PhD Thesis

Lucia Romano

UNIVERSITÀ DEGLI STUDI DI CATANIA DOTTORATO DI RICERCA IN FISICA – XVIII CICLO

Heavily doped Si with B and Ga: electrical properties and clustering

Tesi per il conseguimento del titolo

Tutor: Prof.ssa Maria Grazia Grimaldi

Coordinatore: Prof. Francesco Riggi

This thesis is named after the best teacher I have ever met: My dad.

Cover: Experimental spectrum of Time Resolved Reflectivity measured on a sample of Si 550 nm amorphous thick on a crystalline substrate. More details can be found in Fig. 2.10 within this thesis, on page 45. * Poem of the Italian poetess Maria Luisa Spaziani (Rita Levi Montalcini, Abbi il Coraggio di Conoscere, Rizzoli, Milano, 2004), the English text is a free translation by Lucia Romano.

Heavily doped Si with B and Ga: electrical properties and clustering Lucia Romano Ph.D. Thesis – University of Catania Printed in Catania, 10th December 2005

Non ha colonne d’Ercole il pensiero. La tua anima piccola, diabolica pigrizia, se le crea. Né Ulisse né Colombo sospettavano le mille e mille isole in attesa. Te aspettano interi continenti. Dormono dentro il tuo cervello: osa! Il mondo è da creare.

Maria Luisa Spaziani

No pillars of Hercules has thought. Your tiny soul, diabolic indolence, creates them. Ulysses or Columbus did not suspect the thousands and thousands of isles awaiting them. Whole continents are waiting for you. They are sleeping in your mind: risk it! The world has to be created. *

Contents

Introduction................................................................................................................................ I

CHAPTER 1 ............................................................................................................................... 1 Review of Si doping: incorporation, activation and deactivation of dopants ...................... 1

1.1 Defects in crystalline Si.............................................................................................. 1 1.1.1 Point defects.......................................................................................................... 2 1.1.2 Damage generation: displacement cascades ........................................................ 2 1.1.3 Annealing and Dopant diffusion............................................................................. 4

1.2 Impurity Clustering..................................................................................................... 7 1.2.1 Clustering evidences ............................................................................................. 8 1.2.2 Cluster structures .................................................................................................. 9 1.2.3 Impurity lattice location ........................................................................................ 10

1.3 Solid Phase Epitaxial Regrowth............................................................................... 13 1.3.1 Effect of impurities and regrowth models............................................................. 14 1.3.2 Supersaturated Solid Solutions ........................................................................... 19 1.3.3 Interface segregation........................................................................................... 21

1.4 Impurity ionization in heavily doped Si ..................................................................... 22 1.4.1 Low impurity concentration.................................................................................. 23 1.4.2 High impurity concentration ................................................................................. 23

1.5 References .............................................................................................................. 26

CHAPTER 2 ............................................................................................................................. 31 B and Ga in Si: impurity solubility and distribution............................................................. 31

2.1 Experimental............................................................................................................ 31 2.1.1 Sample preparation ............................................................................................. 31 2.1.2 Characterization .................................................................................................. 32

2.2 Impurity solubility in single doped (B or Ga) Si......................................................... 35 2.2.1 B doped Si........................................................................................................... 35 2.2.2 Ga doped Si ........................................................................................................ 39

2.3 Impurity solubility in B+Ga co-doped Si ................................................................... 41 2.4 SPE rate .................................................................................................................. 43

2.4.1 TRR measurements ............................................................................................ 44 2.4.2 SPE rate of B and Ga doped Si ........................................................................... 47 2.4.3 Ga segregation.................................................................................................... 51

2.5 Stability of the solid solution upon annealing ........................................................... 53 2.6 Concluding Remarks ............................................................................................... 56 2.7 References .............................................................................................................. 56

CHAPTER 3 ............................................................................................................................. 59 Effect of Strain on Carrier Mobility in heavily doped silicon............................................... 59

3.1 Brief review of carrier mobility in semiconductor ...................................................... 59 3.1.1 The BTE and the definition of carrier mobility ...................................................... 60 3.1.2 Strained silicon .................................................................................................... 63 3.1.3 Carrier Mobility in heavily doped Si ..................................................................... 65

3.2 Hall Mobility in Si doped with B and Ga ................................................................... 68 3.3 Strain in Si doped with B and Ga ............................................................................. 70

3.4 Strain effect on Hole Mobility ................................................................................... 73 3.5 Concluding Remarks ............................................................................................... 77 3.6 References .............................................................................................................. 77

CHAPTER 4 ............................................................................................................................. 79 Off-lattice displacement of dopants during ion irradiation ................................................. 79

4.1 Experiment .............................................................................................................. 79 4.1.1 Channeling Method ............................................................................................. 80 4.1.2 Evaluation of the ion energy loss......................................................................... 81

4.2 Off lattice displacement of B and Ga in Si................................................................ 83 4.2.1 Model of impurity- ISi interaction........................................................................... 86

4.3 Off lattice displacement of dopants in B+Ga co-doped Si ........................................ 88 4.3.1 Model of impurity- ISi interaction........................................................................... 88

4.4 Lattice location of impurities after ion irradiation ...................................................... 95 4.4.1 Ga doped Si ........................................................................................................ 96 4.4.2 B doped Si......................................................................................................... 101 4.4.3 B+Ga Co-doped Si ............................................................................................ 102

4.5 Concluding Remarks ............................................................................................. 104 4.6 References ............................................................................................................ 104

CHAPTER 5 ........................................................................................................................... 107 B implanted at RT in crystalline Si: B defect formation and dissolution.......................... 107

5.1 Electrical activation behaviour of B implanted in crystalline Si: literature review .... 107 5.2 Lattice location of B clusters and thermal evolution ............................................... 110

5.2.1 Experimental ..................................................................................................... 110 5.2.2 B lattice location at RT....................................................................................... 111 5.2.3 B clustering evolution during annealing ............................................................. 113

5.3 Concluding Remarks ............................................................................................. 116 5.4 References ............................................................................................................ 116

Conclusions .......................................................................................................................... 119 List of Publications............................................................................................................... 121 Curriculum ............................................................................................................................ 123 Acknowledgments ................................................................................................................ 125

Introduction

The ever-changing nature of silicon-based microelectronic devices demands

material properties must be modified to meet device expectations. The trends in semiconductor advances show little signs of slowing down due to the continuous demand for increased computing power. Therefore, the need for research directed at material design and enhancement calls for science to continue evolving. Innovations by scientists lead to these advances, but these improvements can not be accomplished without an understanding of the work at hand. This chapter presents the motivation behind the research contained within and a brief description of the work and results of interest.

The science and engineering of semiconductor materials have evolved some

remarkable changes over the last several decades. The semiconductor industry is on an eternal hunt for methods to continue Moore’s Law. Since the invention of the transistor (see Figure I.1a) in 1947 by William Shockley, John Bardeen, and Walter Brattain, and the fabrication of the first Metal Oxide Semiconductor Field Effect Transistor (MOSFET) at Bell Labs in 1960, much innovation in the forms of transistor scaling and new materials has led to the recent MOSFET [Tho04,Tho05]. In 1965, Gordon Moore proposed that the number of transistors on an integrated circuit (IC) will approximately double every 2 years [Moo65], the device scaling down is reported in Figure I.2 as function of time.

The MOSFET has been a workhorse for the semiconductor industry for quite some time now. Due to the vast knowledge and understanding of the MOSFET along with its scaling capabilities it has become an important device for current technology. The durable design allows devices to be scaled into the submicron range, which in turn permits higher device densities and increased performance demanded by consumer markets. As scale down continues for future generations there are fundamental limitations that are being met. These limitations call upon scientists to investigate problems and possible solutions to scaling down.

To begin understanding what is needed for scale down it is necessary to examine the MOSFET. Figure I.1b shows a cross sectional view of a typical MOSFET. The

Fig. I.1 First transistor (a) and new generation strained-channel-MOSFET (b)

Polycide

Poly gate

Strained Si channel

Relaxed SiGe (15%) Source

Lch

Drain

50.00 nm

a b

Introduction II

ultimate goal is to shorten the channel length (Lch), thus making the device faster and permitting higher densities of devices. Simply shortening the channel length while leaving other dimensions constant harms the overall performance of the device. One of the main concerns is scaling the source-drain extension depth, xj, while decreasing transistor size. If junction depths remain at deeper levels the lateral depletion under the gate is larger resulting in increased charge sharing leading to short channel effect. While it may be possible to decrease the junction depth, xj, at the same time it is also necessary to maintain a low sheet resistance, Rs, in the implanted layer.

Having low material sheet resistance is crucial since the combination of millions

of transistors can accumulate to very large resistances overall. Guidelines for the desired material properties for future generations of semiconductor devices are given in the International Technology Roadmap for Semiconductors (ITRS) [ITR05].

Figure I.3 shows a plot of sheet resistance, Rs, versus junction depth, xj, for results obtained by conventional implant and annealing techniques along with the requirements each year given by the ITRS. Clearly there is a need to reduce junction depths while maintaining relatively low Rs. This is done by activating higher levels of dopants in silicon. The active dopant levels need to reach are in the range 1020-1021 cm-3, which is well high, considering that the solid solubility limit for As and P in Si is ∼2x1021 cm-3, but for B is ∼3x1020 cm-3 and ∼5x1019 cm-3 for Ga, therefore a notably gap occurs between n-type and p-type doping.

Ion implantation is the most used technique [Rim95] to introduce these levels of dopants in the Si devices, the combination of excellent spatial and dose control, as well as ease of manufacture, has led to a widespread use of this technique by the microelectronic industry. Charged dopant atoms are accelerated through an electric field and directed at the silicon substrate. The energy of the implanted atoms used for the formation of the source, drain and channel regions is thousand of times larger than the silicon bond energy. Because of this, a large numbers of Si atoms are knocked off their lattice sites, in a series of displacement collisions, resulting in an extremely large amount of defects in crystalline Si. In particular an excess of point defects (interstitials and vacancies) with respect of the equilibrium is created in the crystal, these defects can agglomerate to form from extended defects up to amorphous pockets, depending on the implant and substrate conditions. Conventional processing relies on rapid thermal annealing to repair the damage generated by the implantation step and activate dopants. During the post-

Fig. I.2 Scaling down of characteristic device’s size according to Moore’s law.

III

implantation annealing, the dopant atoms diffuse through the silicon lattice to form the final device profile. For highly doped, abrupt and shallow profiles, the dopant diffusion must be minimized. It is well known that atomic diffusion in the silicon crystalline lattice is mediated by point defects. The excess of point defects created by the ion implant greatly enhances the equilibrium dopant diffusion by many orders of magnitude, causing the loss of the desired dopant confinement, and induces the dopant deactivation via the formation of impurity-defects complexes. The greatest limitations occur for the dopant boron, which is known to achieve lower active concentration levels, due to clustering phenomena, and diffuse rapidly by a process known as transient enhanced diffusion (TED) as consequence of the dopant interaction with Si self-interstitials in excess. It is clear that a fundamental understanding of the self-interstitials properties and their interactions with impurity atoms in Si can not be longer disregarded in order to control and preserve the huge dopant concentration gradients required for the near future device generations.

With both low levels of activation and rapid diffusion it becomes more difficult to reach future low Rs and small xj prescribed by the ITRS. Solid phase epitaxial (SPE) regrowth, on the other hand, will propagate at lower temperatures (500-650 oC), thus minimizing diffusion while still activating dopants at concentration higher than the solubility limit. SPE process [Ols88] involves the re-crystallization of an amorphous layer in intimate contact with a crystalline layer upon heating by a planar motion of the interface, with a rate dependent on several factors, such as orientation and impurity concentration. Upon re-crystallization, impurities dissolved in the amorphous phase may become trapped onto substitutional lattice sites allowing metastable conditions to be met. The study of the physical mechanisms involved in the SPE process and the role of the different dopant impurities on SPE features is clearly a point of technological interest.

The last few years [Lee05] have also witnessed rapid growth in the study of

strained silicon due to its potential ability to improve the performance of very large scale integrated (VLSI) circuits independent of geometric scaling. Strain improves MOSFET drive currents by fundamentally altering the semiconductor energy band

20022003

20042007

20102013

2016

2001

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80100

1000

10000

Shee

t Res

ista

nce

[Ω/s

q]

Junction Depth [nm]

conventional pre-amorph. conventional crystalline SPE at T<600°C

Fig. I.3 Sheet Resistance as function of junction depth for p-type Si predicted by the ITRS map. The empty symbols represent the values obtained with conventional processes that include ion implantation into pre-amorphized (circles) and crystalline Si followed by high temperature rapid thermal annealing. The full triangles are data obtained by low temperature SPE processes.

Introduction IV

structure of the channel and can therefore enhance performance even at aggressively scaled channel lengths. Since the advent of the relaxed graded buffer technique in 1991 [Fit91] SiGe alloys have been a proven path to increasing the functionality of the silicon microelectronics platform, playing on the possibility of epitaxial growth of Si on SiGe substrate. Relaxed SiGe virtual substrates have enabled to realize strained Si channels improving the hole mobility up to a factor of 2, this is extremely important in IC technology to couple NMOS and PMOS, because of the lower holes mobility with respect of electrons. An example of the strained-pMOSFET is given in the Figure I.1b. However the effects of mechanical stress can also degrade device characteristics. The proximity and amount of the stress in the silicon substrate limits the density of ICs, and when the too much stress is exerted in the silicon, it will yield by releasing dislocations that lead to leakage currents and degraded device performance. As we enter the nanometer regime, standard process steps, such as source/drain doping, introduce significant stress in the channel of MOSFETs. In PMOS devices, the tensile stress generated in the channel from source/drain boron doping is nearing values large enough to compensate the engineered strain for performance enhancement. Therefore a large interest of the scientific community is devoted to the strain effect and to the relationship between charge carrier mobility and strain of the host material.

In conclusion of this overview we would indicate some of the main requests of microelectronic science and technology that have guided the topics of this work:

High doping levels above all for p-type Si, strengthening the conventional Si processing and elaboration of new strategy to reduce the dopant electrical deactivation;

Improve of the charge carrier mobility, above all for p-type Si; Reliable models of dopant interaction with point defects, electrical activation and deactivation, to simulate the real device properties;

The technological challengers can be pursued thanks to a broad view of the problems and a deep searching in the fundamental physics. For these reasons, near the list of the technological requests we can compile a picture of the main required understandings in order to answer the industrial demand:

Interaction of impurity and point defects that determine the enhanced dopant diffusion and electrical deactivation;

Clustering kinetics of formation and dissolution, therefore investigations about the clusters structures, in order to study efficient processes that could limit the dopant deactivation and the eventually reactivation by thermal treatment;

Strain effect on the conventional processes, also considering the strain induced by dopant itself in heavily doped semiconductors;

Characterization of charge carrier mobility as function of new parameters, like the strain, the chemical species of the dopant, taking into account the effect of different scattering mechanisms over the concentration range of interest and material size.

This dissertation is part of this contest. It is widely recognized that boron is the most used p-type dopant in silicon, but

it strongly interacts with Si self-interstitials [Fah89], and this interaction is really the origin of the well known problems of deactivation, diffusion and clustering [Sto97] that affect this dopant in Si. Precipitation of B atoms, well below the solid-solubility limit in Si, was shown to occur in presence of a high density of self-interstitials, which are also responsible of the well-known B enhanced diffusion. The resulting B clusters severely inhibit the electrical activation of the dopant and could also deteriorate the charge carrier mobility. Moreover, B ion implantation does not amorphize the Si at fluence and energy used in standard processes [Rim95], so it is subjected to channeling phenomena that produces an undesired broadening of the concentration profile. To overcome this problem one can use preamorphized Si, or

V

to reduce the processing steps it is possible to use co-implantation with another dopant that can amorphize the crystalline substrate. Boudinov et al. [Bou99] proposed to use In. Indium (z=49) allows to create shallow profiles (∼100 nm) with moderate implant energy (∼100 keV), but it has a deep level (156 meV) in the energy gap of Si so that only 35% of In impurities are ionized in Si at room temperature, and, moreover, it has a low solubility limit (2x1018 at/cm3) [Sze81]. In this work we have tackled the B doping problems using the co-doping of B with another impurity of the p-type: Ga. Gallium has a shallow level (70 meV) so it is completely ionized at room temperature and its solubility limit (5x1019 at/cm3) can be enhanced of five times by SPE, moreover its implant amorphize the Si (z=31) approximately like the Ge (z=32). The B+Ga co-doped Si is a new material so it is necessary to study its properties. In particular we have investigated the electrical properties, the stability and also the lattice location upon proton irradiation in heavily doped (B concentration ∼1x1019 – 8x1020 at/cm3) samples, realized by conventional ion implantation and SPE processes. The comparison of the investigated properties in the three different systems of B, Ga and B+Ga doped silicon, has permitted to obtain fundamental information about:

the incorporation, the distribution, the activation and the stability of the dopants by SPE in the three different kinds of sample;

the interaction between the two impurity species and with the Si point defects at room temperature;

the different cluster structures formed by the two dopants as consequence of Si point defects injection;

the effect of the strain induced by the dopants themselves on the carrier mobility.

The plan of the present dissertation is the following. In Chapter 1, the general concepts necessary to introduce this thesis work are

given. A brief overview of the state-of-the-art on the damage generated by ion implantation (section 1.1.2) and its effect on dopant diffusion (1.1.3) and clustering during annealing (1.2), is given in the first sections. The interaction between dopant atoms and point defects is schematically depicted as given by the models of diffusion mediated by point defects. The B-interstitials clusters (BICs) formation is presented with particular attention to the observed electrical deactivation of the dopant. The cluster structure of a large population of BICs has been predicted by theoretical calculations, the ion beam channeling technique [Tes95] can be a powerful means of investigation about the lattice location of impurities (1.2.3), and therefore it could be used to study the cluster structure.

In section 1.3 the process of SPE is analyzed as function of the dopant density, temperature of annealing in the light of the main experimental observations and modelling. The incorporation of impurities at concentration higher than the equilibrium solubility limit is explained in term of the trapping at the moving crystal-amorphous interface, impurity distribution profiles and interface segregation are discussed.

The last section of the chapter 1 is devoted to a brief review about the ionization of impurities in Si. The effect of the heavily doping causes the metal-to-insulator transition with the consequently total ionization of the shallow impurities at concentration higher than 1x1019 at/cm3 at room temperature.

Starting from Chapter 2 the results of our work are presented. Many aspects of the solid phase epitaxial process showed a strong dependence on the atomic size of dopant impurities: the interface velocity and the substitutional trapping strictly depend on the type of impurities and the strain effect has been often involved to explain the material properties. Since the solid solubility depends on the atomic size of the impurities we asked if a sort of strain compensation in presence of impurities with different sizes could affect the solubility of the involved dopants. B and Ga

Introduction VI

have been chosen as dopants with different size in order to have a strain compensation that could act positively on the impurity incorporation. Moreover, they are both p-type impurities in Si, therefore the presence of both dopants can enhance the total number of charge carriers. The two impurities have been implanted at high concentration (∼1020 at/cm3) in the same region with overlapping profiles. In this chapter we have described the properties of supersaturated solid solution of three systems: Si(B), Si(Ga) and Si(B+Ga). In particular the dopant distribution during the SPE process, the incorporation into substitutional lattice sites and the stability upon further annealing, have been expounded. The interface velocity of the SPE regrowth has been characterized as function of B and Ga concentration, also in co-doped samples, by time resolved reflectivity method. The measure of the SPE rate in co-doped samples is clearly an original result.

In Chapter 3 the problem concerning the carrier mobility in heavily co-doped B+Ga samples is faced. Firstly a brief review of the scattering mechanisms that limit the carrier mobility is depicted, with a particular focus on the properties at high concentration of impurities. It is well known that under low fields the mobility depends on the doping concentration and on temperature. However, it is less known that the carrier mobility in doped Si depends as well on the chemical nature of the dopant atoms. In this chapter we demonstrate that this difference arises from the strain induced by the dopant itself. The Hall mobility has been measured in samples in which the effective strain has been varied by co-doping Si with B and Ga having overlapping concentration profiles in the 0.1-2x1020 at/cm3 range. The strain distribution has been measured by high resolution x ray diffraction. Co-doped samples with a total (B+Ga) constant carrier concentration (1x1020 at/cm3) have been used to disentangle the effect of the strain on the mobility, and a higher mobility has been measured in tensile strained Si. A linear relationship between the perpendicular strain and the inverse of mobility has been inferred. Using this relationship the mobility relative to B and Ga impurities has been corrected and a unique mobility versus carrier concentration curve for unstrained Si has been determined, as original result of the co-doping experiments.

In Chapter 4 the stability of the supersaturated solid solutions of B and Ga in Si under bombardment of light energetic ions has been investigated, using the channeling technique of lattice location. Substitutional B or Ga in Si undergo off-lattice displacement at room temperature (RT) during irradiation with H+ and He+ beams as consequence of the impurity interaction with the Si self-interstitials (Is) generated by irradiation. The amount of displaced B (Ga) increased with irradiation fluence until saturation, at which point, the formation of B-B (Ga-Ga) pairs stable in presence of Is excess has been supposed. The impurity displacement rate have been studied in a coherent simple model that assumes an interaction between Is generated by the irradiating beam and impurity substitutional atoms. The lattice location of the impurity clusters, formed as consequence of the interaction with Is, has been investigated performing angular scans along <100> and <110> axes. The experimental data are in qualitative agreement with simulations of the simplest stable clusters theoretically predicted (pairs of impurity atoms). In co-doped B+Ga samples, the displacement of each impurity has been investigated and interpreted in terms of a competitive trapping of Is by the two dopants. Channeling method turned out to be very powerful to study the impurity clustering when an excess of point defects is generated in the crystal. It should be noted that clustering characterization can not be performed by other analyses at RT, because the profiling techniques, like the secondary ion mass spectrometry, are not sensitive to the low diffusion length associated at this low temperature regime.

In Chapter 5 we have applied the channeling method to the case of B implanted in crystalline Si, which is of technological interest. The B lattice location has been compared in the two samples: the first is B implanted crystalline Si at RT; the second a B doped SPE regrown sample irradiated with 300 keV He at a fluence that

VII

causes the maximum measured displacement of B atoms, as consequence of the interaction with Is generated by the passing ion beam. Very interesting and surprising results have been shown.

In addition the damage recovery and the electrical activation of such B complexes subjected to thermal treatment in the 200-950 °C range has been presented and discussed. The B complexes dissolve at low temperature if no excess of Si self interstitials (Is) exists or they evolve into large B clusters and then dissolve at high temperature if Is super saturation holds.

These investigations provide a picture of the properties – structural, electrical

and functional – of supersaturated solid solution of B and Ga in Si. Eventually, the conclusions will be drawn.

__________________________________________________________________

[Bou99] Boudinov H., J. P. de Souza, and C. K. Saul, J. Appl. Phys. 86 (1999) 5909

[Fah89] Fahey P. M., P. B. Griffin and J. D. Plummer, Rev. Mod. Phys. 61 (1989) 289

[Fit91] Fitzgerald E. A., Y. H. Xie, M. L. Green, D. Brasen, and A. R. Kortan, Mater. Res. Soc. Symp. Proc. 220 (1991) 211

[ITRS05] International Technology Roadmap for Semiconductors (Semiconductor Industry Association, Austin, TX, 2005)

[Lee05]

Lee M.L., E.A. Fitzgerald, M.T. Bulsara, M.T. Currie, and A. Lochtefeld, J. Appl. Phys. 97 (2005) 11101

[Moo65] Moore G. E., Electronics 38 (1965) 114 [Ols88] Olson G.L. and J.A. Roth, Mater. Sci. Rep. 3 (1988) 1 [Rim95] Rimini E., Ion Implantation: Basics to Device Fabrication (Kluwer

Academic Publishers, Boston, 1995) [Sto97] Stolk P. A., J. H.-J. Gossmann, D. J. Eaglesham, D. C. Jacobson, C. S.

Rafferty, G. H. Gilmer, M. Jaraìz, J. M. Poate, H. S. Luftman and T. E. Haynes, J. Appl. Phys. 81 (1997) 6031

[Sze81] Sze S. M., Physics of Semiconductor Devices (Wiley, New York, 1981) [Tes95] Tesmer J. R. and M. Nastasi, eds., Handbook of modern ion beam

materials analysis, (Materials Research Society, Pittsburg, 1995). [Tho04] Thompson S.E., M. Armstrong, C. Auth, M. Alavi, M. Buehler, R. Chau,

S. Cea, T. Ghani, G. Glass, T. Hoffman, C. H. Jan, C. Kenyon, J. Klaus, K. Kuhn, Z. Ma, B. McIntyre, K. Mistry, A. Murthy, B. Obradovic, R. Nagisetty, P. Nguyen, S. Sivakumar, R. Shaheed, L. Shifren, B. Tufts, S. Tyagi, M. Bohr, and Y. El-Mansy, IEEE Electr. Dev. Lett. 25 (2004) 191

[Tho05] Thompson S.E., R. Chau, T. Ghani, K. Mistry, S. Tyagi, and M. Bohr, IEEE Trans. Semicond. Man. 18 (2005) 1

Chapter 1

Review of Si doping: incorporation, activation and deactivation of dopants

This chapter presents an overview of some current knowledge involved in

integrated circuit (IC) processing and physics of silicon-based materials. Dopant introduction into silicon for IC manufacturing is done predominately by

ion implantation [Rim95]. While implantation offers excellent control of impurity amounts it also produces damage to the silicon crystalline lattice. Therefore, it is necessary to anneal the damage and force dopants onto substitutional sites. Solid phase epitaxial (SPE) regrowth process permits to have the higher concentration of dopant atoms into substitutional sites, moreover the dopant is electrically activated after annealing process at low temperature (<600°C) avoiding undesired transient enhanced diffusion (TED) phenomena. A synopsis of the SPE process and why it is employed is given. Particular attention is devoted to the effects of impurities, like B, on SPE regrowth.

The SPE process at low temperature is not able to eliminate the defects at the end of range (EOR) implant, this kind of extended damage can evolve from point defects to dislocation loops during post-implant annealing. The EOR defects degrade the junction properties favouring leakage current and during annealing they release point defects, that, being high mobile also at room temperature [Kyl96], voyage through the crystal and can reach the doped region. The interaction of the dopant atoms with the excess of point defects can be deleterious causing TED and deactivation of the dopant by the formation of impurity agglomerates, called clusters. Clustering phenomena are actually subjected to deep investigation being the knowledge of their formation and dissolution fundamental to project ultra-shallow junctions where very high concentrations of active dopant (>1020 at/cm3) are necessary to obtain low sheet resistance values. The last part of this chapter is dedicated to the clustering phenomena of B with particular attention to the path of formation and crystallographic structure predicted by theoretical calculations.

Finally a brief review about the ionization of impurities in Si. The effect of the heavily doping causes the metal-to-insulator transition with the consequently total ionization of the shallow impurities at concentration higher than 1x1019 at/cm3 at room temperature (RT).

1.1 Defects in crystalline Si Ion implantation is the most commonly used technique to introduce dopants in

Si. The passage of an energetic ion through the Si lattice initiates a sequence of displacement events that leads to defect production and, at sufficiently high doses, to the c-a transformation of the irradiated area. Post-implant thermal processing is required to anneal out the damage and to electrically activate the introduced dopants. The formation of the amorphous phase is beneficial because it limits ion

Chapter 1 Review of Si doping: incorporation, activation and deactivation of dopants 2

channeling (which can distort the implanted dopant profile) and also it is easily annealed. Annealing, which occurs by SPE growth, results in a low defect density in the recrystallized volume and incorporates the dopants into electrically active positions [Tsa79, Lan98]. This behaviour differs from the regrowth of highly damaged but not continuous amorphous layers. In these cases, annealing temperatures of 800–1000 °C are required to remove extended defects in the implanted region and place all of the dopants into substitutional positions. The diffusion of dopants in implanted Si is affected by the presence of implantation damage.

1.1.1 Point defects A point defect in a crystal can be defined as an imperfection, i.e. an irregularity,

in the periodicity localized at one point. The two basic types of intrinsic point defects are vacancies (V) and interstitials (I). A vacancy is a lattice site with a missing atom. An interstitial is an atom in excess into the lattice. The vacancy-interstitial pair is called Frenkel defect. In particular the interstitial is called pure if it is located into a hollow of the lattice, while two atoms in nonsubstitutional positions configured around a single substitutional lattice site form an interstitialcy. Usually a distinction between an interstitial and an interstitialcy is not made and both are identified as I in literature. At any temperature higher than 0° K, all crystalline solids contain thermally generated native point defects that lower the Gibbs free energy of the system as compared to a defect-free crystal, while impurity-related defects arise from the introduction of foreign impurities into the silicon lattice. The equilibrium concentration of defects in NL lattice sites is given by [Fah89]:

⎥⎦

⎤⎢⎣

⎡−⎥⎦

⎤⎢⎣

⎡=

TkH

kSNc

B

Xf

B

Xf

XLXeq expexpϑ (1.1)

where: X=I,V; XfS and X

fH are the single point defect formation entropy (associated to lattice vibration) and enthalpy (associated to lattice distortion), kB is the Boltzmann constant, and T is the absolute temperature, ϑX is the degree of internal freedom of the defect (for example, spin degeneracy). Bracht et al. [Bra00] experimentally found the following concentrations, in equilibrium conditions, for vacancies and self-interstitials:

⎟⎟⎠

⎞⎜⎜⎝

⎛−×≈−

TkeV

cmcB

eqI

][18.3exp109.2][ 243 (1.2)

⎟⎟⎠

⎞⎜⎜⎝

⎛−×≈−

TkeV

cmcB

eqV

][0.2exp104.1][ 233 (1.3)

It is worth to evidence that at T=1000 °C, for example, the equilibrium concentrations of Is and Vs are about 7x1011 and 2x1015 cm-3, respectively: i.e. they are several or many orders of magnitude lower than the Si density (5x1022 at/cm3). In spite of this, the point defects can be created in excess by ion implantation and they play a key role in the diffusion of silicon impurities, as described in the next sections.

1.1.2 Damage generation: displacement cascades An ion, during its slowing down, interacts anelastically with electrons and

elastically with the other target atoms. If the kinetic energy E’, transferred to the host atom is higher than a certain value, Ed, the displacement threshold energy, the knock-on atom leaves its lattice site and according to the residual kinetic energy, E’-Ed, can move for a certain path length [Rim95]. In silicon threshold energy of

1.1 Defects in crystalline Si

3

∼15 eV is required to create a Frenkel pair [Cor66, Mil94, Cat94]. If the energy transfer is lower only local heating occurs. When ions transfer much higher energy to target Si atoms than needed to create a Frenkel pair, the interaction of displaced atoms with other lattice atoms can lead to further displacements (recoils). Frenkel pair production is therefore a cascade process in which the incident ion is simply the primary damage-producing particle. The total of all such events is commonly referred to as the collision cascade of the ion. High defect densities are generally associated with the vicinity of the ion track, especially near the end of range (EOR) where the ion’s velocity is sufficiently slow so that nearly every atomic interaction results in a displacement event [Bri54]. Local heating can lead to the melting of significant volumes of material [DeL95] and thus it can have an important role on amorphization.

Theoretical models permit us to estimate the number of atoms displaced by a projectile as it comes to rest, and provide an approximate indication of the damage produced by implantation. MD simulation methods [Hai92] and computer simulation codes based on the binary collision approximation (BCA) [Sig72] such as TRIM [Zie77] and MARLOWE [DeL95] as well as analytical descriptions based on linear Boltzmann transport theory [Win70] have generally been used for this purpose.

For light ions, as B in Si, the mean free-path between successive elastic collisions is larger than the interatomic distance, and thus the collision cascade will result in a dilute distribution of defects. Heavy ions at low energy can have a mean free path comparable with the interatomic distance and a dense cascade will be generated. In the case of the B cascade a number of isolated Frenkel pairs and small clusters are observed. Since local melting in the cascade does not take place for low mass ions, defect production is essentially governed by the early ballistic phase of the cascade and therefore agrees well with the BCA predictions at low temperatures [Pel04]. Defects can be reduced over time due to bulk recombination and annihilation at surfaces and internal sinks, and the experimental RBS profiles at room temperature can give smaller amount of defects than those predicted by BCA calculations. In the heavy ion implants the deposited energy density within the cascade becomes large enough that the assumption of isolated binary collisions breaks down and several atoms are set simultaneously in motion sharing a reasonable high kinetic energy.

The distribution of the deposited density into nuclear collision can be converted into a damage distribution, assuming, for instance, that only those recoils receiving energy greater than Ed are displaced. The energy transfer below Ed results in the creation of lattice vibration or phonons. The total number nd of displaced atoms per incident ion in the implanted volume is:

dd E

dxdxdE

n2

0∫∞

= (1.4)

Therefore, if dxdE

is constant and independent of the ion energy, the

concentration Nd of displaced atoms is approximately given by:

dp

dd Edx

dERnN

21φφ == (1.5)

where φ is the ion fluence and Rp is called projected range of the ion implant. This relationship can be used to evaluate the ion fluence necessary to create an amorphous layer assuming that the amorphous is formed when the density of displaced atoms equals that of silicon.

However, point defect, defect complexes, or locally amorphous regions can accumulate as successive cascades are implanted in the target material until highly


damaged c-Si becomes unstable and transforms into a-Si. In fact, RBS measurements indicate that ion-beam-induced amorphization occurred initially near the most heavily damaged region (near the EOR) [Mot92, Mot91, Hol88]. Continued irradiation increases the thickness of the generated amorphous layer. The amorphization process results to be very complex and the kinetics of damage accumulation is controlled by a competition between damage accumulation and dynamic annealing. The mass of the ion species, the temperature of the substrate, the dose and the dose rate of the irradiation all play interdependent roles [Cro70, Wes69, Pic69, Cam93]. It has been observed that damage in Si increases as the ion fluence increases. The implant dose at which a wholly amorphous layer first appears is referred to as the threshold fluence. It was found that the threshold fluence required for light ions is much greater than that for heavy ones and that room temperature implantations require a much higher fluence than those carried out at liquid nitrogen temperatures [Den78, Mor72, Bar75, Ell88, Mor70, Gol93].

As example of the damage generation during ion implantation we report the SRIM [Zie85] simulation of a 50 keV B implant (which will be considered in chapter 5), in Figure 1.1 the number of interstitial Si atoms per incident ion is shown as function of depth. The number of displaced Si, integrated over the depth distribution, is about 500 per ion.

It should be noted that the SRIM simulation does not take into account any I-V

recombination, so the situation depicted in Figure 1.1 is realistic at very low temperature (∼ 70°K) where I-V annihilation is negligible. When we use the SRIM simulation to evaluate the concentration of Is generated by the energetic light ions at room temperature (see chapter 4), we are conscious that this is an overestimation, but no data are reported in literature about the entity of I-V recombination at RT, so the reader must take in mind this condition.

1.1.3 Annealing and Dopant diffusion Ridding the damage created by ion implantation is typically fulfilled by heating

the silicon. This gives the point defects enough energy to migrate such that vacancies and interstitials may combine to annihilate one another. Unfortunately

0 500 1000 1500 2000 2500 30000.00

0.05

0.10

0.15

0.20

0.25 black: Interstitialgray: Vacancies

Depth [Å]

I, V

[ato

m/Å

/ion]

50 keV B+, tilt 7°

Fig. 1.1 SRIM [Zie85] simulation of 50 keV B+ implanted in Si. Point defects (Si interstitials and vacancies) generated by the ion cascade are shown as function of depth.

1.1 Defects in crystalline Si

5

the damage annealing is not as simple as recombination since there are extra interstitials introduced from the implant. It is the net extra interstitials that cause problems upon annealing.

Annealing of ion-implanted silicon at elevated temperatures can cause dopants to diffuse much faster than predicted for equilibrium diffusion. This phenomenon, called transient enhanced diffusion (TED), most severely affects B diffusion, so our discussion will focus on boron. It occurs for a limited period of time, and then equilibrium diffusion takes over again [Mic89]. Models to explain this phenomenon describe how the excess interstitials from ion implantation are responsible for TED [Eag94, Eag95]. The silicon interstitials are also responsible for “kicking out” substitutional boron to interstitial positions allowing rapid diffusion of boron. To understand the phenomenon of “kicking out” it can be helpful to review the mechanisms of dopant diffusion, because these processes clarify the role of Si point defects and their interaction with the dopant atoms. Figure 1.2 illustrates various mechanisms for the diffusion of an element A in a solid, such as silicon. In the upper part (Figure 1.2a) of the figure the direct mechanisms are depicted. The diffusion of mainly interstitially dissolved foreign atoms (Ai) proceeds via interstitial lattice sites. No intrinsic point defects are involved in this direct interstitial mechanism. Direct diffusion of atoms on substitutional sites (As) can occur by means of a direct exchange with an adjacent Si atom or a ring mechanism (note that the diffusion of As by indirect mechanism is usually more favourable). Various indirect diffusion mechanisms, which involve intrinsic point defects, are illustrated in Figure 1.2b. These mechanisms can be expressed by the following point-defect reactions [Bra00, Fah89, Cow91]:

1) As + V ⇔ AV 2) As + I ⇔ AI 3) As + I ⇔ Ai 4) As ⇔ Ai + V

Reactions 1 and 2 represent the vacancy and interstitialcy mechanism, respectively. Isolated intrinsic defects approach substitutional impurities and form AV and AI defect pairs due to Coulomb attraction and/or minimization of local strain. For a long-range migration of As, the AV pair must partially dissociate. In contrast, dopant diffusion via the interstitialcy mechanism only occurs if the AI pair does not dissociate. Reactions 3 and 4 are commonly called the kick-out and the dissociative (or Frank-Turnbull) mechanisms, respectively. They describe the diffusion behaviour of elements that are mainly dissolved on substitutional sites, but that move as interstitial defects (Ai).

A picture of the interaction between an impurity atom and an interstitial (reactions 2 and 3) is shown in Figure 1.3. The diagram represents the total energy of the system as a function of its configuration. At far left, the system consists of a crystal with a free surface and one substitutional impurity atom As. Moving to the right, a point defect (here a self-interstitial) is thermally generated at a large distance from the impurity atom. The energy of the system fluctuates as the self-interstitial migrates between adjacent stable locations in the crystal. The shaded region of Figure 1.3 represents the event where the free self-interstitial encounters and reacts with a substitutional dopant atom As, to form a mobile dopant species Ai (either a dopant-interstitial pair or an interstitial dopant atom).


The mobile species may migrate some distance before dissociating, becoming

again substitutional. For each dopant it is possible to define the fractional interstitial component of diffusion:

A

AIA

I DD

=Φ (1.6)

where DA is the impurity diffusivity and DAAI is the component of the dopant

diffusivity attributable to an I-type mechanism. ΦI depends on temperature and it is specific for each element. For example, if, for a fixed dopant, ΦI was about 1 the dopant would diffuse essentially by means of interstitials, whereas if ΦI was about 0 the dopant would diffuse basically by means of vacancies.

In Figure 1.4, ΦI is plotted for some common silicon dopants, as a function of

their atomic radius normalized to the Si one, at the temperature of 1100 °C. In particular, B [Fah89] and Ga [Fah89b] atoms diffuse essentially by interstitials (ΦI~1). It can be noted in Figure 1.4 that smaller dopants attract self-interstitials and repel vacancies, whereas bigger dopants are more attractive for vacancies than

Fig. 1.3 Configuration diagram showing the energetics of interstitial-mediated dopant diffusion [Cow00]

Fig. 1.2 Schematic two-dimensional representation of (a) direct and (b) indirect diffusion mechanisms of an element A in a solid. Ai, As, V and I denote interstitially and substitutionally dissolved foreign atoms, vacancies and silicon self-interstitials, respectively. AV and AI are pairs of A with the corresponding defects [Bra00]

1.2 Impurity Clustering

7

for self-interstitials, for lattice distortion compensation. But Ga and Al disagree this rule indicating that a charge dependence interaction must be considered, in fact, the interstitial defect may be positively charged with a donor level located at 0.3–0.4 eV above the valence-band edge, so the Coulomb attraction explains the interaction between an I+ and an acceptor impurity which dope the Si being negatively ionized (A-) [Bra00, Fah89].

Several authors [Sad99, Win99, Ali01, Jeo01] demonstrated, by means of

theoretical studies, that boron diffuses by an interstitialcy mechanism (reaction 2). A substitutional B captures an I, forming a complex BI, which is mobile and can diffuse into the silicon lattice, with no need to first kick-out the B into an interstitial channel.

In conditions of non-thermal equilibrium for point defects concentration, the diffusivity of the element A (DA*) will be different to the diffusivity in equilibrium condition (DA) [Bra00, Fah89], since B diffuses essentially by I-mediated mechanism (ΦI~1), it can be demonstrated that:

SCC

DD

eqI

I

B

B =≈*

(1.7)

where CI is the Is concentration and CIeq the equilibrium value, S is called

supersaturation of Is. The diffusion period is certainly controlled by the anneal temperature whereby the greater the temperature the shorter the transient period and diffusion [Cow99, Eag95]. Transient diffusion may last for hundreds of hours at 650 °C or on the order of seconds at 950 °C [Jai02]. With the advent of TED there is a major concern about forming ultra-shallow junctions that have sufficiently activated dopant levels. TED may drive the boron tail too deep to obtain acceptable MOSFET device characteristics. As boron seems to be the limiting dopant, there is much research into attaining high activation while minimizing diffusion. Recent studies show that using ultra-high ramp rates and high temperatures can minimize TED [Bou01, Jai02]. The other approach would use temperatures low enough that diffusion is negligible but still sufficient to activate dopants. SPE regrowth uses this approach to form highly active, shallow junction materials.

1.2 Impurity Clustering The phenomenon of B clustering usually refers to the tendency of B to form

complexes with Si self-interstitials, (the so-called “BIC”, Boron-Interstitial-Cluster, with B atoms and m interstitials, both B and/or Si). Three-to eight-atom clusters can not be seen directly by electron microscopy or x-ray techniques because of their small size. Evidence of the existence of small clusters comes from the

Fig. 1.4 Interstitial-related fractional diffusion components AI for group III, IV and V elements versus their atomic radius in units of the atomic radius rSi for Si [Gös00].


interpretation of TED and electrical measurements and from theoretical calculations [Sto97, Jain02, Hof73, Mic87, Sch99, Gos95, Cow96, Hof74-Sol90, Cow90, Sol91, Hay96, Pel97, Pel 99, Pel 99b, Hua99, Man00, Sol01, Wan00, Man01, Luo98, Cat98, Liu00, Cha01, Luo01]. Some evidence of the existence of interstitial clusters comes from the studies of photoluminescence.

B clustering severely hinders the scaling-down of Si microelectronic devices, which requires very high B concentration fully active. Thus, many efforts have been devoted to this task, but, nonetheless, a detailed scenario of B clusters formation and dissolution is still lacking.

This paragraph will be devoted to an overview of the phenomenon of B clustering in Si under the condition of a high supersaturation of Si self-interstitials.

1.2.1 Clustering evidences While the mechanism of B diffusion under equilibrium conditions is fairly

understood, in presence of a high Is-supersaturation boron could exhibit an anomalous diffusive behaviour characterized by enhanced diffusion, under a certain concentration, in conjunction with immobile and electrically inactive high-concentration regions. These features were already observed, almost thirty years ago, by Hofker et al. [Hof73, Hof74] in B implanted Si: as Figure 1.5 shows, after the post-implantation annealing at 800 °C a considerable, electrically inactive B fraction is revealed in the region of high B concentration, correlated with an immobile B fraction, consisting of unspecified B precipitates. On the contrary, the diffusing part of the B distribution (below the concentration level of about 1×1019

B/cm3) was electrically active. The correlation between electrical activity and diffusion appeared quite strongly. In addition, the immobile B peak became more and more pronounced with increasing implantation fluence and/or decreasing the annealing temperature, being still present, after post-implantation annealing at 1000 °C, provided that the B implantation fluence was high enough [Hof74].

Cowern et al. [Cow90], analyzing the diffusion behaviour of implanted B in crystalline Si, found a “static peak region” above a critical concentration of 3.5×1018 or 8×1018 B/cm3 after annealing at 800 or 900 °C, respectively. This B concentration threshold was much lower than the maximum electrically active B concentration (3.5x1020 at/cm3) determined by Solmi et al. [Sol90], in fact, the “static B peak”, electrically inactive, was correlated to the large non-equilibrium

Fig. 1.5 As-implanted and post-annealing B concentration distributions and charge carrier profile in B implanted Si after annealing at 800 °C [Jai02].


9

point-defects concentration induced by B implantation in crystalline Si. In addition, the static B peak was shown to be released over a time much longer than the TED duration [Cow90]. It is seen that the concentration of active boron under the peak is smaller than the total B concentration by approximately one order of magnitude. In the tail region there is a good agreement between the charge carrier profile and the diffused SIMS profiles which shows that percentage of activation of boron in this region is high. Solmi et al. [Sol91] observed that the critical B concentration (the concentration below which enhanced diffusion and above which B precipitation occur in crystalline Si) was about one order of magnitude lower than the B solubility in Si in a wide range of experimental conditions. Thus, B precipitation could be enhanced inside the damaged region and this lowering of the equilibrium B solubility in Si was explained in terms of a large supersaturation of B atoms in interstitial positions [Cow90].

1.2.2 Cluster structures We discuss here the nature of the clusters that are responsible for the immobile

peak in Figure 1.5. The boron in the immobile peak is electrically inactive. The immobile peak occurs only if concentrations of both B and interstitials are high. Since no clusters can be seen by electron microscopy the size of the clusters must be small. The static peak remains stationary and electrically inactive during TED and dissolves only if annealing continues for several hours at 800 °C after TED has ended.

Pelaz et al. [Pel97, Pel99a] used physical reasoning and experimental results to show that the clusters are not Bs–BI or BI–BI pairs (subscripts s and I indicate substitutional and interstitial positions). Since the clusters are formed only near the surface where Is concentration is large, the cluster must involve both B and I. They suggested that in the initial stages BI2 clusters are formed. However the clusters are not stable when the supersaturation of the interstitials is not large. During annealing at high temperatures, BI2 clusters decay. Apart from energetic considerations, if they did not decay there will not be enough interstitials to cause TED. These clusters act as precursors for the growth of clusters containing a smaller number of interstitials. Larger B clusters were ruled out because the fraction of clustered B atoms does not increase after initial annealing for about 5 s. It was suggested that the most probable stable clusters are B3I and B4I. The diffused profiles were calculated using this mechanism and the agreement with the observed profiles was good. They determined the activated fraction of boron in the marker layers as a function of annealing time at 800 °C and assumed that in the early stages when supersaturation is large the high I content clusters (BI2 ,B2I2 ,B3I3 ,B4I4 ,...) are formed. In later stages of annealing when supersaturation becomes low, these clusters emit interstitials leaving high concentration boron clusters (B3, B4I, B4) behind. The high boron concentration clusters are stable and decay only after a very long anneal. This is consistent with the observation that the immobile peak dissolves only after TED ends and extended defects (like the 311 defects [Eag94]) have been dissolved. The simulated activated fraction of boron based on this model agreed closely with the observed fraction.

Considerable theoretical work on clustering of boron in Si was done in the mid-1980s and early 1990s. Several different models were used to interpret the experiments. Theories of nucleation and growth of precipitates developed to study aging of metal alloys were used. Infrared and electron paramagnetic resonance studies seemed to suggest the existence of BsBI pairs. Some authors assumed that the BsBI pairs were immobile while the others found that it was necessary to assume that the pairs are mobile to interpret the experiments. A review of this work is given by Luo et al. [Luo98].


Since the structure of the small clusters can not be determined by x-ray or electron microscopy techniques, many groups have investigated the structure and stability of the clusters by the theoretical methods. This lack of direct experimental check has fed the theoretical speculations and an extraordinary zoology of B clusters is reported in literature, an example is given by the famous picture of Liu et al. [Liu00] (see Figure 1.6).

In chapters 4 and 5 we will propose that the channeling and ion backscattering technique can be used as a powerful method to investigate the nature of the impurity clusters formed as consequence of interaction with point defects in excess. The lattice location of the impurity atoms can give precious information about the cluster configuration, for these reasons a brief description of the channeling phenomenon and its characteristic parameters will be given in the next section.

1.2.3 Impurity lattice location It is well known that the ion backscattering spectroscopy associated with

channeling technique can provide very precise information about the lattice location of impurity atoms dispersed in a crystalline material [Nas95]. The channeling phenomenon has been studied since the 1960’s and it has been combined with various ion beam analysis methods, e.g. Rutherford Backscattering Spectroscopy (RBS) [May77, Fel82, Mor73], proton induced x-ray emission, nuclear reaction analysis [Ras94, Mey95], elastic recoil detection [Nol98] and charged particle activation analysis [Sch94]. Even if the basic principles of this technique are very intuitive, the right interpretation of the experimental data can be very complex and needs of a simulation code that will be exposed in chapter 4. When the direction of the impinging ion beam is aligned along a well defined crystallographic axis the rate of backscattered ions is remarkably reduced, because in a single crystalline material, charged particles travelling along atomic rows or planes experience a steering force induced by the regular crystal structure. In the crystal lattice, atomic rows or planes form channels and this steering phenomenon is thereby called

Fig. 1.6 Structure and energetics of the calculated BICs. The small white balls are B atoms, the large gray balls are Si atoms involved in the cluster. All other Si atoms are shown as a stick-only network. The energy values (eV) next to each picture are calculated using different models [Liu00].


11

channeling. Due to the steering potential, the flux of charged particles travelling along a channel in the lattice is not homogeneous and therefore the nuclear encounter probability between the incoming particles and the atoms in the host lattice depends strongly on the incoming angle of the particles.

The channeling analyses are very sensitive to the presence of crystalline defects because they modified the periodic structure of the crystal and consequently alter the rate of backscattered ions with respect of a perfect crystal. The impurity atoms that are displaced from the substitutional sites are looked as defects by a channeled ion beam, as shown by the picture in Figure 1.7.

In ion channeling experiments, typical quantities, describing how well ions

channel in a crystal, are the channeling minimum yield χmin and the full-width half maximum (FWHM) of an angular scan Ψ1/2 (Figure 1.8) [May77]. Angular scan is the detected yield as a function of the sample tilt angle with respect to a main axial or planar direction. The minimum yield is the yield along the channel direction normalised with the yield in a random direction, i.e. the yield obtained from an amorphous material.

Fig. 1.7 Schematic of channeling effect of ion beam aligned along a crystal axis. When the incoming ions are scattered by interstitial atoms the backscattered component increases, permitting the location of the impurities.


Analytic models for ion channeling date back to the 1960’s [Rob63]. In

Lindhard’s model [Lin65] the critical angle for axial channeling is given by the following equation:

2/1221

12

⎟⎟⎠

⎞⎜⎜⎝

⎛=Ψ

EdeZZ

(1.8)

where Z1 and Z2 are the atomic numbers of the bombarding ion and the host atom, e the unit charge, E the energy of the ion and d the distance between atom rows in the lattice projected to the plane perpendicular to the channel direction. Lindhard [Lin65] has derived the following equation for Ψ1/2 for axial channeling:

2/12

1112/1 1ln

21)( ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛Ψ=Ψ

uCau (1.9)

In this equation, the minimum distance of ions from the atom rows is approximated to be equal to the thermal motion amplitude u1 of the lattice atoms. The factor C is a function of the angular divergence of the incoming ion beam and a is the Bohr’s screening length. The equation for the channeling minimum yield based on Barrett’s Monte Carlo simulations [Bar71] is:

2/1221min )1(8.18 −+= ξχ Ndu (1.10)

where

du

2/1

1126ψ

ξ = (1.11)

and N is the atomic density, Ψ1/2 is given in degrees.

Fig. 1.8 Backscattering spectra a) and angular scan b). Typical channeling quantities: Ψ1/2 and χmin are illustrated [May78].

-1 1

1.3 Solid Phase Epitaxial Regrowth

13

Channeling effects measurements have been widely used to determine the

lattice location of foreign atoms in crystals [Pic75]. By simultaneous measurement of the signals from the lattice and foreign atoms, one can often determine the crystallographic site location of the foreign atoms. To specify site location it is necessary to measure angular scans about more than one axial direction. Figure 1.9 shows a two dimensional crystal with an interstitial impurity and schematic angular profiles about two axes. About the <11> axis, the yield from the interstitial atom matches that of the host crystal since the interstitial foreign atom lies along the <11> rows. Along the <10> direction there is a narrow peak in the foreign atom signal rather than a broad dip. The peak is a consequence of the enhancement of the ion flux in the centre of the channel when the beam is well aligned with the crystallographic axis. Because of this flux enhancement (or flux peaking) the channeling effect can be used to distinguish between specific interstitial sites. If the foreign atoms were substitutional, the angular scan around the <11> axis would also match that of the host lattice. The analysis becomes more complicated when the impurity atoms are not in well-defined positions.

1.3 Solid Phase Epitaxial Regrowth Solid phase epitaxial growth process involves an amorphous layer in intimate

contact with a crystalline layer, which upon heating to sufficient temperatures allows the amorphous layer to crystallize using the crystalline layer as a seed (see the sketch of Figure 1.10). A well-defined crystalline-amorphous (c-a) interface moves toward the surface, at a rate dependent on several factors, such as orientation and impurity concentration.

The tendency for amorphous silicon (a-Si) to crystallize is a consequence of the fact that the free energy is lower for the crystalline state than for the amorphous state. Silicon forms strongly covalent, directional bonds, and in a solid the condition of minimum free energy is achieved by having these bonds arranged in a tetrahedral configuration. When this arrangement is extended in three dimensions, the diamond lattice characteristic of crystalline silicon (c-Si) can be formed. At room temperature and atmospheric pressure this is the configuration of lowest free energy. In contrast, the amorphous phase of silicon maintains a local order, arising from the strong energy minimum associated with tetrahedral bonding, but has not the long-range order seen in the crystal (i.e. beyond 2 interatomic distances).

Fig. 1.9 Conceptual angular scans for a two dimensional crystal [May78].


The amorphous layer may be deposited onto a crystalline layer or substrate via

chemical vapour deposition or similar technique. The obvious disadvantage to using deposition techniques would be the need to highly control the amount of impurities on the surface of the substrate to ensure good quality growth later. A more common approach involves bombarding the surface of a crystalline substrate or layer with a heavy ion at sufficient fluence to amorphize part of the crystalline material. Generally this is done using ion implantation, which has the advantage of producing a cleaner amorphous layer and c-a interface. If only part of the crystalline layer is amorphized, then the remaining crystalline layer can act as a seed to recrystallize the amorphous layer upon heat treatment. This approach is typically employed and is the basis for work in this dissertation. The amorphous layers are generated by ion implanting the surface of silicon wafers with heavy ions, such as Si. Implant energies are typically chosen to amorphize a layer from the surface down to some desired thickness. After amorphization another impurity may be introduced into the material. Upon recrystallization, impurities may become trapped onto substitutional lattice sites allowing metastable conditions to be met. Typical SPE regrowth begins to occur at temperatures as low as ~450 °C [Poa84, Wil83c, Wil83d] on up to temperatures below the melting point of a-Si with regrowth rates dramatically increasing for increasing temperature. It is particularly interesting to examine temperatures ≤650 °C where diffusion is minimal.

Thermal heating [Nar82e, Nar83, Poa84, Wil83c, Wil83d], electron beam heating [Tim85, Tim86], ion beam assisted regrowth [Ell87a, Ell87b, Ker86, Wil85], and laser heating [Kok82, Ols84, Ols85a, Ols85b] techniques aid in regrowing the amorphous layer by giving the system enough energy for reorganization. Since regrowth observes an Arrhenius dependence, the time scale to complete recrystallization of an amorphous layer may become very small at temperatures >650 °C. This limits experimental observations to lower temperatures unless in-situ measurements and very high temperature ramp rate equipment is used. Timans et al. [Tim85] accomplished this by using electron beam heating, Olson et al. used a cw laser for heating to higher temperatures and took data using time resolved reflectivity (TRR) measurements [Ols85a, Ols85b]. The TRR technique has been used in this work and will be described in details in chapter 2.

1.3.1 Effect of impurities and regrowth models In their pioneering studies, Csepregi et al. [Cse75, Cse76, Cse77, Ken77, Cse78]

showed that over the temperature range from 450 to 575 °C the velocity of the interface motion during SPE of silicon is thermally activated and also depends on the crystallographic orientation of the substrate and on the presence of impurities in the amorphous layer. The regrowth is a process thermally activated, as shown

Fig. 1.10 Schematic illustration of the solid phase epitaxy (SPE) process in a-Si [Ols88].


15

experimentally for the first time by Csepregi et al. [Cse75, Ols88], well described by an Arrhenius-type expression:

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

TkEvvB

aexp0 (1.12)

where v is the SPE growth rate; v0 is the pre-exponential factor; Ea is the

activation energy of the process; kB is the Boltzmann's constant; T is the temperature. The values for Ea and v0, for the Si implanted layers are Ea=2.68±0.05 eV and v0= 3.1x108 cm/s [Ols88] over an extremely wide range of rates (10-2-106 Å/s) and temperatures (500-1000 °C).

The regrowth rate can be expressed [Nar83] in term of the free energy of the amorphous-crystal phase transition.

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

Tk∆G

Tk∆GAv

BB

*0exp1expλη (1.13)

where A is a geometrical factor, λ is the planar spacing, η is the frequency of vibration of atoms, ∆G* is the excess of free energy of the state relative to the a-Si (see Figure 1.11), ∆G0 the net free energy change between the amorphous and the crystalline phase. For SPE in Si ∆G0/kBT>>1 and the final factor of the (1.13) can be dropped, yielding the (1.12).

The presence of impurities in an amorphous layer, at concentrations > 0,1 at%, can dramatically affect the SPE rate. Csepregi et al. found B concentrations of ~2.5x1020 cm-3 increase the regrowth rate 20 times that of intrinsic silicon [Cse77]. Olson et al. [Ols88] reported (see Figure 1.12) the SPE rate of B doped Si in the concentration range between 1x1018 and 1x1021 at/cm3 at temperatures of 610, 710 and 840 °C.

The other elements of group III (aluminium, gallium, indium, and thallium)

increase the regrowth rate, but not as much, and maximum incorporation limits are usually smaller. These elements also have the disadvantage of being very mobile upon recrystallization if concentration become too high. The work of Narayan and co-workers also examines the effect Ga has on SPE regrowth. Essentially, Ga will behave very similar to that of In [Nar82a, Nar82d, Nar82e, Nar83]. Low concentrations allow enhanced, complete regrowth and almost total incorporation while higher concentrations inhibit regrowth and may induce polycrystalline formation. Redistribution of Ga is possible by similar “push out” effects as well as precipitation. The maximum substitutional concentration is estimated to be 2.5x1020 cm-3, which is about an order of magnitude higher than equilibrium. Kerkow et al. [Ker84] find the maximum regrowth enhancement at concentrations of ~2-3x1020 cm-3 at 515 °C.

∆G*

∆G0

amorphous crystal

Fig. 1.11 Schematic Gibbs energy difference between amorphous and crystalline phases.


Experiments by Suni et al. [Sun82a, Sun82b, Sun82c] look at the effect of

intrinsic as well as B, P, As, and P+As implants with compensated regions where B concentrations are similar to either P or As concentrations exhibit regrowth rates very close to intrinsic rates. Temperatures of 475 and 500 °C are used. Olson et al. [Ols88] investigated the compensation effect over a temperature range from 575 to 900 °C in films containing uniform concentration (~1.8x1020 cm-3) of B and P. The rate versus temperature data are shown in Figure 1.13. The activation energies are 2.52, 2.68 and 2.68 eV for B, P, and B+P respectively. Studies using In and Sb for compensating implants also show regrowth rates close to intrinsic silicon [Tho89, Wil83b]. Finally, Ga and As compensated implants are used by Kerkow et al. showing concentrations below ~1020 cm-3 leave the regrowth rate close to intrinsic but above this the rate begins to decrease [Ker84]. Non-doping impurities such us O, N, C and F significantly reduce the SPE rate [Ken77, Cse78, Tsa79].

Fig. 1.12 SPE rate of B doped Si versus B concentration at three different growth temperatures [Ols88]


17

The compensation effect suggests that the SPE velocity variation could be

attributed to electronic phenomena. Suni et al. [Sun82b] hypothesized that the SPE rate is controlled by the concentration of vacancies at the c-a interface. In heavily doped films, the total Vs concentration is dominated by charged vacancies, the concentration of which is established by the relative numbers of n- and p-type impurities in the layer. Since the charged vacancy concentration responds to the Fermi level position, it becomes apparent that the SPE rate will increase when the Fermi level moves towards either band edge. When the Fermi level is driven to mid-gap, by the presence of both n- and p-type impurities, the total vacancies concentration is reduced and the SPE rate should revert to its intrinsic value. An alternative description for impurity-induced rate enhancement, which does not require motion of vacancies to the interface, has been put forward by Williams et al. [Wil83a]. This model extended the ideas of Spaepen and Turnbull [Spa78, Tur82], in which dangling bonds are generated at the interface and migrate along the interface reconstructing the random network into the crystalline network, therefore epitaxial crystallization is viewed as a simple bond rearrangement and continues as the defect propagates along a crystalline edge. Williams and Elliman include the doping effects by showing how the concentration of kink sites at the interface might depend on Fermi level position. However, these models can furnish only a qualitative explanation of the impurity effects. In fact a variation of the Fermi level from the mid-gap position of 0.3-0.4 eV should be change the activation energy of the same quantity. Such variation has never been experimentally observed. Moreover, when the temperature increases it is expected that the number of thermally generated charge carriers increases and the Fermi level should move toward mid-gap, we should expect less rate enhancement with increasing temperature, while no deviation from Arrhenius behaviour in the temperature range 500-1000 °C has been ever observed [Ols88]. Another interesting question is the

Fig. 1.13 Dependence of the SPE rate on temperature for a-Si containing either B or P, and for both impurities in equal (compensating) concentration (peak concentration=1.8x1020 cm-3) [Ols88].


different SPE rate enhancement produced by the various doping impurities. Campisano [Cam82] noted an interesting relationship between regrowth rate, at constant impurity concentration, and the absolute covalent radius difference between the particular impurity and silicon |rI-rSi|. This correlation is shown in Figure 1.14 for dopant (As, P, Sb and B) concentration of 0.125 at% (~6.3x1019 at/cm3) and regrowth temperature 500°C. In addition at low impurity concentration, the regrowth rate increases linearly with the impurity concentration [Cam82] up to the solubility limit. Campisano suggested that the impurity-induced regrowth rate effects result from strain-enhanced recrystallization. Suni et al. [Sun82a] pointed out that the accumulation of local strain surrounding an impurity atom may develop into a macroscopic strain in the lattice, thus providing a driving force for migration, such process may enhance regrowth by facilitating atom motion, notably Si interstitials, across the interface a-c. Although the strain model does not explain the compensation effect observed with dopant impurities of opposite charge.

The work of Lu et al. [Lu89, Lu91] showed that at temperature in the range of

520 – 570 °C and hydrostatic pressure up to 3.2 GPa the growth rate of intrinsic Si is enhanced by up a factor of 5 over that at atmospheric pressure. The strain induced by 0.1 at% of impurity concentration is in the range 0.01-0.02 %, while 2 GPa results in a strain of 0.7%, considering this difference Lu et al. suggested that the impurity effect is substantially electronic. They showed the SPE rate increases exponentially with pressure, and is characterized by a negative activation volume of -0.28 the atomic volume in Si. The activation volume is independent of both dopant concentration and dopant type. This result is inconsistent with the bulk point defects mechanism proposed by Suni et al. [Sun82b], but supports the interface point defects model of Williams et al. [Wil83a].

In conclusion of this overview we can note that a complete model of the SPE process that explain all the observed effects (electronic and strain) is actually lacking.

0.0 0.1 0.2 0.30

25

50

Si

As P

Sb

B

SP

E ra

te [A

ng/m

in]

|rI-rSi| [Ang]

T=500°C

Fig. 1.14 500°C SPE growth velocity of a-Si doped with different impurities at 0.125 at% as function of absolute covalent radius difference between the impurity and silicon |rI-rSi| [Cam82].


19

1.3.2 Supersaturated Solid Solutions The ability both to anneal impurities that have been ion-implanted in Si and to

create a high concentration of electrically active impurities is an extremely important aspect of the SPE process.

It is well known that ionized impurities of group III and V provide the charged carriers when they are located into substitutional sites of the Si lattice, the concentration of substitutional impurities can be seen as the solid solubility of the solute in a binary alloy. The phase diagram of the impurity-Si system describes the variation of the substitutional impurity concentration as function of the thermodynamical parameters (temperature, pressure, composition). Sb, In, Bi, Ga, As exhibit retrograde solubility, i.e., maximum in the solid curve, as draft in Figure 1.15. The Figure 1.16 reports the solid solubility of several species in Si [Sze81]. Under equilibrium conditions the limits on maximum substitutional concentrations are set by the retrograde solubility limits. After the SPE process, instead, a metastable phase is reached and long time annealing needs to relax the system into a stable, equilibrium phase. This metastable condition permits to overcome the impurity solubility limit realizing supersaturated solid solutions, for example Narayan et al. [Nar83] obtained a maximum concentration of Ga of 2.5x1020 at/cm3 into substitutional sites in Si by SPE at 550°C, being the retrograde solubility limit of Ga 4.5x1019 at/cm3 as shown in Figure 1.16. White et al. [Whi80] reached a value of 4.5x1020 at/cm3 by liquid phase epitaxial regrowth.

Campisano et al. [Cam80a, Cam80b] showed that incorporation of above-

equilibrium concentration of impurities onto silicon lattice sites can take place if the diffusivity of the impurity in Si is negligible compared with the epitaxial regrowth time. This condition is verified if the time required for one monolayer regrowth τint=λ/v (λ is the crystal plane spacing and v the interface velocity) is negligible with respect of the time that an impurity atom spends at the interface τimp=λ2/Dint (Dint is the diffusion coefficient at the interface). During SPE growth, dopant diffusion length varies typically from 10-12 cm at 550°C to 10-9 cm at 1400°C in the time interval the crystallizing interface advances by one plane spacing (~2Å). Therefore, most of the dopant impurities will be engulfed by the advancing interface.

Fig. 1.15 Schematic phase diagram of a solution as function of the concentration of solute. The CS

0 indicates the maximum of the solid curve that is called “maximum retrograde solubility”.


However, if the gain in free energy from the amorphous-crystalline

transformation becomes equal to the increase in free energy associated with size, chemical, and electronic effects of dopants in the crystalline lattice, then the net ∆G0 in equation 1.13 will be zero and the advancing interface will stop. Narayan et al. [Nar83] used this condition to set the maximum limit on the dopant concentration, neglecting the changes in chemical free energy and the electronic effects they considered only the ∆G0 associated to the impurity size effect. In this approach the solute concentration corresponds to the intersection of free-energy curves of amorphous and doped crystalline silicon on free energy versus composition plots. Experimentally observed concentrations tend to the calculated maxima in Si-Sb and Si-As systems, but for other systems (Si-In, Si-Ga) this is not verified indicating that, eventually, other effects are involved.

A summary of observed (by RBS-channeling analyses) substitutional impurity concentrations by various authors is reported in table 1.1, elements with radii close to silicon (rC=1.17 Å) are more readily incorporated onto lattice sites.

Table 1.1

Impurity Max substitutional concentration by SPE

Covalent radius

[Å]

Ref.

As 9.0x1021 1.20 [Wil82b]

Ga 2.4 x1020 1.26 [Nar83]

Sb 1.3 x1021 1.40 [Nar83]

In 5.5 x1019 1.44 [Nar83]

Bi 8.9 x1019 1.46 [Nar83]

Pb 7.8 x1019 1.47 [Wil82b]

Tl 3.9 x1019 1.48 [Wil82b] Williams and Elliman [Wil82a] suggested a model of SPE where the maximum

soluble concentration is controlled by process occurring at the regrowth interface rather than by impurity diffusion and incipient precipitation in the amorphous and

Fig. 1.16 Solid solubility as function of temperature for several impurities in Si [Sze81].


21

crystalline phase. During bond breaking and atomic rearrangement at the amorphous-crystal interface, the size differences, in terms of covalent radius, between impurity and Si atoms would give rise to local bond distortion and hence to interfacial strain, when impurities are incorporated onto substitutional sites. The level of interfacial strain increases with both impurity concentration and mismatch in covalent radius between impurity and Si atoms and this strain may provide the driving force for rejection of impurity atoms into less dense amorphous phase rather than for their incorporation onto substitutional sites in the denser crystalline phase. The interface segregation of the impurity atoms, similar to a push out effect, can be very disadvantageous for the realization of structure with sharp and well defined dopant profiles, this process correlated to the movement of the c-a interface will be discussed in the following section.

In conclusion, the influence of the strain on the substitutional impurity concentration can not be negligible. In the chapter 2 we will investigate the effect of co-doping the Si with impurities that have different covalent radii with respect of Si (rC=1.17 Å), like B (rC=0.82 Å) and Ga (rC=1.26 Å), in order to enhance the maximum dopant concentration by strain compensation.

1.3.3 Interface segregation The interface planar motion can alter the impurity concentration profile because

of the different solute solubility between the crystalline and amorphous phases of the solvent. The segregation coefficient at equilibrium k0 is defined as the ratio of the concentration of solute soluble in crystal (Cx) and in amorphous (Ca).

bulka

x

CCk =0 (1.14)

Cx and Ca can be determined from the phase diagram for Si, where Gibbs free-energy differences for the crystal, liquid, and amorphous phases are represented as a function of temperature [Don85]. Being the SPE a non equilibrium process, an interfacial segregation coefficient k’ can be expressed as:

Inta

x

CCk =' (1.15)

where the values of Cx and Ca are defined at the interface. In Figure 1.17 [Whi82] is schematically described a process where k0<1, initially

the solute distribution has a uniform concentration n0, during the interface coming the solute is rejected in the lower dense amorphous phase and a quantity of solute atoms are accumulated at the interface. The final concentration profile of the picture can be calculated by solving the diffusion equation of the Fick’s law:

2

2 ),(),(x

txCDt

txC aam

a

∂∂

=∂

∂ (1.16)

Where Ca(x,t) is the impurity concentration in the amorphous phase at the depth x at time t, D is the diffusivity of the impurity in the amorphous phase. The boundary conditions [Bae82] are:

00

==x

a

dxdC

(1.17)

to limit the diffusion at the outer surface of the sample; and

0),()1( ' =−+ txvCkdx

dCaa (1.18)

to take into account the surface segregation.


Analytical solution is possible only if the initial concentration profile is uniform

and it is expressed by the following formula:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ ′′−−−

′′−

+′=am

s Dvxkk

kkCkC )1(exp1110 (1.19)

where x is the distance from the starting position of the interface, v is the interface velocity and C0 the initial concentration. In Figure 1.17, when the steady state is reached the concentration of segregated solute is n0/k0 and the peak thickness is ∼D/v.

A numerical solution [Bae82, Woo81, Whi80] can be elaborated to calculate the profile starting from a non uniform solute distribution as it will be shown in chapter 2 for Ga implanted Si.

The stepwise growth model [Rei94] gives the following relationship between k’ and k0 and the interface velocity:

v)/)-(1' 0 λDexp(kkk 0 −+= (1.20)

where λ is defined as the atomic jump distance.

1.4 Impurity ionization in heavily doped Si The final goal of all the studies briefly sketched here is the optimization of the

electrical properties of the doped Si layers. Since an intimate relationship exists between the bulk properties and that of the material in a device structure, in the concluding remarks of this chapter it is important to give some skills about the electrical properties of doped Si. The ionization of shallow impurities is described in the first section, but we are especially interested in the high doping regime (section

Fig. 1.17 Schematic of a segregation process induced by SPE growth. k0 indicates the segregation coefficient at equilibrium, n0 the initial concentration of impurity in the amorphous phase, x is the depth from the surface. The fours pictures represent the situation at different times during the c-a interface movement from left to right.

1.4 Impurity ionization in heavily doped Si

23

1.4.2) at room temperature (RT), being these conditions into focus of the technological challengers.

1.4.1 Low impurity concentration In a bulk doped semiconductor substitutional donors and acceptors have an

excess or deficit electron in their outer electron shell, respectively, as compared to the replaced lattice atoms. Donors have one excess electron that can be donated to the conduction band. Acceptors have one less electron than the replaced lattice atom and can accept an electron from the filled valence band of the semiconductor [Con82, See73, Yu99]. In the discussion about the ionization of doping impurities in Si we will often use the description of the donor-like impurities, this is only a convenient way because the argument is completely specular for acceptor-like impurities, but the electron’s representation is often more intuitive with respect of the hole’s one. The charge state of donors is neutral (ND

0) when occupied by an electron and positively charged (ND

+) if the electron is excited to the conduction band, the total charge neutrality of the semiconductor impose that the total concentration of impurities equal the sum of neutral and ionized impurities, i.e. ND= ND

0+ND+, similarly for acceptors NA=NA

0+NA−. The probability of occupation of an

acceptor or donor follows Fermi-Dirac statistics, consequently ND0= NDƒF(ED) and NA

0= NA(1-ƒF(EA)), being ƒF the Fermi-Dirac distribution and ED and EA the energy levels of donor and acceptor in the energy gap, respectively. The free carrier concentration due to the ionization of dopant impurities is given by the concentration of ionized impurities, which is calculated using the Fermi-Dirac distribution as function of temperature by the following formulae [Sze81]:

⎟⎠⎞

⎜⎝⎛ −+

=⎟⎠⎞

⎜⎝⎛ −+

= −+

KTEE

g

NN

KTEEg

NNFA

AA

DF

DD

exp11exp1 (1.21)

where g is the ground state degeneracy of the impurity (g=2 for electrons and 4 for holes); EA, ED and EF are measured with the zero of the energy fixed at the valence band edge. The condition of complete ionization is obtained when ED>EF and EA<EF, at low temperature the Fermi level approaches the band edge and the impurities become partially ionized, this effect is called freeze−out regime.

The Fermi level depends on the impurity concentration and can be determined by the condition of charge neutrality: p+ NA

−=n (if NA>>ND), where n and p are the electron and hole concentration in the conduction and valence band, respectively. At RT in silicon the free carrier concentration is essentially determined by the ionized fraction of the dopants, being the intrinsic carrier concentration negligible (∼1.6x1010cm-3) [Sze81].

Boron and gallium in silicon have shallow energy levels (for this reason they are called shallow impurities) of 45 meV and 70 meV [Mad96] from the valence band edge, respectively. In a p-doped Si with NA∼1017 at/cm3 one can evaluate EF∼110 meV at RT, and therefore the ionized fraction of B and Ga impurities at RT, using the equation 1.21, are 98% and 95%, respectively. Instead, an acceptor with deep energy level in the gap, like In for example (EA∼160 meV), has ionization of 35% at RT.

Note that the equation 1.21 is limited to concentration below the Mott transition. Above the Mott transition, which will be discussed in the next section, impurities can not bind charge carriers, i.e. donors and acceptors can not be in the neutral charge state.

1.4.2 High impurity concentration At RT the ionization of shallow impurities is quite complete in the case of non

degenerate semiconductor. As the p-doping concentration increases the Fermi level


moves towards the valence band edge, and the ionization efficiency progressively decreases, for B and Ga this can occur at doping concentration of ~1018 at/cm3. However, when the impurity concentration approaches the critical value of the Mott transition the impurity atoms are so closed that the Coulomb potentials of impurities overlap resulting in a reduction of the ionization energy. At this point, phenomena like the hopping conduction, impurity band conduction and strong screening effect due to the high concentration of free carriers must be taken into account [Sch05].

The Mott transition [Mot61, Mot81a, Mot81b] refers to the insulator-to-metal

transition occurring in semiconductors at high doping concentrations. Consider an n-type semiconductor (for simplicity, the case of p-type has a symmetrical description) with low doping concentration. At low temperatures (T→0), shallow impurities are neutral, i.e. electrons occupy the ground state of the donor impurities. All continuum states in the conduction band are unoccupied. In this case, the semiconductor has insulator-like properties. As the doping concentration increases, the Coulomb potentials of impurities overlap as schematically shown in Figure 1.18. As a result of the overlapping impurity potentials, electrons can transfer more easily from one donor to another donor. Electrons transfer from one donor state to a state of an adjacent donor by either tunneling or by thermal emission over the barrier. The probability of both processes increases with decreasing donor separation. In other words, the activation energy for electron transport is reduced. In the extreme case, the activation energy approaches zero, i.e. the conductivity remains finite even for T→0. The semiconductor has metal-like properties. Screening of impurity potentials is a second contribution to the reduction of the impurity ionization energy. Impurity potentials are effectively screened at high free carrier concentrations. Screened potentials are less capable of binding electrons. Thus, the effective ionization energy decreases due to screening. The insulator-to-metal transition occurs at the impurity concentration at which the distance between impurities becomes comparable to the Bohr radius. If donors with concentration N occupied sites in a simple cubic lattice, their separation would be N−1/3. The Mott transition would then occur at a concentration

3/1*2 −= critB Na (1.22)

where aB is the effective Bohr radius and Ncrit is called the critical concentration. However, equation 1.22 does not give the correct result, because impurities are distributed randomly in semiconductors. Using a Poissonian distribution of impurities, one can show that Bohr orbital of an impurity is likely to overlap with the orbitals of one, two, or three neighbouring impurities if

3/1*

232 −= critB Naπ

(1.23)

Rearrangement of the equation 1.23 yields the Mott criterion:

Fig. 1.18 Picture representative of the ionization energy reduction due to the energetic band overlap of the nearest donor atoms when the impurity concentration is about the critical Mott transition [Sch05].

1.4 Impurity ionization in heavily doped Si

25

24.03/1* ≈critB Na (1.24)

As an example the critical concentration for Si doped with P, with an effective Bohr radius of aB*=17 Å [Ros83], is Ncrit=2.8x1018 at/cm3.

However, the insulator-to-metal transition does not occur abruptly at the critical concentration. Instead the transition is gradually evolving with increasing the impurity concentration. Qualitatively, the gradual nature of the Mott transition can be expressed in terms of continuously changing impurity activation energy. Experimental donor activation energies have been described by the equation [Deb54]:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

3/1

0 1crit

DDD N

NEE (1.25)

where ED0 is the donor activation energy for ND<<Ncrit. The reduction in donor ionization energy is thus proportional to the distance between the donor atoms.

At impurity concentration well below the critical Mott concentration, impurities can be considered as isolated, non-interacting entities. As the concentration increases but is still well below the Mott concentration, impurities begin to interact. Carrier transport at low temperatures occurs via thermally assisted tunneling between impurity states. This transport process is called hopping conduction. At still higher impurity concentrations but below the critical Mott concentration, overlapping impurity states form an impurity band. At low temperatures, carriers can propagate within the impurity band without entering the conduction band. This transport process is known as impurity band conduction [Mot87, Mot90, Shk84].

Consider a semiconductor with a donor density well below the critical Mott transition density. Upon cooling the semiconductor to low temperature, the conductivity is expected to decrease as free electrons freeze out onto localized donor states. For kBT<< ED the conductivity of an n-type semiconductor is expected to become vanishing small. Experimentally, zero conductivity is not observed in semiconductors containing a net concentration of shallow impurities. Instead, the temperature dependence of the conductivity is less dramatic than expected for free carrier freeze-out. The conductivity in this regime is not given by electrons excited to the conduction band but rather by electrons hopping from neutral donors to ionized donors. The conductivity is referred to as hopping conductivity. When the donor impurities are closely spaced, their energy levels split. Electrons can tunnel from a donor state to an empty state of an adjacent donor. A so-called Coulomb gap develops between filled donor states and empty donor states. The Coulomb gap is caused by the long-range Coulomb interaction of localized electrons [Kno74; Efr75], and occurs at the Fermi level. The tunneling from filled donor states to adjacent empty donor states therefore requires small thermal activation energy. The activation energy can be interpreted as the energy from the Fermi level to the energy of the maximum of the density of empty state distribution. Typically the activation energy is much smaller than the donor ionization energy. Figure 1.19 schematically represents the dispersion relationships and donor impurity states at different doping densities. At low doping density, states of adjacent impurities do not interact (N<<Ncrit) and impurity ground states are discrete and energetically well-defined levels. As the doping concentration increases, states of adjacent impurities interact, split, and finally form an impurity band (N≤Ncrit). At even higher doping concentrations, the impurity band widens and merges with the continuum band (N>Ncrit).

The insulator-to-metal transition has deeply investigated in B doped Si by measuring the hopping conductivity and the critical concentration has been determined in the 3-5x1018 at/cm3 range [Edw99, Bog99, Dai91]. Mamontov and Willander [Mam94] evaluated the ionized fraction of B impurities in Si at room temperature as function of dopant concentration in the range 1013-1020 at/cm3


applying the Fermi-Dirac statistics and the existing models of band gap narrowing due to many body effects [Lee83], taking into account the effect of Mott transition and the impurity band formation. The ionization has a minimum of 75% at 2x1018 at/cm3 and increases at 100% at 2x1019 at/cm3 maintaining this value for higher concentration. No studies has been found about Ga doped Si but we believe that the critical concentration is of the same order of magnitude.

Concluding for Si doped with B and Ga at concentration higher than 1x1019 at/cm3 a metallic regime is realized at RT and the ionization of impurities can be considered complete. In this contest it is important to underline that the phenomenon of the so called “de-activation” of the dopants is due to causes different from the ionization efficiency and it is completely adduced to the clustering effects and impurity precipitation we have mentioned before.

1.5 References

[Ali01] Alippi P., L. Colombo, P. Ruggerone, A. Sieck, G. Seifert and Th. Frauenheim, Phys. Rev. B 64 (2001) 75207.

[Bae82] Baeri P., S.U. Campisano, in Laser annealing of Semiconductor, J.M Poate and J.W. Mayer eds. (Academic Press, New York, 1982)

[Bar71] Barrett J. H., Phys. Rev. B 3, 1527 (1971). [Bar75] Baranova E. C., V. M. Gusev, Y. V. Martynenko and I. B. Haibullin, Radiat. Eff. 25

(1975) 157. [Bog99] Bogdanovich S., D. Simonian, S.V. Kravchenko, M.P. Sarachik, Phys. Rev. B 60

(1999) 2286 [Bou01] Bourdelle K. K., A. T. Fiory, H.-J. L. Gossmann and S. P. McCoy, in Si Front End

Processing – Physics and Technology of Dopant-Defect Interactions III, Mat. Res. Soc. Proc. J8.1.1 (2001) 669

[Bra00] Bracht H., Mater. Res. Soc. Bull. 25 (2000) 22. [Bri54] Brinkman J. A., J. Appl. Phys. 25 (1954) 961. [Cam80a] Campisano S.U., E. Rimini, P. Baeri and G. Foti, Appl. Phys. Lett. 37 (1980) 170

Fig. 1.19 Schematic representation of the energy bands in a n-doped Si when the impurity concentration increases from the low level (left), at which the donor energy levels are isolated in the band gap and classical electrical conduction due to the electrons in the conduction band happens, to the critical level concentration, at which the hopping conduction (centre) and then the impurity band conduction (right) occur [Sch05].

EC

EV

∆ED EC

EV

+

- EC

EVN<<NC N≤NC N∼NC

1.5 References

27

[Cam80b] Campisano S.U., G. Foti, P. Baeri, M.G. Grimaldi and E. Rimini, Appl. Phys. Lett., 37 (1980) 719

[Cam82] Campisano S. U., Appl. Phys. A 29 (1982) 147 [Cam93] Campisano S. U., S. Coffa, V. Raineri, F. Priolo, and E. Rimini, Nouv. J. Chim.

80/81 (1993) 514. [Cat94] Caturla M.-J, T. D. de la Rubia, and G. H. Gilmer, in Materials Synthesis and

Processing using Ion beams, R. J. Culburison, O. W. Holland, Jones K. S., and K. Maiz eds., MRS Symposia Proceedings No. 316 (Material Research Society, Pittsburgh, 1994) 141.

[Cat98] Caturla M. J., M. D. Johnson, and T. D. de la Rubia, Appl. Phys. Lett. 72 (1998) 2736

[Cha01] Chakravarthi S. and S. T. Dunham, J. Appl. Phys. 89 (2001) 3650. [Con82] Conwell E., in Transport: The Boltzmann equation, Handbook on Semiconductors,

(North-Holland Publishing Company, USA, 1982) 513 [Cor66] Corbett J. W., Solid State Physics Vol. 7. (Academic, New York, 1966) [Cow90] Cowern N. E. B., K. T. F. Janssen, and H. F. F. Jos, J. Appl. Phys. 68 (1990) 6191. [Cow91] Cowern N. E. B., G. F. A. van de Walle, D. J. Gravesteijn and C. J. Vriezema, Phys.

Rev. Lett. 67 (1991) 212. [Cow96] Cowern N. E. B., A. Cacciato, J. S. Custer, F. W. Saris, and W. Vandervorst, Appl.

Phys. Lett. 68 (1996) 1150. [Cow99] Cowern N. E. B., G. Mannino, P. A.Stolk, F. Roozeboom, H. G. A. Huizing, J. G.

M. van Berkum, F. Cristiano, A.Claverie and M. Jaraiz, Phys. Rev. Lett. 82 (1999) 4460

[Cro70] Crowder B. L., R. S. Title, M. H. Brodsky, and G. D. Pettit, Appl. Phys. Lett. 16 (1970) 205.

[Cse75] Csepregi L., J. W. Mayer and T. W. Sigmon, Phys. Lett. A 54 (1975) 157. [Cse76] Csepregi L., J. W. Mayer and T. W. Sigmon, Appl. Phys. Lett. 29 (1976) 92. [Cse77] Csepregi L., E. F. Kennedy, T. J. Gallagher, J. W. Mayer and T. W. Sigmon, J.

Appl. Phys. 48 (1977) 4234. [Cse78] Csepregi L., E. F. Kennedy, J. W. Mayer and T. W. Sigmon, J. Appl. Phys. 49

(1978) 3906. [Dai91] Dai P., Y. Zhang, M.P. Sarachik, Phys. Rev. B 66 (1991) 1914 [Deb54] Debye P.P. and E. M. Conwell, Phys. Rev. 93 (1954) 693 [DeL95] De la Rubia T. D. and G. H. Gilmer, Phys. Rev. Lett. 74 (1995) 2507. [Den78] Dennis J. R. and E. B. Hale, J. Appl. Phys. 49 (1978) 1119. [Don85] Donovan E. P., F. Spaepen, D. Turnbull, J. M. Poate, and D. C. Jacobson, J. Appl.

Phys. 57 (1985) 1795. [Eag94] Eaglesham D. J., P. A. Stolk, H. J. Gossman and J. M. Poate, Appl. Phys. Lett. 65

(1994) 2305 [Eag95] Eaglesham D. J., P. A. Stolk, H. J. Gossman, T. E. Haynes, and J. M. Poate, Nucl.

Inst. and Meth. B 106 (1995) 191 [Edw99] Edwards P.P., R.L. Johnston, F. Hensel, C.N.R. Rao, D.P. Tunstall, Solid State

Physics 52 (Accademic Presse, USA, 1999) 229 [Efr75] Efros A. L. and B. I. Shklovskii, J. Phys. C: Solid State Phys. 8 (1975) L49 [Ell87a] Elliman R. G., J. S. Williams, W. L.Brown, A. Leiberich, , D. M. Maher and R. V.

Knoell, Nuclr. Inst. and Meth. B19/20 (1987) 435 [Ell87b] Elliman R. G., J. S. Williams, S. T.Johnson and E. Nygren, Mat. Res. Soc. Symp.

Proc. 74 (1987) 471 [Ell88] Elliman R. G., J. Linnros, and W. L. Brown, in Fundamentals of Beamsolid

Interactions and Transient Thermal Processing (M.J. Aziz, L. E. Rehn, and B. Stritzker eds) MRS Symposia Proceedings No. 100 (Materials Research Society, Pittsburgh, 1988) 363.

[Fah89] Fahey P. M., P. B. Griffin and J. D. Plummer, Rev. Mod. Phys. 61 (1989) 289 [Fah89b] Fahey P. M., S.S. Iyer, G.J. Scilla, Appl. Phys. Lett. 54 (1989) 843 [Fel82] Feldman L. C., J. W. Mayer, and S. T. Picraux, Materials analysis by ion

channeling (Academic Press, New York, 1982). [Goe00] Gösele U., P. Laveant, R. Scholz, N. Engler and P. Werner, Mater. Res. Soc. Symp.

Proc. B7.1 (2000) 610


[Gol93] Goldberg R. D., R. G. Elliman, and J. S. Williams, Nucl. Inst. Methods Phys. Res. B 80/81 (1993) 596.

[Gos95] Gossmann H.-J., C. S. Rafferty, F. C. Unterwald, T. Boone, T. K. Mogi, M. O. Thompson, and H. S. Luftman, Appl. Phys. Lett. 67 (1995) 1558.

[Hai92] Haile J. M., Molecular Dynamics Simulations: Elementary Methods (Wiley, New York, 1992)

[Hay96] Haynes T. E., D. J. Eaglesham, P. A. Stolk, H.-J. Gossmann, D. C. Jacobson, and J. M. Poate, Appl. Phys. Lett. 69 (1996) 1376.

[Hof73] Hofker W. K., H. W. Werner, D. P. Oosthoek, and H. A. M. de-Grefte, Appl. Phys. 2 (1973) 165.

[Hof74] Hofker W. K., H. W. Werner, D. P. Oosthoek, and N. J. Cowman, Appl. Phys. 4 (1974) 125.

[Hol88] Holland O. W., M. K. El-Ghor, and C. W. White, Appl. Phys. Lett. 53 (1988) 1283. [Hua99] Huang M. B. and I. V. Mitchell, J. Appl. Phys. 85 (1999) 174. [Jai02] Jain S. C., W. Schoenmaker, R. Lindsay, P. A. Stolk, , S. Decoutere, M. Willander

and H. E. Maes, J. Appl. Phys. 91 (2002) 8919 [Jeo01] Jeong J.-W. and A. Oshiyama, Phys. Rev. B 64 (2001) 235204. [Ken77] Kennedy E. F., L. Csepregi, J. W. Mayer and T. W. Sigmon, J. Appl. Phys. 48

(1977) 4241. [Ker84] Kerkow H., G. Kreysch and B. Lukasch, Phys. Stat. Sol. (a) 82 (1984) 125 [Ker86] Kerkow H., G. Kreysch, , G. Wolf and K. Holldack, Phys. Stat. Sol. (a) 94 (1986)

793 [Kyl96] Kyllesbech Larsen K., V. Privitera, S. Coffa, F. Priolo, S. U. Campisano, and A.

Carnera, Phys. Rev. Lett. 76 (1996) 1493 [Kno74] Knotek M. L. and M. Pollak, Phys. Rev. B 9 (1974) 664 [Kok82] Kokorowski S. A., G. L. Olson and L. D. Hess, J. Appl. Phys. 53 (1982) 921 [Lan98] Landi E., A. Armigliato, S. Solmi, R. Köghler, and E. Wieser, Appl. Phys. A: Mater.

Sci. Process. A47 (1998) 359 [Lee83] D.S. Lee and J. G. Fossum, IEEE Trans. Electron. Dev. ED-30 (1983) 626 [Lin65] Lindhard J., K. Dan. Vidensk, Selsk. Mat. Fys. Medd. 34, (1965) 1. [Liu00] Liu X.-Y., W. Windl, and M. P. Masquelier, Appl. Phys. Lett. 77 (2000) 2018. [Lu89] Lu G.Q., E. Nygren, M. Aziz, D. Turnbull, C.W. White, Appl. Phys. Lett. 54 (1989)

2583 [Lu91] Lu G.Q., E. Nygren, M. Aziz, J. Appl. Phys. 70 (1991) 5323 [Luo01] Luo W. and P. Clancy, J. Appl. Phys. 89 (2001) 1596. [Luo98] Luo W., P. B. Rasband, P. Clancy, and B. W. Roberts, J. Appl. Phys. 84 (1998)

2476. [Mad96] Madelung O., ed., Semiconductors group IV elements and III-V compounds, in

Data in Science and Technology, R.Poerschke ed. (Springer – Verlag, Germany, 1996)

[Mam94] Mamontov Y.V. and M. Willander, IEICE Trans. Electron. E77-C (1994) 287 [Man00] Mannino G., N. E. B. Cowern, F. Roozeboom, and J. G. M. van Berkum, Appl.

Phys. Lett. 76 (2000) 855. [Man01] Mannino G., S. Solmi,V. Privitera, and M.Bersani, Appl. Phys. Lett. 79 (2001)

3764. [May77] Mayer J. W. and E. Rimini, eds., Ion Beam Handbook for Material Analysis,

(Academic Press, New York, 1977). [Mey95] Meyer J. D., R. W. Michelmann, F. Ditroi, and K. Bethge, Nucl. Instr. and Meth. B

99 (1995) 440 [Mic87] Michel A. E., W. Rausch, P. A. Ronsheim, and R. H. Kasti, Appl. Phys. Lett. 50

(1987) 416. [Mic89] Michel A. E., Nuclr. Inst. and Meth. B 37/38 (1989) 379 [Mil94] Miller L. A., D. K. Brice, A. K. Prinja, and S. T. Picraux, Radiat. Eff. Defects Solids

129 (1994) 127. [Mor70] Morehead F. F.and B. L. Crowder, Radiat. Eff. 6 (1970) 27. [Mor72] Morehead F. F., B. L. Crowder, and R. S. Title, J. Appl. Phys. 43 (1972) 1112. [Mor73] Morgan D. V. ed., Channeling Theory, Observation and Application, (John Wiley &

Sons, New York, 1973).

1.5 References

29

[Mot61] Mott N. F. and W. D. Twose, Adv. Phys. 10 (1961) 107 [Mot81a] Mott N. F., Phys. Rev. B 44 (1981) 265 [Mot81b] Mott N. F. and M. Kaveh, J. Phys. C 14 (1981) L177 [Mot87] Mott N., J. Phys. C: Solid State Phys. 20 (1987) 3075 [Mot90] Mott N., Phil. Mag. 62 (1990) 37 [Mot91] Motooka T. and O. W. Holland, Appl. Phys. Lett. 58 (1991) 2360 [Mot92] Motooka T. and O. W. Holland, Appl. Phys. Lett. 61 (1992) 3005 [Nar82a] Narayan J. and O. W. Holland, Appl. Phys. Lett. 41 (1982) 239 [Nar82b] Narayan J. and O. W. Holland, Phys. Stat. Sol. (a) 73 (1982) 225 [Nar82c] Narayan J., J. Appl. Phys. 53 (1982) 8607 [Nar83] Narayan J., Holland, O. W., and Appleton, B. R., J. Vac. Sci. Technol. B1 (1983)

871 [Nol98] Nolte H., W. Assmann, H. Huber, S. A. Karamian, and H. D. Mieskes, Nucl. Instr.

and Meth. B 136-138 (1998) 587. [Ols84] Olson G. L., Roth, J. A., Hess, L. D., and Narayan, J., Mat. Res. Soc. Symp. Proc.

23 (1984) 375 [Ols85a] Olson G. L., Mat. Res. Soc. Symp. Proc. 35 (1985) 25 [Ols85b] Olson G. L., Roth, J. A., Rytz-Froidevaux, Y., and Narayan, J., Mat. Res. Soc.

Symp. Proc. 35 (1985) 211 [Ols88] Olson G.L. and J.A. Roth, Mater. Sci. Rep. 3 (1988) 1, and references therein. [Pel97] Pelaz L., M. Jaraìz, G. H. Gilmer, H.-J. Gossmann, C. S. Rafferty, D. J. Eaglesham,

and J. M. Poate, Appl. Phys. Lett. 70 (1997) 2285. [Pel99a] Pelaz L., G. H. Gilmer, H.-J. Gossmann, C. S. Rafferty, M. Jaraìz, and J. Barbolla,

Appl. Phys. Lett. 74 (1999) 3657. [Pel99b] Pelaz L., V. C. Venezia, H.-J. Gossmann, G. H. Gilmer, A. T. Fiory, C. S. Rafferty,

M. Jaraìz, and J. Barbolla, Appl. Phys. Lett. 75 (1999) 662. [Pel04] Pelaz L., L. A. Marqués, and J. Barbolla, J. Appl. Phys. 96 (2004) 5947 [Pic69] Picraux S. T., J. E. Westmoreland, J. W. Mayer, R. R. Hart, and O. J. March, Appl.

Phys. Lett. 14 (1969) 7. [Pic75] Picraux S.T., in New Uses of Ion Accelerators, J.F. Ziegler ed. (Plenum Press, New

York 1975) [Poa84] Poate J. M. and Williams, J. S., in Ion Implantation and Beam Processing,

Williams, J. S. and Poate, J. M., eds. (Academic Press, New York 1984), p. 27 [Ras94] Rasmussen F. B. and B. B. Nielsen, Phys. Rev. B 49 (1994) 16353. [Rei94] Reitano R., P. M. Smith, and M. J. Aziz, J. Appl. Phys. 76 (1994) 1518 [Rim95] Rimini E., Ion Implantation: Basics to Device Fabrication (Kluwer Academic

Publishers, Boston, 1995) [Rob63] Robinson M. T. and O. S. Oen, Phys. Rev. 132 (1963) 2385 [Ros83] Rosembaum T.F., R.F. Milligan, M.A. Paalanen, G.A. Thomas, R.N. Bhatt, W. Lin,

Phys. Rev. B 27 (1983) 7509 [Sad99] Sadigh B., T. J. Lenosky, S. K. Theiss, M.-J. Caturla, T. D. de la Rubia and M. A.

Foad, Phys. Rev. Lett. 83 (1999) 4341 [Sch94] Schenkel T., H. Hebert, J. D. Meyer, R. W. Michelmann, and K. Bethge, Nucl. Instr.

and Meth. B 89 (1994) 79 [Sch99] Schroer E., V. Privitera, F. Priolo, E. Napolitani, and A. Carnera, Appl. Phys. Lett.

74 (1999) 3996. [Sch05] Schubert E.F., Physical Foundations of Solid-State Devices (New York, 2005);

http://www.rpi.edu/~schubert [See73] Seeger K., Semiconductor Physics (Springer-Verlag, New York-Wien, 1973) [Shk84] Shklovskii B. and A. L. Effros, Electronic Properties of Doped Semiconductors

(SpringerVerlag, Berlin, 1984) [Sig72] Sigmund P., Rev. Roum. Phys. 17 (1972) 823. [Sol01] Solmi S., L. Mancini, S. Milita, M. Servidori, G. Mannino, and M. Bersani, Appl.

Phys. Lett. 79 (2001) 1103 [Sol90] Solmi S., E. Landi, and F. Barrufaldi, J. Appl. Phys. 68 (1990) 3250 [Sol91] Solmi S., F. Barrufaldi, and R. Canteri, J. Appl. Phys. 69 (1991) 2135 [Spa78] Spaepen F., Acta Metal., 26 (1978) 1167


[Sto97] Stolk P. A., J. H.-J. Gossmann, D. J. Eaglesham, D. C. Jacobson, C. S. Rafferty, G. H. Gilmer, M. Jaraìz, J. M. Poate, H. S. Luftman and T. E. Haynes, J. Appl. Phys. 81 (1997) 6031

[Sun82a] Suni I., G. Goltz, M. G. Grimaldi, M.-A. Nicolet and S. S. Lau, Appl. Phys. Lett. 40 (1982) 269.

[Sun82b] Suni I., G. Goltz, M.-A. Nicolet and S. S. Lau, Thin Solid Films 93 (1982) 171. [Sze81] Sze S. M., Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981) [Tes95] Tesmer J. R. and M. Nastasi, eds., Handbook of modern ion beam materials analysis

(Materials Research Society, Pittsburg, 1995). [Tho89] Thornton R.P., R.G. Elliman and J.S. Williams, Nuclr. Inst. and Meth. B37/B38

(1989) 387 [Tim85] Timans P. J., R. A. McMahon and H. Ahmed, Mat. Res. Soc. Proc. 45 (1985) 337 [Tim86] Timans P. J., R. A. McMahon and H. Ahmed, Mat. Res. Soc. Proc. 52 (1986) 123 [Tsa79] Tsai M. Y. and B. G. Streetman, J. Appl. Phys. 50 (1979) 183. [Tur82] Turnbull D. and F. Spaepen, in Laser Annealing of Semiconductor, J.M. Poate, J.W.

Mayer eds. (Academic Press, New York, 1982) 15 [Wan00] Wang T.-S., A. G. Cullis, E. J. H. Collart, A. J. Murrell, and M. A. Foad, Appl.

Phys. Lett. 77 (2000) 3586 [Wes69] Westmoreland J. E., G. W. Mayer, F. H. Eisen, and B. Welch, Appl. Phys. Lett. 15

(1969) 3088 [Whi80] White C.W., R.S. Wilson, B.R. Appleton, F.W. Young, J. Appl. Phys. 51 (1980)

738 [Whi82] White C.W., B.R. Appleton, S.R. Wilson, in Laser annealing of Semiconductor,

J.M. Poate and J.W. Mayer eds. (Academic Press, New York, 1982) [Wil82a] Williams J. S. and R. G. Elliman, Appl. Phys. Lett. 40 (1982) 266 [Wil82b] Williams, J. S., and K. T. Short, in Metastable Materials Formation by Ion

Implantation, S. T. Picraux and W. J.Choyke , eds. (North Holland, New York, 1982) 109

[Wil83a] Williams J. S., and R. G. Elliman, Phys. Rev. Lett. 51 (1983) 1069 [Wil83b] Williams, J. S., and K. T. Short, Nuclr. Inst. and Meth. 209/210 (1983) 767 [Wil83c] Williams J. S., Nuclr. Inst. and Meth. 209/210 (1983) 219 [Wil83d] Williams J. S., in Surface Modification and Alloying, J. M. Poate, G. Foti and D.C.

Jacobson eds. (Plenum Press, New York, 1983) 133 [Wil85] Williams J. S., W. L. Brown, R. G. Elliman, R. V. Knoell, O. M. Maher and T. E.

Seidel, Mat. Res. Soc. Proc. 45 (1985) 79 [Win70] Winterbon K. B., P. Sigmund, and J. B. Sanders, K. Dan. Vidensk, Selsk. Mat. Fys.

Medd. 37 (1970) 14. [Win99] Windl W., M. M. Bunea, R. Stumpf, S. T. Dunham and M. P. Masquelier, Phys.

Rev. Lett. 83 (1999) 4345. [Woo81] Wood R.F., J.R. Kirkpatrick, G.E. Giles, Phys. Rev. B 23 (1981) 5555 [Yu99] Yu P.Y., M. Cardona, Fundamentals of semiconductors : physics and materials

properties (Springer, New York, 1999) [Zie77] Ziegler J. F., Stopping and Ranges of Ions in Matter (Pergamon, New York, 1977) [Zie85] Ziegler J. F., J. P. Biresack, and U. Littmark, The Stopping and the Range of Ions in

Solids (Pergamon, New York, 1985); http:// www.srim.org

Chapter 2

B and Ga in Si: impurity solubility and distribution

Many aspects of the solid phase epitaxial process presented a strong dependence on the atomic size of dopant impurities, the interface velocity and the substitutional trapping strictly depend on the type of impurities and the strain effect has been often involved to explain the material properties. The main idea of the co-doping comes from the observation that also the solid solubility depends on the atomic size of the impurities, therefore a sort of compensation operated by the presence of impurities with different sizes could affect this property. B and Ga have been chosen as dopants with different sizes in order to have a strain compensation that can act positively on the impurity incorporation. Moreover, they are both p-type impurities in Si, therefore the presence of both dopants can enhance the total number of charge carriers. The two impurities have been implanted at high concentration (∼1020 at/cm3) in the same region with overlapped profiles.

In this chapter we will describe the properties of supersaturated solid solution of three systems: Si-B, Si-Ga and Si-B-Ga. In particular the dopant distribution during the SPE process, the incorporation into substitutional lattice sites, the electrical activation and the stability upon further annealing, will be expounded.

2.1 Experimental In this section the sample preparation and characterization will be described. All

experiments presented in the following chapters refer to this experimental procedure, so we will give the details of all the several samples prepared in this work (section 2.1.1). The experimental details of the characterization technique mainly used in this work, ion beam analyses and Hall effect measurements, are reported in section 2.2.2, while the details about other characterizations strictly used to study specific peculiarities will be given at the right time.

2.1.1 Sample preparation The substrate used for all samples was a <100> oriented Cz-Si, n-type, ρ=1.5-4

Ωcm, it was amorphized from the surface to a depth of 550 nm, by implanting Si ions (3x1015 at 250 keV plus 2x1015 at/cm2 at 40 keV). The second implant was made to ensure the complete amorphization up to the surface. The silicon implants were managed at the liquid nitrogen temperature (T=77 °K). This low temperature was chosen in order to strongly reduce the dynamic recombination of the point defects during the implantation itself; in fact, this effect plays an important role against the realization of an amorphous layer [Rim95]. The Si amorphization implants were performed at the section of Catania of the IMM-CNR, by a 1.7 MV High Voltage Engineering Europe (HVEE) Tandetron accelerator.

The Si wafer was subsequently implanted with 11B+ and 69Ga+ at room temperature (RT) in order to realize a list of samples doped with B, or Ga, or both B and Ga in the same layer. B and Ga implantation was realized by the HVEE 400 kV ion implanter of the Physics Department of the University of Catania. Double

Chapter 2 B and Ga in Si: impurity solubility and distribution 32

implantation energies and appropriate ion fluences of B and Ga were chosen in order to obtain a dopant profile with a region of maximum concentration larger than a Gaussian peak. This shrewdness better warranties the study of the properties that depend on the maximum dopant concentration, for example the solid solubility or the carrier mobility. Moreover the energy and the fluence of each ion were accurately selected using SRIM simulations [Zie85] to have overlapping impurities concentration profiles into 250 nm thick layer in the co-doped B+Ga samples. Energies and fluences of B and Ga ions used for the several implants are scheduled in the following table (table 2.1) with the corresponding maximum impurity concentration. In the following text the “co-doped” samples will indicate that samples implanted with B and Ga in the same layer, and the relative B and Ga maximum concentrations will be given as parameters to identify the implantation conditions using the table 2.1.

Table 2.1

Impurity E1 [keV]

Fluence1 [1015 at/cm2]

E2 [keV]

Fluence2 [1015 at/cm2]

Tot Fluence [1015at/cm2]

Max conc. [1020at/cm3]

B 17 0.05 29 0.19 0.24 0.2 B 17 0.18 29 0.66 0.84 0.7 B 17 0.25 29 0.92 1.17 1.0 B 17 0.32 29 1.20 1.52 1.3 B 17 0.50 29 1.85 2.35 2.1 B 17 0.58 29 2.14 2.74 2.5 B 17 1.25 29 4.66 5.90 5.5 B 17 1.37 29 5.08 6.45 6.0 B 17 1.42 29 5.27 6.70 6.3 B 17 1.80 29 6.80 8.60 8.0 B 17 2.00 29 7.40 9.40 8.7

Ga 90 0.05 160 0.31 0.36 0.3 Ga 90 0.10 160 0.57 0.67 0.5 Ga 90 0.12 160 0.68 0.80 0.6 Ga 90 0.16 160 0.91 1.07 0.8 Ga 90 0.18 160 1.03 1.21 0.9 Ga 90 0.20 160 1.14 1.34 1.0 Ga 90 0.22 160 1.25 1.47 1.1 Ga 90 0.27 160 1.54 1.81 1.3 Ga 90 0.40 160 2.28 2.68 2.0 Ga 90 0.44 160 2.51 2.95 2.2 Ga 90 0.84 160 4.76 5.60 4.2

Finally samples were annealed in a vacuum furnace (p∼10-7 mbar) at 580 °C for

1 hr to crystallize amorphous Si by SPE. The crystal quality of the regrown samples was detected by channeling analyses with 2 MeV He beam (explained in the following section), it was that of a good Si virgin crystal for almost all samples.

2.1.2 Characterization Ion beam analyses (IBA) based on backscattering spectroscopy, extensively

used in this work to characterize the properties of the materials, have been performed using an HVEE coaxial Cockroft–Walton Singletron accelerator with a

2.1 Experimental

33

maximum terminal voltage of 3.5 MV. The beam spot dimensions are about 1-3 mm2, the typical current is 50 nA.

In particular standard RBS with a 2 MeV 4He+ beam has been used to check the crystalline quality of the regrown samples and to determine the distribution profile of Ga atoms. The scattering geometry is the IBM [Tes95] and refers to the scattering configuration where the incident beam, surface normal, and detected beam are all coplanar. For 2 MeV He RBS analyses the scattering angle is 165°, the detector has an active area of 30 mm2 and is placed at about 10 cm from the target. An example of the RBS spectra in normal incidence are reported in Figure 2.1 for a sample doped with 1x1020 Ga/cm3: the spectrum of the as implanted sample has been collected aligning the beam along the <100> axis and the amorphous thickness is about 550 nm; the spectrum of the sample after SPE shows a Ga profile very similar to that implanted (random spectrum) with a crystalline quality comparable to that of a not-implanted Si crystal (channeling spectra). In order to improve the depth resolution of the Ga concentration profiles, we used a glancing geometry with a tilt angle between the incident beam and the surface normal of 60°, and the solid angle of the detector has been reduced with a slit of 2 mm, obtaining a depth resolution of 80 Å against the 230 Å of the normal incidence.

The lattice location of impurities has been performed using the channeling

technique explained in section 1.2.3. The channeling analyses are very delicate because the impurity undergoes an off-lattice displacement during the ion beam irradiation and this phenomenon will be discussed in chapter 4. To perform the channeling analyses, the beam is first aligned parallel to the selected crystal axis, subsequently intercepted by a shutter while the sample is shifted to start recording the channeling spectrum on a non-irradiated spot. The beam alignment along the main crystallographic axes of the Si requires the following tilt angles: 0° for <100>, 45° for <110> and 54.75° for <111>. The normalized channeling yield χ is defined as the ratio of aligned yield to a randomly directed beam yield and the aligned

250 300 350 4000

5

10

15

20

25

550 600

300 200 100 0

500 250 0<

Random

2 MeV He+ on Sialigned <100>

as implanted after SPE not implanted

Nor

mal

ized

Yie

ld

Channel

Ga x50

Energy [KeV]

800 900 1000 1100 1200 1500 1600

Depth [nm]

<

Depth [nm]

Fig. 2.1 Energy spectra of a 2 MeV He beam incident on a Ga-implanted (1.3x1015 Ga/cm2) silicon: () random; (×, , ⎯) <100> channeling. The spectra are relative to: (×) as implanted sample, (, ) after annealing at 580°C for 1h, (⎯) not implanted crystal. Ga signal is magnified (x 50), the peak concentration is ∼1x1020 Ga/cm3.


fraction of the solute atoms along a particular <uvw> axis in the Si host lattice is defined as [Tes95]:

)(1)(1)(

min

min

Sisolutesolutef uvw

uvwuvw

aligned ><

><><

−−

=χ

χ (2.1)

where ><uvwminχ is the minimum channeling yield measured on the impurity and Si

signals, respectively. The aligned fraction furnishes in first approximation the fraction of impurity atoms located in substitutional sites. However, there are particular interstitial sites of the diamond lattice that are shadowed only along some directions, to avoid that such kind of interstitial impurity could be assumed as substitutional it is necessary to measure the aligned fraction along the <110> and <100> (or <111>) axes [Mor73]. More details about the channeling lattice location, investigated performing the angular scans, will be given in chapter 4.

The detection of B density in Si, instead, requires the use of a particular nuclear reaction because the Rutherford scattering cross section decreases as z2 and, for this reason the presence of 0.1 at% of B in Si is completely undetectable by standard RBS analyses.

The nuclear reaction 11B(p,α)8Be at 650 keV proton beam is usually used [May77, Tes95] to detect B in Si at concentration higher than 1x1014 B/cm2.

The reaction of protons with a 11B nucleus has four exit channels [Ajz90]: 1) 11B+p→12C* → α0+8Be → α01+α02+α03 2) 11B+p→12C* → α1+8Be* → α11+α12+α13 3) 11B+p→12C*→ α2+α3+α4 4) 11B+p→12C*→12C +γ

The intermediate 8Be formed in reaction channels 1) and 2) disintegrates into 2 α particles. The energy released in the first step of reaction channel 1) is 8.583 MeV [Seg65]. In reaction channel 2) the 8Be is left in its first excited state at 2.90 MeV [Seg65]. Reaction channel 4) has only a small maximum total cross section of 10 µb in the energy range 2.0-2.7 MeV [Seg65]. The reaction 1) has a maximum cross section of ~7 mb/sr at a proton energy of 2600 keV [May98]. The channel 2) has a high cross section: ~100 mb/sr [Vol96] at 650 keV, it is 300 keV wide. We have used this reaction to detect B in Si. The emitted α particles have energy in the range from 5 keV to 5.5 MeV. This reaction does not allow to determine the B concentration profile being three the particles of the reaction final product. An example of a RBS spectrum of 650 keV protons normal incident on a Si target doped with B at 5x1015 at/cm2 is reported in Figure 2.2. The yield due to protons backscattered by Si atoms is about 4 orders of magnitude higher than the yield of the emitted α particles by the nuclear reaction 11B(p,α)8Be, the α coming from the reaction channels 1) and 2) are indicated in the Figure 2.2.

In our analyses a 1.3 MeV H2+ beam (equivalent to two 0.650 MeV protons) has

been used. The α particles detector, with an active area of 450 mm2, has been placed at 160° with respect to the incident beam direction and it has been covered with a 10-µm-thick aluminised mylar film to prevent backscattered protons to reach the detector. A second detector, at 165°, was used to detect backscattered protons and to perform the alignment procedure. The normalized channeling yield χB is obtained from the energy integrated α particles yield normalized to the random yield.

The error which affects this kind of analyses (both B and Ga detection) is given by the Poisson statistics, typically an error of 3% must be considered on the dopant density measured by the IBA techniques and indicated in this work.

Hall measurements [Van58, Sch90, Ast01] and the four point probe resistance measures were performed by a Hall system BioRad HL5560. The magnetic field intensity was of 0.322 T. The samples patterned according to Van der Pauw geometry were cut into squares of 0.8x0.8 cm2. The carrier fluence measured by

2.2 Impurity solubility in single doped (B or Ga) Si

35

Hall effect are affected by a maximum error of 5%. We have eventually used the Helium cryostat the to perform the measurement as function of temperature in the range of liquid nitrogen to room temperature, in this case very small In-Zn contacts were soldered on the corners of the square sample.

2.2 Impurity solubility in single doped (B or Ga) Si The implanted impurity concentrations exceed in a lot of samples the solubility

limit we discussed in section 1.3.2, so it is important to check the substitutionality of B and Ga in the various samples. In this section the measurements of substitutionality performed by lattice location techniques will be shown for the three cases of B (2.2.1), Ga (2.2.2) and B+Ga (2.3) doped samples. The substitutional fraction of B and Ga atoms obtained by the channeling analyses will be compared with the carrier concentration measured by Hall effect method.

2.2.1 B doped Si The B concentration profile has been measured by secondary ion mass

spectrometry (SIMS) using a CAMECA IMS 4f instrument (at the University of Padova), with a 3 keV O2

+ analysing beam. In Figure 2.3 the SIMS profiles of the samples after SPE are reported for three implant conditions (see table 2.1), the SRIM simulation for the lowest B concentration is also shown evidencing the good agreement of experimental and expected results. No differences has been observed between samples as implanted and after SPE, as expected due to the negligible B diffusion at 580°C and the efficient solute trapping (see section 1.2.2). The doped region is about 250 nm thick and the maximum concentration is peaked at 100 nm from the surface.

The aligned fraction of B atoms, defined by the formula (2.1), has been measured along the <100> and <110> crystal axes for a set of selected samples among that prepared. Table 2.2 reports the χSi and χB along the two axes and the relative aligned fractions. In first approximation the substitutional fraction has been

0 200 400 600 800 1000100

101

102

103

104

105

106

1000 2000 3000 4000 5000 6000

α0

Cou

nts

Channel

α1

650 keV H+, normal incidence, ϑ=165°B (5x1015 at/cm2) in Si

Energy [KeV]

Fig. 2.2 Energy spectra of a 650 keV H+ beam incident on a B-implanted (5x1015 B/cm2) silicon. The α particles emitted in the nuclear reaction 11B(p, α)Be8 are also indicated.


estimated as a medium value between the aligned fractions, but for the highest B concentration the χB values are very high and differs about 20% along the two axes. In this last case the evaluated substitutional fraction is affected by a large error because the B atoms that do not occupy substitutional sites can be displaced in particular lattice location that false the intuitive explanation; a similar phenomenon will be discussed in chapter 4. At highest B concentration the substitutional fraction has been assumed equal to the lower aligned fraction.

Table 2.2

Max conc. [1020at/cm3]

<100>χB <100>χSi <110>χB <110>χSi f<100> f<110> Sub. fraction

0.2 0.090 0.06 0.075 0.05 0.98 0.98 0.98 1.0 0.091 0.06 0.077 0.05 0.97 0.97 0.97 2.1 0.168 0.06 0.166 0.05 0.89 0.88 0.88 5.5 0.560 0.06 0.500 0.05 0.47 0.52 0.47 6.3 0.680 0.07 0.570 0.05 0.34 0.45 0.34

The Hall carrier fluence of several samples is reported in table 2.3. The fraction

of electrically active B atoms is not easily given by the ratio of the Hall carrier fluence and the total implanted fluence because we would obtain an electrical activation that exceeds the unity at low B concentration, but it should be considered the multiplicative Hall scattering factor. The Hall scattering factor (rH) depends on many parameters like the magnetic field, the energy bands of the semiconductor and the scattering mechanisms that limit the charge carrier transport (see section 3.1.1 for details). A lot of works in literature report about 0.75 for B concentration up to 1x1019 at/cm3 [Rom03], but there are no experimental data that confirm the same value for higher B concentration. The rH value of 0.75 has been used to calculate the electrically active fraction of B atoms that is reported in the 4th column of the table 2.3.

0 50 100 150 200 2500

2

4

6

8

Con

cent

ratio

n [x

1020

at/c

m3 ]

Depth [nm]

B profiles after SPE measured by SIMS SRIM simulation

Fig. 2.3 B concentration profile measured by SIMS (solid lines) after SPE at 580°C 1h. The SRIM simulation (dot line) of the sample with lowest concentration is also shown.


37

Table 2.3 Max B conc. [1020at/cm3]

Implanted B fluence

[1015at/cm2]

Hall carrier fluence

[1015at/cm2]

Electrically active B fraction

0.2 0.24 0.32 1.00 0.7 0.84 1.20 1.07 1.0 1.17 1.50 0.96 1.3 1.64 2.10 0.96 2.1 2.35 2.76 0.88 2.5 2.74 4.01 1.10 5.5 5.90 5.42 0.69 6.0 6.45 4.12 0.48 6.3 6.70 4.83 0.54 8.0 8.60 5.96 0.52 8.7 9.40 4.12 0.33

For comparison the fractions of electrically active and substitutional B atoms are

reported in Figure 2.4 as function of the maximum B concentration. The substitutional fraction and the electrical fraction almost coincide up to a B concentration of 2x1020 at/cm3, but at higher concentration the two values diverge. Glass et al. [Gla00] observed a similar B electrical activation in B doped Si grown by gas source molecular beam epitaxy in the B concentration range 1x1017<CB<2x1022 at/cm3. The data from Glass et al. are also reported (full triangles) in Figure 2.4, and show intermediate values between our measurements of substitutional and electrical fractions. For low CB, all the B atoms are ionized. But for samples with CB>2.5x1020 at/cm3, the increase of electrically active B is significantly smaller than that of total B concentration. The maximum concentration of electrically active B is 1.3x1021 at/cm3 at room temperature. However, unlike previous studies on p- or n-type dopants in Si [Rad94, Rev96], here no carrier saturation ever takes place. An example is shown in Figure 2.5: the hole fluence is reported as function of the impurity implanted fluence for B and Ga in Si (the data of Ga will be discussed in the next section). The carrier concentration continues to increase in the B doped samples, while saturates in Ga doped Si. The origin of this effect is actually not well understood: Glass et al. proposed that the B electrically inactive atoms are incorporated as sp2 bonded trigonally coordinated B pairs located at single substitutional Si sites. The B pairs formation reduces the in-plane tensile strain and explains the non linear decrease of the out-of-plane lattice parameter as function of CB at CB>2.5x1020 at/cm3 observed by HRXRD [Gla00, Gla99]. Luo et al. [Luo03], instead, attributed this phenomenon only to a partial ionization of the B atoms due to an electron chemical potential effect, dismissing the B clustering as the main cause of the partial electrical activation at least in the 2x1020<CB<1x1021 at/cm3 concentration range. The measured χB, instead, indicate the presence of displaced B atoms with respect to the substitutional sites. The fact that the substitutional fraction (in Figure 2.4) is lower than the electrical fraction can be due to a non random displacement of the B atoms. In this case, in fact, the evaluation of the substitutional fraction can be very complicated with respect to the easy formulation of expression 2.1. The displacement of B atoms in particular positions is also indicated by the different values of χB along the two axes at CB>2x1020 at/cm3, as shown in table 2.2.


However, even if the minimum between the values of the aligned fraction along

the two axes, has been assumed as the substitutional value, a large error can be committed in this evaluation. In conclusion, our observations support the idea of the formation of B clusters at high concentration of B atoms, but the identification of the kind of cluster and its structure needs of an in depth study, like that will be shown in chapter 4, where the B clusters are formed as consequence of a super-saturation of Si self interstitials.

0.2 0.4 0.6 0.81.0 2.0 4.0 6.0 8.00.2

0.4

0.60.81.0

2.0

4.0

6.0

B Ga

Hol

e flu

ence

[cm

-2]

Impurity implanted fluence [cm-2]

Fig. 2.5 Hole fluence in B and Ga doped samples, measured by Hall effect, as function of the impurity implanted fluence. The lines are guide for eyes.

Fig. 2.4 Fraction of electrically active (full squares) B atoms measured by Hall effects and Fraction of substitutional B atoms measured by channeling (empty squares) in B doped Si obtained by SPE process. The solid and dot lines are guide of eyes. Data (full triangles) from Glass et al. [Gla00] refer to B doped Si grown by molecular beam epitaxy.

1019 1020 10210.2

0.3

0.4

0.5

0.60.70.80.9

1

This work Electrically active B fraction Substitutional B fraction

from Glass et al. [Gla00] Electrically active B fraction

Ele

ctric

al o

r Sub

stitu

tiona

l Fra

ctio

n

B maximum concentration [at/cm3]


39

2.2.2 Ga doped Si Figure 2.6 shows the Ga profile measured by RBS (glancing geometry) in some

samples doped with different Ga concentrations as implanted and after SPE. A surface segregation is clearly detectable in the sample with 2x1020 Ga/cm3 and this component increases with increasing Ga concentration, so the sample implanted with 4.2x1020 Ga/cm3 has a real maximum Ga concentration of 3.5x1020 Ga/cm3. The profile of the sample with 1x1020 Ga/cm3 presents a very low Ga redistribution and the dopant approximately maintains the as implanted profile also after the annealing.

The lattice location of Ga in supersaturated solid solutions of Si-Ga has been

investigated using the channeling technique with a 2 MeV He beam. Table 2.4 reports the χSi and χGa along the crystal axes <100>, <110> and <111>. The substitutional fraction (last column of table2.4) has been calculated as the medium value between the aligned fractions, being the χGa approximately the same along the three axes. This behaviour clearly marks the difference between the two dopants. In fact the substitutional fraction of Ga atoms permits to evaluate a maximum soluble concentration of Ga of about 1.8-2x1020 at/cm3 that is one order of magnitude higher than the retrograde solubility limit of Ga (4.5x1019 at/cm3, see section 1.3.2).

Table 2.4 Max conc.

[1020at/cm3] <100>χGa <100>χSi <110>χGa <110>χSi <111>χGa <111>χSi Sub.

fraction

1.0 0.07 0.030 0.10 0.027 0.09 0.030 0.94 2.2 0.13 0.032 0.13 0.030 0.12 0.031 0.90 4.2 0.55 0.090 0.60 0.010 0.56 0.080 0.44

The lattice location measurements are in agreement with the electrical active

fraction of Ga atoms investigated by Hall effect measurements reported in table 2.5. The electrical active fraction of Ga atoms has been calculated as the ratio of the Hall carrier and the implanted fluences, assuming rH=1, because there are very

0 50 100 150 200 250 3000.00.51.01.52.02.53.03.54.04.5

Con

cent

ratio

n [x

1020

at/c

m3 ]

Depth [nm]

as implanted after SPE

Fig. 2.6 Ga concentration profiles measure by RBS in samples as implanted (empty circles) and after SPE at 580°C (solid lines).


poor data about the Hall effect on Ga doped Si. Considering that at low concentration the differences between the values of the Hall carrier fluence and the implanted fluence are very small and the measured substitutional fraction is higher than 90%, we can estimate that the assumption of rH=1 can affect the measure of the carrier fluence with a maximum error of about 10%, instead of the 5% used for B analyses. One could ask if this is an effect of partial ionization of Ga atoms, as we discussed in section 1.4.2 we can exclude this case. Moreover a confirmation of the metal-to-insulator transition comes from the measurement of the carrier concentration as function of temperature reported in Figure 2.7 for two samples doped with a maximum Ga concentration of 6x1019 and ~1x1020 at/cm3, respectively. The sample with lowest Ga concentration shows a particular oscillation, which is due to the formation of the band impurity [Mam94] and disappears at high concentration. In both cases the classical freeze-out does not exist due to the reduction of the ionization energy caused by the high density of impurity atoms.

Table 2.5

Max Ga conc. [1020at/cm3]

Implanted Ga fluence

[1015at/cm2]

Hall carrier fluence

[1015at/cm2]

Electrically active Ga fraction

0.3 0.36 0.38 1.04 0.6 0.84 0.83 0.99 0.8 1.07 0.97 0.90 0.9 1.21 1.25 1.04 0.9 1.21 1.32 1.10 1.0 1.34 1.42 1.06 1.3 1.81 1.96 1.08 2.0 2.68 2.58 0.96 2.2 2.95 2.63 0.89 4.2 5.60 2.25 0.40

The electrical activation of Ga starts to decreases, as shown also in Figure 2.5,

when the maximum concentration exceed the value of ~2x1020 at/cm3. The saturation trend of the Ga soluble concentration started when the critical

concentration of ~2x1020 at/cm3 is reached, the carrier concentration does not increases even if the doping concentration increases, so we can accept this limit value as the maximum solubility of Ga in Si obtainable by SPE process. This behaviour is clearly completely different with respect of B doping, for B the carrier concentration continues slowly to increase at concentration higher than 2x1020 at/cm3. The Ga solubility limit (~2x1020 at/cm3) we have obtained by SPE is well in agreement with the experimental data of Narayan et al. [Nar83], they observed a maximum substitutional Ga concentration of about 2.4x1020 at/cm3 in samples implanted in the concentration range 3-6.5x1020 at/cm3 and regrowth by SPE.

2.3 Impurity solubility in B+Ga co-doped Si

41

2.3 Impurity solubility in B+Ga co-doped Si Figure 2.8 shows the overlapping profiles of B and Ga atoms at concentration of

1x1020 at/cm3, the presence of the two dopants does not affect the distribution of each one. However, we have just observed that Ga atoms at high concentration tend to segregate, the Ga profile substantially changes with increasing the B concentration up to a remarkable decrease of the Ga incorporation. In Figures 2.9 it is reported the Ga profiles of the co-doped samples with CB=5.5x1020 at/cm3 and CGa=2.2x1020 at/cm3. The maximum Ga concentration incorporated in the Si host decreases to 1.65x1020 at/cm3. In section 2.4.3 this effect will be studied in co-doped samples at low Ga concentration (1x1020 at/cm3) where the segregation effect appears when B concentration exceeds 2x1020 at/cm3. The B concentration profile has not been remarkably changed in presence of Ga.

The substitutional fraction, determined measuring the aligned fraction of B and Ga by channeling technique, is reported in table 2.6 for both dopants. The maximum Ga concentration is also reported to take into account the decrease of this value with respect of as implanted samples. The substitutional fraction of Ga is about 90% up to a concentration of 2x1020 at/cm3 even if there is a B concentration of 5.5x1020 at/cm3. The channeling analyses evidenced that the Ga atoms in the segregated peak are essentially random located, so the substitutional fraction reported in the table refer to the 95% of Ga atoms that are distributed outside of the segregated peak. Taking into account the decrease of the maximum Ga concentration shown in Figure 2.9, the maximum substitutional concentration of Ga changes from 1.9 to 1.5 when a CB=5.5x1020 at/cm3 is added.

50 100 150 200 250 3000.50.60.70.80.91.01.11.21.31.41.51.6

CMax=1x1020 at/cm3

CMax=6x1019 at/cm3

Hal

l car

rier c

onc.

[x10

15 c

m-2]

Temperature [°C]

Ga doped Si

Fig. 2.7 Hall carrier concentration in samples doped with Ga at concentration of 6x1019 and at/cm3 as function of temperature. At low concentration the oscillation is typical of band impurity conduction, while at high concentration the concentration is constant indicating that metal conduction has been established.


Table 2.6

Max B conc. as implanted [1020at/cm3]

Max Ga conc. as implanted [1020at/cm3]

Max Ga conc. After SPE

[1020at/cm3]

Sub. Fraction of B

Sub. Fraction of Ga

2.1 1.0 0.80 0.90 0.91 5.5 1.0 0.75 0.46 0.90 5.5 2.2 1.70 0.45 0.90 5.5 4.2 3.00 0.46 0.50

The lattice location of B does not show any substantial variation in presence of

Ga co-doping. The presence of two impurities with different covalent radius has not influenced the B lattice location so we have not observed the substitutional fraction increase we hoped in the sample with CB=5.5x1020 at/cm3. It can be pointed out

0 50 100 150 200 250 300

0.5

1.0

1.5

2.0

2.5

Con

cent

ratio

n [x

1020

at/c

m3 ]

Depth [nm]

As implanted after SPE after SPE +B

Fig. 2.9 Ga concentration profiles measured by RBS in samples implanted with Ga (solid line) and after SPE at 580°C (dashed lines) and co-doped with B at a maximum concentration of 5.5x1020 at/cm3 (dot lines).

0 100 200 3001017

1018

1019

1020

SIMS profile of B (1.20x1015 B/cm2)

RBS profile of Ga (1.34x1015 Ga/cm2)

Con

cent

ratio

n [a

t/cm

3 ]

Depth [nm]

Fig. 2.8 Ga (empty circles) and B (solid line) concentration profiles measured in a co-doped sample by RBS and SIMS, respectively.

2.4 SPE rate

43

that B maintains the same maximum substitutional concentration of the pure B doped samples, while a reduction of the solubility of Ga has been evidenced.

The Hall carrier fluences (pH) measured in B+Ga co-doped samples (5th column) are reported in table 2.7 with the values relative to samples doped with pure B (3rd column) and Ga (4th column).

Table 2.7

Max B conc. as implanted [1020at/cm3]

Max Ga conc. as implanted [1020at/cm3]

pH (B doped)

[1015at/cm2]

pH (Ga doped) [1015at/cm2]

pH (B+Ga co-doped)

[1015at/cm2] 1.3 0.3 2.1 0.4 2.5 1.3 0.6 2.1 0.8 3.3 1.3 0.8 2.1 1.3 3.5 1.3 1.3 2.1 2.0 3.8 2.5 2.2 4.0 2.5 6.4 5.5 1.1 5.4 1.2 6.2 5.5 2.2 5.4 2.5 7.5 5.5 4.2 5.4 2.3 8.6 8.0 2.2 6.0 2.5 7.8 2.1 0.5 2.8 0.7 3.3 6.0 0.5 4.1 0.7 4.5 8.7 0.5 4.1 0.7 5.0 2.1 1.0 2.8 1.3 3.9 6.0 1.0 4.1 1.3 5.3 8.7 1.0 4.1 1.3 5.3

The comparison immediately follows looking at the last three columns; the pH of

co-doped samples is about (within the 10%) the sum of the pH in single doped samples, indicating that both impurities are doping the semiconductor and the total number of charge carriers is given by the sum of the two contributions. The only exception is about the sample doped with the highest Ga concentration (4.2x1020 at/cm3), the pH of co-doped sample is 20% higher the sum pH(B)+pH(Ga). However, we observed that at this high Ga percentage the maximum Ga concentration was reduced from 4.2 to 3.5x1020 at/cm3 and is further reduced in presence of B (3x1020 at/cm3). Therefore the increase of carrier concentration can be due to the strong redistribution of the dopant.

Even by electrical analyses no additional increase of the B electrical activation has been observed. In addition, the electrical characterization showed that there is no evidence of any interaction between the two impurities that modify the carrier concentration in the co-doped systems. However to complete the picture of the electrical characterization we need to investigate the other fundamental electrical property of the semiconductor, the carrier mobility, which will be presented in chapter 3.

2.4 SPE rate The velocity of the crystalline-amorphous (c-a) interface is well know in B doped

Si in the temperature range 500-900 °C and B concentration between 1x1019 and 1x1021 at/cm3, as shown in section 1.3.1., but few data are available about Ga doped Si and even if a lot of measurements have been performed on B and P co-doped Si, the SPE has never been measured in co-doped Si with B and Ga. In order


to cover this lack we have measured the SPE rate in co-doped samples with B concentration of 1, 2 and 6x1020 at/cm3 and Ga concentration of 1x1020 at/cm3 by using the time resolved reflectivity (TRR) method. The TRR technique will be described in the section 2.4.1, while the SPE rate as function of B and Ga concentration will be presented in section 2.4.2. The analysis of the Ga segregation phenomenon observed in co-doped samples will be discussed in section 2.4.3 by the light of the SPE rate measurements.

2.4.1 TRR measurements A sample heater HeatWave has been allocated in a vacuum chamber equipped

with a quartz window and an adjustable mirror. The temperature of the heater is controlled by a thermocouple. A 5 mW He-Ne laser beam (λ=633 nm) strikes on the amorphous sample; the reflected light goes to the mirror, comes back to the sample and finally exits the chamber and is collected by a photodiode detector positioned outside the vacuum chamber. The intensity of the reflected light (or the square of the reflectivity, because of the double reflection) is acquired as function of the time. The use of real-time reflectivity measurements to monitor the solid phase crystallization of Si is based on the fact that the index of refraction of a-Si in the visible portion of the spectrum substantially exceeds that of c-Si. This index difference causes an easily detected difference in surface reflectivity and also results in a reflection from the interference between amorphous and crystalline regions [Ols88]. When the laser beam is directed at the surface, some of the light will be reflected from the outer surface of the a-Si and some will penetrate and be reflected from the c-a interface because of the discontinuity in the refractive index at that boundary. If the interface and the surface are smooth compared to the wavelength of the light, interferences will occur between the two reflected beams. When epitaxial crystallization occurs, the a-Si film thickness decreases continuously as the a-c interface moves toward the outer surface. This changing film thickness causes the net reflectivity to go through cycles of constructive and destructive interference, and leads to a reflectivity that varies with the time as shown in Figure 2.10. The separation d between successive peaks and valleys of reflectivity is given by:

11 cos4 φλ

nd = (2.2)

where λ=633 nm, n1=4.85 is the refraction index of the a-Si and φ1 is the angle between the incident light and the a-c interface. The angle φ1 can be calculated using the Snell’s rule:

1100 sinsin φφ nn = (2.3)

where n0=1 is the air refraction index and φ0 is the angle of the incident light on the sample. φ0~74°, about the Brewster angle, has been set in order to minimize the component of the reflected light at the surface and consequently to enhance the ratio of the signal and the background, d~330 Å results from 2.2. The amplitude of reflectivity oscillations is reduced for thicker amorphous films because absorption in the film attenuate the beam reflected from the c-a interface, the motion of the c-a interface can only be detected when the interface is within 3000 Å from the outer surface. The incident light is partially reflected by the surface (r1) and partially transmitted (t1). This last component is partially transmitted by the c-a interface (t1t2) and partially reflected (t1r2). In its turn the component t1r2 is partially transmitted by the surface (t1t1’r2) and makes interference with r1 and is partially reflected again (t1r1’r2). The total reflectivity is obtained summing the several terms:

2.4 SPE rate

45

2

221

2211

1242

21112

21111

111

1'.....'' δ

δδδ

i

iii

errerttrerrtterttrR −

−−−

++=+−+= (2.4)

In this expression: δ1 accounts for the phase change of the wave passing the amorphous film: δ1=(2π/λ)n1zcosφ1, where z is the amorphous film thickness. For σ polarized light and using the Maxwell equations the expressions of t1, t1’ and r1 are given by:

1100

11001

1100

111

1100

001

coscoscoscoscoscos

cos2'

coscoscos2

φφφφφφ

φφφ

φ

nnnnr

nnnt

nnnt

+−

=

+=

+=

(2.5)

where n0=1, n1=4.85-0.6i (refraction index of a-Si), n2=4.16-0.012i (refraction index of c-Si).

In Figure 2.10 the reflectivity spectrum versus time of a sample doped with Ga 1x1020 at/cm3 is reported, it is possible to well distinguish 5 valleys and 5 peaks in the range 1200-2400 s. The Ga profile is confined in the first 2500 Å so the first oscillations between 1200-1700 s show the velocity regrowth of intrinsic Si and can be used to monitor the sample temperature, which is about 570°C. The time separation between successive valleys and peaks decreases when the c-a interface moves through the doped layer indicating an enhancement of the SPE rate due to the presence of the dopant. Figure 2.11 and 2.12 represent the experimental procedure followed to extract the SPE rate as function of depth and dopant concentration: the time positions of valleys and peaks were marked (Figure 2.11) and compared (Figure 2.12) with a simulated spectrum of reflectivity versus amorphous depth z obtained by the formula (2.4), the correspondence time-depth was well defined for each point of the spectrum, obtaining a z(t) function. Differentiating this z(t) function the measurement of the SPE rate was extracted as function of the depth, as shown in Figure 2.13 of the section 2.4.2. The SPE rate was then reported as function of the dopant concentration being known the dopant profile concentration in the sample by SIMS or RBS analyses (see Figure 2.14 of section 2.4.2).

Fig. 2.10 A draft of the TRR experiment: the c-a interface moves toward the outer surface giving interference with the incident laser light. An example of the reflectivity spectrum acquired during the SPE process as function of the time is shown on the right.

500 1000 1500 2000 25000.2

0.3

0.4

0.5

0.6

0.7

0.8

Ref

lect

ivy

[a.u

.]

Time [s]

experimental data FFT smoothed data

SPE

c-Si a-Si

Laser


Fig. 2.12 The experimental and simulated spectra were normalized and compared, a point of the curve on the left at a time t correspond to a point of the curve on the right at a depth z. A collection of points (z, t) is so created, the time derivative of this function z(t) is the interface velocity as function of depth.

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000

Nor

mal

ized

Inte

nsity

[a.u

.]

Time [sec]

Depth [Ang]

Experimental Simulation

0 1000 2000 3000 40000.00.10.20.30.40.50.60.7

0 200 400 600 800 1000 12000.0

0.1

0.2

0.3

0.4

0.5

0.6

283

639

984

13351683

20332381273030793428

161.48

244.14

301.98

363

432.37517.94

626.48752.09886.491008.59

Inte

nsity

[a.u

.]

Depth [Ang]

Simulation peak position

Inte

nsity

[a.u

.]

Time [sec]

experimental peak position

Fig. 2.11 Experimental (top figure) reflectivity spectrum obtained by TRR measurement of a sample doped with Ga at 1x1020 at/cm3 as function of the annealing time at 570°C. The positions of peaks and valleys are marked and compared with that of a simulated spectrum (bottom figure) as function of depth of the c-a interface from the surface.

2.4 SPE rate

47

2.4.2 SPE rate of B and Ga doped Si The SPE rate at 570°C of Ga doped Si (1x1020 at/cm3) is reported in Figure 2.13

as function of depth, the Ga concentration profile measured by RBS is also shown. The increase of the SPE rate as the Ga concentration increases is clearly visible, the maximum of SPE rate is reached at the peak concentration and it is about 6.3 Å/s, while that of intrinsic Si is ~2.5 Å/s. The same measurements has been repeated at 550°C and gives a maximum SPE rate of ~2.4 Å/s (see Figure 2.16). The SPE rate as function of Ga concentration is shown in Figure 2.15.

Boron is the dopant that most enhances the SPE rate of amorphous Si, the

experimental data are reported in Figure 2.14 for the two temperatures 568 and 550 °C for the sample doped with 6x1020 B/cm3. The maximum SPE rate is 32 and 15 Å/s at 568 and 550°C, respectively, our data are in agreement with the values that can be extrapolated by the measurements of Olson and Roth [Ols88]. They had 174 Å/s at regrowth temperature of 610°C and B concentration 5x1020 at/cm3, using their activation energy of 2.52 eV a SPE rate of 15.5 Å/s at 550°C is obtained.

0 500 1000 1500 2000 2500 3000 35001016

1017

1018

1019

1020

1021

1022

0.1

1

10

100 B SIMS profile

Con

cent

ratio

n [a

t/cm

3 ]

Depth [Å]

Interface Velocity [Å

/s]

T=568°C T=550°C

Fig. 2.14 B concentration profile (solid line) of a B doped sample and SPE rate measured by TRR as function of depth at regrowth temperature of 568°C (full squares) and 550°C (empty squares).

0 500 1000 1500 2000 2500 3000 35001017

1018

1019

1020

1021

1

2

3

4

5678910

Con

cent

ratio

n [a

t/cm

3 ]

Depth [Å]

Ga RBS profile

Interface Velocity [Å/s]

Fig. 2.13 Ga concentration profile (solid line) of a Ga doped sample and SPE rate measured by TRR as function of depth (full squares) at regrowth temperature of 570°C.


Figure 2.15 shows the SPE rate as function of the dopant (B or Ga) concentration, the enhancement of the SPE rate in B doped samples is clearly visible in the region 1x1019-2x1020 at/cm3, at higher concentration a saturation trend is observed in agreement with the curve (solid line) measured by Olson and Roth [Ols88] at a regrowth temperature of 610°C. The SPE rate enhancement of the Ga doped samples is completely different with a small rising that anticipates the saturation at a concentration of 1x1020 at/cm3.

The SPE rate measured at 550°C in B+Ga co-doped sample is reported in Figure

2.16, the data about B and Ga doped samples are also shown for comparison. The SPE maximum is about 7.5 Å/s in the co-doped samples that is an intermediate value between the 15 and 2.4 Å/s of B and Ga doped samples, respectively. A similar effect has been observed for P and As doped Si [Sun82a]: the SPE rates measured at 475°C are 31.7, 12.2 and 20 Å/min for P, As and P+As (~2x1020 at/cm3 for each dopant) doped Si, respectively. Using the observation of Campisano (see section 1.3.1) that the SPE rate increases with the absolute difference of dopant and Si sizes, the co-doped samples (P+As or B+Ga) can be seen as materials doped with impurity that has an intermediate covalent radius between the two dopants. The regrowth velocity is enhanced with respect of lowest rate. However, the medium covalent radius is clearly an intuitive representation and has no physical meaning, so we have calculated the perpendicular strain associated to the B and Ga doping of the Si matrix. The strain (see section 3.3) can be evaluated considering the crystal parameter (a0) of a relaxed crystalline alloy Si1−xBx or Si1−xGax that follows the Vegard’s rule [Veg21]:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

=

+−=

⊥ 177.0

38

)1(

0

0

aa

ra

xaxaa

Si

CI

ISi

ε

(2.6)

where aSi=5.431 Å, x=CI/CSi (CI=impurity concentration and CSi=5x1022 at/cm3), rC is the covalent radius of the impurity: rC=0.82 and 1.26 Å for B and Ga,

1018 1019 1020 1021

100

101

102

Inte

rface

Vel

ocity

[Å/s

]

Concentration [at/cm3]

B T=570°C B T=550°C Ga T=570°C

B [Olson-Roth] T=610°C

Fig. 2.15 Regrowth velocity of Si doped with B (empty symbols) and Ga (full squares) as function of dopant concentration and different regrowth temperatures: 570°C and 550°C. The data of B doped Si at 610°C from Olson et al. [Ols88] are also shown (solid line).

2.4 SPE rate

49

respectively [Kit96]. The perpendicular strain (ε⊥) is deduced (see section 3.3) using the elastic coefficients of Si [Fis96].

This calculation is acceptable for B concentration lower than 2.5x1020 at/cm3 and

has been verified by HRXRD analyses that will be shown in chapter 3. In Figure 2.17 we have reported the SPE rate at 570°C, measured in B and Ga doped and co-doped samples with 1-2x1020 at/cm3 of each dopant (see the figure labels for details), as function of the absolute value of perpendicular strain. In this way the number of ionized impurities is similar in all samples and the SPE rate is compared in samples with nearly the same Fermi level.

The SPE rate relative to samples doped with 1x1020 at/cm3 of B and Ga is also

shown for comparison. The points with constant number of ionized impurities are

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

B+Ga(1+1)

Ga(2)

B(2)

Ga(1)

B(1)

Inte

rface

Vel

ocity

[Å/s

]

|ε| [x10-4]

T=570°C

Si this work

Fig. 2.17 Regrowth velocity at 570°C of Si doped with B and Ga as function of absolute value of perpendicular strain induced by the impurities. The numbers in brackets indicate the concentration of each dopant in unity of 1020 at/cm3. The dashed line is a guide of eyes and joints the points relative to a constant total impurity concentration.

0 500 1000 1500 2000 2500 3000 35001016

1017

1018

1019

1020

1021

0.1

1

10

Con

cent

ratio

n [a

t/cm

3 ]

Depth [Å]

B SIMS profile Ga RBS profile

Interface Velocity [Å

/s]

T=550°C B + Ga B Ga

Fig. 2.16 Regrowth velocity at 550°C of Si doped with B (empty squares), Ga (empty triangles) and co-doped B+Ga (full squares). The dopant concentration profiles of the three samples are also shown: B (solid line), Ga (dot line).


jointed by a straight line, indicating a linear dependence of the SPE rate and the strain induced by the impurities. In order to bear out this observation we have plotted in a similar graph (Figure 2.18) the experimental points from Suni et al. [Sun82a] about the SPE rate of P, As and As+P doped Si at 475°C. The perpendicular strain has been calculated using the covalent radii of 1.20 and 1.07 Å for As and P, respectively [Kit96]. Also in this case the medium position of the co-doped point agrees with our idea.

Figure 2.19 shows the SPE rate of co-doped samples with Ga concentration of 1x1020 at/cm3 and different B concentrations, the SPE rate increases with increasing B concentration because both effects, doping and strain, act in the same

0 1 2 3 4 5 62

3

4

5

6

7

8

Inte

rface

Vel

ocity

[Å/s

]

B conc. [x1020 at/cm3]

T=550°CGa+B co-doped Si

Fig. 2.19 Regrowth velocity at 550°C of Si co-doped with Ga concentration of 1x1020 at/cm3 as function of the B concentration.

0 1 2 3 4 5 60

25

50

P+As(2+2)

As(4)

P(4)

As(2)

P(2)

Si

Inte

rface

Vel

ocity

[Å/m

in]

|ε| [x10-4]

T=475°C

Suni et al. [Sun82]

Fig. 2.18 Regrowth velocity of Si doped with P and As as function of absolute value of perpendicular strain induced by the impurities. The data are from Suni et al. [Sun82a] and refer to a regrowth temperature of 475°C. The numbers in brackets indicate the concentration of each dopant in unity of 1020 at/cm3. The dashed line is a guide of eyes and joints the points relative to a constant total impurity concentration.

2.4 SPE rate

51

direction. This result permits to draw some important conclusions about the Ga segregation observed in co-doped samples, which will be discussed in the next section.

2.4.3 Ga segregation We showed (see Figure 2.9) that the Ga profile undergoes redistribution with a

visible surface segregation when Ga is implanted with B in the co-doped samples. In Figure 2.9 the Ga concentration in the as implanted sample is 2x1020 at/cm3, which is a critical value and a small segregation is detectable also when there is no B, the presence of B enhances the Ga segregation. We have investigated this effect in samples with a lower Ga concentration. Figure 2.20 reports the Ga profiles of samples doped with Ga concentration of 1x1020 at/cm3 and B concentration of 2, 5.5 and 8x1020 at/cm3. The sample doped only with Ga does not show any surface segregation. In the co-doped samples, instead, the maximum Ga concentration decreases as observed in samples doped with higher Ga concentration and the segregation peak at the surface increases with increasing B concentration. Considering that the SPE rate increases in co-doped sample with increasing the B concentration, as shown in Figure 2.19, and the stronger segregation the higher ratio between the impurity diffusivity and interface velocity D/v (see section 1.3.3), the presence of B atoms changes the Ga diffusivity.

The Ga distribution has been simulated with a model that numerically resolves [Bae82, Woo81, Whi80] the one dimensional diffusion equation (see section 1.3.3) with the condition of a moving c-a interface. The concentration of the solute C(t+δt) at the time t+δt is given by:

( ) (t))vCk(δxδt(t)C(t)C(t)C

δxδtD(t)Cδt)(tC i

'iiiii −+−++=+ −+ 12112 (2.7)

Ci(t) represents the solute concentration in the amorphous layer (δx thick) at the depth i at the time t, v is the interface velocity, k’ is the segregation coefficient, D is the diffusion coefficient of Ga in the amorphous Si. The initial Ga profile used for simulation is that of the as implanted sample (dashed line in Figure 2.20), the interface velocity in the co-doped samples has been evaluated by the TRR measurements. We have evaluated D using the reported data about Ga diffusivity in pure amorphous Si [Str87], k’ is the free parameter that has been determined by fitting the experimental data with the simulated concentration profiles.

The diffusivity of Ga in amorphous Si has been evaluated about 20 Å2/s at the temperature of the annealing process (580°C), using the diffusion coefficients published in literature [Str87]. The diffusion in the crystal phase is about 5 orders of magnitude lower than that in the amorphous [Zag93] at 550°C. The Ga diffusion coefficient in crystal Si was measured by neutron activation and SIMS in the temperature range 700-1100°C giving D0∼0.005 cm2/s and an activation energy of 2.7 eV [Hari80], the extrapolated value at 580°C is D∼5x10-3 Å2/s, while Ghoshtagore et al. [Gho71] gave D∼3.4x10-5 Å2/s and Fuller et al. [Ful56] D∼5.5x10-5 Å2/s. Therefore the diffusion in the crystal phase can be neglected and only the diffusion of the impurities in front of the advancing interface is crucial for segregation modelling.


The regrowth velocity has been measured for the co-doped samples at T=550°C,

while the standard annealing treatment we performed on all samples presented so far was at T=580°C. We have evaluated the SPE velocity at T=580°C using the data at T=550°C and the activation energy of 2.68 eV reported by Olson and Roth [Ols88]. For example the SPE rate of the sample doped with Ga (1x1020 at/cm3) and B (6x1020 at/cm3) is ∼29 Å/s and no further increase is expected for higher B concentration, as indicated by the saturation trend of Figure 2.19.

Figure 2.21 shows the simulated profile of the sample with concentration 1x1020 at/cm3 of Ga and 8x1020 at/cm3 of B, the simulation parameters are v=29 Å/s, D=20 Å2/s and k’=0.35. The k’ values obtained fitting the three Ga profiles of Figures 2.20, are reported in the table 2.8, k’ decreases with increasing the B concentration, as expected.

Table 2.8

Max B conc. [1020at/cm3]

2.0 5.5 8.0

k’ 0.60±0.02 0.45±0.02 0.35±0.02 k’ is the segregation coefficient at the interface, it depends on the segregation

coefficient in equilibrium conditions (k0) by the following relationship (see section 1.3.3):

v)/)-(1' 0 λDexp(kkk 0 −+= (2.8)

where λ=1.36 Å is the is the crystal plane spacing. The equilibrium solid solubility of impurities [Ell93] in amorphous Si is known to be very much higher than in crystal Si, so it is plausible to have k0<<1. Using the equation 2.8 we can evaluate that the k’ decreasing is correlated to a D increasing at least of a factor of 2. However, we can estimate a variation of the diffusion length of 50 Å by changing D from 20 to 40 Å2/s, considering the time for which the doped amorphous layer was subjected to annealing before the a-c interface arrived (600 s to regrow 2500 Å of undoped Si at 580°C). With a depth resolution of 80 Å in the RBS spectra of Ga we are clearly unable to evaluate the variation of D caused by the presence of the B atoms.

0 50 100 150 200 250 3000.0

0.5

1.0

Con

cent

ratio

n [x

1020

at/c

m3 ]

Depth [nm]

as implantedafter SPE:

Ga Ga+B(2) Ga+B(5.5) Ga+B(8)

Fig. 2.20 Ga concentration profiles measured by RBS in samples implanted with Ga (solid line) and after SPE at 580°C (dashed line) and co-doped with B at a maximum concentration of 2x1020 at/cm3 (solid line), 5.5x1020 at/cm3 (dash line), 8x1020 at/cm3 (dash-dot line).

2.5 Stability of the solid solution upon annealing

53

2.5 Stability of the solid solution upon annealing The thermal stability of the supersaturated solid solutions of B and Ga doped Si

has been investigated by rapid thermal annealing (RTA) at temperature of 700°C, 800°C and 900°C for 10 s. We have studied the samples doped at maximum with 2x1020 at/cm3 of each dopant, in order to be sure that the impurity atoms are completely substitutional in the starting solid solutions.

The stability of Si-B solutions is well known since many years, the milestone of Armigliato et al. [Arm77] reported the precipitation of B atoms in very heavily doped bulk Si (5x1020 at/cm3) upon annealing at temperature higher than 700°C and very long time (22h), while no electrical deactivation was observed for dopant concentration of 2x1020 at/cm3 and annealing at 900°C for 500 h. When the dopant is implanted in amorphous layer the situation is completely different because the annealing treatments causes the emission of point defects from the end of range defects, the injection of Si self interstitials becomes considerable at temperature of 800°C, in such conditions clustering phenomena induced by the interaction between B and point defects (see section 1.2) give rise to electrical deactivation of B. In B doped with 1.3x1020 at/cm3 the carrier concentration reduces of about 6% after the annealing at 900°C 10 s.

Si-Ga solutions are, instead, very unstable. Ga is subjected to a quickly precipitation still after annealing at low temperature. The Figure 2.22 shows the sheet resistance and the Hall carrier fluence as function of the implanted fluence of Ga measured after SPE and after RTA treatment at 900 °C 10 s. The sheet resistance of Ga-doped Si after SPE (filled symbols Fig. 2.22a) decreases from 500 to 200 Ω/sq as Ga concentration increases from 3×1019 to 2×1020 at/cm3 because of the enhancement of the carrier surface concentration (filled symbols Fig. 2.22b).

0 50 100 150 200 250 3000.0

0.5

1.0

Con

cent

ratio

n [x

1020

at/c

m3 ]

Depth [nm]

Ga+B(8x1020cm-3) as implanted after SPE simulated

Fig. 2.21 Ga concentration profiles measured by RBS in co-doped sample with B at a maximum concentration of 8x1020 at/cm3 as implanted (empty circles) and after SPE at 580°C (+). The simulated (solid line) has been calculated with k’=0.35, D=20 Å2/s, v=29 Å/s (see the text for details).


The solid line in Figure 2.22b marks the carrier concentration expected in case of complete Ga activation; the experimental data are consistent with a complete activation up to a Ga concentration of ∼2×1020 at/cm3, above this value the carrier surface concentration saturates. The sheet resistance increases after annealing, as previously reported by Harrison et al. [Har86], but the electrical deactivation is independent of the annealing temperature in the 700 - 900 °C range, in fact a difference lower than 20% has been observed after the various annealings. As expected, the thermal treatment produces the electrical deactivation of Ga exceeding the solubility limit and the maximum active carrier concentration reduces down to 4x1019 at/cm3, which is about the retrograde solubility (see section 1.3.2). The results of the RBS channeling analyses after RTA at 900°C are reported in table 2.9.

Table 2.9

Max Ga conc.

[1020cm-3] Treatment χ<100> χ<110> χ<111> fsubst Subst. Ga conc.

[1020cm-3]

Carrier conc.

[1020cm-3]

1.0 SPE 0.07 0.12 0.09 0.95 0.95 0.94

2.0 SPE 0.13 0.14 0.12 0.90 1.80 1.70

1.0 SPE+RTA 0.36 0.36 0.35 0.66 0.66 0.35

2.0 SPE+RTA 0.57 0.58 0.55 0.45 0.90 0.40 The χ(Ga) along the different axes increases with respect to the not-annealed

samples and about 65% and 45% of the implanted Ga remains substitutional for Ga concentration of 1x1020 and 2x1020 at/cm3, respectively. The Ga channeling yield χ

0 1 2 3 4 5 60

1

2

3

40

100

200

300

400

5001 2 3 4

Hal

l flu

ence

[1015

at/c

m2 ]

Ga fluence [1015 at/cm2]

b)

a)

SPE +RTA

Shee

t Res

ista

nce

[Ω/s

q]

Ga max concentration [1020at/cm3]

Fig. 2.22 a) Sheet Resistance as function of the Ga implanted fluence measured on samples after SPE (full symbols) and after RTA at 900°C 10 sec (empty symbols). b) Surface carrier concentration measured by Hall effect as function of the implanted Ga fluence for samples after SPE (full symbols) and after RTA at 900°C 10 sec (empty symbols). The solid line indicates the complete activation of the implanted fluence.

2.5 Stability of the solid solution upon annealing

55

increases identically in all the high-symmetry directions, indicating a random location of not-substitutional Ga atoms. It should be noted that the concentration of substitutional Ga was always higher than the carrier concentration and this could be an indication of the formation of complexes involving substitutional Ga atoms that are not electrically active. However no agglomerates have been observed in the sample implanted at a concentration of 2x1020 at/cm3 (or lower) by plan view transmission electron microscopy (TEM) analyses at a magnification of 106. This is consistent with previous results on the deactivation of supersaturated solid Si solutions doped with As [Par90] or Sb [Tak04], in which the formation of complexes not electrically active and not visible by TEM involving substitutional dopant atoms has been demonstrated. The formation of large agglomerates visible by TEM requires thermal treatments at very high temperatures and/or very high dopant concentration. In particular Ga precipitates have been detected by TEM for a Ga concentration of ∼5x1020 Ga/cm3 [Nar83, Shi92]. The tendency of Ga to precipitation and the effect of point defects injection from the EOR probably collaborate to the observed Ga deactivation upon RTA. In fact, a large concentration of Si self interstitials is generated by the dissolution of the EOR defects during annealing [Mad84, Rim95] and, on the other hand, enhanced impurity diffusion must be invoked to account for complex formation in the experimental conditions. The stability of the Si-Ga solid solution in presence of a controlled rate of point defects will be studied in chapter 4.

The Ga precipitation has been observed also in co-doped samples. Figure 2.23 shows the carrier fluence measured by Hall in co-doped samples as function of the Ga implanted fluence. These samples were doped with B concentration of 1.3x1020 at/cm3 and Ga concentration between 0.3 and 1.4x1020 at/cm3, as indicated in table 2.1. We noted (see section 2.3) that the carrier concentration in co-doped samples is approximately given by the sum of the two contributions from each dopant, after RTA treatment at 900°C the carrier fluence in co-doped samples (full triangles in Fig. 2.23c) decreases by the same factor of the reduction observed for Ga doped samples (empty circles in Fig. 2.23). The same trend has been detected for the low RTA temperatures (see Fig. 2.23b). In conclusion the thermal stability of B in Si-B-Ga solutions seems to be not affected by the precipitation of Ga that occurs, even in presence of B, upon rapid annealing.

0 1 20

1

2

3

4

1 2 1 2

Hal

l car

rier [

1015

cm

-2]

Ga implanted fluece [1015 cm-2]

Ga

B

B+GaSPE

a) b) c)

Ga

B

B+Ga

+RTA 700°C

Ga

B

B+Ga

+RTA 900°C

Fig. 2.23 Hall carrier fluence as function of Ga implanted fluence for samples doped with B (empty squares), Ga (empty triangles) and co-doped samples (full squares) with a fixed B concentration of 1.3x1020 at/cm3 and Ga concentration of 0.3, 0.6, 0.9, 1.3 x1020 at/cm3. The measurements are shown after SPE regrowth (a), after RTA treatment at 700 °C (b) and 900 °C (c) for 10 s.


2.6 Concluding Remarks We showed that our B and Ga doped Si samples are supersaturated solid

solutions. The electrical activation of B doped Si continued to increase at concentration higher than 2x1020 at/cm3, while Ga reached this value as the maximum substitutional and electrically active concentration in Si. The measurements of the substitutional fraction of B atoms by channeling technique indicated that B atoms are displaced from substitutional sites when the B concentration exceeds the value of 2x1020 at/cm3, supporting the idea that the B cluster formation is responsible of the B deactivation.

When both dopants were present in the solution the Ga solubility decreased even at concentration of 1x1020 at/cm3 and a strong segregation at surface with increasing the B concentration was observed. The B dopant, instead, did not change its electrical and structural properties in presence of Ga. The carrier concentration in the co-doped samples was given by the ionization of both impurities.

The measurements of the SPE rate in co-doped B+Ga samples showed that the SPE rate in presence of B increases with respect of pure Ga doping. We reported a dependence of the SPE rate on the lattice strain induced by the dopant itself. The increase of SPE velocity in presence of B allowed to conclude that the Ga segregation is due to an increase of the Ga diffusivity at the interface.

The stability of the supersaturated solid solution was studied using RTA treatments in the temperature range 700-900°C. While B maintained its electrical activation and lattice location during annealing, Ga was subjected to a rapid precipitation also in presence of B, which, however, did not affect the charge carrier concentration due to the ionized B impurities.

2.7 References

[Ajz90] Ajzenberg-Selove F., Nucl. Phys. A 506 (1990) 1. [Arm77] Armigliato A., D. Nobili, P. Ostoja, M. Servidori, S. Solmi, in Semiconductor

Silicon 1977, 77-2, H. Huff and E. Sirtl eds. (The Electrochemical Society, Princeton, N. J. 1977) 638.

[Ast01]

ASTM Standard F76, “Standard Test Method for Measuring Resistivity and Hall Coefficient and Determining Hall Mobility in Single-Crystal Semiconductors” 2001 Annual Book of Standards (Am. Soc. Test. Mat., Philadelphia, 2001)

[Bae82] Baeri P., S.U. Campisano, in Laser annealing of Semiconductor, J.M Poate and J.W. Mayer eds. (Academic Press, New York 1982)

[Ell93] Elliman R.G. and Z.W. Fang, J. Appl. Phys. 73 (1993) 3313 [Fis96] Fischetti M.V., S.E. Laux, J. Appl. Phys., 80 (1996) 2234. [Ful56] Fuller C.S. and J. Ditzenberger, J. Appl. Phys. 27 (1956) 544 [Gho71] Ghoshtagore R.N., Phys. Rev. B 3 (1971) 2507

[Gla00] Glass G., H. Kim, P. Desjardins, N. Taylor, T. Spila, Q. Lu, and J. E. Greene, Phys. Rev. B 61 (2000) 7628

[Har80] Haridoss S. and F. Beniere, J. Appl. Phys. 51 (1980) 5833

[Har86] Harrison H.B., J. Narayan, D. Fathy and S.R. Wilson, Appl. Phys. Lett. 51 (1986) 905

[Kit96]

Kittel C., Introduction to Solid State Physics (John Wiley & Sons, New York, 1996)

[Luo03] X. Luo, S. B. Zhang and S. H. Wie, Phys. Rev. Lett. 90 (2003) 26103 [Mad84]

Mades S., in Ion implantation: Science and Technology, J.F. Ziegler ed. (Academic Press, Orlando, 1984) 109

[Mad96] Madelung O. ed., Semiconductors group IV elements and III-V compounds, in Data in Science and Technology, R.Poerschke ed. (Springer – Verlag, Germany, 1996)

[Mam94] Mamontov Y.V. and M. Willander, IEICE Trans. Electron. E77-C (1994) 287

2.7 References

57

[May77] Mayer J. W. and E. Rimini, eds., Ion Beam Handbook for Material Analysis, (Academic Press, New York, 1977).

[May98] Mayer M., A. Annen, W. Jacob, S. Grigull, Nucl. Instr. and Meth. in Phys. Res. B 143 (1998) 244

[Mor73] Morgan D. V. ed., Channeling Theory, Observation and Application, (John Wiley & Sons, New York, 1973).

[Nar83] Narayan J., Holland, O. W., and Appleton, B. R., J. Vac. Sci. Technol. B1 (1983) 871

[Ols88] Olson G.L. and J.A. Roth, Mater. Sci. Rep. 3 (1988) 1 [Par90] Parisini A., A. Bourret, A. Armigliato, M. Servidori, S. Solmi, R. Fabbri, J. R.

Regnard, and J. L. Allain, J. Appl. Phys. 67 (1990) 2320 [Rad94] Radamson H. H., M. R. Sardela, L. Hultman, and G. V. Hansson, J. Appl. Phys. 76

(1994) 763. [Rev96] Revenant-Brizard A., J. R. Regnard, S. Solmi, A. Armigliato, S. Valmorri, C.

Cellini and F. Romanato, J. Appl. Phys. 79 (1996) 9037 [Rim95] Rimini E., Ion Implantation: Basics to device fabrication (Kluwer, USA, 1995) [Rom03] Romano L., E. Napoletani, V. Privitera, S. Scalese, A. Terrasi, S. Mirabella, M.G.

Grimaldi, Mater. Sci. Eng. B 102 (2003) 49. [Sch90] Schroder D.K., Semiconductor Material and Device Characterization, John Wiley

& Sons Inc., USA, 1990 [Seg65] Segel R.E., S.S. Hanna, R.G. Allas, Phys. Rev. 139 (1965) B818. [Shi92] Shiryaev Y., A.N. Larsen, and M. Deicher, J. Appl. Phys. 72 (1992) 410 [Str87] Streit D.C., E.D. Ahlers, F.G. Allen, J. Vac. Sci. Technol. B 5 (1987) 752 [Sun82a] Suni I., G. Goltz, M. G. Grimaldi, M.-A. Nicolet and S. S. Lau, Appl. Phys. Lett.

40 (1982) 269. [Tak04] Takamura Y., A. F. Marshall, A. Mehta, J. Arthur, P.B. Griffin, J.D. Plummer. J.R.

Patel, J. Appl. Phys. 95 (2004) 3968 [Tes95] Tesmer J. R. and M. Nastasi, eds., Handbook of modern ion beam materials

analysis, (Materials Research Society, Pittsburg, 1995). [Vai99] Vailionis A., G. Glass, P. Desjardins, David G. Cahill, and J. E. Greene., Phys.

Rev. Lett. 82 (1999) 4464 [Van58] Van der Pauw L.J., A Method of Measuring specific Resistivity and Hall Effect of

Discs of Arbitrary Shape, Philips Res. Repts. 13 (1958) 1 [Veg21] Vegard L., Z. Phys. 5 (1921) 17 [Vol96] Vollmer M., J.D. Mayer, R.W. Michelmann, K. Bethge, Nucl. Instr. and Meth. B.

117 (1996) 21 [Whi80] White C.W., R.S. Wilson, B.R. Appleton, F.W. Young, J. Appl. Phys. 51 (1980)

738 [Woo81] Wood R.F., J.R. Kirkpatrick, G.E. Giles, Phys. Rev. B 23 (1981) 5555 [Zag93] Zagwin P., Ph. D thesis, University of Amsterdam (1993) [Zie85] Ziegler J. F., J. P. Biresack, and U. Littmark, The Stopping and the Range of Ions

in Solids (Pergamon, New York, 1985); http:// www.srim.org

Chapter 3

Effect of Strain on Carrier Mobility in heavily doped silicon.

The carrier mobility in silicon is an important parameter for device design and analysis. Accurate mobility models are necessary for predictive simulation due to the direct dependence of the charge current on mobility, which is often the most desired quantity in a device. Conductivity of heavily doped silicon is significant in design and analysis for the high density of the devices since the scaling rules allow the doping concentration to increase by the scaling factor in a short-channel MOSFET.

Strained Si material emerged as a strong contender for developing transistors for the next generation electronics. Strain lifts the degeneracy of the valence and conduction bands which can be used to deliver superior transport properties in comparison to bulk Si. Transistors fabricated using strained Si channels have reported larger drive currents capabilities [Lee05] due to the enhanced electron and hole mobilities. However, the strain technology has never been applied to reduce the sheet resistance in the heavily doped region of ultra-shallow junctions; the effect of strain in presence of a high concentration of charge carriers is still unknown.

In the device simulation, the empirical formulae given by Caughey and Thomas [Cau82] have been firstly used for the carrier mobilities. Some corrected formulae extending to heavily doped region has been figured out by Arora et al. [Aro83] and Masetti et al. [Mas83], Li has made some theoretical approaches for low impurity doping region [Li78]. Recently, more fine analytical expression has been derived from the study of Monte Carlo method for heavily doped n-type silicon [Kai98]. It is well known that under low fields the mobility depends on the doping concentration and on temperature. However, it is less known that the carrier mobility in doped Si depends as well on the chemical nature of the dopant atoms. In this chapter we demonstrate that this difference arises from the strain induced by the dopant itself. The Hall mobility has been measured in samples in which the effective strain has been varied by co-doping Si with B and Ga having overlapping concentration profiles in the 0.1-2x1020 at/cm3 range. The strain distribution has been measured by high resolution x ray diffraction (HRXRD). Co-doped samples with a total (B+Ga) constant carrier concentration (1x1020 at/cm3) have been used to disentangle the effect of the strain on the mobility, and a higher mobility has been measured in tensile strained Si. A linear relationship between the perpendicular strain and the inverse of mobility has been inferred. Using this relationship the mobility relative to B and Ga impurities has been corrected and a unique mobility versus carrier concentration curve for unstrained Si has been determined.

3.1 Brief review of carrier mobility in semiconductor A brief review of the scattering mechanisms and the carrier transport description

is reported in section 3.1.1, a detailed description of the scattering processes is

Chapter 3 Effect of Strain on Carrier Mobility in heavily doped silicon. 60

beyond our purpose so we refer to the many works by the expertises [Con82, See73, Yu99] about this argument, but we would like to underline some important skills that usually are poor characterized in literature and can help to set this work in a right background.

The most important results about the hole mobility enhancement in strained Si is reported in section 3.1.2, while the effect of high doping concentration is discussed in section 3.1.3.

3.1.1 The BTE and the definition of carrier mobility At the most basic level, electrons in semiconductors are quantum mechanical

waves propagating through the device under the influence of the crystal, applied, and scattering potentials. When the scale of the device is large enough, the electron can be treated much as a classical particle. Electron scattering, however, is the result of short-range forces and must be treated quantum mechanically. The drift-diffusion equation can be written as follow:

neDEneJ nnn ∇+=rr

µ (3.1)

where J is the charge carriers current, Er

is the applied electric field, n the electron concentration, e the electron charge, µ the carrier mobility, D the diffusion coefficient. At the macroscopically level, the equation 3.1 results by averaging an enormous number of nearly chaotic trajectories. Alternatively, one may simply ask: what is the probability of finding an electron at r with (crystal) momentum hk? The answer is ƒ(r, hk, t), the distribution function, which defines the state of the device. The equation, which describes the way free carriers (electrons in the conduction band, holes in the valence band) move in a semiconductor under the action of an electric field, determines ƒ and is called “Boltzman transport equation” (BTE). The BTE, considering the electrostatic potential φ(r), is:

[ ]∑ −+

+∇⋅∂∇+∂∇⋅∇−=∂

∂

'

),,(),'(),',()',(

),,(),(),,()(1),,(

k

krrk

tkrfkkPtkrfkkP

tkrftretkrfkEt

tkrf

vvrvrrrr

vrrrrr

h

rr

φ (3.2)

In general, such an equation should be derived starting from the Schrödinger equation for a many particle (the free carriers) system, including the lattice potential as well as the perturbations which represent scattering. The problem is daunting and still largely unsolved, among the approximations that are usually made to solve the problem, we would like to underline that all collision processes are assumed to be independent, instantaneous, local in space, and are perturbations weak enough to justify the use of the first-order (in perturbation theory) Fermi Golden Rule. As a consequence, all collision processes depend only on the local, instantaneous electron variables, without retaining memory of where and when the previous collision happened. At very large value of impurity concentration (1x1019 at/cm3 in Si) the Fermi Golden Rule (equivalent to what’s know as the Born approximation for Coulomb scattering) breaks down; scattering with several impurities can not be considered as a succession of independent scattering events, in other words the impurities are so close that the electrons wavelength is longer than the average separation of impurities. In this case numerical solutions of the BTE must be performed using Monte Carlo simulations.

Let’s define the momentum relaxation time τp,i(k) along the direction i (=x,y,z) via the integral equation:

),'()()()'()'(

1)2()(

1

,

,3

,

kkPkkvkkvkd

k ipi

ipi

ip

rrrr

rrv

r ∫⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

ττ

πτ (3.3)

3.1 Brief review of carrier mobility in semiconductor

61

If the scattering process is elastic and the band-structure of the semiconductor is isotropic, then k=k’, vi(k)=vi(k’), the relaxation time itself depends only on the magnitude of k, so that the term in square bracket becomes 1 − cosθ, where θ is the angle between k and the xi-axis. Thus the expression for τp,i simplifies to:

[ ] ),'(cos1)2()(

13

,

kkPkdkip

rrv

r ∫ −= θπτ

(3.4)

This is the scattering rate ‘weighted’ by change of the ith component of the velocity. For small-angle scattering (such as Coulomb scattering) small θ dominate inside P(k’, k), the term (1−cosθ) is small and the effect of the scattering process is weak. In other words, even if scattering is frequent, each collision changes the ith component of the velocity by such a small amount that the time required to relax the velocity to its equilibrium value is very long. On the contrary, for large-angle scattering (such as optical-phonon scattering) each collision is very effective, the term cosθ vanishes after integration over the polar angle and the momentum relaxation time becomes identical to the scattering rate.

The mobility tensor is defined by:

>∂∂

<−=fk

fvej

iipij1

,τµh

(3.5)

so along the x-axis, without loss of generality in the isotropic limit, we have:

[ ]∫∞

−>=∂∂

<−=0

)(1)()()(*3

21 EfEfEEEdETknm

efk

fveFDFDp

Bxxpij τρτµ

h (3.6)

where ƒFD is the equilibrium Fermi-Dirac distribution. This expression is known as the “Kubo-Greenwood” equation. A simpler expression is useful, since it is related to the simpler Drude’s model of conduction. Note that:

Fig. 3.1 Schematic list of several scattering mechanisms that limit carrier mobility in a semiconductor grouped in three classes evidenced by the grey squares. The coupling among the different classes of scatterings is represented by the white squares [Lun90].

Carriers • Binary: electron-electron; electron-hole • Collective: plasmons Coupled

Plasmons and phonons

Defects • Neutral Impurities • Dislocations • Alloy scattering • Ionized Impurities

Phonons • Acoustic/optical: deformation potential • Acoustic/optical: polar

Screening


>><<=><><

>→<>≈∂∂

<−= pp

xxpBx

xpij me

EE

mevv

Tke

fkfve τ

τττµ

**1

h (3.7)

we obtain the Drude’s mobility by defining the Drude’s τ as the ‘energy weighted average’ of the momentum relaxation time < τpE>/<E>.

Common scattering mechanisms can be classified as shown in Figure 3.1. The relaxation time has a power law dependence on E for each scattering mechanism that is resumed in the table 3.1

s

TkkEE

Bp ⎥

⎦

⎤⎢⎣

⎡=

)()( 0

v

ττ (3.8)

Table 3.1 Scattering mechanism Exponent s Hall factor

Acoustic phonon -1/2 1.18 Ionized Impurity (weakly

screened) +3/2 1.93

Ionized Impurity (strongly screened)

-1/2 1.18

Neutral Impurity 0 1.00 Piezoelectric +1/2 1.10

The Hall factor will be discussed later. The screening of the ionized impurities is

due to the presence of the valence electrons, which is accounted for by the macroscopic dielectric constant of the semiconductor, and the free carriers, which is accounted for by the Yukawa’s potential instead of the Coulomb’s form [See73].

Using 3.7 and 3.8 it is possible to express the temperature dependence of carrier mobility for each scattering process. The most important contributions are due to ionized impurity in the limit of weak screening (positive exponential) and acoustic phonon (negative exponential) scatterings, and give the well known exponential law µ∝T±3/2, respectively.

The expression of the carrier mobility limited by the ionized impurity scattering is given by the Brooks–Herring formulation [Bro51]:

22

2

2

222/13

2/322/15 24

1)1ln(3

)(2DB

BSIMP LTkm

Nme

Tk⋅=

⎥⎦

⎤⎢⎣

⎡+

−+=

hβ

βββ

πµ ε1/2

(3.9)

Where εS is the semiconductor dielectric function, m is the effective mass of charge carriers, N is the impurity concentration, LD is the Debye’s length, which express the characteristic length of screening of the Yukava’s potential.

Acoustic phonon scattering gives the following mobility [See73]:

2/322/52/1

24

)(23 Tkmce

BAc

SAc ∆⋅

=ρπµ h1/2

(3.10)

Where cS is the average sound velocity, ρ is the crystal density, ∆Ac is the deformation potential from the model of Bardeen and Shockley [Kit96] that values 10 eV [Fis96].

The total scattering rate is the sum of the rates for each of the individual process:

∑=i ieff ττ

11 (3.11)

Where the index, i, label the various scattering mechanisms listed in Figure 3.1. Scattering occurs by defects, by phonons, and by other carriers. Defect scattering


63

includes scattering by both ionized and neutral impurities and by crystal defects such as dislocations. For semiconductors alloys, variations in the alloy composition also produce scattering. Phonon scattering occurs by the deformation potential in covalent semiconductors and by both the deformation potential and polar interactions in compound semiconductors. Carrier-carrier scattering includes both binary collisions and interactions with the carrier plasma. Free carriers can also influence the other scattering processes by screening the perturbing potential. In polar semiconductors, free carrier plasma oscillations can also couple with longitudinal optical phonons.

If we consider two scattering mechanisms the effective mobility is given using the formulae 3.11 and 3.7, and if the two scattering mechanisms have the same exponent s (see equation 3.8) the resulting mobility is simply given by:

21

111µµµ

+= (3.12)

that is known as Mathiessen’s rule and states that the mobility may be deduced from the mobility due to each mechanism acting alone. Mathiessen’s rule is often used to evaluate mobility when multiple scattering mechanisms are present, but it must be stressed that Mathiessen’s rule applies only when s1=s2. Since independent scattering mechanisms rarely have the same energy dependence, the use of Mathiessen’s rule is rarely justified in practice. Nevertheless, it is commonly used because it is often easy to evaluate the mobility for various scattering mechanisms independently, but difficult to do so when the processes occur simultaneously. An example of the application of 3.12 is the case of acoustic phonon and ionized impurities scatterings that are the main mechanisms limiting the carrier mobility in common Si based devices at room temperature. For n-type impurity concentration of 1x1019 at/cm3 in Si the phonon limited mobility of electrons is ∼ 1500 cm2/Vs at RT [Fis96] and the ionized impurity term gives ∼500 cm2/Vs, according to formula 3.12 the lowest mobility determines the total mobility of about ∼380 cm2/Vs that must be compared to the measured value of ∼120 cm2/Vs [Mas83]. Fischetti et al. [Fis03] noted also the dramatic failure of the Mathiessen’s rule when the subband structure plays an important role and the scattering mechanisms differ substantially in each subband, because, for example, of the competing effects of different effective masses.

When a weak magnetic field is applied, the force –ev∧B must be included in the BTE, and the result is a set of four transport tensors that are function of B. Developing the BTE, it is possible to obtain the following relationship between the carrier mobility in presence of a magnetic field, called Hall mobility, and the drift mobility:

µµττµ HH r=

>><<>><<

= 2

2

(3.13)

rH is a function of the factor s and is called Hall factor and the calculated values

for common scattering mechanisms are reported in table 3.1. However, these calculations do not take into account the shape of the energy bands of the semiconductor. Theoretical and experimental works showed that rH∼1.1 for As and P doped Si [Mes63, Mor54] and rH∼0.75 for B doped Si [Mor54, Szm86, Lu96, Car94, McG99].

3.1.2 Strained silicon The past several years have witnessed rapid growth in the study of strained

silicon (ε-Si) due to its potential ability to improve the performance of very large scale integrated (VLSI) circuits independent of geometric scaling [Ant02, Hoy02]. Strain improves MOSFET drive currents by fundamentally altering the band


structure of the channel and can therefore enhance performance even at aggressively scaled channel lengths. A relaxed Si1−xGex graded buffer creates a larger lattice constant on a Si substrate (i.e., “virtual substrates”) and can be used as an epitaxial template for depositing Si-rich layers in a state of biaxial tension. Such band-engineered heterostructures can be optimized to allow mobility enhancement factors over bulk Si of 2 for electrons and as high as 10 for holes [Lee05].

In the 1980’s, improvements in epitaxial technique and, in particular, molecular beam epitaxy (MBE), allowed researchers to determine the band offsets of tensile and compressive SiGe heterostructures. However, success in attaining high hole and electron mobilities was limited by critical thickness considerations, high-defect densities, or both. In the early 90’s, the advent of relaxed, graded Si1−xGex buffers simultaneously allowed considerably lower-defect densities and much greater flexibility in tailoring strained-layer composition, strain state, and band offset. Through the use of compositional grading at high temperatures, Fitzgerald et al. [Fit91] lowered the dislocation density in the active area of a ε-Si modulation-doped structure from 108 to 106 cm−2, allowing the record for 4 K 2DEG mobility to be improved from 1.9x104 to 9.6x104 cm2/Vs. In 1993, Nayak et al. [Nay93] published the first report of a ε-Si p-MOSFET with enhanced µeff. Nayak et al. reasoned that the strain-induced breaking of the heavy-hole (HH)–light-hole (LH) degeneracy could be used to fabricate a p-MOSFET with higher µeff. In 2002, Leitz et al. [Lei02] increasing the Ge content in the Si1−xGex relaxed buffers to values as high as x=0.5, attained much larger hole mobility enhancements than had previously been reported [Rim95, Cur01] in ε-Si single heterostructures.

Surveying the most recent research in the field of ε-Si, -SiGe, and -Ge channels reveals that there are two major research paradigms in operation: one is focused on scalability and manufacturing issues and the other is focused on the physical fundamentals of hole mobility enhancement. Essentially, as more and more research groups were able to demonstrate high electron mobility in ε-Si, the mobility enhancement itself became an empirical fact. As a result, the focus shifted to short-channel design, process integration, and characterization, as well as attempting to extend the scalability of ε-Si channels through the use of “on-insulator” technologies and high-k gate dielectrics.

It should be noted that the mobility measurements in ε-Si have been performed using device structure with an undirected evaluation of the mobility from device characteristic quantities. The mobility enhancement in ε-Si has been observed by the comparison in the same operating conditions of the device characteristics with bulk-Si instead of SiGe virtual substrate. No data are available in literature about carrier mobility in ε-Si measured by Hall effect technique in samples without the MOSFET structure. Even if the technological efforts favour the device realization, the lack of a study on the bulk properties of ε-Si materials does not improve the scientific understanding of the problem.

Figure 3.2 reports the single-channel PMOS mobility enhancements for hole density in the inversion layer of Ninv=1x1013 cm−2 from the MIT group [Lei02, Cur01, Lee03] and the IBM group [Rim03]. They revealed similar trends in mobility enhancement as a function of strain for x=0.1–0.5 from. The drop in enhancement for x=0.7 is believed to be caused by excessive dislocation nucleation in the highly mismatched ε-Si [Lee05]. While the reported enhancement factors of Rim et al. [Rim03] are lower than those from the MIT group, this is almost certainly due to differences in channel doping; the MIT group typically had ND=1016 cm−3, while the IBM group had ND=2x1017 cm−3. Since high channel doping is required to suppress short-channel effects, the enhancement values of Rim et al. may be considered the more relevant data set from the perspective of ultra-large scale integration implementation. Typically the thickness of the ε-Si layer is between 4-30 nm, the perpendicular strain component can be easily calculated using the Vegard’s rule and


65

the tetrahedral distortion described in section 3.3, to have an order of magnitude of the strain in Figure 3.2, the reader can consider that the perpendicular strain in the ε-Si layer is given by the product of the Ge fraction x and the factor 0.03, therefore a scale of strain 0.3-3 %. It should be noted that no strain measurement is reported in literature about the effective strain of the ε-Si channel.

Theoretical studies of the hole mobility in Si inversion layers have lagged

substantially behind those dedicated to electron transport. Oberhuber et al. [Obe98] speculated correctly that this may be attributed to the complicated nature of the valence bands –not amenable to a simple analytic description–. Fischetti et al. [Fis03] proposed a six-band k⋅p model to study the mobility of holes in Si inversion layers for different crystal orientations, for both compressive or tensile strain applied to the channel, and for a varying thickness of the Si layer, taking into account scattering assisted by phonons and surface roughness. Satisfactory qualitative agreement is found between experimental data and theoretical results for the density and temperature dependence of the mobility. Both compressive and tensile strain are found to enhance the mobility, while confinement effects result in a reduced hole mobility for a Si thickness ranging from 30 to 3 nm. It should be noted that the theoretical calculations do not consider the effect of impurity scattering, being the channel a low doped region, therefore we have not theoretical evaluation of the strain effect when the mobility is limited by ionized impurity scattering mechanism, as in the heavily doped semiconductors.

3.1.3 Carrier Mobility in heavily doped Si At room temperature it is particularly important to keep in mind the plot of

carrier mobility versus carrier concentration, this is a function of all the scattering processes we have mentioned and its analytical expression is only empirical due to the evident difficulty to predict the effect of all the scattering events. Several empirical expressions and Monte Carlo simulations are available in literature [Cau82, Aro83, Li78, Kai98, Mat00] about the mobility versus carrier concentration, but we retain that the most complete work is that of Masetti et al. [Mas83], which collect all the previous experimental data and fit them with a unique expression in the whole range of concentration (about eight decades) for As, P and B doped Si. In Figure 3.3 we report the plot of the carrier mobility versus the carrier concentration using the Masetti’s parameters.

MIT IBM

Fig. 3.2 Single-channel PMOS mobility enhancement at Ninv=1x1013 cm−2 of ε-Si p-MOSFETs vs Ge content [Lee05]. Triangles are from Rim et al. [Rim95] and circles are from MIT research group [Cur01, Lei02, Lee03].


In the high concentration regime the assumption of the independence of the following scattering events comes to break down, from the experimental point of view both the electron and hole mobilities have a well defined and verified function of the dopant concentration in the range of 1x1013-1x1019 at/cm3. At concentration higher than 1x1019 at/cm3 the mobility of both carriers shows a dependence on the chemical species of the doping atoms. There is no theoretical model to date which explains the lower mobility data for As-doped samples compared to P-doped Si for impurity concentrations higher than 1018 at/cm3.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.060

70

80

90

100

110

120

Elec

tron

Mob

ility

[cm

2 /Vs]

Carrier Concentration [1020 cm-3]

P As

Si, 300 °K

Fig. 3.4 Room temperature drift mobility of electrons in Si doped with P (solid line), As (dot line) as function of carrier concentration in the range 1x1019-1x1020 cm-3 using the empirical formulae from Masetti et al. [Mas83]

1014 1015 1016 1017 1018 1019 102020

406080

100

200

400600800

1000

2000

T=300 K

Carrier Concentration [cm-3]

Mob

ility

[cm

2 /Vs]

Masetti et al. [Mas83] P As B

n-Si

p-Si

Fig. 3.3 Room temperature drift mobility of electrons (n-Si) and holes (p-Si) as function of carrier concentration in Si doped with P (solid line), As (dot line), B (dash line) using the empirical formulae from Masetti et al. [Mas83]


67

The difference between the electron mobility in As- and P-doped samples

monotonically increases from 6% at NI=1019 at/cm3 up to 32% for NI=4X1021 at/cm3 [Mas83], as depicted in Figure 3.4.

Similarly a difference of about 30% is reported for B and Ga doped Si at 1x1019

at/cm3 [Mas83, Sas88, Cas86]. The Hall mobility in Si doped with B and Ga from Sasaki et al. [Sas88] is reported in Figure 3.5, our data, which will be described in section 3.2, are also shown for comparison in the region 1x1019-1x1020 at/cm3.

There were several attempts in the past to explain these differences by impurity-core effects [Dag72, Csa61]. Ralph et al. [Ral75] introduced a central-cell scattering potential determined empirically using bound state energies of donors. Later, El-Ghanem and Ridley [ElG80] employed a square-well impurity core potential. Both approaches cannot explain experimental data sufficiently. Bennett and Lowney made extensive studies of the majority and minority electron mobility in Si [Ben83, Ben92] and GaAs [Low91]. They used phase shift analysis to calculate the ionized impurity scattering cross sections of minority and majority electron scattering. They introduced different scale factors in the interaction potential for majority and minority electrons. The well-known Brooks–Herring [Bro51] approach neglects the chemical nature of dopant species by assuming point-like dopant atoms, thus not being able to explain the above mentioned experimental observations.

Kaiblinger-Grujin et al. [Kai98] calculated the electron charge distribution of the impurities by the Thomas–Fermi theory using the energy functional formulation. They treated the ionized impurity scattering within the Born approximation, taking into account for degenerate statistics, dispersive screening and pair scattering, which become important in heavily doped semiconductors; they performed Monte Carlo simulations including all important scattering mechanisms in the doping concentration range from 1015 to 1021 cm-3, obtaining a good agreement with the experimental data. However Fischetti et al. [Fis99] severely criticized the calculations by Kaiblinger-Grujin et al: the macroscopic dielectric constant was used even inside the impurity core, screening by valence electrons was double counted, and the distribution of the valence electrons around the impurity was assumed to be isotropic. Fischetti et al. modified the model and found that the dependence on the doping element becomes too weak to explain the experimental results.

According to the published works we can conclude that a complete understanding of the chemical species effect on carrier mobility is still missing. In the next section we present the experimental results about the hole mobility in Si doped with B and Ga in the high concentration regime 0.1-2x1020 at/cm3 and we propose (section 3.3) a relationship between carrier mobility and lattice strain induced by the substitutional dopants.


3.2 Hall Mobility in Si doped with B and Ga Samples were prepared by implantation of 11B+ and 69Ga+ ions in n-type Si (100)

substrates (4-10 Ωcm) previously amorphized by Si implantation, as described in chapter 2. Thermal annealing at 580°C for 1h was performed to crystallize Si by solid phase epitaxy and to activate the implanted dopants.

The mobility measured at room temperature by Van der Pauw and Hall effect techniques is reported in Figure 3.6 as a function of carrier fluence for B doped Si (full dots), Ga doped Si (full triangles) and co-doped Si (empty symbols). The impurity peak concentration is reported on the top axis of Figure 3.6. The Hall mobility of B and Ga doped samples is in good agreement with the literature data [Mas83; Cas86; Sas88] (see Figure 3.5) and the hole mobility in Ga doped samples is about a factor 2 smaller than in B doped Si. The mobility of co-doped Si is intermediate between that of B and Ga doped samples. The abscissa of the starting point of the dashed lines indicates the carrier concentration due to B in co-doped samples, the abscissa of each empty symbol indicates the total carrier concentration due to B and Ga atoms, according to the electrical activation shown in chapter 2. It must be noted that for a given Ga concentration the mobility is higher in co-doped samples with respect to pure Ga despite of the higher total impurity concentration. This is a surprising result that is in contrast with the Mathiessen’s rule (eq. 3.12). In fact, the lower mobility in Ga doped Si can be explained in term of screened Coulomb scattering, which depends on the charge distribution of the ionized impurity scatter. If we consider the carrier mobility in co-doped samples given by the independent contributions of B and Ga scatterings, the total effective mobility should be given by the Mathiessen’s rule, which predict a lower mobility with respect of the lowest term. For example, consider the samples doped with ∼1x1020 at/cm3 of B and Ga, the sample doped with only B has a mobility of µ(B)∼40 cm2/Vs, the sample doped with only Ga has µ(Ga)∼20 cm2/Vs, for B+Ga co-doped sample the mobility is µ(B+Ga)∼24 cm2/Vs, while applying the Mathiessen’s rule we obtain an effective mobility of ∼13 cm2/Vs

VscmGaB eff

eff

/13)(

1)(

11 2≈→+= µµµµ

(3.14)

1017 1018 1019 1020 102110

20

40

6080

100

200

400

Ga

B, this work Ga this work B, [Sas88] Ga, [Sas88]

Hal

l Mob

ility

[cm

2 /Vs]

Hole Concentration [cm-3]

Si, T= 300 K

B

Fig. 3.5 Hall mobility in B (circles) and Ga (triangles) doped Si as function of the Hall carrier concentration from Sasaki et al [Sas88] (empty symbols) and from this work (full symbols).

3.2 Hall Mobility in Si doped with B and Ga

69

On the failure of the Mathiessen’s rule we can make two considerations: The two scattering events can not be independent because the high

concentrations of scattering centres. In this regime the BTE can not be easy solved because the Fermi Golden rule is based on the assumption of independent scattering events, and Monte Carlo simulations are necessary to predict the transport properties as function of the carrier concentration.

The presence of the two impurities can modify a bulk property that is not additive for the scattering probability, or can modify the relaxation time dependence of the energy introducing a different s factor with respect of the simple ionized impurity scattering.

However, the effect of chemical species can not be univocally identified from Figure 3.6 since we are comparing the mobility in samples having different carrier concentrations. In order to disentangle this effect we prepared a set of samples with a total impurity concentration CGa+CB=1x1020 at/cm3 (where CGa, CB are the Ga, B concentration, respectively) varying the relative amount of B and Ga impurities. The fraction of Ga is quantified by the parameter ξ: ξGa=CGa/(CGa+CB). The Hall mobility as a function of ξGa is shown in Figure 3.7: the mobility decreases progressively from 41 cm2/Vs of pure B to 20 cm2/Vs of pure Ga doped Si.

Fig. 3.6 Hall mobility as function of carrier fluence measured in B (full circles), Ga (full triangles) and B+Ga (empty squares) doped Si. Lines are guide of eyes.

0 1 2 3 40

10

20

30

40

50

60

70

80

900 1 2

Ga

CMax [1020at/cm3]

B Ga B+Ga

µ H H

all M

obili

ty [c

m2 /V

s]

Hall fluence [1015at/cm2]

B


3.3 Strain in Si doped with B and Ga In a first attempt one can suppose that the strain induced by the dopants is

responsible of the effect of chemical species on carrier mobility, visible in Figures 3.5 – 3.7. This would justify the observation that it becomes progressively more relevant with increasing dopant concentration as the strain does. Moreover, in co-doped samples the strain is expected to vary progressively from tensile (B doping) to compressive (Ga doping) being the covalent radius of B (rB=0.82 Ǻ) smaller than that of Si unlike Ga (rGa=1.26 Ǻ).

The strain introduced by the impurities at high concentration (1x1020 at/cm3) in the Si lattice is detectable by high resolution x ray diffraction (HRXRD). A detailed description of the HRXRD analyses is beyond the aim of this work, so we will give only some skills about the quantities that have been directly used to characterize the strain in B and Ga doped Si.

When an x-ray beam strikes the surface of a crystal, strong diffraction occurs when all the scattered waves add up in phase. By considering an entire crystal plane as the scattering entity, rather than each individual electron, the Bragg’s rule gives that strong diffraction results when:

λϑ ndsen =2 (3.15) where n is an integer representing the order of diffraction, λ is the wavelength of

the radiation, d the interplanar spacing of the reflecting plane and ϑ the angle of incidence and of diffraction of the radiation relative to the reflecting plane.

The deformation of the film is described by the strain matrix. In the case of a pure tetragonal distortion (see Figure 3.8) the significant elements of the strain matrix are only two:

1;100

//// −=−= ⊥

⊥ aa

aa εε (3.16)

where a// and a⊥ are the lattice parameter of the layer parallel and perpendicular to the growth direction, respectively; ε// and ε⊥, the parallel and perpendicular strain, respectively, quantify the deformation of the film, with respect to the relaxed lattice parameter a0, in a direction parallel or perpendicular to the film-

0 20 40 60 80 10010

20

30

40

50

µ H

Hal

l Mob

ility

[cm

2 /Vs]

ξGa [%]

CMaX(B+Ga)=1x1020 at/cm3

Fig. 3.7 Hall mobility as function of the ξGa (see the text) for a fixed carrier concentration and total impurity (maximum) CB+CGa concentration of about 1x1020 at/cm3.

3.3 Strain in Si doped with B and Ga

71

substrate interface. The relaxed lattice parameter a0 of a generic alloy A1−xBx can be calculated using the Vegard’s rule [Veg21]:

xaxaa BA +−= )1(0 (3.17)

where aA and aB are the lattice parameter of the solids A and B, respectively, in the same crystallographic structure.

When the material has a cubic symmetry and the growth is along the <100>

axis, the elasticity theory of the continuum medium [Tu92] predicts that the above two quantities are related by the following equation:

////11

122 αεεε −=−=⊥ CC

(3.18)

This relationship is called Poisson effect; C11 and C12 are elastic constants characteristic of the material, their values for Si are: C11=16.577x1011 dyn/cm2, C12=6.393 x1011 dyn/cm2 [Mad96] and α=0.771 [Fis96].

In our samples the epitaxial constraint of the c-a interface forces the doped layer to have a//= aS (aS is the substrate lattice parameter, 5.431 Å for Si) and the effect of the impurities results in a reduction of the a⊥ with respect of Si (for B doping ε⊥<0, tensile strain of the lattice) or an increase (for Ga doping, ε⊥>0, compressive strain of the lattice).

Differentiating the Bragg’s law (eq. 3.15), it is easy to obtain the following formula:

1)(

−=∆

=∆

− ⊥

SB aa

dd

tg ϑϑ

(3.19)

where aS is the lattice parameter of the substrate, ∆ϑ is the angular distance between the layer peak and the substrate peak in the diffraction spectrum and ϑB is the Bragg angle for the considered reflection. Since the typical uncertainty in the peak position is about 0.001°, the error associated to a⊥ is about 0.04 Å.

HRXRD measurements were performed with a Philips X-Pert Pro Diffractometer at the University of Padua. Figure 3.9 shows the HRXRD spectra of co-doped samples with a total impurity concentration CGa+CB=1x1020 at/cm3, the Ga compressive strain is indicated by the shoulder on the left (∆ω<0). As the B concentration increases a peak on the right (∆ω>0) grows up indicating the tensile strain increases.

a0

aS

a//

a⊥

Fig. 3.8 Schematic two-dimensional representation of an epitaxial strained film of SiGe alloy on a Si substrate. The film is tetrahedrally deformed to follow the epitaxial constraint of the substrate. Characteristic lattice parameters a0, a//, a⊥ are indicated.


The diffraction spectra were simulated with the help of RADS MERCURY code [Wor99, Bis04]. According to this code, one can insert an arbitrary number of layers in order to simulate an experimental diffraction profile; the strain status and the thickness of every layer are the free parameters of the simulation. The simulation procedure is based on a trial and error approach and it ends when all the main features exhibited by the diffraction pattern are reproduced. The dopant concentration profile is not really a free parameter because it is finally compared with the measured SIMS or RBS concentration profile. The simulated spectra are shown by the solid lines in Figure 3.9. The perpendicular strain (ε⊥) has been extracted as fitting parameter of the diffraction spectrum and its profile as function of depth is reported for the various samples in Figure 3.10. The strain changes from tensile (negative value) of pure B doped layer (ξGa=0%) to compressive (positive value) of pure Ga doped layer (ξGa=100%), indicating that the strain level depends on the relative B and Ga concentrations, a strain compensation over the entire profile for co-doped samples occurs for ξGa=80%.

The ε⊥ has been evaluated for pure B or Ga doped Si at the maximum

concentration of 1x1020 at/cm3 using the Vegard’s law (equation 3.17) to evaluate the lattice parameter of the relaxed alloy Si−B or Si−Ga. In equation 3.17 the lattice parameter aA refers to Si, that has the crystalline structure of the diamond, aB refers to a solid compounded of B (or Ga) atoms in the diamond structure, which really does not exist. The aB can be evaluated considering the covalent radius of B (or Ga):

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

exp fit

ξGa=0%

ξGa=30%

ξGa=60%

ξGa=80%

ξGa=100%

∆ω [deg]

Inte

nsity

[a.u

.]

Fig. 3.9 HRXRD spectra (circles) measured in samples co-doped with B+Ga according to the ξGa parameter indicated for each spectrum. The total impurity concentration is CB+CGa=1x1020 at/cm3. Solid lines are the fitted curves (see text for details).

3.4 Strain effect on Hole Mobility

73

CB ra3

8= (3.20)

for rC(B)=0.82 and rC(Ga)=1.26 Ǻ we have a(B)=3.78 and a(Ga)=5.81 Ǻ, respectively. We have calculated ε⊥(B)∼-4.8x10-4 and ε⊥(Ga)∼+1x10-4 for B or Ga concentration x=2at%, in well agreement with the measured peak values shown in Figure 3.10.

3.4 Strain effect on Hole Mobility The results so far presented, relative to co-doped Si, demonstrate that the

carrier mobility (Figure 3.7) and the strain (Figure 3.10) they both depend on the percentage of Ga (ξGa) once the concentration of ionized impurity is fixed. In particular, the mobility decreases and the strain turns from tensile to compressive with increasing ξGa. The merging of these findings gives evidence of the mobility enhancement in tensile strained Si. A similar trend has been observed in Si and SiGe alloys lightly doped with B. For example, at B concentration of 2×1017 cm3 the mobility increases from 110 cm2/Vs in strained Si0.8Ge0.2 to 143 cm2/Vs in Si0.79Ge0.2C0.01 [Kar00]. Such variation has been explained in terms of partial strain compensation (due to C) that in turn modifies the valence band of SiGeC. The alloy scattering play a relevant role in determining the absolute value of mobility. Most of the experiments on strained Si channels end up with a mobility that is a factor 2 higher with respect to unstrained Si. It must be noted that the available literature regarding the effect of strain on mobility is limited to the regime of low dopant concentration where phonon scattering is the main scattering process. Strain is expected to modify significantly the band shape and related variables as for example the effective mass. We can not compare our data with literature since in our samples the mobility is limited by the scattering with ionized impurities.

In Figure 3.11 we can see that the inverse of mobility depends linearly on ε, and the continuous line is the fit of the experimental data using:

βεαµ

+=1

(3.21)

0 50 100 150 200 250 300 350-60

-50

-40

-30

-20

-10

0

10

20

ξGa=100% ξGa=90% ξGa=80% ξGa=60% ξGa=30% ξGa=0%

P

erpe

ndic

ular

stra

in [1

0-5]

Depth [nm]Fig. 3.10 Perpendicular strain versus depth obtained by HRXRD analyses of B and Ga co-doped samples at a fixed total impurity (maximum) concentration of about 1x1020 at/cm3. ξGa (see the text) represents the Ga percentage with respect of total impurities (B+Ga) concentration.


α=0.047±0.002 Vs/cm2 and β=47.4±6.7 Vs/cm2. The hole mobility of unstrained Si can be extracted from the plot of Figure 3.7, and it results to be about 50% lower than that of B doped Si. Modelling the mobility at so high carrier concentration is a very hard task (see section 1.4 and 3.1) and is well behind the scope of this work. For simplicity we can assume that at room temperature the strain contribution to the mobility can be simply added to the other terms entering in the calculation of 1/µ. Our data allow then to correct the measured mobility for the strain.

In fact, the mobility of a not strained doped layer µUnstrained can be empirically

calculated using the mobility measured in a strained material µStrained by the following expression:

),(11GaB

Strainedunstrained

CC⊥⋅−= εβµµ

(3.22)

where β is the slope of the fit shown in Figure 3.11. The strain ε⊥(CB, CGa), when not directly measured by HRXRD, has been estimated as a linear combination of the strain induced by Ga and B separately. The formula reported above corrects the measured mobility µStrained for the strain effect according to the slope β estimated. The mobility of unstrained Si as function of the mean carrier concentration is reported in Figure 3.12. The mean carrier concentration has been evaluated considering the peak values of the dopant concentration profiles shown in chapter 2 and the total electrical activation of the substitutional impurities. The uncertainty about the Hall scattering factor, which is attested to be rH=0.75 for B and rH=1 for Ga (see chapter 2), can affect the concentration scale of the Figure 3.12 with an error of 10% that is, however, well beyond the divergences between B and Ga mobilities observed in Figure 3.6. With the strain correction all the points of Hall mobility in B and Ga doped Si collapse on a unique curve, and the dependence of carrier mobility on the chemical species of the dopants is remarkably reduced in the concentration region 1x1019-1x1020 at/cm3.

The formula 3.22 and the plot of Figure 3.12 have been empirically calculated assuming that a linear relationship 3.21 is valid over all the impurity concentration

-60 -50 -40 -30 -20 -10 0 10

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.055

0.060

ε ⊥ [ 10-5]

1/µ H

Fig. 3.11 Inverse of the Hall mobility (reported in Figure 3.7) of B+Ga co-doped samples at a fixed B+Ga concentration of about 1x1020 at/cm3 as a function of the perpendicular strain at about 100 nm depth (Figure 3.10). The linear fit (1/µ=α+βε⊥) is obtained with the following parameters: α=0.047 Vs/cm2 and β=47.4 Vs/cm2.

3.4 Strain effect on Hole Mobility

75

range of our measurements. Considering the heavily calculations necessary to evaluate the carrier mobility in presence of an high carrier concentration and the effect of strain that has been usually calculated in low carrier concentration regime, we can not apply the theoretical results to explain our experimental values. However, the main effect of strain is the variation of the effective mass of carriers, being the energy band structure strongly affected. This effect can be accounted introducing a deformation potential in the mobility tensor calculation, the simulations made by Fischetti and Laux [Fis96] are available for strained Si in the low carrier concentration regime where the mobility is phonon limited.

From a qualitative point of view we can make the following considerations. Using

the Kubo-Greenwood’s equation 3.6 and 3.7 the mobility can be always expressed as:

)()(),(

ετεµ ∗

>><<=

mNeN (3.23)

where N and ε between brackets indicates the generic functional dependence on carrier concentration and strain, respectively. The values of the effective mass m* can not be made explicit without the knowledge of the energy band structure as function of the strain. The relaxation time <<τ>> takes into account all the scattering process involved, but no analytical expression is available for heavily doping. In first approximation we can assume that τ does not strongly depend on the strain, being the scattering of ionized impurities dominant.

Developing in series the function m*(ε), the first order approximation gives:

εε ⋅+≈ ')( *0

* mmm (3.24)

Combining 3.23 and 3.24 one can have:

ετττ

εµ >><<

+>><<

≈>><<

=∗

)('

)()()(1 *

0

Nem

Nem

Nem

Strained

(3.25)

therefore at ε=0 we have that:

0 1x1020 2x1020 3x10200

10

20

30

40

50

60

70

80

90

Hal

l Mob

ility

[cm

2 /Vs]

Hole Concentration [cm-3]

Ga B B+Ga

Fig. 3.12 Hall mobility versus carrier concentration in unstrained material, obtained by the measured Hall mobility corrected by the strain effect. The solid line is an eye guide.


>><<=

)(1 *

0

Nem

Unstrained τµ (3.26)

while from our data:

βεαµ

+=Strained

1 (3.27)

αµ

=Unstrained

1 (3.28)

thus equalling the second term of 3.27 and 3.25, and considering 3.26 and 3.28,

we can extract the following relationship:

1*0

*

+≈ εαβ

mm

(3.29)

The ratio β/α we have measured is about 103 while ε is negative in the 10-5-10-4 range, the second term of equation 3.29 is compatible with the calculation of Fischetti and Laux [Fis96] reported in Figure 3.13. In fact, Figure 3.13 shows the hole effective masses as function of the ratio a///a0. The authors considered a strained Si grown on a relaxed SiGe substrate, so a0 is the Si lattice parameter and a// changes with the applied strain according to formula 3.16. Therefore, the tensile strain range for the positive values of the bottom scale in Figure 3.13 is 10-3-10-2. Even if the strain range is two orders of magnitude with respect of the ε values involved in our data, the linear trend of the effective mass is detectable around a///a0=1 (i.e. ε=0), indicating that the calculation of m* as function of ε in a more sensitive strain scale could be promising to explain the observed mobility data in heavily doped Si.

Fig. 3.13 Calculated hole density-of-states effective masses in strained <100> Si as a function of biaxial in-plane strain [Fis96]. The effective mass is reported in the units of the electron mass. v1 is for light holes, v2 for heavy holes, v3 for the spin-orbit term, the strain lifts the degeneracy of the valence band at the Γ point.

3.6 References

77

3.5 Concluding Remarks In conclusion we have shown that the dopant atoms induce a local strain of the

Si lattice that affects the hole mobility. This strain effect modifies the carrier mobility introducing a not negligible contribution that can explain the dopant-dependent hole mobility in heavily doped p-Si and it could be probably useful also for electron mobility in n-Si. In fact the strain term of the mobility has completely explained the different mobilities observed in Si doped with B or Ga in the high concentration (1x1019-2x1020 at/cm3) regime. Moreover we have obtained a unique curve of mobility versus carrier concentration for unstrained material using the relationship between the strain and the mobility in co-doped Si with B and Ga.

At this point, considering the electrical properties and structural characterization of B and Ga co-doped silicon shown in chapters 2 and 3, a possible application of Ga doping can be inferred. In fact, even if Ga can not be used to improve the electrical performances of B doping because it does not affect the B solid solubility limit, the effective mobility in co-doped samples is not too low with respect of pure B doping. This effect can be a not trivial advantage if we consider that Ga implantation can be used to pre-amorphize the Si crystal instead of Si ion implantation. We have studied this possibility realizing two samples doped with Ga and Ga+B at Ga and B concentration of 1x1020 at/cm3 with the same scheme of energies and fluences illustrated in chapter 2, first Ga ions have been directly implanted in Si single crystal at room temperature without Si pre-amorphization, and B has been successively implanted. The Ga ion fluence (∼1015 at/cm2) used in this experiment exceeds the amorphization threshold and the entity of crystal damage produced by the Ga ion, which has a mass 2.5 times bigger than Si, allows to obtain an amorphous layer ∼300 nm thick without freezing the substrate at liquid nitrogen temperature. The crystalline quality after the annealing treatment at 580°C is that of a good Si crystal, indicating a fine SPE planar re-growth without extended defects. The electrical properties measured in these samples are in well agreement with that presented for Si pre-amorphized samples, denoting the real possibility of a technical application of B+Ga co-doped Si.

3.6 References [Ant02]

Antoniadis D. A., Symposium on VLSI Technology Digest of Technical Papers (Honolulu, HI, 2002) 2

[Aro82] Arora N., J.R.Hauser, and D.J.Roulston, Ieee Trans. Electron Devices, Ed-29 (1982) 292

[Ben83] Bennett H., Solid-State Electron. 26 (1983) 1157 [Ben92] Bennett H. and J. Lowney, J. Appl. Phys. 71 (1992) 2285 [Bis04]

Bisognin G., Strain, clustering and diffusion of B in highly doped Si-based epitaxial systems, PhD thesis, University of Padova (2004)

[Bro51] Brooks H., Phys. Rev. 83 (1951) 879 [Car94]

Carns T.K., S.K. Chun, M.O. Tanner, K.L. Wang, T.I. Kamins, J.E. Turner, D.Y.C. Lie, M.A. Nicolet, and R. Gwilson, IEEE Trans. Electron Dev. 41 (1994) 1273

[Cas86] Casel A., H. Jorke, E. Kasper, and H. Kibbel, Appl. Phys. Lett. 48 (1986) 922 [Cau82] Caughey D.M. and R.E.Thomas, Proc. Ieee, 55 (1982) 2192 [Con82] Conwell E., Transport: The Boltzmann equation, in Handbook on Semiconductors,

(North-Holland Publishing Company, USA, 1982) 513 [Csa61] Csavinsky P., J. Phys. Soc. Jpn. 16 (1961) 1865 [Cur01]

Currie M. T., C. W. Leitz, T. A. Langdo, G. Taraschi, D. A. Antoniadis, and E. A. Fitzgerald, J. Vac. Sci. Technol. B 19 (2001) 2268

[Dag72] Daga O. and W. Khokle, J. Phys. C 5 (1972) 3473 [ElG80] El-Ghanem H. and B. Ridley, J. Phys. C 13 (1980) 2041

[Fis03] Fischetti M. V., Z. Ren, P. M. Solomon, M. Yang, and K. Rim, J. Appl. Phys. 94 (2003) 1079


[Fis96] Fischetti M.V., S.E. Laux, J. Appl. Phys., 80 (1996) 2234 [Fis99] Fischetti M. V., S. E. Laux, J. Appl. Phys. 85 (1999) 7984 [Fit91]

Fitzgerald E. A., Y. H. Xie, M. L. Green, D. Brasen, and A. R. Kortan, Mater. Res. Soc. Symp. Proc. 220, 211 (1991)

[Hoy02]

Hoyt J.L., H. M. Nayfeh, S. Eguchi, I. Aberg, G. Xia, T. Drake, E. A. Fitzgerald, and D. A. Antoniadis, Technical Digest-International Electron Devices Meeting (San Francisco, CA, 2002) 23

[Kai98] Kaiblinger-Grujin G., H. Kosina, and S. Selberherr, J. Appl. Phys. 83, 3096 (1998) [Kar00]

Kar G. S., A. Dhar, S. K. Ray, S. John, and S. K. Banerjee, J. Appl. Phys. 88 (2000) 2039

[Kit96] Kittel C., Introduction to Solid State Physics (John Wiley & Sons, New York, 1996) [Lee03] Lee M.L. and E.A. Fitzgerald, J. Appl. Phys. 94, 2590 (2003) [Lee05]

Lee M.L., E. A. Fitzgerald, M.T. Bulsara, M.T. Currie, A. Lochtefeld, J. Appl. Phys. 97 (2005) 11101.

[Lei02]

Leitz C. W., M. T. Currie, M. L. Lee, Z. Y. Cheng, D. A. Antoniadis, and E. A. Fitzgerald, J. Appl. Phys. 92 (2002) 3745

[Li78] Li S.S., Solid-State Electron. 21 (1978) 1109 [Low91] Lowney J. and H. Bennett, J. Appl. Phys. 69 (1991) 7102 [Lu96] Lu Q., M.R. Sardela, T.R. Bramblett, and J.E. Greene, J. Appl. Phys. 80 (1996) 4458 [Lun90] M. Lundstrom, Fundamentals of Carrier Transport, in Modular Series on Solid State

devices, G.W. Neudeck and R.F. Pierret eds. (Addison-Wesley Publishing Co., USA, 1990)

[Mad96] Madelung O. ed., Semiconductors group IV elements and III-V compounds, in Data in Science and Technology, R.Poerschke ed. (Springer – Verlag, Germany, 1996)

[Mas83] Masetti G., M. Severi, S. Solmi, IEEE Trans. Electron Dev. ED-30 (1983) 764 [Mat00] Matsuda K., Y. Kanda, Proceedings of CIMTEC Mass and Charge Transport in

Inorganic Materials (Venice Jesolo Italy, May 2000) [McG99]

McGregor B.M., R.J.P. Lander, P.J. Phillips, E.H.C. Parker, and T.E. Whall, Appl. Phys. Lett. 74 (1999) 1245

[Mes63] Messier J. and J.M. Flores, J. Phts. Chem. Solids 24 (1963) 1539 [Mor54] Morin F.J. and J.P. Maita, Phys. Rev. 96 (1954) 28 [Nay93]

Nayak K., J. C. S. Woo, J. S. Park, K. L. Wang, and K. P. MacWilliams, Appl. Phys. Lett. 62 (1993) 2853

[Obe98] Oberhuber R., G. Zandler, and P. Vogl, Phys. Rev. B 58 (1998) 9941 [Ral75] Ralph H., G. Simpson, and R. Elliot, Phys. Rev. 11 (1975) 2948 [Rim03]

Rim K. et al., Technical Digest-International Electron Devices Meeting (Washington, DC, 2003) 49

[Rim95]

Rim K., J. Welser, J. L. Hoyt, and J. F. Gibbons, Technical Digest- International Electron Devices Meeting (Washington, DC, 1995) 517

[Sas88] Sasaki Y., K. Itoh, E. Inoue, S. Kishi, T. Mitsuishi, Solid-St. Electron., 31 (1988) 5 [See73] Seeger K., Semiconductor Physics (Springer-Verlag, New York-Wien, 1973) [Szm86] Szmulowicz F., Phys. Rev. B 34 (1986) 4031 [Tu92]

Tu K.N., J.M. Mayer, L.C. Feldman, Electrical Thin Film Science (Macmillan Publishing Company, USA, 1992)

[Veg21] Vegard L., Z. Phys. 5 (1921) 17 [Wor99]

Wormington M., C. Panaccione, K. M. Matney, and K. Bowen, Phil. Trans. R. Soc. Lond. A 357 (1999) 2827

[Yu99] Yu P.Y., M. Cardona, Fundamentals of semiconductors : physics and materials properties (Springer, New York, 1999)

Chapter 4

Off-lattice displacement of dopants during ion irradiation

We investigate here the stability under point defects injection of Si(B/Ga) supersaturated solid solutions by measuring the off-lattice displacement during irradiation with H and He beams at room temperature. To this end, we irradiated the B/Ga doped crystal with ion beams at different energies, while we measured the B/Ga off-lattice displacement by channeling technique.

More than ten years ago, it was shown that ion-beam analyses could induce an off-lattice displacement for different dopants such as B [Swa89, Smu90], Ga, Sb, and As [Wig78] in crystalline Si. The microscopic mechanism responsible for this process was not clarified, although there is evidence that dopant displacement induced by ion irradiation has a great impact on the electronic device manufacturing processes and on the analysis of materials for their development. In fact, from a device manufacturing perspective, irradiation-induced dopant displacement could be a strategic subject of research because every device application in space, such as satellite telecommunications, suffers from a persistent cosmic irradiation. On the other hand, ion-beam irradiation has been used in ultra-shallow junction fabrication by tuning the vacancy-self-interstitial balance in the point defects engineering approach [Sha03]. Therefore, an accurate knowledge of the physical mechanism underlying ion-beam irradiation and related damage is highly demanded. Many experimental observations of dopant enhanced diffusion, clustering and electrical deactivation occurring during ion implantation have been interpreted as effect of the interaction between dopant atoms and Si point defects.

The impurity displacement rate and its dependence on the irradiation energy have been studied in a coherent simple model that assumes an interaction between Si- self interstitials (Is) generated by the irradiating beam and impurity substitutional atoms. This interaction has been prevalently observed through the anomalous and enhanced diffusion of the impurities, thanks to diffusion studies it has been determined that B and Ga prefer to interact with Is with respect of vacancies [Fah89, Fah89b]. However, diffusion based investigations, by Secondary Ion Mass Spectrometry, are limited to the high temperature regime, where B diffusion is detectable [Man00, Mir03, Ven04]. Nevertheless, the lattice location of the impurity clusters, formed as consequence of the interaction with Is, is actually predicted only by theoretical calculations [Ali04, Zhu96, Liu00, Mel04, Lop04] and has not experimentally evidenced.

4.1 Experiment The samples described in this chapter followed the same preparation procedure

described in chapter 2 (see section 2.1.1): pre-amorphized Si wafer were implanted with B and Ga, and then annealed to re-crystallize by SPE. In particular we refer to two samples doped with B or Ga with a peak concentration of 2x1020 B/cm3 (2.3x1015 B/cm2) and 1e20 Ga/cm3 (1.35x1015 Ga/cm2) in a 250 nm surface region.

Chapter 4 Off-lattice displacement of dopants during ion irradiation 80

These samples have been chosen because they have the maximum concentration of active and substitutional impurities. In particular the sample with Ga concentration of 1e20 at/cm3 has been selected in order to avoid Ga segregation effects. Single Ga or B doped Si (sections 4.2-4.3) and co-doped samples (4.4) have been characterized.

In the following sections we will describe the experimental method used to study the impurity displacement under ion irradiation (4.1.1) and some preliminary considerations about the damage generated by the impinging ions on the samples (4.1.2).

4.1.1 Channeling Method We have just explained the channeling technique (see section 1.3.3) and the

experimental setup (see section 2.1.2) to determine the lattice location of impurities in Si host. In this section we will briefly sketch the method we have followed to study the stability of supersaturated solid solutions under ion beam irradiation. Whigger and Saris [Wig78] observed that Ga atoms undergo a progressive off-lattice displacement as function of the He implanted fluence. We performed a similar experiment using 650 keV H+ and 2 MeV 4He+ beams to study the displacement of B and Ga atoms, respectively. The beam spot was 1 mm2 and the typical current was 50 nA. First of all the alignment conditions for a particular crystal axis and the tilt angle to have random incidence were determined, and then the sample was shifted to start recording the channeling spectrum on a not-irradiated spot. The nuclear reaction 11B(p,α)8Be at 650 keV proton energy was used to reveal B in Si, standard RBS-channelling analyses using a 2 MeV He+ to detect the Ga lattice location. After SPE the substitutional fraction of B and Ga were ∼90%. The samples were then irradiated by the ion beam (H+, He+) incident at a random direction, and subsequently aligned spectra were acquired as a function of the irradiation fluence. We tested that the impurity displacement rate was independent of the beam current in the 5–100 nA range. Care was taken to ensure a good thermal contact between the sample and the holder in order to avoid beam heating effect. A thermocouple placed close to the sample indicated a maximum temperature rise of 20 °C. We have monitored the channeling yield (χ) of the impurity and of the Si as function of the fluence of the ion beam randomly impingent on the sample. This procedure has been performed many times on several samples giving excellent repeatability within 10% for both B and Ga impurities, and the relative displacement will be discussed in section 4.2. The main uncertainty derives from the statistical error of the channeling spectra. In fact, the statistical error can be reduced by increasing the integrated charge that, on the other hand, must be kept as low as possible in order to avoid off-lattice displacement during the analysis itself. We used fluences of 5x1015 H/cm2 and 1x1015 He/cm2 for the analyses. We checked the effect of the channeled beam on the impurity displacement by measuring the χ as function of the channelled fluence and no B displacement could be detected in the investigated range unlike Ga. The χGa under irradiation with <110> channeled beam is reported (empty symbols) as a function of the He fluence in Figure 4.1 and it is compared to that obtained for random incidence (full symbols). As expected, the occurrence of Ga displacement under irradiation with channeled beam requires higher fluences compared to random irradiation, and in order to reach the same χGa the ion fluence in channeling incidence φch must be about 130 times the random ion fluence φrn. From the data of Figure 4.1 we have evaluated that the effect of a channelling irradiation at a fluence φch is equivalent to a random irradiation at a fluence φrn=0.015xφch and we have used this quantity to correct the measurements that will be shown in the next section.

4.1 Experiment

81

4.1.2 Evaluation of the ion energy loss SRIM simulations [Zie85] have been performed to evaluate the details of the

energy loss of the incident ions in the surface layer. The projected range of 650 keV H+ and 2 MeV He+ beams resulted about 8.7 and 7.3 µm, respectively, well above the thickness of the doped layer (250 nm). In Figure 4.2 the elastic (nuclear) and anelastic (electronic) energy loss profiles for 650 keV H+ and 2 MeV He+ randomly incident on a Si substrate are shown. For both ions the anelastic energy loss is dominating and constant for the shown thickness (1 µm), while the elastic term is 3x103 times smaller. Elastic collisions become predominant at the end of range and the small damage pockets produced by irradiation have been observed by electron microscopy analyses at a depth of ∼ 7 µm.

In order to explain the impurity displacement (discussed in the next section) induced by the ion beam, we could assume a direct interaction between the ion beam and the impurity atom or, alternatively, an indirect effect related to the beam energy loss. Despite of the large amount of energy lost by anelastic processes, Smulder and Swanson [Swa89, Smu90] demonstrated that B off-lattice displacement (details are discussed in the following section) is not due to the anelastic energy loss of the ions and for this reason we will only consider the elastic term. We are interested to evaluate the probability of a direct knock-on displacement of impurities by the incident ions. The concentration of B atoms is CB∼2x1020 at/cm3. Assuming a Coulomb interaction and impurity displacement energy of the same order of the Si displacement (15 eV) [Rim95] it is possible to roughly estimate the number of displaced impurities referred to Si displacement:

42

105 −

−

− ×≈⎟⎟⎠

⎞⎜⎜⎝

⎛∝

+

+

Si

B

Si

B

SiH

BH

ZZ

CC

pp

(4.1)

where CSi=5x1022 at/cm3 is the atomic concentration of silicon; ZB, ZSi the atomic number of B and Si, respectively. In a surface layer 250 nm thick, where B atoms are confined, about 0.15 Si atoms were displaced per each incoming ion of the 650

1015 1016 10170.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7He+ 2 MeV

χ(G

a)

Ion fluence [cm-2]

<110>

random

channeling

Fig. 4.1 <110> Ga normalized yields as a function of the irradiation fluence of 2 MeV He beam in random (full squares) and in channeling (empty squares) incidence on the sample doped with 1x1020 Ga/cm3.


keV H+ beam, as can be evaluated by integration of the Is profile of the Figure 4.3. Thus, a fluence of 5x1016 H+/cm2 at 650 keV displaces approximately 3x1020 Si/cm3 so that 1x1017 B/cm3 are displaced, i.e. 1‰ of the total B concentration, indicating that the direct knock-on displacement of B atoms is negligible.

The same consideration holds for Ga in Si. In our sample CGa∼1x1020 at/cm3 and

therefore:

32

108.9 −

−

− ×≈⎟⎟⎠

⎞⎜⎜⎝

⎛∝

+

+

Si

Ga

Si

Ga

SiHe

GaHe

ZZ

CC

pp

(4.2)

For a 2 MeV He+ beam impinging on Si about ∼ 1 Si atom is displaced by each ion in the doped surface layer. A fluence of 5x1015 He/cm2 at 2 MeV displaces approximately 1x1020 Si/cm3 so that 1x1018 Ga/cm3 are displaced, i.e. 1% of the total Ga concentration. Therefore, also in this experiment the direct knock-on displacement of Ga atoms is negligible.

In order to compare the experimental data realized by irradiation with different ions, we could use the energy loss by elastic collisions integrated over the doped region (250 nm) as the characterizing parameter of irradiation. However, for a more physical perception of the phenomenon we used, instead, the self interstitials (Is) concentration integrated over the same depth. In fact, the displacement energy relates the elastic energy loss to the concentration of point defects, reported in Figure 4.3, and the concentration of vacancies (V) and interstitials are very similar in this regime of light ions and high energy, and being known that B and Ga dopants strongly interact with Is, we have chosen the Is concentration as damage parameter.

0.0

0.1

0.2

0.3

0.4

Ane

last

ic d

E/d

x[e

V/Å/

ion]

Elas

tic d

E/dx

[x10

-2eV

/Å/io

n]

0.65 MeV H+

Depth [x104 Å]

a) b)

0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

25c) d)

0.0

0.5

1.0

1.5

2.0

Elastic dE

/dx[x10

-2eV/Å/ion]

2 MeV He+

0.2 0.4 0.6 0.8 1.00

5

10

15

20

25 Anelastic dE/dx[eV

/Å/ion]

Fig. 4.2 SRIM simulation of specific energy loss by elastic (a, b) and anelastic (c, d) collisions of 650 keV H+ (a, c) and 2 MeV He+ (b, d) beams randomly incident on Si substrate as function of depth.

4.2 Off lattice displacement of B and Ga in Si

83

4.2 Off lattice displacement of B and Ga in Si The channelling yield (χB and χGa) along the <110> crystallographic direction is

reported in Figure 4.4 as function of ion fluence (H+ and He+), and increases progressively with increasing ion fluence for both B (fig. 4.4a) and Ga (fig. 4.4b) impurities.

0

1

2

3

I, V

[ato

m/µ

m/io

n]

0.65 MeV H+

Depth [µm]

grey: Vacanciesblack: Interstitials

0.00 0.25 0.50 0.75 1.000

5

10

2 MeV He+

Fig. 4.3 SRIM simulation of interstitials (black) and vacancies (grey) generated by elastic collisions of 650 keV H+ (top figure) and 2 MeV He+ (bottom figure) beams randomly incident on Si substrate as function of depth.

0 1 2 3 4 5 6 7 8 9 100 50 100 150 2000.0

0.1

0.2

0.3

0.4

0.5

0.6

2 MeV He+

Ga Si

<110>

b)a)

650 keV H+

B Si

<110>

Nor

mal

ized

yie

ld (χ

)

Ion fluence [1015 cm-2]Fig. 4.4 <110> B (a) and Ga (b) normalized yields measured with 650 keV H+ beam (a) and 2 MeV He+ beam (b) as a function of the ion irradiation fluence. The minimum Si yield (empty squares) is also reported.


In Figure 4.4a it is also reported the normalized Si channelling yield below the surface peak in the proton spectrum. The χSi is ∼4%, typical of a free-of-defects crystal, and it remains constant under irradiation, indicating that no damage is accumulated in the Si lattice. The B yield startes to increase monotonically with H fluence above 1×1016 cm-2, until saturation occurs at a fluence of ∼7.5×1016 cm-2. A similar progressive displacement is observed during irradiation with a 2.0 MeV He+ beam of the Ga implanted samples. Even in this case the Si channelling yield remains constant to ∼4% during irradiation (see fig. 4.4b). The saturation occurs at a fluence of ∼2×1015 He/cm2.

In order to explain the impurity displacement induced by the ion beam, we could assume a direct interaction between the ion beam and the impurity atom or, alternatively, an indirect effect related to the beam energy loss. We have just shown in section 4.1 that the probability of a direct interaction ion-impurity is negligible in both cases of H and He irradiations. Thus, an indirect effect related to the beam interaction with the Si matrix, through elastic or anelastic energy loss, has to be invoked. Earlier work from Smulder and Swanson [Swa89, Smu90] demonstrated that no B off-lattice displacement occurs at very low temperature. In fact, they did not detect any B displacement after irradiation at 35 K with a 700 keV H+ beam at a fluence of 4x1016 H+/cm2, while a strong B displacement was observed after the sample thermalization at RT. Therefore, the B displacement did not occur during the irradiation but after it, so that it can not be due to the anelastic energy loss of the beam. On the other hand, it is well known that the elastic energy loss of the beam produces point defects along the ion path. Even if a high percentage of the generated interstitials and vacancies annihilate, it is possible that a B atom can interact with an ISi generated near its lattice site and the B off-lattice displacement is due to this interaction, because a mobile B-ISi pair (see section 1.1.3) is formed. Being the Ga enhanced diffusion of the same kind of B, i.e. mediated by ISi, it is likely that the Ga displacement follows a similar mechanism. The fluence of ISi generated for the two cases of H and He irradiation in the doped region has been calculated by integrating the ISi concentration profile (see figure 4.3) over the 250 nm region where the impurities are confined. Using this quantity as independent variable it is possible to compare the displacement rate of the two impurities.

Figure 4.5 reports the B and Ga displacement along the <110> and <100> axes as function of the ISi fluence. The χB increases up to a saturation value of 0.5 along the <110> axis at a Is fluence of ∼1.5×1016 ISi/cm2, this displacement could be due to a dynamical equilibrium of the B atoms substitutional located and randomly displaced. A random displacement produces a χB∼1. This condition should be the same along each crystallographic axis, but the saturation value of 0.7 the along the <100> axis clearly discredits this hypothesis. The difference in the saturations values 0.5 and 0.7 for <100> and <110> channeling, respectively, is a clear indication of a not-random B displacement, but the B atoms must be located in a particular lattice site. The χGa versus ISi fluence has been plotted taking into the account the effect of channeling irradiation, considering that channelling irradiation at a fluence φch is equivalent to a random irradiation at a fluence φrn=0.015xφch.


85

The Ga displacement is faster than that of B and the saturation occurs at ∼4×1015

ISi/cm2. For Ga case the saturation value for <110> channeling is ∼0.6 definitely higher with respect to <100> channeling, indicating, as in the case of B, a non-random displacement of Ga. It should be noted that the Ga channelling yield at saturation is higher along the <110> with respect to the <100> axis, opposite to the B case. This inversion indicates that the lattice location of displaced Ga atoms is different from that of B atoms [Tes95, May77]. The lattice location of both impurities after ion irradiation at the saturation value of the channeling yield has been performed by means of the angular scans and will be discussed in section 4.4.

The solid lines of Figure 4.5 are the best-fit curves of the experimental data and have been obtained using the following expression for both impurities:

( ) INFF e σχχχχ −−−= 0 (4.3)

where χ0 is the χ of the non-irradiated sample, NI is the ISi fluence, and σ is a fitting parameter. The σ values are reported in the table 4.1 for the two impurities and the two axes.

Table 4.1

Impurity σ<100> [10-16 cm2]

σ<110> [10-16 cm2]

B 1.3±0.1 1.2±0.1 Ga 5.2±0.1 5.4±0.2

The σ values are independent of the channeling axis and are 4 times higher for

Ga with respect of B. This parameter has been interpreted as an effective cross section of the ISi trapping process by the impurity atoms, which is described in the following section. It should be noted that the Is fluence (NI) is calculated using the results of the SRIM simulation, where no I-V recombination is taken into account. Therefore, the term NI is certainly overestimated and consequently the absolute value of σ is underestimated, but the relative values of σ for B and Ga express the really different efficency of Is-trapping of the two dopants. However we have just

0 1 2 3 4 5 6 7 8 90 10 20 30 40 50 600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 MeV He+

Ga <110> Ga <100> Si <110> fit

<110>

<100>

b)a)

650 keV H+

B <100> B <110> Si <100> fit

<110>

<100>

Nor

mal

ized

yie

ld (χ

)

Si Interstitials fluence [1015 cm-2]

Fig. 4.5 <100> and <110> B (a) and Ga (b) normalized yield as function of the Si self interstitials fluence generated by 650 keV H (a) and 2 MeV He (b) beams. The solid lines are the best fit curves described in the text.


observed that the impurity displacement depend on the elastic energy loss of the irradiating beam, so the Is fluence could be certainly adopted as a convenient parameter, instead of the energy loss term, to compare the impurity displacement in the two cases. Moreover, as it will be explained in the next section, the fluence of Is has a more appropriate physical meaning in term of the interaction between impurities and Si self interstitials.

4.2.1 Model of impurity- ISi interaction The model used to describe the off-lattice displacement process [Pir05a,

Rom05b, Pir05b, Rom05c] has been inspired by the impurity diffusion assisted by point defects [Fah89], which we have introduced in section 1.1.3.

Essentially, we propose the following mechanism to depict the off-lattice displacement process:

1) the impurity A binds an interstitial I by forming a mobile pair AI; 2) A migrates in this complex form (AI), (the estimated migration

barrier are ∼ 1 eV); 3) AI migration ends when the mobile A atom binds the substitutional A

atom forming a stable A-A complex; 4) the process ends when there are no more unpaired substitutional

impurities. It should be noted that the average distance between two substitutional A atoms

is ∼2 nm at this concentration (∼1x1020 at/cm3), so the high dopant density favourites that a mobile A meets a substitutional A and forms a stable A-A complex 1. The main difference between the off-lattice displacement under irradiation and the enhanced impurity diffusion is the temperature of the process. In fact, the enhanced diffusion is clearly observable upon annealing at high temperature in presence of an excess of Is. At RT the impurity complexes, even if a supersaturation of Is is maintained, are stable; in the diffusion experiment the cluster dissolution is competitive with the cluster formation and a high concentration of impurity atoms is recovered into substitutional sites [Pel99b].

Assuming that the limiting step is the ISi capture process, the variation of the displaced impurity concentration (CD) can be expressed by:

SITD CG

dtdC σ= (4.4)

where GI is the rate of the interstitial fluence generated by the impinging beam (GI∼1.9x1013 cm-2s-1 for 650keV H+ and GI∼5.3x1013 cm-2s-1 for 2MeV He+), CS is the substitutional impurity concentration, which can interact with the Is; σT is the trapping cross section. The CS at time t can be expressed as

)()( tCCtC DTS γ−= (4.5)

where CT is the total impurity concentration and γCD is the concentration of atoms that have formed stable complexes. The parameter γ is a clustering factor that we have introduced to take into account the formation of impurity agglomerates. For example γ=2 if the stable complex contains a pair, while γ=1 if it contains only one A atom. Theoretical calculations suggest that impurity pairs are the most probable agglomerates to be formed when an excess of Is is injected in a B [Zhu96, Ali01] or Ga [Lop04] doped Si crystal.

1 It should be noted that the local temperature rise due to anelastic excitation during irradiation can not account for a diffusion length of 2 nm that is the mean distance between two impurity atoms. In fact, the thermal regime in a collision cascade lasts less than a 1x10-9 s [Rim95], hence diffusion over 2 nm would require a diffusion coefficient of ∼5x10−5 cm2/s, several orders of magnitude higher than that of B or Ga at the Si melting point. Therefore the impurty migration due to thermal diffusion can be excluded.


87

The condition to solve the equation 4.4 is that before irradiation the dopant is completely substitutional, while at saturation the concentration of unbounded substitutional atoms is null. This means:

0)0(0 0

=⇒∞→−=⇒=

S

DTS

CtCCCt

(4.6)

CD0 is the initial displaced concentration, in an ideal case it should be zero, it is about 10% of the total concentration in our samples.

Thus the solution of the equation 4.4 is: )exp()()( 0 tGCCCtC ITDDFDFD γσ−−−= (4.7)

CDF is the concentration of displaced atoms at the saturation (i.e. at CS=0). It is known that when there is a concentration C’ of off-lattice atoms, the channeling yield along a particular crystallographic axis <hkl> is given by the following expression [Tes95]:

><><= hkl

hklT

fCC χ'

(4.8)

where f<hkl> depends on the ion flux distribution of the particular channel. Note that at saturation the concentration of substitutional impurities vanishes (CS→0) and the equation 4.5 gives CDF= CT/γ, therefore the final displaced concentration depends on the clustering factor γ. At the saturation the relationship 4.8 gives:

><>< = hklF

hklfγχ

1 (4.9)

that is the condition to evaluate the factor f<hkl> from experimental data (that will be used in section 4.3), in fact, χF is the measured χ at saturation. It should be noted that for random displacement f<hkl> =1 for every crystallographic directions 2.

Substituting relationship 4.8 in the 4.7 one obtains the following expression for χ:

)exp()()( 0 tGt ITFF γσχχχχ −−−= (4.10)

which is the expression 4.3 used to fit the experimental data, by setting σ=γσT and GIt=NI. In this way the fitting parameter σ is the trapping cross section by the factor γ. In this description the trapping cross section σT depends on the impurity species; the product γσT depends on the cluster configuration and it is independent of the channeling axis; χF depends on both impurity species and cluster configuration. The above mentioned functional dependences are in agreement with the experimental observations, which discussed in the previous section. It should be noted that the formulae 4.10 and 4.3 can be used to fit the experimental data but one can not decouple the product γσ, because there is only one equation for two unknowns, γ and σT.

The difference among the I-trapping cross section of B and Ga reported in table 4.1 should be searched in the peculiarities of the dopant-I interaction that is beyond our aim. However, it should be noted that the ratio of the cubic covalent radii of the two impurities (rB=0.82 and rGa=1.26 Å) is about 3.6 and we intuitively expect that σ is proportional to the volume occupied by the impurity.

2 Really the relationship 4.9 should take into account the effect of the initial off-lattice displacement that is not due to the irradiation. Assuming that the initial displacement is

random, the corrected relationship 4.9 is: ><><

><

>< −−

×= hklhklF

hkl

hklf0

011χχ

χγ


4.3 Off lattice displacement of dopants in B+Ga co-doped Si The displacement rate has been studied also in co-doped samples with

CB=2x1020 at/cm3 and CGa=1x1020 at/cm3. The channeling yield of B and Ga along the <110> axis is reported in Figure 4.6 as function of ISi fluence for B and Ga doped (full symbols) and co-doped samples (empty symbols). The dechanneling rate appears to be slower for both dopants in the case of co-doping and also the saturation values are different with respect of single B and Ga doped samples. This can not be attributed to a direct interaction between the different atoms in not-irradiated samples, since we have seen, in section 2.3, that the carrier concentration in co-doped samples was simply given by the sum of the carrier concentration due to each dopant (like in the single doping case). This observation exclude a pre-irradiation B-Ga interaction, on the contrary the electrical properties should be modified. The displacement process in the case of co-doping is more complex to explain in terms of the I-trapping model of section 4.2.1. The lower displacement rate could be due to a competition in the I-trapping process, in fact, each impurity compete to the I capture with the other one, therefore the concentration of Is available for each impurity decreases with respect of the absence of the other one. A modified model of I-trapping that takes into account the effect of the co-presence of two capture centres has been developed and is shown in section 4.3.1.

4.3.1 Model of impurity- ISi interaction We assume that the I-trapping process by an impurity atom is not modified since

an impurity atom of different chemical species is nearly located in the crystal. In another words, the I-trapping occurs in the same way of the single doping case. With this assumption we can write the equation rate for each impurity simply introducing a term that decreases the concentration of Is due to the capture by the other impurity. Also in this case, assuming that the limiting step is the ISi capture process, the variation of the displaced impurity concentration (CD) can be expressed by:

0 1 2 3 4 5 6 7 8 9 100 10 20 30 40 50 600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ga in single doped Si Ga in B+Ga doped Si

2 MeV He+<110>

b)a)

650 keV H+

<110>

Nor

mal

ized

yie

ld (χ

)


B in single doped Si B in B+Ga co-doped Si

Fig. 4.6 <110> B (a) and Ga (b) normalized yield as function of the Si self interstitials fluence generated by 650 keV H+ (a) and 2 MeV He+ (b) beams in B (full squares), Ga (full squares) and B+Ga co-doped (empty squares) samples.

4.3 Off lattice displacement of dopants in B+Ga co-doped Si

89

⎪⎪⎩

⎪⎪⎨

⎧

=

=

SGaIGaTGaDGa

SBIBTBDB

CGdt

dC

CGdt

dC

σ

σ (4.11)

where CD, CS and σT, have the same meaning of the equation 4.4 for single doping case, but the subscripts B and Ga indicate that each quantity is referred to the relative impurity. GIB (and GIGa) is not simply the rate of the interstitial fluence generated by the impinging beam, but it represents the number of Is that can be bound by each impurity in the time unit, therefore it is given by the generation term of Is by the impinging beam minus the term of Is trapped by the competitive centre, the other impurity. According to this representation, GIB and GIGa can be expressed as following:

⎩⎨⎧

−=−=

))(1()())(1()(

tCGtGtCGtG

SBTBIIGa

SGaTGaIIB

σσ

(4.12)

where GI is really the rate of the interstitial fluence generated by the impinging beam, that does not depend on the presence of particular impurities in the crystal; while the terms GIB and GIGa are correlated to the capture of Is by the Ga and B impurities, respectively. With the conditions 4.12, the equations 4.11 become to be coupled. The decreasing of CS in the time interval is due to the increasing of the concentration of impurities in the clusters, therefore:

⎪⎪⎩

⎪⎪⎨

⎧

−=

−=

dtdC

dtdC

dtdC

dtdC

DGaGa

SGa

DBB

SB

γ

γ (4.13)

where γB and γGa are the clustering factor for B and Ga, respectively. γ has the same meaning of that in section 4.2.1, with the additional case that also mixed B-Ga clusters can be formed.

By deriving the equations 4.11 and combining the conditions 4.12 and 4.13 we obtain two coupled equations of second order in t with two unknowns (CDB and CDGa) and the four parameters σTB, σTGa, γB and γGa. Like in the case of single doping, we can consider the product γσT as a single parameter. The boundary conditions are the same of the single doping case:

⎩⎨⎧

==

⇒∞→

⎩⎨⎧

−=−=

⇒=

00

)0()0(

00

0

SGa

SB

GaTGaSGa

BTBSB

CC

t

CCCCCC

t (4.14)


We have numerically solved the equation 4.11 and the CD as function of t has

been calculated for 650 keV H+ and 2 MeV He+ irradiations at ion current of 50 nA. Like the single doping case, CD depends on the parameter γ, an example of the calculation is shown in Figure 4.7 for the B doped Si case. We have considered the 650 keV H+ irradiation, the B implanted fluence of 2.3x1015 at/cm2, the measured values of the parameter γBσTB=1.3x10-16 cm2. The Figure 4.7 shows the plots for two values of γB=2 and 1.5, the saturation value of CDB is CDB∼0.5CTB and CDB∼0.66CTB for γB=2 and γB=1.5, respectively.

In Figure 4.8 we have reported the calculated CDB and CDGa of B and Ga atoms as

function of the time of irradiation with 650keV H+ beam. The parameters of the simulations are the values measured for the displacement of B and Ga atoms in

0 500 1000 1500 2000 2500 30000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4σT(B)=0.65x10-16 cm2 γ=2

σT(Ga)=2.6x10-16 cm2 γ=2

H+ 650 keV

CD [x

1015

at/c

m2 ]

Time [s]

B total conc.=2.35x1015 at/cm3

Ga total conc.=1.34x1015 at/cm3

single doping

B

Ga

Fig. 4.8 Simulated displaced concentration of B (solid line) and Ga (dot line) atoms as function of the time of irradiation with 650 keV H+ beam in samples single doped with B or Ga. The two curves have been simulated with trapping cross section σT(B)=0.65x10-16 cm2, σT(Ga)=2.6x10-16 cm2 and γB=γGa=2.

0 500 1000 1500 2000 2500 30000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

σT(B)=0.65x10-16 cm2

H+ 650 keV

CD

B [x

1015

at/c

m2 ]

Time [s]


single doping

γ=1.5

γ=2.0

Fig. 4.7 Simulated displaced concentration of B atoms as function of the time of irradiation with 650 keV H+ beam in a sample doped with B. The two curves have been simulated with a trapping cross section σT(B)=0.65x10-16 cm2 and two values of γ factor: γB=2 and γB=1.5.


91

single doped samples: γBσTB=1.3x10-16 cm2 and γGaσTGa= 5.2x10-16 cm2, with γB=γGa=2. The time necessary to obtain the saturation of CDGa is 3x102 s, while the saturation of CDB is reached after 103 s. This indicates that when the two impurities are together present in the sample, Ga is much faster displaced than B, moreover the concentration of Ga is about half of that of B, so the presence of Ga atoms alter sensitively the displacement of B only in the first ∼3x102 s of the irradiation, while the displacement of Ga in practically unaffected by the B presence. To clarify this point we have reported in Figure 4.9 the CDB in single e co-doped case, as anticipated the simulations of the two cases slightly differs in the initial ∼3x102 s of H+ irradiation.

As in the case of single doping described in the previous section, the measured χ is related to the CD for each impurity by the expression 4.8.

><><= hkl

hklT

D fCC χ (4.15)

In order to compare the simulated CD in co-doped cases we need to express χ as

function of time. The parameter f<hkl> can be evaluated using the relationship 4.9 that binds the final experimental χ to the factor f<hkl> for the particular axis. The χB(t) simulated for B doped Si is shown in Figure 4.10, the saturation value is fixed by the product γBf<hkl>, while the rate of the increasing χ is given by the product γBσTB. The comparison with the experimental data can be made considering that the time scale can be converted into Is fluence (NI) using the relationship GIt=NI, for 650 kev H+ GI∼1.9x1013 cm-2s-1. Clearly we can not determine all the three parameters f<hkl>, γB and σTB, but only two of them, we have chosen to use the product f<hkl>γB and γBσTB, and analogously for Ga. In Figure 4.11 there are the experimental data of for B in single and co-doped samples, the lines are the simulations obtained with the described procedure. The simulated curves of co-doped sample have been calculated fixing γGaσTGa=5.2x10-16 cm2 and varying γBσTB between 0.81 to 1.3 x10-16 cm2 in order to obtain a good agreement with the experimental data. The same procedure has been used for Ga data, reported in Figure 4.12, the simulated curve refer to a fixed γBσTB=1.3 x10-16 cm2 and various γGaσTGa between 3.4 and 5.2 x10-16 cm2.

0 500 1000 1500 20000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


Ga total conc.=1.34x1015 at/cm3

σT(B)=0.65x10-16 cm2 γ=2

σT(Ga)=2.6x10-16 cm2 γ=2

H+ 650 keV

CD

B [x

1015

at/c

m2 ]

Time [s]

single doping co-doping

Fig. 4.9 Simulated displaced concentration of B atoms as function of the time of irradiation with 650 keV H+ beam in a sample doped with B (solid line) and co-doped with Ga (dot line). The two curves have been simulated with trapping cross section σT(B)=0.65x10-16 cm2, σT(Ga)=2.6x10-16 cm2 and γB=γGa=2.


0 10 20 30 40 50 60 700.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7single doped Bγσ

Τ(B) = 1.3x 10-16cm2

Si Interstitial fluence [1015 cm-2]

χ(B

)

co-doped B+Gaγσ

Τ(Ga) = 5.2x 10-16cm2

γσΤ(B) = 1.3x10-16cm2

γσΤ(B) = 0.97

γσΤ(B) = 0.81

Fig. 4.11 Experimental χ(B) as function of I-fluence in single (full squares) and co-doped (empty squares) samples. The calculated curves for different set of parameters γσT are shown. The calculated curves for co-doped samples has been obtained with one fixed value of γσT(Ga)= 5.2x10-16 cm2 and three different values of γσT(B)=1.3 (dash line), 0.97 (dot line), 0.81 x10-16 cm2 (dash-dot line).

0 500 1000 1500 2000 2500 30000.0

0.2

0.4

0.6

0.8

1.0


σT(B)=0.65x10-16 cm2 γ=2H+ 650 keV

χ(Β

)

Time [s]

<110>

Fig. 4.10 Simulated channelling yield of B along the <110> axis as function of the time of with 650 keV H+ beam in a sample doped with B. The curve has been simulated with trapping cross section σT(B)=0.65x10-16 cm2 and γB=2.


93

The best conditions obtained for B and Ga displacement are reported in Figure

4.13 and clearly there is no agreement between the χB curve calculated with the best parameters of χGa and vice versa. Therefore, both γBσTB and γGaσTGa must be changed simultaneously to have a set of parameters that agree with both B and Ga displacement.

This condition is obtained for γBσTB=0.94x10-16cm2 and γGaσTGa=3.2x10-16 cm2, the curves relative to this condition are reported in Figure 4.14 for both <100> and <110> axes. This result permits two possible interpretations: either

1) the factor γ is always equal to 2 for both cases (single and co-doping) and consequently the values of σT must be changed to justify the observed values of the product γσT, this condition is resumed in table 4.2 (light grey columns); or

2) the trapping cross sections maintain the values of the single doping case and the clustering factor must change when B and Ga are co-doping the sample, this second interpretation is resumed in the table 4.2 (dark grey columns).

Table 4.2

γσT [10-16cm2]

γ σ T [10-16cm2]

σ T [10-16cm2]

γ

B 1.3 2 0.65 Ga 5.2 2 2.6 B in B+Ga

0.94 2 0.47 0.65 1.44

Ga in B+Ga

3.2 2 1.6 2.6 1.23

The first implicates that the trapping cross section of Is by B and Ga atoms is

reduced in presence of another competitive trapping centre. The second interpretation needs to more explanations about the physical meaning of the

0 1 2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Si Interstitial fluence [1015 cm-2]

χ(G

a)

single doped Gaγσ

Τ(Ga) = 5.2x 10-16cm2

co-doped B+Gaγσ

Τ(B) = 1.3x 10-16cm2

γσΤ(Ga) = 5.2x10-16cm2

γσΤ(Ga) = 3.9

γσΤ(Ga) = 3.4

Fig. 4.12 Experimental χ(Ga) as function of I-fluence in single (full squares) and co-doped (empty squares) samples. The calculated curves for different set of parameters γσT are shown. The calculated curves for co-doped samples has been obtained with one fixed value of γσT(B)= 1.3x10-16 cm2 and three different values of γσT(Ga)=5.2 (dash line), 3.9 (dot line), 3.4 x10-16 cm2 (dash-dot line).


clustering factor γ we have introduced to take into account the formation of impurity agglomerates.

Theoretical calculations suggest that impurity pairs are the most probable

agglomerates to be formed when an excess of Is is injected in a B or Ga doped Si crystal. For definition (see 4.2.1) when no impurity clusters are formed it is γ=1; if

0 5 10 15 200 10 20 30 40 50 600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

<100>

<110>

<100>

b)a)

B Ga

<110>

Nor

mal

ized

yie

ld (χ

)


Fig. 4.14 Experimental χB (a) and χGa (b) along the <100> (circles) and <110> (squares) axes as function of I-fluence in B+Ga co-doped (empty squares) samples. The calculated curves have been calculated with γσT(B)=0.94 and γσT(Ga)=3.2x10-16 cm2.

0 1 2 3 4 5 6 7 8 9 100 10 20 30 40 50 600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

<110>

γσΤ(B) = 0.81x10-16cm2

γσΤ(Ga) = 5.2x10-16cm2

γσΤ(B) = 1.3x10-16cm2

γσΤ(Ga) = 3.4x10-16cm2

b)a)

B Ga best for B best for Ga

<110>

Nor

mal

ized

yie

ld (χ

)


Fig. 4.13 Experimental χ(B) (a) and χ(Ga) (b) along the <110> axis as function of I-fluence in B+Ga co-doped (empty squares) samples. The calculated curves are the best conditions obtained for B (solid line) and Ga displacement (dash line) with two sets of parameters γσT. The best condition for B displacement has been calculated with γσT(B)=0.81 and γσT(Ga)=5.2 x10-16 cm2. The best condition for Ga displacement has been calculated with γσT(B)= 1.3 and γσT(Ga)=3.4 x10-16 cm2.

4.4 Lattice location of impurities after ion irradiation

95

at the end of the displacement process all the displaced impurity atoms are bonded in pairs it must be γ=2. In an intermediate case, 1<γ<2, γ−1 fraction of CD is bonded into pairs, while the rest, i.e. a fraction of CD equal to 2−γ, is bonded into different clusters. The easiest hypothesis is that only three kinds of defects can be formed in the co-doped samples: B-B, Ga-Ga and B-Ga pairs. With this assumption, we have evaluated the densities of B atoms clustered in the B-Ga pairs at the saturation of the displacement process. In fact, at saturation CD is about the total impurity concentration, therefore if the implanted fluence of B in the sample is 2.35x1015 B/cm2 the clustered density is given by the product of “2−γ” and the total B density, using the value γB=1.44 from the table 4.2 the density of B atoms bonded to Ga atoms is 8.9x1014 B/cm2, i.e. the 38% of the total B concentration. Considering the total Ga density (1.34x1015 Ga/cm2) and the γGa=1.23, the same calculation gives that the density of Ga atoms bonded to B atoms is 8.2x1014 Ga/cm2, i.e. the 63% of the total Ga concentration. The calculated concentration of B and Ga atoms bonded into B-Ga clusters are self consistent within the 10% that is a very appreciable result, considering the roughness of the calculations and the experimental errors (~ 5%) that affect the measurements of χB and χGa.

4.4 Lattice location of impurities after ion irradiation Angular scans (see section 1.2.3) through the <100> and <110> axes along

(100) plane have been performed for B and Ga doped Si samples after irradiation at fluence above the χB and χGa saturated, respectively. In Figure 4.15 the normalized yields from the B (fig. 4.15a and 4.15b) or Ga (fig. 4.15c and 4.15d) impurity atoms and the Si atoms in the doped region as function of the angle between the incident beam (650 keV H+ or 2 MeV He+) and the <100> and <110> axes along the (100) plane are reported. The angular scan of B shows a lot of differences with respect of Ga. In particular for B along the <100> axis the scan is larger than that of Ga, and along the <110> axis there is a significant attenuation in the scattering yield of B with a minimum at mid-channel. From a quantitative comparison of the angular scans of the irradiated samples through the two axes a B random position in the Si lattice can be excluded. In fact, if we assume that the displaced B atoms are randomly located and the remaining are still substitutional, we expect an increase of the χB after irradiation maintaining the same ratio χ<100>/χ<110> and Ψ1/2

should be the same in the damaged and in the undamaged sample. This is in contrast with our data, in which χB

<100>/χB<110> = 1.4 after irradiation (~1 before

irradiation, see section 2.2.1). Moreover, Ψ1/2(B) =0.39° for <110> scan, smaller than that of Si (Ψ1/2(Si) =0.47°), unlike the <100> scan in which Ψ1/2(B)≈ Ψ1/2(Si)=0.43°. Therefore, disregarding the hypothesis that a fraction of B is still substitutional and the remaining fraction is randomly dispersed, the only reasonable hypothesis concerns the formation of a B complex, as will be discussed in section 4.4.2.

The <100> angular scan for Ga shows a pronounced attenuation with a minimum at 0° tilt with a narrower dip with respect to the Si, whilst a significant peak is observed in the <110> channel in contrast to the B signal, indicating that a fraction of the Ga atoms occupy a position which is shadowed along the <100> direction and near to the centre of the <110> channel, such position is indicative that a component of the Ga atoms occupy the tetrahedral interstitial site. Along the <100> channel the χGa is definitively lower with respect the <110> and only a small displacement toward the interior of the channel can be inferred. As reported by first principle calculations the tetrahedral interstitial site is a lowest energy position for Ga atoms interacting with Is, in particular it is very probable the formation of pairs with a Ga atom in substitutional site (GaSi) bonded to a Ga atom in tetrahedral site (GaT), this kind of configuration will be shown in section 4.4.1.


The determination of the impurity cluster structure is not easy because the

observed angular scans give some indications about the lattice location of the impurities, like the tetrahedral site for Ga, but the angular scan is the result of the distribution of all atoms in the doped layer. The features of the angular scans indicate the distribution of the impurity atoms in various positions, therefore it is necessary to calculate the ion flux distribution inside each channel and to simulate the angular scans of the predicted impurity locations using the cluster structures reported in literature. To this end the FLUX code [Smu87], based on a Monte Carlo calculation algorithm has been used to simulate the angular scans through different axes. Firstly, the flux distribution of 650 keV H+ or 2 MeV He+ beam through a crystallographic channel was calculated by setting all the parameters of the simulation (crystal temperature, beam divergence) in order to match our experimental setup and measurement conditions. Each ion trajectory calculated by Monte Carlo method was followed through the Si crystal that was modelled considering both binary collision with thermally vibrating host atoms and a surrounding string potential to approximate the effect of the neighbour atomic strings. The potential used was the standard ZBL [Zie85] potential and the electron energy loss and the electron angular scattering were taken into account. The flux distribution was calculated collecting a large number of those trajectories (greater than 104). Secondly, suitable and reasonable B and Ga sites in the Si lattice have been chosen to calculate the angular scans. The calculated angular scans have been compared to the experimental ones for Ga and B in section 4.4.1 and 4.4.2, respectively.

4.4.1 Ga doped Si In first-principles calculations [Mel04, Lop04] it was found that, in analogy to

boron, GaSi binds a ISi into a GaSi-ISi trigonal complex, gaining 1.5 eV in the process. This complex transforms spontaneously (with a 0.5 eV energy gain) into GaT, which migrates (by transiently forming the GaSi-ISi complex [Mel04, Lop04]) with a jump rate of 0.15 s-1 at room temperature, resulting from the calculated [Mel04, Lop04]

Fig. 4.15 Channelling angular scans for B (full symbols) in B doped sample (a, b) and Ga (full symbols) in Ga doped sample (c, d) measured after ion irradiation at saturation. <100> scan along a (100) plane (a, c), <110> scan along a (100) (b, d). The Si scans (empty symbols) are also shown.

-0.5 0.0 0.50.0

0.2

0.4

0.6

0.8

1.00.0

0.2

0.4

0.6

0.8

1.0

-0.5 0.0 0.5

b)

<110>

Nor

mal

ized

yie

ld (χ

)

Tilt angle [deg]

B Si

a)

<100>

B Si

c)

<100>

2 MeV He+650 keV H+

Ga Si

d)

<110>

Ga Si


97

migration barrier of 0.8 eV and an assumed attempt frequency of 10 THz. Given the high Ga density (average Ga-Ga distance ~2 nm), this migration rate - albeit low- is sufficient to cause, within the observation time, the formation of a further complex: the migrating Ga binds with GaSi with an additional 1.0 eV gain to form an approximately trigonal GaSi-GaT complex. Upon formation of this complex, the diffusion-driving ISi is annihilated, as one Ga remains interstitial. This complex is depicted in Figure 4.16a.

Fig. 4.17 Schematic energetics of the Ga-Si complexes cascade generated by one Ga and one ISi originally far apart. As indicated, the bottom step requires a second remote ISi per center.

a) b)

Fig. 4.16 Ground-state configuration along a direction <110> of the GaT-GaSi sad and Ga2-I complexes in Si. The Ga atoms are in dark grey, the Si self interstitial is in light grey, the sticks represent the Si bonds. Refer to Fig. 4.5 and text for the energetics.


The same calculation indicates that the GaSi-GaT complex is electrically neutral, so that both the participating Ga atoms are electrically deactivated. Note that self-interstitials, which are donors (double, according to theory, e.g. [Mel04, Lop04]), compensate the Ga acceptors even before the latter are displaced off-site or clustered. As a result, Ga-ISi complexes and self-interstitials migrate in their neutral charge state, which is important because their diffusivity in the positively-charged configuration (typical of p-type conditions) would be small at room temperature (e.g. the migration barrier for ISi is 1.2 eV in the 2+ state vs. 0.3 eV in the neutral state respectively [Mel04, Lop04]). The energetics of the whole cascade of events is summarized [Rom05a] in Figure 4.17 (including the three-body Ga2I complex discussed next). Assuming now the Is super-saturation to exceed significantly the impurity density (as in the case of high-temperature annealing with release from end of range defects), one expects further channels such as e.g. Ga2I clustering to come into play [Rom05a]. Further calculations enabled us to identify a Ga2I complex bound by about 1 eV compared to a GaSi-GaT pair (see Figure 4.17) and a remote ISi. This complex is depicted in Figure 4.16b. The Ga atoms are not placed at sites of high symmetry, so that Ga in this complex should give rise to a high peak in the <110> channeling.

In order to have more information about the Ga lattice location we have performed the angular scan also through <100> axis along the (110) plane, the width of the Ga dip is smaller with respect of Si also in this case, indicating a small displacement inside the <100> channel. The collection of the three experimental angular scans of Ga doped Si is reported in Figure 4.18.

The simulation of the angular scan of a particular site requires the determination

of all the symmetric positions of this site in a crystal cell of the silicon. The simulated angular scans for Ga in tetrahedral site (T) and the symmetric positions for each projection are reported in Figure 4.19.

-0.5 0.0 0.50.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.5 0.0 0.5 -0.5 0.0 0.5

χ

a)

<100> (100)

Si Ga

Tilt angle [deg]

b)

<100> (110)

Si Ga

c)

<110> (100)

Si Ga

Fig. 4.18 Channelling angular scans for Ga (full squares) and Si (empty squares) measured in the irradiated samples at saturation through <100> axis along a (100) plane (a), <100> axis along a (110) plane (b), <110> axis along a (100) plane (c).


99

In the <110> channel the T site is projected in positions near the channel

centre, causing a high flux peaking, while in the <100> channel the T site is

-0.5 0.0 0.50.0

0.5

1.0

1.5

-0.5 0.0 0.5 -0.5 0.0 0.5

a)

<100> (100)

χ

Ga Si

Tilt angle [deg]

b)

<100> (110)

c)

<110> (100)

Fig. 4.20 Simulated angular scans for Ga in Y site (see text for details), through <100> axis along a (100) plane (a), <100> axis along a (110) plane (b), <110> axis along a (100) plane (c). The projection of all the symmetric positions along the <100> and <110> directions are shown: Si atoms are empty circles, Ga atoms are the stars, the crystalline planes are indicated.

-0.5 0.0 0.50.0

0.5

1.0

1.5

-0.5 0.0 0.5 -0.5 0.0 0.5

a)

<100> (100)χ

Ga

Tilt angle [deg]

b)

<100> (110)

c)

<110> (100)

Fig. 4.19 Simulated angular scans for Ga in Tetrahedral site, through <100> axis along a (100) plane (a), <100> axis along a (110) plane (b), <110> axis along a (100) (c). The projection of all the symmetric positions along the <100> and <110> directions are shown: Si atoms are empty circles, Ga atoms are the stars, the crystalline planes are indicated.


completely shadowed by the host atoms resulting in a scan similar to that of Si. We have simulated also another kind of interstitial, the site called “Y”, because it was observed for ytterbium in silicon [Mor73]. Figure 4.20 shows the projection of the Y site for the <100> and <110> channels and the simulated angular scans, also in this case a high flux peaking is evidenced for the <110> scan.

The angular scan relative to a GaSi-GaT complex is given by the linear combination of the angular scans relative to substitutional Ga and tetrahedral Ga, weighted for the relative concentrations of Ga in the two positions. The χ resulting from two sites (substitutional and tetrahedral) is given by [Tes95]:

subsubTTtot ff χχχ ⋅+⋅= (4.16)

where fT and fsub represent the fractions of impurity atoms displaced in the T sites and in substitutional sites, respectively; χT and χsub are the channeling yields if all the impurity atoms occupy T sites or substitutional sites, respectively.

The angular scans for <100> and <110> axes of the pair GaSi-GaT are reported

in Figure 4.21, the simulation of the Si signal is also shown. In Figure 4.21 there are also the scans relative to the pair GaSi-GaY that has been calculated using the relationship 4.16 and the simulated χY, even if this complex has never been considered for first principle calculations, its projection along the <110> axis is very similar to the GaSi-GaT shown in Figure 4.16a. The scan of the defect G2I has, instead, been calculated putting all the symmetric positions of the two Ga atoms in the FLUX code, the scan is also showen in Figure 4.21, the signal of the ISi is clearly undetectable. Excluding the presence of only the G2I defects, all the simulated defects are in qualitative agreement with the experimental data, supporting the idea of pair formation, but none among the simulated defects can fit the experimental data. Moreover, there is neither a simple mix of the simulated defects or a simple displacement along the bond direction that can explain the data. Therefore, we suppose that the Ga complex could be distorted with respect of the predicted bond direction and such distortion should cause the narrowing of the dip along both <100> and <110> axes with respect of that obtained for the predicted defects.

-0.5 0.0 0.5 1.0-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

Tilt angle [deg]

exp: Ga Si

simulations: Ga

SiGa

T

Ga2I GaSiGaY

<110>

<100>

χ

a) b)

Fig. 4.21 Angular scans for Ga measured in the irradiated samples at saturation through <100> axis along a (100) plane (a), <110> axis along a (100) (b). The simulated scans are reported for three defects: GaSiGaT (solid line), Ga2I (dashed line), GaSiGaY (dash-dot line). The simulation of the Si signal is also shown (dot line).


101

4.4.2 B doped Si The channelling analyses shown in Figure 4.15a and 4.15b allow to evaluate the

projection of B lattice position inside the analyzed axis. It turned out that our data indicate small displacement inside the <110> channel and large displacements inside the <100> channel. We now compare the angular scans with those expected for the simplest and stable complex predicted by ab initio calculations [Ali04, Zhu96, Liu00]: the B2I defect, named B dumbbell <100> or B-B split<100>. This defect (see Figure 4.22), constituted by two B atoms sharing a substitutional lattice site, is oriented along the <100> directions, and it is characterized by a (calculated) bond length of 1.54 Å [Ali04] or 68% of the Si first-neighbour distance [Zhu96]. It is stable at room temperature, due to its formation energy of about 2 eV [Ali04]. Figure 4.23 reports the calculated angular scans of the B2I pair with different bond lengths between 1.3 and 1.6 Å.

This defect clearly presents some details that are no compatible with the

experimental data, the calculated minimum χB along the <100> is always greater than the real one, and the calculated angular half-width for both axes is narrower than the experimental ones. Furthermore, every linear combination of random dispersed B, substitutional B atoms and B2I with a bond length varying in the range 1.30–1.60 Å can not fit the experimental data. The experimental data can be reproduced assuming a linear combination of B displacements along the <100> directions. In Figure 4.24 the experimental angular scans are compared to our best fit that has been obtained assuming that 40% of B atoms is displaced by 0.30 Å from the substitutional site, 40% is displaced by 1.25 Å along the same direction [Pir05c] and the remaining 10% are randomly displaced. It is evident that the main features of the angular scans are reproduced by the simulations. However, such a defect configuration was not predicted by ab initio calculations, and it might be thought as a fictitious way to describe a more complex defect, always involving a couple of B atoms, or a metastable defect.

a) b)

Fig. 4.22 Ground-state configuration along a direction <100> (a) and <110> (b) of the B2I complex in Si. The B atoms are in dark grey, the sticks represent the Si bonds.


4.4.3 B+Ga Co-doped Si The formation of different cluster in the co-doped samples has been confirmed

by the lattice location analyses. The lattice location of B and Ga in co-doped samples at saturation of the displacement process has been investigated by angular scans along the <100> and <110> axes. Figure 4.25 shows the angular scans of B and Ga in single and co-doped samples. The comparison between the single and co-doping cases reveal that the main difference are evidenced in the <110> dip of Ga. The well evident peak of the <110> dip in sample doped with Ga is clearly disappeared in presence of B.

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

-0.5 0.0 0.5 1.0

χ

Tilt angle [deg]

B simulation Si simulation

a) b)

<110><100>

Exp B Si

Fig. 4.24 Channelling angular scans for B measured in the irradiated sample at saturation. <100> scan along a (100) plane (a), <110> scan along a (100) (b). The fitting scans of B are obtained from a linear combination of both a small displacement (0.3 Å) and a larger displacement (1.25 Å) into the ion channel along the <100> direction (solid line). The simulation of the Si scan is also shown (dot line).

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

-0.5 0.0 0.5 1.0

χ

Tilt angle [deg]

B-B split 100 1.30 Å 1.40 Å 1.50 Å 1.60 Å

a) b)

<110><100>

Exp B Si

Fig. 4.23 Channelling angular scans for B measured in the irradiated sample at saturation. From left to right: <100> scan along a (100) plane, <110> scan along a (100) plane. The simulated scans are referred to a B dumbbell oriented along <100> with a bond length of 1.30 Å (dash line), 1.40 Å (dot line and open circle), 1.50 Å (solid line) and 1.60 Å (dot line). The simulation of the Si scan is also shown (dash-dot line).


103

The changes of the B dips are, instead, less marked, in compliance with the fact

that the fraction of Ga atoms involved in different defects is higher with respect of B. However, the impurity lattice location can not go beyond these qualitative observations because very few data are available about the clustering in B and Ga co-doped Si. Preliminary simulations showed that the pair of B and Ga into nearest neighbours substitutional sites is favoured with respect of Ga into tetrahedral site bonded to B in substitutional site, the formation energy of these configurations is reported in Figure 4.26 as function of the Fermi energy level [Lop04b]. The decrease of the channeling peak along the <110> axis, that is indicative of Ga into tetrahedral site, seems to be consistent with calculations. However, further calculations with B and Ga into different interstitial locations are needed to explain the observed angular scans of the co-doped samples.

0.0 0.2 0.4 0.6 0.8 1.0 1.2-1

0

1

2

3BSiGaT

GaSiGaT

Form

atio

n E

nerg

y [e

V]

Fermi Energy [eV]

BSiGaSi

Fig. 4.26 Absolute formation energy of BSiGaSi (solid line), GaSiGaT (dash line) and BSiGaT (dot line) complexes vs the Fermi level [Lop04b].

0.0

0.2

0.4

0.6

0.8

1.0

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0.2

0.4

0.6

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χ

B B+Ga

<100> (100)

Tilt angle [deg]

a)

B Ga

d)

c)

b)

Ga Ga+B

<100> (100)

Fig. 4.25 Channelling angular scans for B (a, b) in B doped sample (full symbols) and in B+Ga co-doped sample (empty symbols). Angular scans for Ga (c, d) in Ga doped sample (full symbols) and in B+Ga co-doped sample (empty symbols). All scans are measured after ion irradiation at saturation. <100> scan along a (100) plane (a, c), <110> scan along a (100) plane (b, d). The Si scans (squares and diamonds) are also shown.


4.5 Concluding Remarks The off-lattice displacement of impurities in Si during ion beam analyses has

been investigated using channeling technique, this effect was well known since twenty years but has never been studied in details. By the light of recent investigations about the interaction of dopant impurities with Si point defects we have correlated the off-lattice displacement with an indirect effect of the incident ion beam, i.e. the point defects generated by the incoming ions are responsible of the impurity displacement. Therefore this effect has permitted to study the stability of the supersaturated solid solutions of B and Ga in Si under injections of point defects in the doped region. In this contest we have developed a model of the displacement process that is able to furnish the exponential increases of the impurity channeling yield as function of the incident ion fluence. The experimental data have been fitted using some parameters, like the trapping cross section of the Is by impurity atoms. The trapping cross section is 4 times higher for Ga than B atoms and the displacement rate becomes slower when both impurities are put together in the same samples. The co-doped case has been investigated using a model in which the two impurities compete to trap the Is generated by the beam.

The saturation of the impurity χ as function of the ion fluence suggested the formation of stable clusters that end the impurity migration, the performed angular scans after irradiation have been compared with the predicted cluster structure of B and Ga dopants in Si, revealing a qualitative agreement with the most stable pairs of impurities. Moreover, the channeling studies suggested the presence of distorted structures of clusters and gave important inputs for theoretical investigations, demonstrating the powerful skills of this experimental method in very actual fields of science and technology.

4.6 References [Ali01] Alippi P., L. Colombo, P. Ruggerone, A. Sieck, G. Seifert and Th. Frauenheim,

Phys. Rev. B 64 (2001) 75207. [Ali04] Alippi P., P. Ruggerone, L. Colombo, Phys. Rev. B 69 (2004) 125205. [Fah89] Fahey P. M., P. B. Griffin and J. D. Plummer, Rev. Mod. Phys. 61 (1989) 289 [Fah89b] Fahey P. M., S.S. Iyer, G.J. Scilla, Appl. Phys. Lett. 54 (1989) 843 [Liu00] Liu X.-Y., W. Windl, and M. P. Masquelier, Appl. Phys. Lett. 77 (2000) 2018. [Lop04] Lopez G. M. and V. Fiorentini, Phys. Rev. B 69 (2004) 155206. [Lop04b]

Lopez G., Understanding and controlling Native-Defect-Assisted diffusion of acceptors in Silicon: a theoretical study, PhD thesis, University of Cagliari (2004)

[Man00]

Mannino G., N. E. B. Cowern, F. Roozeboom, J. G. M. van Berkum, Appl. Phys. Lett. 76 (2000) 855

[May77] Mayer J. W. and E. Rimini, eds., Ion Beam Handbook for Material Analysis, (Academic Press, New York, 1977).

[Mel04] Melis C., G. M. Lopez, and V. Fiorentini, Appl. Phys. Lett. 85 (2004) 4902 [Mir03]

Mirabella S., E. Bruno, F. Priolo, D. De Salvador, E. Napolitani, A. V. Drigo, A. Carnera, Appl. Phys. Lett. 83 (2003) 680

[Mor73] Morgan D. V., ed., Channeling Theory, Observation and Application, (John Wiley & Sons, New York, 1973).

[Pel99b] Pelaz L., V. C. Venezia, H.-J. Gossmann, G. H. Gilmer, A. T. Fiory, C. S. Rafferty, M. Jaraìz, and J. Barbolla, Appl. Phys. Lett. 75 (1999) 662.

[Pir05a] A. M. Piro, L. Romano, S. Mirabella, M. G. Grimaldi, Appl. Phys. Lett. 86 (2005) 81906.

[Pir05b] A. M. Piro, L. Romano, P. Badalà, S. Mirabella, M. G. Grimaldi, E. Rimini, Journal of Physics: Condensed Matter 17 (2005) S2273.

[Pir05c] A. M. Piro, L. Romano, S. Mirabella, and M. G. Grimaldi, Mat. Sci. Eng. B 124-125 (2005) 253

[Rim95] Rimini E., Ion Implantation: Basics to Device Fabrication (Kluwer Academic Publishers, Boston, 1995)

4.6 References

105

[Rom05a] L. Romano, A.M. Piro, M.G. Grimaldi, G.M. Lopez, V. Fiorentini, Phys. Rev. B 71 (2005) 165201.

[Rom05b] L. Romano, A.M. Piro, R. De Bastiani, M.G. Grimaldi, E. Rimini, Nucl. Instr. Meth. B 242 (2006) 646.

[Rom05c] L. Romano, A.M. Piro, M.G. Grimaldi, E. Rimini, Journal of Physics: Condensed Matter 17 (2005) S2279.

[Sha03] Shao L., J. Liu, Q. Y. Chen, and W. K. Chu, Mater. Sci. Eng., R. 42 (2003) 65. [Smu87] Smulders P. J. M. and D. O. Boerma, Nucl. Instr. and Meth. B 29 (1987) 471. [Smu90]

Smulders P. J. M., D. O. Boerma, B. Bench Nielsen, and M. L. Swanson, Nucl. Instr. Meth. B 45 (1990) 438.

[Swa89] Swanson M. L., Vacuum 39 (1989) 87. [Tes95] Tesmer J. R. and M. Nastasi, eds., Handbook of modern ion beam materials analysis

(Materials Research Society, Pittsburg, 1995). [Ven04]

Venezia V.C., L. Pelaz, H.J.L. Gossmann, A. Agarwal and T.E. Haynes, Phys. Rev. B 69 (2004) 125215

[Wig78] Wigger L. W. and F. W. Saris, Nucl. Instr. Meth. 149 (1978) 399. [Zhu96]

Zhu J., T. Diaz dela Rubia, L. H. Yang, C. Mailhiot, and G. H. Gilmer, Phys. Rev. B 54 (1996) 4741

[Zie85] Ziegler J. F., J. P. Biresack, and U. Littmark, The Stopping and the Range of Ions in Solids (Pergamon, New York, 1985); http:// www.srim.org

Chapter 5

B implanted at RT in crystalline Si: B defect formation and dissolution.

Ion implantation has became a standard industrial technique to selectively introduce dopants in crystalline Si [Rim95]. However, at the fluences used for Si doping by B implantation (1015 cm-2), the crystalline lattice is heavily damaged and B is electrically inactive. During the post implant thermal treatments required to activate the dopant and recover the lattice damage, undesired effects, such as Transient Enhanced Diffusion (TED) of B atoms [Sto97] and precipitation into electrically inactive Boron-Interstitial-Clusters (BICs) [Pel97, Abo05] well below the B equilibrium solid solubility [Arm77], occur. This behaviour has been modelled in terms of interaction of B with Si self-interstitials (Is), with the concentration of the latter in ion implanted Si being several orders of magnitude higher than at equilibrium. Many theoretical efforts have been spent to detail BICs nature, location and energies [Abo05, Liu00, Ali04] while a few experimental works evidenced their composition, thermal dissolution and electrical activation [Man00, Mir03, Lil02]. Diffusion based investigations, by Secondary Ion Mass Spectrometry, are limited to the high temperature regime, where B diffusion is detectable [Man00, Mir03]. Nevertheless, some crucial information about the lattice location of BICs and their thermal evolution from the room temperature (RT) to 800°C are still missing.

In the chapter 4 we showed that substitutional B in Si undergoes off-lattice displacement at RT during irradiation with H+ beams as a consequence of B interaction with Is generated by irradiation. The amount of displaced B increased with irradiation fluence until saturation, at which point, the formation of B-B pairs stable in presence of excess Is was supposed. In this chapter we study the lattice location of B implanted in crystalline Si at room temperature. The angular scans along the <100> and <110> axes indicate the formation of a particular B complex with B atoms not randomly located. The same defect has been observed also for B doped Si where the B atoms, initially substitutional and electrically active, have been displaced as consequence of the interaction with the point defects generated by proton irradiation. This is surprising because of the different scenario involved in the two cases.

In addition the damage recovery and the electrical activation of such B complexes subjected to thermal treatment in the 200-950 °C range will be presented and discussed. The B complexes dissolve at low temperature if no excess of Si self interstitials (Is) exists or they evolve into large B clusters and then dissolve at high temperature if Is super saturation holds.

5.1 Electrical activation behaviour of B implanted in crystalline Si: literature review

The electrical activation behaviour of B implanted at room temperature in a Si substrate presents interesting features. When B+ is implanted at fluences lower than 3x1013 cm-2 the sheet carrier concentration increases monotonically with the

Chapter 5 B implanted at RT in crystalline Si: B defect formation and dissolution. 108

increasing of the annealing temperature. However, when the B+ fluence exceeds 3x1013 cm-2, reverse annealing (decreasing of the sheet carrier concentration with the increasing of the annealing temperature) takes place in the temperature range of 500-650 °C, as shown in Figure 5.1 [Rim95].

The mechanisms for the reverse annealing are not fully established at present.

North and Gibson [Nor70] suggested that interstitial Si atoms released from defect aggregates during annealing replace substitutional B atoms to interstitial sites and render them electrically inactive, so the reverse annealing is though to occur because of a competition between the native interstitial point defects and the B atoms for lattice sites. Blamires [Bla70] proposed that the reverse annealing is a consequence of substitutional-interstitial B pairing. Gibbons [Gib72] explained the reverse annealing assuming B segregation to dislocation lines and loops to relieve the strain energy associated with the large covalent radius mismatch between substitutional B and Si atoms (~25% mismatch). Huang and Jaccodine [Hua86] demonstrated that the reverse annealing is present similarly both in float zone and in Czochralski grown Si. Since float zone Si has low oxygen concentration, the findings of Huang and Jaccodine apparently disagree with the model proposed by Gregorkiewicz and Ammerlaan [Gre85], which suggested that oxygen and oxygen-related complexes may be involved in reverse annealing. Huang and Jaccodine [Hua86] further noticed that the reverse annealing phenomenon is absent in the B+ implanted Si that underwent rapid thermal annealing (RTA). Based on the observed enhanced electrical activation of B after RTA, the authors suggested that the formation of B-point defects complexes should be the main cause for the reverse annealing because it can be affected efficiently by the heating rate.

De Souza and Boudinov [DeS93] observed that the electrical activation in B+ (5.0x1014 cm-2 at 50 keV) implanted Si samples submitted to furnace annealing can be noticeably affected by a C co-implantation. C+ implanted to a fluence equal to or ten times higher than the B+ fluence contributed, respectively, to the reduction or enhancement of the electrical activation of B after annealing in the temperature range of 450-700 °C. The reverse annealing of B in the temperature range of 500-650°C is attenuated in the co-implanted samples and suppressed in samples where

Fig. 5.1 Electrical activation as function of annealing temperature of B implanted in crystalline Si at room temperature for different B fluences [Rim95].

5.1 Electrical activation behaviour of B implanted in crystalline Si: literature review

109

the C implantation damage was annealed prior to the B+ implantation. This effect is due to the gettering of Is by C atoms [Ter90, Mir02], which is proved by many experimental works where C doping is used to reduce the implant damaging [Tam91, Won88, Cac96] and the B-TED [Sto95, Cow96, Nap01] and, indicating that the reverse annealing is primarily caused by the interaction of B atoms and Is.

Recent theoretical works about BICs have proposed the explanation of the B electrical activation behaviour in terms of formation and dissolution of a complex BIC’s population. In particular, the B activation measured in a sample implanted with 2x1014 B/cm2 at 40 keV after annealing treatments is reported in the Figure 5.2 from Windl et al. [Win01], the simulation has been obtained considering the concentration of several BICs (shown in the figure labels) that are formed and dissolved as function of temperature.

In this way the reverse annealing is essentially due to the disappearance of B4I4

and to the increasing concentration of B2I2. The deactivation and reactivation mechanisms for high B concentration profiles were analysed using atomistic simulations based on kinetic Monte Carlo modeling of dopant diffusion and defect interactions in Si by Aboy et al. [Abo03, Abo05]. They proposed different boron-interstitial cluster (BnIm) pathways as function of the Is concentration, in order to explain the different experimental observations about B reactivation for B implants in crystalline Si and B implants in pre-amorphized Si as function of the annealing time. According to Pelaz’s model [Pel99b] several stages can be distinguished in the temporal evolution of damage and B clustering during the post-implant anneal:

The formation of B clusters occurs at the very early stages of the anneal in the presence of a high concentration of point defects. The growth of B clusters takes place by adding mobile interstitial B to the pre-existing B clusters. The initial B complexes have a high Is content (comparable number of Is and B atoms).

As the anneal proceeds and the Si interstitial supersaturation decreases, B clusters emit Is, reducing their interstitial content. Also, some interstitial B atoms are emitted from the B clusters. The stable B clusters have a larger number of B atoms than Is (a ratio of approximately four B atoms per Si interstitial), and survive longer than the Is clusters 311 [Sto97].

The complete dissolution of the more stable B clusters takes place in a quasi-equilibrium condition by the capture of thermally generated Si interstitials

Fig. 5.2 Simulated (lines) and experimental (circles) B activation after a 40 keV, 2x1014 cm-3 B implant, for 30 min anneals at varying temperatures [Win01]. Contributions of the various BnIm clusters as function of the post-implant annealing temperature are indicated.


and then the release of an interstitial B. Therefore, long-time or high-temperature anneals are needed to activate the B completely, in agreement with experimental observations [Sie71].

This brief review indicates that the effect of B clustering has been indirectly observed by the electrical activation of B implanted in crystalline Si during annealing treatments.

In literature also other phenomena of reverse annealing (involving dopants unlike B) have been explained in term of the formation and dissolution of impurity clusters, for example in As doped Si systems [Sol00]. In supersaturated solid solution of As in Si after equilibrium the reverse annealing phenomenon consists of a transient increase of the carrier density taking place when the system, previously annealed at the temperature T1, is further annealed at the higher temperature T2 with respect to which it is still supersaturated. In these conditions the transient dissolution of aggregates occurs because they become unstable with respect to another population in equilibrium at the higher temperature. A well-known example is given by the early stages of precipitation; in this case the temperature rise makes the critical size of the nuclei to increase, hence, part of the population of smaller particles becomes unstable with respect to the larger ones.

5.2 Lattice location of B clusters and thermal evolution In this section we will present the study of the lattice location of B implanted in

crystalline Si at room temperature. In addition the damage recovery and the electrical activation after thermal treatment in the 400–950 °C range will be presented and discussed.

5.2.1 Experimental In chapter 4 we have observed that B clustering occurs in samples where B is

initially substitutional located and electrically active and is displaced after injection of Is. In this chapter we study the clustering phenomenon of B in samples implanted with B at RT using channeling analyses and electrical measurements. The evolution of B location and electrical activation is particularly interesting during annealing, therefore in order to compare the two different situations we refer to two set of samples realized with (100) n-type Si (4-10 Ωcm) substrates:

Proton-irradiated samples. They consist of 400 nm thick Si layer uniformly doped with a B concentration of 1x1020 at/cm3 irradiated with a 650 keV H+ beam at a fluence of 1x1017cm-2 (above the saturation fluence, see chapter 4). The B doped layer was obtained either by molecular beam epitaxy (MBE) or SPE regrowth of B implanted at multiple energies into pre-amorphized Si.

B implanted samples. A 50 keV 11B+ beam was implanted (7° tilt) at RT into crystalline substrate at a fluence of 2x1015 cm-2. The B concentration profile calculated by SRIM [Zie85] is reported in Figure 5.3 and presented a peak concentration of 1.5x1020 B/cm3 at the projected range (∼200 nm).

The B electrical activation has been measured by Van der Pauw and Hall effect techniques. A Hall scattering factor rH=0.75 has been used to determine the carrier concentration; the active fraction is the ratio of the actual carrier fluence to the implanted fluence, i.e. with respect of a full B activation.

5.2 Lattice location of B clusters and thermal evolution

111

The B lattice location was determined by channeling measurements using the

11B(p,α)8Be nuclear reaction at 650 keV H+ beam. Angular scans have been performed by measuring the normalized B or Si yield as function of the tilt angle swept by the proton beam around a crystal axis (<100> or <110>) inside the (100) plane, as described in chapter 2 and 4. Channeling analyses using 2 MeV He+ beam were in addition performed to detect with a better resolution the recover of crystalline quality of the Si substrate after thermal treatments.

Isochronal (45 min each) thermal annealing was performed in the temperature range between 200°C to 950°C in N2 atmosphere.

5.2.2 B lattice location at RT The angular scans, relative to both a proton irradiated sample and a B implanted

sample, are reported in Figures 5.4a and 5.4b. They have been obtained by measuring the integrated B yield (χB) and the Si yield just below the surface peak (χSi), as function of the tilt angle swept by the proton beam about a crystal axis (<100> in Figure 5.4a or <110> in Figure 5.4b) inside the (100) plane. An error of 5% and 3% affects the minimum yield of B and Si, respectively.

In proton irradiated samples the B χmin is 65% and 50% along the <100> and <110> axes, respectively, because of B off-lattice displacement depicted in chapter 4. The χSi in irradiated samples is identical to that of a not-irradiated crystal (not shown), indicating that the Si lattice is not affected by the proton irradiation at least within the channelling sensitivity. The half-width of the B angular scan is Ψ1/2(B) =0.39° for <110> scan, smaller than that of Si – Ψ1/2(Si)=0.47° –, unlike the <100> scan in which Ψ1/2(B)≈ Ψ1/2(Si)=0.43°. As we have minutely discussed in chapter 4, this means that in these samples the displaced B is not randomly located, since one would expect in this case similar angular half-width and χmin regardless of the channeling axis. Moreover the features of the angular scans indicated that part of the B atoms undergo large displacement towards the centre of the <100> axis and small displacement along the <110>. The symmetry of the displaced B could be an indication that the complex or defect involves a very limited number of B atoms, since it is likely that in large B-Is clusters the several possible configurations will generate a B random signal in channelling analyses. In chapter 4 we have shown that our data are compatible with the formation of B-B pairs aligned along <100> directions, even if the contribution to the measured yield of other B2Ix (x>1) complexes can not be excluded.

Fig. 5.3 B concentration profile (by SRIM simulation) of 50 keV 11B 2x1015 at/cm2 implanted in (100) Si (7°tilt).

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Figures 5.4a and 5.4b. They are identical to those recorded on proton irradiated samples, indicating the same B location in the two samples. The Si χmin (0.1) is slightly higher than that of the unimplanted sample, and the angular half-width (Ψ1/2) remains unchanged. It must be pointed out that it is practically impossible to obtain the same collection of angular scans along the two <100> and <110> channels with two different lattice locations of B atoms in the Si crystal [Tes95, Mor73]. Thus, channelling analyses indicate that the same kind of B complex is formed at RT any time that an excess of Is is produced although different scenarios compete to proton irradiated and B implanted samples. In fact, in proton irradiated samples, B atoms are sitting on substitutional sites with thermal energy and they only see an increase of the concentration of vacancies and interstitials being the probability of direct knock-on by the incoming ions negligible. We calculated by SRIM [Zie85] that ∼3x1016 Si/cm2 are displaced in the doped layer by the 650 keV H+ ions at a fluence of 1x1017 H+/cm2. During implantation of B in Si, B ions with energy of the order of 10 keV are slowed down, interact with the matrix and for each incoming B ion ∼ 500 Si atoms are displaced. This means that ∼5x1017 Si/cm2 are displaced during implantation of ∼1015 B/cm2. Therefore, in the proton irradiated sample the ratio Is/B is ∼10 and to be compared with 500 in the 50 keV B+ implantation. Although these are huge difference the B atoms appear to be

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113

similarly displaced. The question is to identify this common B configuration. We propose that the B atoms form at RT a very small complex, with two B atoms, such as the B-B pair oriented along the <100> axis, that is, according to first principle calculation [Ali04, Pel99b], the lowest energy configuration accessible in presence of an excess of Si self-interstitials. This complex, once formed, is stable even in presence of an excess of point defects and it could qualitatively account for the measured angular scans. We have shown (see chapter 4) that in proton irradiated samples the fraction of clustered B atoms increases continuously with the H+ fluence (with Is fluence) until B is completely clustered and stable upon further irradiation. In B implanted samples we could imagine that some mobile B-Is pairs are formed in the collision cascade and, even in a dynamical situation in which interaction with other Is can occur, the final product is still a B-B pair.

5.2.3 B clustering evolution during annealing We have investigated the evolution of the B complex after isochronal annealing

(45 min, in N2) in the temperature range 200-950°C for both proton-irradiated and implanted samples.

The angular scans of the implanted samples annealed at 700°C for 45 min are shown in Figures 5.4c and 5.4d. The B yield raises up to 0.95 along the both <100> and <110> axes and gives a featureless angular scans, indicating that most of the B atoms are almost randomly located. The reduction of the Si χmin with respect to the as implanted is due to the recovery of the implantation induced defects. After 900°C annealing about 50% of B is substitutional located as attested by the angular scans shown in Figures 5.4e and 5.4f that exhibite identical χmin(B) and angular half-width close to that of the host lattice. For proton-irradiated samples at 700°C the angular scans (not shown) indicate that the B atoms are almost substitutional located.

To summarize the results relative to B implanted samples we have reported in Figure 5.5 the B minimum yield, χmin(B), measured in <100> (full squares) and <110> (full circles) axes as function of the annealing temperature. χmin(B) increases after annealing up to 700 °C, and it suddenly drops at higher temperatures reaching a value of 0.1 after 950 °C annealing. In the same figure we have reported by empty symbols the electrically active B fraction determined by Hall carrier concentration measurements. The active B fraction was calculated as the ratio of the measured Hall carrier fluence to that expected for a complete activation of the implanted B fluence (2x1015 at/cm2). The carrier concentration measurements indicate that only 10% of the implanted B is active up to 800 °C, and the total activation is achieved after annealing at 950 °C, in agreement with the B lattice location. The phenomenon of reverse annealing, described in section 5.1, is clearly evident in the 500 – 700 °C range. Therefore in B implanted sample we have two regimes: at low temperatures the B lattice location evolves toward a nearly random distribution up to 700 °C; at higher temperatures a quick recovery of B in substitutional sites occurs.

The comparison with the thermal evolution of B in the proton-irradiated samples is shown in Figure 5.6 where χmin(B) for proton beam impinging along the <100> axis is reported for both (proton-irradiated and B implanted) samples. The trend of the B lattice location evolves in an opposite way. In fact, the χB of the proton-irradiated samples monotonically decreases as the temperature increases, indicating a progressive dissolution of the B complex; at T higher than 500 °C a consistent fraction of B is substitutional and the minimum χB along the <100> and <110> (not shown) axes coincides. The location of B in substitutional sites at low temperature is also supported by measurements of the carrier concentration. B is completely inactive after irradiation, after 200 °C annealing a ~15% of B is active, and electrical activation is almost complete after 500 °C annealing. Therefore the


B-B pairs dissolve at relatively low temperature and the electrical activation of B requires a limited thermal budget.

The different thermal evolution of B complexes in the two samples can be

correlated to the defects concentration in the Si host lattice. In fact, the damage could be detected by channeling in the proton irradiated samples unlike the B implanted. The thermal evolution of the damage produced by the B implant is visible in Figure 5.7 where are reported the <100> channeling spectra of a 2 MeV He+ beam relative to the as-implanted and annealed samples. The as-implanted spectrum shows a peak between channels 370-410 due to direct scattering from point defects, and it corresponds to 7.5x1016 displaced Si/cm2. A smaller damage peak is visible in the spectra of the annealed samples and it is scarcely visible after 700 °C annealing, indicating that at low temperature annealing of point defects occurs. At 900 °C the sharp step at channel 390 indicates the formation of a dislocation band due to the dissolution of the 311 defects [Sto97]. The spectrum of the 950 °C annealed sample indicates most of the damage has been annealed out. The thermal evolution of the B complex is different in the two sets of samples. This difference might be attributed to the interaction of B complex with the residual defects. In the proton-irradiated samples the B complex evolves in a nearly free-of-defects matrix since the density of point defects produced by the H+ beam is quite low, as also indicated by the channelling yield. In the B implanted sample large amount of damage is left in the layer: the channelling analyses of Figure 5.7 show a disorder peak due to direct scattering from point defects corresponding to ~1017 displaced Si/cm2. The peak area decreases as the annealing temperature increases, and no defects have been detected after annealing at 700 °C. Many authors [Sto97, Gil93, Cow99] showed that implantation induced damage evolves during annealing sustaining an Is supersaturation up to 800 °C. We believe that the increase of the minimum χB is indicative of the formation of large B-Is clusters (due to excess of Is) and B atoms in the clusters appear randomly displaced in channelling analyses. Therefore the simple B-B complex (see section 4.4.2) stable at RT evolves at high temperature: it dissolves if no Is supersaturation is maintained (proton-irradiated samples) or it grows by trapping Is if they are available (B implanted samples).

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Fig. 5.5 Channeling yield of B (right axis) in B implanted Si along the <100> (squares) and <110> (circles) axes as function of the annealing temperature. The fraction of B electrically active is reported (empty triangles) on the left axis.


115

This is the first experimental evidence of the model proposed by Pelaz et al. [Pel99b] (see section 5.1) who predicted the B cluster growth if an external Is supersaturation holds, otherwise B clusters dissolution. At higher temperature the large B clusters start to dissolve and B becomes substitutional and electrically active.

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Fig. 5.6 Minimum channeling yield B χmin (squares) measured along the <100> axis and electrical activation (triangles) vesus the annealing temperature for proton-irradiated (1x1017 H+/cm2) samples (empty symbols) and B implanted samples (full symbols). Each annealing step is 45 min.


5.3 Concluding Remarks In conclusion, we have shown that a well defined, stable B complex, involving

probably two B atoms, is formed at room temperature in the presence of a supersaturation of Is. At higher temperature this complex evolves into large B clusters if a substantial Is super saturation is present or dissolves (at temperature ~500°C) if no excess of Is exists. The thermal budget necessary to activate B depends on the cluster size and it is significantly higher when B is bonded in larger B-Is clusters. The results so far presented indicate that in order to achieve B activation with reduced thermal budget one has to develop strategy to keep the Is concentration as low as possible.

5.4 References [Abo03] Aboy M., L. Pelaz, L. A. Marqués, J. Barbolla, A. Mokhberi, Y. Takamura, P. B.

Griffin, and J. D. Plummer, Appl. Phys. Lett. 83 (2003) 4166

[Abo05] Aboy M., L. Pelaz, L. A. Marqués, P. López, J. Barbolla, R. Duffy, J. Appl. Phys. 97 (2005) 103520

[Ali04] Alippi P., P. Ruggerone, L. Colombo, Phys. Rev. B 69 (2004) 125205. [Arm77] Armigliato A., D. Nobili, P. Ostoja, M. Servidori, S. Solmi, in Semiconductor Silicon

1977, 77-2, H. Huff and E. Sirtl eds. (The Electrochemical Society, Princeton, N. J. 1977) 638.

[Bla70] Blamires N. G., European Conference on Ion Implantation (Peregrinus, Stevenage, England, 1970) 52.

[Cac96] Cacciato A., J. G. E. Klappe, N. E. B. Cowern, W. Vandervorst, L. P. Birò, J. S. Custer, and F. W. Saris, J. Appl. Phys. 79 (1996) 2314.

[Cow96] Cowern N. E. B., A. Cacciato, J. S. Custer, F. W. Saris, and W. Vandervorst, Appl. Phys. Lett. 68 (1996) 1150.

[Cow99] Cowern N. E. B., G. Mannino, P. A.Stolk, F. Roozeboom, H. G. A. Huizing, J. G. M. van Berkum, F. Cristiano, A.Claverie and M. Jaraiz, Phys. Rev. Lett. 82 (1999) 4460

[DeS93] De Souza J. P. and H. Boudinov, J. Appl. Phys. 74 (1993) 6599 [Gib72] Gibbons J. F., Proc. IEEE 60 (1972) 1062. [Gil93] Giles M.D., Appl. Phys. Lett., 62 (1993) 1940. [Gre85] Gregorkiewicz T. and C. A. J. Ammerlaan, Radiat. Eff. Lett. 85 (1985) 249. [Hua86] Huang J. and R. J. Jaccodine, in Rapid Thermal Processing, T.O. Sedgwick, T. E.

Seidel, and B.-Y. Tsaur eds. 52 (Materials Research Society, Pittsburgh, 1986) 57. [Lil02] Lilak A.D., M.E. Law, L. Radic, K.S. Jones, M. Clark, Appl. Phys. Lett. 81 (2002)

2244 [Liu00] Liu X.-Y., W. Windl, and M. P. Masquelier, Appl. Phys. Lett. 77 (2000) 2018. [Man00] Mannino G., N. E. B. Cowern, F. Roozeboom, J. G. M. van Berkum, Appl. Phys.

Lett. 76 (2000) 855 [Mir02] Mirabella S., A. Coati, D. De Salvador, E. Napolitani, A. Mattoni, G. Bisognin, M.

Berti, Carnera, A. V. Drigo, S. Scalese, S. Pulvirenti, A. Terrasi, and F. Priolo, Phys. Rev. B 65 (2002) 45209

[Mir03] Mirabella S., E. Bruno, F. Priolo, D. De Salvador, E. Napolitani, A. V. Drigo, A. Carnera, Appl. Phys. Lett. 83 (2003) 680

[Mor73] Morgan D. V. ed., Channeling Theory, Observation and Application, (John Wiley & Sons, New York, 1973).

[Nap01] Napolitani E., A. Coati, D. De Salvador, A. Carnera, S. Mirabella, S. Scalese, and F. Priolo, Appl. Phys. Lett. 79 (2001) 4145

[Nor70] North J. C. and W. M. Gibson, Appl. Phys. Lett. 16 (1970) 126 [Pel97] Pelaz L., M. Jaraìz, G. H. Gilmer, H.-J. Gossmann, C. S. Rafferty, D. J. Eaglesham,

and J. M. Poate, Appl. Phys. Lett. 70 (1997) 2285 [Pel99b] Pelaz L., V. C. Venezia, H.-J. Gossmann, G. H. Gilmer, A. T. Fiory, C. S. Rafferty,

M. Jaraìz, and J. Barbolla, Appl. Phys. Lett. 75 (1999) 662 [Rim95] Rimini E., Ion Implantation: Basics to device fabrication (Kluwer, USA, 1995) [Sie71] Seidel T. E. and A. U. Mac Rae, Radiat. Eff. 7 (1971) 1

5.4 References

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[Sol00] Solmi S., D. Nobili and J. Shao, J. Appl. Phys. 87 (2000) 658 [Sto95] Stolk P. A., D. J. Eaglesham, H.-J. Gossmann, and J. M. Poate, Appl. Phys. Lett. 66

(1995) 1370. [Sto97] Stolk P. A., J. H.-J. Gossmann, D. J. Eaglesham, D. C. Jacobson, C. S. Rafferty, G.

H. Gilmer, M. Jaraìz, J. M. Poate, H. S. Luftman and T. E. Haynes, J. Appl. Phys. 81 (1997) 6031

[Tam91] Tamura M., T. Ando, and K. Ohyu, Nucl. Instr. Meth. B 59/60 (1991) 572. [Ter90] Tersoff J., Phys. Rev. Lett. 64 (1990) 1757. [Tes95] Tesmer J. R. and M. Nastasi, eds., Handbook of modern ion beam materials analysis

(Materials Research Society, Pittsburg, 1995). [Win01] Windl W., X.-Y. Liu and M.P. Masquelier, Phys. Stat. Sol. (b) 226 (2001) 37 [Won88] Wong H., N. W. Cheung, P. K. Chu, J. Liu, and J. W. Mayer, Appl. Phys. Lett. 52

(1988) 1023. [Zie85] Ziegler J. F., J. P. Biresack, and U. Littmark, The Stopping and the Range of Ions in

Solids (Pergamon, New York, 1985); http:// www.srim.org

Conclusions

Aim of this work was the investigation of the properties of Si doped with B and Ga and eventually co-doped with both impurities in the concentration range 1x1019-8x1020 at/cm3. In order to achieve dopant concentration well above the equilibrium solid solubility, the samples were prepared by solid phase epitaxy at low temperature. The electrical and structural characterization of the supersaturated solid solutions is reported in chapters 2 and 3. However, these solutions are not stable and deactivation of dopants it is known to occur upon thermal annealing. In chapter 4 we demonstrated that the dopant deactivation occurs even at room temperature, provided that the concentration of point defects exceeds the equilibrium value. The experimental data supported that the formation of small dopant-Is complexes is responsible of the deactivation. The evolution at high temperature of such complexes is discussed in chapter 5.

The partial conclusions of each part of this dissertation were given in the concluding remarks at the end of each chapter. In this conclusive section, we want to summarize the most significant results presented so far.

First of all we reported the strain effect on the epitaxial regrow velocity and carrier mobility. In fact, at this high concentration of dopants a considerable strain, detectable by HRXRD, is developed in the Si lattice. The settled down model (see section 1.3.1) for the epitaxial regrowth of Si predicts a dependence of the regrow velocity on the Fermi level position inside the band gap. Our data (see section 2.4.2) indicated that even the strain affects the regrow velocity. In fact, the strain in co-doped samples can be changed continuously by varying the relative amount of B and Ga, and, once the Fermi level was fixed, the regrowth velocity in co-doped samples increased with strain. This could be an important point to be considered in a more complete model for the epitaxial regrowth.

Even the hole mobility depends on strain (see section 3.4) and high mobility is associated to tensile strain. In fact, for a given Ga concentration the mobility is higher in co-doped samples with respect to pure Ga despite of the higher total impurity concentration. To disentangle the effect of strain on mobility we measured the mobility at a fixed concentration of ionized impurities varying the concentration of B and Ga and, from that, we determined the relationship between mobility and strain. The effect of chemical species on carrier mobility was interpreted as a display of the strain effect and the measured values were corrected in order to determine the mobility of unstrained Si versus carrier concentration.

The other point we want to mention here is the accurate determination of the deactivation of dopants in Si during irradiation at room temperature with energetic light ions (chapter 4). The concentration of displaced dopant atoms was measured by channeling techniques as a function of the excess of point defects generated by the beam. The progressive increase of the impurity channeling yield was simulated on the basis of the interaction between the dopants and the Si self interstitials generated by the ion irradiation (section 4.2.1). This interaction was modelled assuming a mechanism similar to the impurity diffusion assisted by Si self interstitials (Is), with the further assumption that the diffusion ends when the mobile impurity forms a stable complex. This accounted for the displacement rate experimentally determined, being the fitting parameter the trapping cross section of the Is by impurity atoms. The lattice location (section 4.4) of B and Ga bonded in not-active complexes was determined by angular scans along the main Si axes and

Conclusions 120

it was in qualitative agreement with the most stable pairs of impurities proposed by several theoretical groups, although, the channeling analyses suggested the presence of a minor distortion with respect to the proposed configurations. This constitutes an input for theoretical investigations, demonstrating the powerful skills of this experimental method in very actual fields of science and technology.

Channeling method turned out to be very effective to study the impurity clustering phenomena. It should be noted that clustering characterization can not be performed by other techniques at RT, since the profiling methods, like the secondary ion mass spectrometry, are not sensitive to the low diffusion length associated to the low temperature regime.

Finally (chapter 5) we applied the channeling method to the case of B implanted in crystalline Si, which is of technological interest. The lattice location of the as-implanted B was identical to that of the B displaced by ion irradiation, suggesting that the same B complex is formed in presence of an excess of point defects in spite of the different conditions. The damage recovery, the B complex evolution and the electrical B activation during thermal treatment in the 200 – 950 °C range indicated that the complexes dissolved at 500 °C if no excess of Is exists or they evolve into large B clusters if Is super saturation holds. Annealing at high temperature (~800 °C) is necessary to dissolve the latter. This is the first experimental evidence of the cluster evolution in a large range of temperatures that will allow validation of the several models proposed by theoretical groups.

List of Publications

This thesis is based on the following publications:

1. L. Romano, A.M. Piro, M.G. Grimaldi, G.M. Lopez, V. Fiorentini, Influence of point defects injection on the stability of supersaturated Ga-Si solid solution, Phys. Rev. B 71 (2005) 165201.

2. A. M. Piro, L. Romano, S. Mirabella, M. G. Grimaldi, Room Temperature Boron Displacement in Crystalline Silicon induced by Proton Irradiation, Appl. Phys. Lett. 86 (2005) 81906.

3. L. Romano, A. M. Piro, E. Napolitani, A. Spada, M. G. Grimaldi, E. Rimini, Electrical activation and lattice location of B and Ga impurities implanted in Si, Nuclear Instruments and Methods B 219-220 (2004) 727.

4. L. Romano, A.M. Piro, M.G. Grimaldi, E. Rimini, Impurities – Si interstitials interaction in Si doped with B or Ga during ion irradiation, Journal of Physics: Condensed Matter 17 (2005) S2279.

5. A. M. Piro, L. Romano, P. Badalà, S. Mirabella, M. G. Grimaldi, E. Rimini, Cross section of the interaction between substitutional B and Si self-interstitials generated by ion beams, Journal of Physics: Condensed Matter 17 (2005) S2273.

6. L. Romano, A. M. Piro, S. Mirabella, M. G. Grimaldi, E. Rimini, Lattice location and thermal evolution of small B complexes in crystalline Si, Appl. Phys. Lett. 87 (2005) 201905.

7. L. Romano, A. M. Piro, S. Mirabella, M. G. Grimaldi, B implanted at room temperature in crystalline Si: B defect formation and dissolution, Materials Science and Engineering B 124-125 (2005) 253.

8. A. M. Piro, L. Romano, S. Mirabella, and M. G. Grimaldi, Boron lattice location in room temperature ion implanted Si crystal, Materials Science and Engineering B 124-125 (2005) 249.

9. L. Romano, A.M. Piro, R. De Bastiani, M.G. Grimaldi, E. Rimini, Group III impurities – Si interstitials interaction caused by ion irradiation, Nuclear Instruments and Methods B 242 (2006) 646.

10. A. M. Piro, L. Romano, P. Badalà, S. Mirabella, M. G. Grimaldi, E. Rimini, Role of Si self-interstitials on the electrical de-activation of B doped Si, Nuclear Instruments and Methods B 242 (2006) 656.

11. L. Romano, A.M. Piro, M.G. Grimaldi, E. Rimini, Room-temperature B off-lattice displacement and electrical deactivation induced by H and He implantation, Nuclear Instruments and Methods B (in press).

Other publications:

12. G. Impellizzeri, S. Mirabella, L. Romano, E. Napolitani, A. Carnera, M.G. Grimaldi, F. Priolo, Fluorine incorporation during Si solid phase epitaxy, Nuclear Instruments and Methods B 242 (2006) 614.

List of Publications 122

13. L. Romano , E. Napolitani, V. Privitera, S. Scalese, A. Terrasi, S. Mirabella, M.G. Grimaldi, Carrier Concentration And Mobility In B Doped Si1-XGex, Materials Science and Engineering B102 (2003) 49.

14. A. M. Piro, L. Romano, A. Spada, F. La Via, M. G. Grimaldi, E. Rimini, Structural characterization and oxygen concentration profiling of Co/Si multilayer structure, Nuclear Instruments and Methods B 219-220 (2004) 732.

15. S. Mirabella, G. Impellizzeri, E. Bruno, L. Romano, M. G. Grimaldi, F. Priolo, E. Napolitani, A. Carnera, Fluorine segregation and incorporation during solid phase epitaxy of Si, Appl. Phys. Lett. 86 (2005) 121905.

Curriculum

Lucia Romano was born on 30th of July 1977 in Augusta (Siracusa, Italy). In 1996 she obtained the General Certificate of Education at the Scientific Secondary School “Leonardo da Vinci" of Floridia (SR), with mark 60/60. She studied Physics at the University of Catania (Italy) winning the scholarship every year. She attained her Master Degree in Physics (110/110 cum laude) on 20th of December 2001. In January 2001 she was involved in the 3.5 MeV Singletron accelerator at the Physics Department of the University of Catania. In January 2003 she was admitted to the three-year Ph.D. course in Physics at the University of Catania. In November 2005 she had a post-doc position at the University of Catania. She has also collaborated with several groups: INFM-MATIS and the University of Padova (Italy), INFM-SLACS and the University of Cagliari (Italy), CNR-IMM of Catania, STMicroelectronics of Catania, Los Alamos National Laboratory (USA). Lucia Romano has been mainly involved in experimental studies concerning ion beam implantation and analyses, electrical characterization and processing of crystalline silicon doped with B and Ga, under the supervision of Prof. Maria Grazia Grimaldi.

During the Ph.D. course she attended national and international conferences (EMRS Spring meeting, 2002 France; IBA conference, 2003 USA; International Summer School Nicolás Cabrera, 2003 Spain; IBMM conference, 2004 USA; 1st CADRES workshop, 2004 Italy; EMRS Spring meeting, 2005 France; IBA conference, 2005 Spain), giving oral and poster contributions. She won the young scientist award at EMRS-2002. Moreover, Lucia Romano is author or co-author of several articles, published in international referred scientific journals.

Acknowledgments

There have been many people along the way that have given me the support

and guidance necessary to complete the work within this dissertation. First, I would like to thank my tutor, Professor Maria Grazia Grimaldi (University of Catania), for her supervision and friendly support given to my research and life in these years. I owe to her the extraordinary experience to assemble bit by bit the 3.5 MV Singletron accelerator, which allowed this thesis work and my personal technical ability about IBA. She loves to stay in laboratory and she taught me a lot of things. But above all I appreciated her because she is frank and an easygoing person.

Heartfelt thanks go to my friend and collaborator Dr. Alberto Piro. The major results of this work have been reached with his collaboration. We lived this adventure together, we studied and worked hard side by side, we enjoyed happy days and suffered bad moments. Thanks to Alberto to have been a good fellow traveller, in every sense.

During my educational course I have had the opportunity to meet very greet people, who, together with the Prof. M.G. Grimaldi, taught me all that I know and hold me in high esteem, I owe much to them. First of all I would like to thank Prof. Emanuele Rimini (University of Catania and director of CNR-IMM) for the innumerable suggestions and encouragements, and above all his paternal backing. I am also sincerely grateful to Prof. Francesco Priolo (University of Catania and director of MATIS) for his unique ability to focus the problems. I have learned very much from his way of presenting and management.

Special thanks go to people from the University of Padova: Dr. Enrico Napolitani for the numerous SIMS, Dr. Gabriele Bisognin for the enlightening HRXRD analyses and his patience, Prof. Alberto Carnera for useful discussions; to prof. Vincenzo Fiorentini and Dr. Giorgia Lopez from the SLACS-INFM laboratory of the University of Cagliari for their substantial contributions. I would like to acknowledge Dr. Marco Camalleri, Dr. Dario Salinas and Dr. Giuseppe Arena (STMicroelectronics, Catania site); Dr. Mike Nastasi and Dr. Jung Kun Lee (Los Alamos National Laboratory, USA) for their collaboration. Thanks to many members of the CNR-IMM center of Catania: Antonio Marino for his special ion implants; Aldo Spada for his special help; Salvo di Franco, Corrado Bongiorno, Dr. Vittorio Privitera, Dr. Vito Raineri, Dr. Francesco La Via, Dr. Paola Alippi and the director Dr. Corrado Spinella.

I’d like to especially thank Salvo Tatì and Carmelo Percolla (MATIS, Catania) for their technical expertise and their friendship and support, without them working into the ion beam laboratory should be impossible! Thanks also to John Fallon (HVEE) who taught me to assemble an accelerator in spite of Etna’s eruption and tremors.

Moreover very special thanks go to Dr. Salvo Mirabella, for his collaboration and motivations that allowed me to keep moving even in times when it seemed there was no end, but above all because he is a really good friend; to Dr. Giuliana Impellizzeri for her candour and kindness, but especially for her constant closeness in my life and the long discussions that allowed to clarify my opinions; to Dr. Elena Bruno for her naturalness, for many happy moments we enjoyed together; to Prof. Tony Terrasi, he taught me to screw bolts, because the laboratory is not a place only for strong men, but also for fine girls! Thanks to all MBE’s group for special assistance at furnace and liquid nitrogen supplying.

Acknowledgments 126

Heartfelt thanks go to my friend Dr. Domenico Pacifici, in spite he was far away he found the way to encourage me during this hard work, I really missed him; to Dr. Riccardo De Bastiani for the long “gallium’s story” he had the patience to write and especially because he made me understand my carelessness could eventually hurt deeply; to Dr. Daniele D’Angelo for his special work at the TRR and to be always present in case of need. Thanks for everything!

I can not forget all the people that shared their life with me at the Department of Physics: Prof. Giovanni Piccitto, Dr. Giuseppe Angilella, Mr. Natale Marino, Dr. Giorgia Franzò, Dr. Maddalena Spadafora, Dr. Alessia Irrera, Dr. Maria Miritello, Dr. Isodiana Crupi, Dr. Andrea Canino, Dr. Roberto Lo Savio, Dr. Paolo Badalà, Dr. Francesco Ruffino, Dr. Simona Boninelli.

I would like also to thank the other members of the “lunch time group”: Dr. Alessandra La Greca and Dr. Giuseppe Politi to have enjoyed with me the so many days at the dining hall.

I wish to thank also some people I met at the IBA conference and made my stay pleasant and interesting: Dr. Federico Mazzei, Dr. Massimo Chiari, Dr. Lorenzo Giuntini, Dr. Mirko Massi, Dr. Silvia Nava, Dr. Novella Grasso, Dr. Marco Bianconi, Dr. Giorgio Lulli, Dr. Tiziana Cesca, Prof. Andrea Gasparotto, Prof. Leonard Feldman.

Thanks to Dr. Fabrizio Mangano, for his kindness and friendship. Thanks to my dear co-tenants Clara, Gloria and MariaAntonietta for the kind cohabitation. Thanks to Mirko, for his spiritual affinity and understanding.

Finally I wish to thank my family that loved and stand by me: my mum to be

every day so charming and to have taught me my strong character, my sister, Silvia, to be so different and so exceptional! Thanks to Paolo because he simply, always, loves me. Heartfelt thankyou to everyone!

PhD Thesis

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