MASTER'S THESIS Mode Structure in the Light Emission from Planar Waveguides with Silicon

Charles University in PragueFaculty of Mathematics and Physics

M ASTER’S THESIS

Eva Skopalová

Mode Structure in the Light Emission from Planar Waveguides with Silicon Nanocrystals

Department of Chemical Physics and Optics

Supervisor. Prof. RNDr. Ivan Pelant, DrSc.Institute of Physics, Academy of Sciences of the Czech Republic

Study programme: Physics, Optics and Optoelectronics

2007

Acknowledgem ents

2

Firstly, I would like to thank my supervisor Prof. RNDr. Ivan Pelant, DrSc. for his excellent guidance, providing me with his invaluable experiences and giving advice.

Furthermore, I am grateful to RNDr. Kateřina Herynková, Ph.D. who introduced me to the work in laboratory and helped me a lot with my first measurements. I am also thankful to RNDr. Kateřina Dohnalová for her assistance with the building of experimental setup and discussion concerning the measurement and processes in silicon nanocrystals. Thanks are due to Prof. Robert Elliman (Australian National University, Canberra), Prof. Leonid Khriachtchev (University of Helsinki) and Prof. Lorenzo Pavesi (University of Trento) for providing us with high quality samples, and to Ing. Vlastimil Jurka for fabrication of the rib waveguides. I want to express my gratitude to RNDr. Tomáš Ostatnický, Ph.D. for his consultation about the theoretical model of the rib waveguide. Moreover, I want to thank Ing. Ondřej Cibulka for technical help with the experimental setup, mainly with the Nd:YAG laser. Besides, I am indebted to Ing. Jan Pejchal for providing transmission measurements on our samples. I acknowledge Doc. RNDr. Jan Valenta, Ph.D. for providing supportive photoluminescence measurements on the rib sample. I am also grateful to all the staff of the Department of Thin Films at the Institute of Physics of the Academy of Sciences of the Czech Republic who have created very good atmosphere for work.

My special thanks belong to my parents who have supported me throughout the whole period of my studies.

I hereby state that I have written this master’s thesis by myself using only the cited references. I agree to lend it.

Prague, April 2007

Contents

Abstract 5

1 Introduction. Light Emission in Silicon 61.1 Zone Folding in SiGe Superlattices.................................................................. 61.2 Luminescence via A lloying................................................................................. 71.3 Luminescence via Impurities.............................................................................. 71.4 Quantum Confinement........................................................................................ 81.5 Aims of this Work .............................................................................................. 8

2 Luminescence of Semiconductors 102.1 Bulk Semiconductors.......................................................................................... 10

2.1.1 General Properties of Bulk Silicon........................................................ 122.2 Semiconductor Nanocrystals.............................................................................. 14

2.2.1 Cubic Quantum D o t .............................................................................. 142.2.2 Breakdown of the k-conservation Rule ............................................... 152.2.3 Role of the Surface of Nanocrystals..................................................... 162.2.4 Luminescence Time Decay of Nanocrystals......................................... 17

2.3 Optical Gain ....................................................................................................... 172.3.1 General Considerations........................................................................... 172.3.2 Variable Stripe Length Technique........................................................ 182.3.3 Artifacts of the VSL Technique........................................................... 192.3.4 Shifting Excitation Spot Technique..................................................... 20

2.3.5 Optical Gain in Silicon Nanocrystals.................................................. 21

3 Asymmetrical Planar Optical Waveguide 233.1 Guided Modes....................................................................................................... 233.2 High-Loss Waveguide........................................................................................... 273.3 Leaky M o d e s ....................................................................................................... 273.4 Matrix Formulation.............................................................................................. 29

4 Results: Planar Waveguides with Si-ncs 314.1 Sam ples................................................................................................................ 31

4.1.1 Samples Prepared by Si+ Ion Implantation.........................................314.1.2 Samples Prepared by Reactive D eposition .........................................32

3

CONTENTS 4

4.2 Experimental Setup..............................................................................................334.3 Light Emission from the Samples Prepared by Si+ Ion Implantation . . . . 34

4.3.1 Mode Structure of the Emission............................................................344.3.2 Modes under Different Ambient Conditions.........................................37

4.4 Light Emission from the Sample Prepared by Reactive D eposition.............424.4.1 Mode Structure of the Emission and the Physical Properties of the

Sample....................................................................................................... 424.4.2 Modes under Different Ambient Conditions.........................................45

4.4.3 Angular Dependence of the Modes ..................................................... 504.5 Summary on the Mode Emission........................................................................ 52

5 Results: Rib Optical Waveguide 545.1 Rib Waveguide Sam ple........................................................................................ 545.2 Experimental Observation of Light Emission.................................................. 55

5.2.1 Excitation with a S tr ip e ........................................................................ 555.2.2 Evanescent Wave Excitation..................................................................57

5.2.3 Summary on Experimental Observation............................................... 575.3 Theoretical Model................................................................................................. 59

5.3.1 Labeling and Useful Geometric Relations............................................595.3.2 Wave Model of Leaking Modes...............................................................615.3.3 Results of Numerical Calculation........................................................ 63

6 Results: Pulsed Excitation 676.1 Time Resolved Photoluminescence..................................................................... 67

6.1.1 Experimental Setup................................................................................. 676.1.2 Slow (microsecond) PL Com ponent..................................................... 686.1.3 Fast (nanosecond) PL Component........................................................ 68

6.2 Results of the VSL Measurements..................................................................... 706.2.1 Experimental Setup................................................................................. 706.2.2 VSL on Rhodamine 6 1 0 ........................................................................ 716.2.3 VSL on a Ruby Sample........................................................................... 726.2.4 VSL on Silicon Nanocrystals.................................................................. 74

7 Conclusions 79

Bibliography 81

Published Articles 84

ABSTRACT 5

Název: Modová struktura emise v planárních vlnovodech s křemíkovými nanokrystalyAutor. Eva SkopalováKatedra: Katedra chemické fyziky a optikyVedoucí diplomové práce: Prof. RNDr. Ivan Pelant, DrSc., Fyzikální ústav AV ČRe-mail vedoucího·, [email protected] V této práci studujeme luminiscenční vlastnosti křemíkových nanokrystalů vS1O2 matrici připravených dvěma různými metodami: iontovou implantací a reaktivní depozicí na S1O2 substrát. Tyto vrstvy nanokrystalů tvoří planarní vlnovody, protože mají vyšší index lomu než substrát. Vlnovodné vlastnosti vzorků silně ovlivňují tvar fotoluminiscenčních spekter měřených z hran vzorků, v těchto spektrech byla pozorována zvláštní modová struktura. V minulosti byly navrženy dvě teorie s cílem vysvětlit tuto strukturu: teorie vybírání vedených vlnových délek ve vysoce ztrátových vlnovodech a teorie prosakujících modů, které opouští jádro vlnovodu a šíří se dál substrátem. Hlavním cílem této práce je experimentální určení, která ze dvou navržených teorií popisuje nejlépe pozorovaný spektrální tvar. Výsledky ukazují, že je to teorie prosakujících modů. Dále byla studována emise světla z kanálkových vlnovodů s křemíkovými nanokrystaly, a to jak experimentálně, tak teoreticky. Protože mody pozorované z hrany vzorku mají významný vliv na interpretaci výsledků metody VSL pro měření optického zisku, byla provedena VSL meření studující chovám prosakujících modů.Klíčová slova: křemíkové nanokrystaly, fotoluminiscence, planární vlnovody, optický zisk

Title: Mode Structure in the Light Emission from Planar Waveguides with Silicon Nano- crystalsAuthor. Eva SkopalováDepartment Department of Chemical Physics and OpticsSupervisor. Prof. RNDr. Ivan Pelant, DrSc., Institute of Physics of the ASCRSupervisor’s email address: [email protected]: In this work we study luminescence properties of silicon nanocrystal (Si-nc)layers in S1O2 matrix prepared by two different methods: Si+ ion implantation and reactive Si deposition on S1O2 substrate. These Si-nc layers have higher refractive index than the S1O2 substrate, thus forming planar waveguides. The waveguiding properties of the samples strongly influence the spectral shape of the light (photoluminescence) emitted from the sample edge and a peculiar mode structure has been observed. In order to explain this observation two theories were proposed some time ago: a theory of wavelength selective waveguiding in high-loss waveguides, and a theory of leaky modes leaving the waveguide core and propagating in the substrate. The main goal of this work is the experimental test which of the theories describes best the nature of the modes. The results show that it is the theory of leaky modes. Furthermore, light emission from rib waveguides with silicon nanocrystals is studied both experimentally and theoretically. Finally, since the modes emitting from the sample edge have a significant effect on the interpretation of Variable Stripe Length (VSL) measurements of optical gain, some VSL measurements were provided in order to reveal the behaviour of leaky modes.Keywords: silicon nanocrystals, photoluminescence, planar waveguides, optical gain

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Chapter 1

Introduction. Light Emission inSilicon

Nowadays the major material used for fabrication of integrated circuits is silicon. It is the most examined material, it is inexpensive, chemically stable, non-toxic and there are sufficient silicon supplies in nature. Modern technologies of producing silicon monocrystals with diameter up to 300 mm have been developed. On the silicon chips very high densities of transistors can be reached and the number of transistors on a chip follows the empirical Moore’s law: it doubles every 18 months. Today more than 10® transistors can be integrated on a single silicon chip. As the density of transistors, and thus interconnects, on a chip gets larger and larger, the problem of propagation delay and overheating arises which is the main limiting factor for proceeding the Moore’s law. One way to overcome the problem of overheating of integrated circuits is combining electronic and photonic devices on one silicon chip. Photonics, which replaces electronic interconnects by optical ones, has the advantage that it does not produce heat, unlike microelectronics. Contrary to microelectronics where the leading material is silicon, there are a variety of materials used in photonics (e.g. InP, GaAs). Photonics based on silicon would be a promising way how to rapidly decrease the heat dissipation and propagation delays and thus increase the speed of devices. There axe many photonic devices made of silicon, such as detectors, optical modulators, low-loss waveguides [1], However, the key device for silicon photonics is still missing: the Si based source of light. A silicon laser would be a revolutionary device for modern photonics which would rapidly increase the effectiveness of the devices.

The problem is that silicon is an indirect band-gap semiconductor and thus a very poor emitter of light. Several approaches have been made to overcome the indirect band-gap and to achieve efficient luminescence from silicon at room temperature. We will briefly mention the most important of them.

1.1 Zone Folding in SiGe SuperlatticesModern epitaxial technologies can produce high quality SimGe„ superlattices, where m isthe number of silicon monolayers and n is the number of germanium monolayers. These su

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CHAPTER 1. INTRODUCTION. LIGHT EMISSION IN SILICON 7

perlattices can be used to converse the indirect band-gap in silicon to the direct band-gap [1,2]. The real periodicity of the lattice is replaced by new periodicity of the superlattice in the growth direction. This results in smaller Brillouin zone with size of ±n/d, whered is the period of the superlattice. For an appropriate d the minimum of conductionband can be folded to the center of the Brillouin zone yielding a quasi-direct band-gap. However, in practice, the strain within the SimGe„ superlattice caused by lattice constant mismatch in Si/Ge systems, plays an important role. Theory has shown that for certain periodicity a direct band-gap can be realized in the SimGe„ superlattice with strain, but the transition probability of radiative recombination is rather low. Another problem is that at room temperature luminescence is quenched due to exciton dissociation. LEDs based on the superlattices have been made but their external quantum efficiency at room temperature is only ~ 10-5 [1].

1.2 Luminescence via AlloyingAnother way of electronic band structure engineering is alloying of germanium with silicon [3]. The band gap of Sii-^Ge* structure varies from 1.15 eV to 0.74 eV depending on the germanium concentration x. The photoluminescence spectra at low temperature can thusbe tuned with the changing of x. However, the luminescence at room temperature is thermally quenched. The Sii-xGe* structures eure usually grown by an epitaxy method on a silicon substrate. Because of the lattice mismatch between Si and Ge the strain within the Sij-xGex layer limits its maximum thickness. When the layer thickness is above the critical thickness, dislocations and other lattice defects are formed. The critical thickness of Sii-xGex layer rapidly decreases with increasing x yielding a very thin absorbing/emittingregions in devices. This problem can be overcome by producing multiple quantum well structure instead of a single layer. Light emission at room temperature has been observed from these structures but their external quantum efficiency is very low (~ 10-7) [2]. SiGe alloys can be used as detectors of infrared radiation.

1.3 Luminescence via ImpuritiesRoom temperature luminescence of silicon can be enhanced, in principle, by introducing isoelectronic impurities. When an electron and a hole are tightly localized in the real space (Δχ —* 0), from the Heisenberg uncertainty principle AxAp > h/2 it follows thatthe particles must be delocalized in the reciprocal space (Δ ρ —* oo). Accordingly, the overlap of the wave functions of localized electron and hole can be large enough to allow radiative recombination in an indirect band-gap semiconductor without participation of a phonon (so called quasi-direct transitions). Moreover, luminescence quenching due to Auger effect is eliminated in isoelectronic impurities because only one electron-hole pair on the isoelectronic impurity is present.

Silicon may be doped indeed with isoelectronic impurities (which have the same number of electrons in valence band as silicon), such as carbon or tin. The isoelectronic


impurities bind excitons which then can recombine radiatively. However, contrary to excellent performance of this mechanism in other semiconductors (e.g. GaP doped with nitrogen), the luminescence efficiency of such bound excitons in Si is weak and decreases with temperature due to the thermal dissociation of excitons and the outset of nonradia- tive processes. Theoretical reason of this is not fully clear.

Second type of impurities used to dope silicon are rare earth elements, particularly Er3+ ions. The mechanism of luminescence in Er doped silicon is different from the previous mechanism. The 4f states in free Er3+ ions are degenerate and the optical transitions are not allowed by the dipole selection rule. However, when introduced to a solid matrix, degeneration is partially removed, the 4f states become mixed, and optical transitions between the first excited state in 4f shell and the ground state may occur. The emission wavelength 1.54 μτη almost does not depend on the surrounding matrix because the 4felectrons are screened from the host matrix by the electrons in outer shells. After the upper 4f state in erbium is excited (by a rather intriguing process) the system can relax radiatively to the ground state.

Many approaches have been made to produce efficient LEDs based on Er-doped silicon working at room temperature [4, 5] and internal efficiency of ~ 10-4 has been achieved. The emission wavelength 1.54 μπι of these LEDs matches the standard wavelength for telecommunications which makes them very interesting for applications.

1.4 Quantum ConfinementObjects having at least one size of the order of several nanometers, such as quantum wells, quantum wires and quantum dots (nanocrystals) are widely studied because of their new physical properties that are different from that of bulk materials. Since 1990, when photoluminescence of porous silicon at room temperature was reported for a first time [6], silicon nanostructures have been investigated as a promising source of light for photonics. Due to quantum confinement the quasi-direct transitions in silicon nanocrystals become allowed and the band-gap energy gets larger with decreasing size of nanocrystals. Room temperature photoluminescence from Si nanocrystals (Si-ncs) has been observed along the whole visible spectrum in dependence of the nanocrystal size and surface passivation. In addition to the spontaneous emission from Si-ncs, optical gain in Si-ncs has also been demonstrated [7]. This is an important step to fabrication of a laser based on silicon.

1.5 Aims of this WorkIn this work we deal with study of photoluminescence from samples with silicon nanocrystals embedded in S1O2 matrix. Due to the refractive index contrast between Si-ncs and S1O2 many of these planar and rib-like samples exhibit waveguiding properties. A peculiar mode structure of emission from the waveguiding samples has been observed. Two theories were proposed to explain the experimental observation: a theory of wavelength- selective guided modes in high-loss waveguides and a theory of leaky modes. The main


objective of this work is to decide which one of these theories is valid. The detailed understanding of the nature of the modes is important for interpretation of the experimental results from the Variable Stripe Length technique.

Chapters 2 and 3 present an introductory background of luminescence of bulk semiconductors, semiconductor nanocrystals, optical gain in semiconductors and waveguiding properties of planar waveguides. Chapters 4, 5, and 6 contain the experimental results on mode emission in planar waveguides with Si-ncs, both experimental and theoretical results on emission in rib waveguides with Si-ncs and experimental results from time-resolved photoluminescence and measurements of optical gain with Variable Stripe Length technique. Chapter 7 concludes the work. At the end of this thesis, articles published by the author are enclosed.

Chapter 2

Luminescence of Semiconductors

KNIHOVNA MAT.-FYZ. FAKULTY Knihovna Fr Zavisny ilyi. odd.)

Ke Kanovu 3 121 16 Praha 2

Luminescence, also called cold light, is defined as non-equilibrium light emission over the blackbody radiation, that lasts at least 10“13 s after the excitation. There are many ways to excite luminescence, e.g. photoluminescence (excited by light), electroluminescence (excited by electrical current), chemoluminescence (excited by chemical reaction), cathodoluminescence (excited by high energy electrons emitted from a cathode impacting on a luminescent material), sonoluminescence (excited by sound waves). The most common type of luminescence, on which we focus in this work, is photoluminescence (PL).

2.1 Bulk Sem iconductorsTo describe luminescence mechanisms in bulk semiconductors we use the band model of solid state [8]. We consider electrons and holes as free particles and the influence of periodical potential of crystal lattice is included in their effective masses m* and m*h. A simple 1-dimensional band structure of a semiconductor is plotted in Fig. 2.1(a). This diagram consists of conduction band, valence band and between them energy gap Eg. After excitation of the semiconductor free carriers in conduction band are created. They relax to lower energy states and then they can recombine radiatively after mean life time Tr with creation of a photon or non-radiatively after mean life time rnr. To describe luminescence we define internal quantum efficiency of luminescence

In order to have a good light emitting material we need rr rnr.There is a big difference between the semiconductors with direct and indirect band-

gap (Fig. 2.1). In optical transitions momentum conservation rule must be fulfilled. The wave number of a photon is fcph = 2π/λ « 1.3 107 m-1 for λ = 500 nm and the wave number of the electron in the 1. Brillouin zone is ke » π/α « 6.3 109 m-1 for lattice constant a — 0.5 nm. Since the wave number of a photon is considerably smaller than the ke of the electron, in E - k diagrams the transitions must be vertical.

10

CHAPTER 2. LUMINESCENCE OF SEMICONDUCTORS 1 1

Figure 2.1: Band structure of one dimensional semiconductor, (a) direct gap, (b) indirect gap. CB and VB stands for conduction and valence band.

In direct band-gap semiconductors the maximum of valence band coincides with the minimum of conduction band in fc-space. Thus direct radiative recombination occurs and the energy of a photon emitted by recombination of a free electron-hole pair is

where h is Planck constant, h = Λ./2π.In indirect band-gap semiconductors the maximum of valence band occurs for different

k than the minimum of conduction band. To satisfy the k conservation rule, the process of free electron-hole pair recombination must be accompanied with absorption or emission of a phonon. The energy of emitted photon is

where ω is frequency of the phonon, -I- stands for absorption and — for emission of the phonon. The probability of this process is low because three particles (an electron, a hole and a phonon) must take part in it. It is a process of higher order than the recombination in direct band-gap semiconductor. In indirect band-gap semiconductors mostly rr » rnr and non-radiative processes are dominant.

An important intrinsic channel of luminescence in semiconductors is radiative recombination of excitons [9, 10]. Exciton is a quasi-particle consisting of an electron and a hole which are attracted by Coulomb interaction. It is a neutral particle that carries energy but not electric charge. The most common types of excitons in semiconductors are excitons with large radius (Wannier excitons) [10]. Solving the problem of energy states of an electron and a hole with Coulomb interaction is similar to the solution of electron states in a hydrogen atom. But there are two differences.

Firstly, contrary to the hydrogen atom, we do not have a light electron in the potential of a heavy proton but the effective masses of the electron and the hole in a semiconductor


are comparable. Thus we have to replace the mass mo of an electron in the hydrogen atom with the reduced mass ττν of the exciton

2.1.1 General Properties of Bulk SiliconSilicon (atomic number 14) crystallizes in diamond structure which consists of two interpenetrating face centered cubic lattices displaced by one quarter of the length of body diagonal [2]. The lattice constant is 0.534 nm. Band structure of silicon can be calculated by empirical pseoudo-potential method [11]. The maximum of valence band is in the centre of the Brillouin zone (point Γ), while the absolute minimum of conduction band is near point X along the (001) direction. Thus, silicon is an indirect band-gap semiconductor. Its energy gap is 1.12 eV at the temperature of 300 K. In order to fulfill the momentum conservation principle a phonon must participate in the radiative recombination process. A typical mean time of this process is of the order of milliseconds [2]. Competitive non- radiative processes play an important role in silicon and mostly have considerably shorter lifetimes than the radiative processes (typically 1 ns). From equation (2.1) we see that the

The second difference is that the electron and the hole in semiconductor are not in vacuum but in an environment with relative dielectric constant ετ. Considering these two differences, the radius r* of Wannier exciton can be calculated using modified solution of the hydrogen atom

where a s « 0.05 nm is the Bohr radius and n is the quantum number. Typical values in semiconductors are er « 10, ττν/τηο « 0.1 and from equation (2.5) we have for the ground state (n = 1) r* « ΙΟΟαβ « 5 nm, which is several times larger than the lattice constant.

The energy spectrum E* of the exciton states can be calculated in a similar way

where EH = —13.6 eV is the binding energy of the electron in the hydrogen atom. Typical values of binding energy of the exciton from equation (2.6) axe of the order of 10 meV. Excitons exist in bulk semiconductors only at low temperatures when they are not thermally dissociated. The presence of excitons in a direct band-gap semiconductor is manifested in the absorption spectrum that contains exciton lines at the energies Eg — E* below the absorption edge. These lines correspond to creations of excitons in states with energies given by equation (2.6). However, the luminescence of excitons is a more complicated processes and cannot be treated analogically to the absorption. The exciton-photon interaction must be taken to account and also non-phonon and phonon-assisted transitions are possible. More detailed study of exciton luminescence in bulk semiconductors can be found [9].

CHAPTER 2. LUMINESCENCE OF SEMICONDUCTORS 13

Figure 2.2: Examples of Auger processes in semiconductors, (a) eeh process, electron recombines with a hole and the energy is carried out by a second electron, (b) ehh process, electron recombines with a hole and energy is carried out by a second hole.

internal quantum efficiency of luminescence of bulk silicon is of the order of 10-6 which is very poor. We will now mention some non-radiative processes occurring in silicon.

Shockley-Read-Hall recombination [3] takes place in silicon which has deep trap states in band-gap caused by impurities. An electron and a hole can be captured on these states yielding recombination process. The lifetime depends on the concentration of deep states, its typical value is of the order of nanoseconds.

Recombination on defects and surface states depends on the quality of samples, good surface passivation can avoid this process.

Very important non-radiative process in silicon is Auger recombination where the energy of the electron-hole pair is not given to the photon but it is transferred to the third particle in the form of kinetic energy (Fig. 2.2). We distinguish eeh process, where the energy is transferred to a second electron and ehh process, where the energy is carried off by a hole. When the concentrations of excited electrons and holes are equal (n = p) the Auger recombination can be described by a rate equation

where G is the generation rate and C ,t is the Auger constant. Furthermore, we define the Auger decay time rA as

I he Auger recombination rate 1/r^ is proportional to the concentration of excited electrons, thus it is a dominant process in highly excited and/or heavily doped samples.

Another phenomenon which limits silicon for light amplification is the free carrier absorption [3J. In this process photons are absorbed by excited electrons instead of electrons


in the valence band. Similar process can occur for holes in the valence band. It yields a decrease of population inversion and an increase of losses suffered by the light beam. The free carrier absorption coefficient is proportional to the free carrier density and the square of the wavelength. It is a significant process that limits light amplification in bulk silicon.

2.2 Semiconductor NanocrystalsSemiconductor nanocrystals are objects between bulk crystals and simple molecules. They have different physical properties from bulk crystals due to the localization in space. There are several methods to theoretically describe electronic and optical properties of nanocrystals [2]. The most common methods are: effective mass approximation (EMA), Hartree-Fock calculations, empirical tight-binding, empirical pseudo-potential method, and first-principle techniques such as density functional theory. In this section we mention the main properties of nanocrystals resulting from their dimensions.

2.2.1 Cubic Quantum DotIn order to study optical properties of nanocrystals we assume a model of a cubic quantum dot which reflects the most important properties of nanocrystals. In this model to describe the electronic states in nanocrystals, we use effective mass approximation [2, 12]. We suppose that the dimension of the nanocrystal is much larger than the lattice constant. The influence of periodical potential on the electron and hole states is included in their effective masses m* and m*h. Depending on the relation between the dimension a of the nanocrystal and the bulk exciton Bohr radius τχ we distinguish three confinement regimes [13]:

Strong confinement: a <£. r* . The Coulomb interaction between electrons and holes can be neglected and the particles can be described independently. A model of a cubic nanocrystal in strong confinement regime is described below.

Weak confinement: a rx . The Coulomb interaction between the electron and the hole is significant. The problem reduces to solving Schrödinger equation for an exciton confined in a nanocrystal.

Intermediate regime: a « r* lies between the strong and the weak confinement. This problem requires numerical solution.

We now examine a cubic nanocrystal in strong confinement regime. We regard an electron and a hole as independent particles. Their motion is restricted by external potential V(r). Neglecting Coulomb interaction between the electron and the hole, the Hamiltonian of the electron has the form

where r = (x, y, z) is the position vector of the electron. To describe a cubic nanocrystal,


where Eg is the bulk band-gap. It is important to point out that Eg ° is proportional to 1/a2, thus the energy gap gets larger with decreasing size of the nanocrystal. In contrast to the energy band structure in bulk semiconductors the electron states in nanocrystals become quantized.

it follows that when we restrict the particle in the real space, its wave function must spread in the k—space (Fig. 2.3). Thus the overlap of the wave functions of the electron and the hole in a nanocrystal made of an indirect band-gap semiconductor is not negligible and quasi-direct transitions are possible. This effect significantly increases the efficiency of luminescence of nanocrystals.

As for the non-radiative processes, the quantum confinement significantly affects the Auger rates in nanocrystals. In a nanocrystal the carriers are confined in space so the Coulomb interaction between them is enhanced leading to increased Auger rates. On the contrary, the discrete electronic states in nanocrystals complicate satisfying the energy conservation rule and a participation of a phonon in the Auger process is often required to conserve energy. A detailed experimental study of the Auger processes in the CdSe quantum dots was made [14]. It has been demonstrated that the Auger decay time ta is proportional to R3 (R is the radius of the nanocrystal). However, the theory of Auger

2.2.2 Breakdown of the k-conservation RuleThe restriction in space has a very important influence on the luminescence of semiconductors with indirect band-gap. FVom Heisenberg’s relation


Figure 2.3: Quantum confinement effect in a semiconductor with indirect band-gap. Quasi- direct transitions are possible.

recombination in bulk semiconductors predicts the Ä6 dependence of the ta (see equation(2.8) and note that n ~ R~3 and CU is independent of R in bulk material). The observed dependence of ta demands the Auger constant to be size dependent: Ca ~ Ä3· The Auger recombination rate 1/ta increases as R~3 with decreasing radius R of the nanocrystal. However, in indirect band-gap nanocrystals, such as silicon nanocrystals, when the size is decreased under certain value, the quasi-direct non-phonon optical transitions become important and can possibly prevail over the Auger recombination [15].

2.2.3 Role of the Surface of NanocrystalsUnlike bulk semiconductors, where we can neglect the surface states, in nanocrystals the proportion surface/volume is not negligible. The smaller the nanocrystal is, the more important the surface states are. On the silicon nanocrystal surface there can be dangling Si bonds or there can be various types of chemical bonds (e.g. Si-H, Si-OH, Si-O-Si and Si=0). The forming of the bonds on nanocrystal surface depends on its preparation (e.g. surface passivation by annealing or oxidation) and on the matrix in which nanocrystals are embedded.

Porous silicon samples exposed in air are passivated forming S i=0 bonds [16]. The presence of S i=0 bonds forms energy states in band-gap and the recombination mechanism is affected by trapped electrons. The states in band-gap cause red-shift of photoluminescence spectrum in small nanocrystals (smaller than ~ 3 nm) compared to photoluminescence of these crystals before oxidation. H-passivated nanocrystals show blue shift of photoluminescence with decreasing nanocrystal size, which agrees with theoretical band-gap broadening. However, oxidized nanocrystals exhibit luminescence which practically does not depend on the crystallite’s size [17]. This can be explained assuming the fact that the excited electrons relax to the lower states associated with S i=0 bonds and after that they recombine radiatively.

The passivation of the sample surface enhances photoluminescence because non-radiative


centres on the surface are reduced. The states caused by bonds on the surface are important for light amplification and a 4-level model involving surface states has been developed [18].

2.2.4 Luminescence Time Decay of NanocrystalsWhen an isolated nanocrystal is excited one would expect a single exponential decay shape from the exciton recombination. However, in porous silicon and in the systems with Si-ncs in S1O2 matrix the time decay of photoluminescence does not follow a single exponential function but it can be described with a stretched exponential function [19]

I(t) = Io exp { - { t / τγ ), (2.15)

where Io is the initial PL intensity, r is the lifetime and ß < 1 is the dispersion factor which represents a broad distribution of lifetimes. Both r and ß depend on the wavelength of the emitted light. A number of measurements have indicated that the recombination rate is faster at shorter wavelengths (it means smaller r) and slower at longer wavelengths [19, 20]. The stretched exponential behaviour reflects the complexity of mechanisms inside the Si-ncs in the matrix. Pavesi [20] has proposed a model based on migration of excitons among the nanocrystals in order to explain the observed time decay of photoluminescence. This model considers a disordered system of nanocrystals with different transition energies and different mutual distances. The hopping of excitons between the nanocrystals yields a random distribution of times in which the exciton reaches the nanocrystal in which it recombines. This process results in ’stretching’ of the decay line shape and introduces factor ß < 1.

2.3 Optical Gain

2.3.1 General ConsiderationsIt is well known that electromagnetic wave can interact with matter in three ways: absorption, spontaneous emission and stimulated emission [21]. In the process of stimulated emission light is amplified when travelling through the material. In this case when an electron is in the upper level and an electromagnetic wave with appropriate frequency is incident on the material the electron can undergo a transition to the lower level by emitting a photon with energy equal to the energy difference between the electron initial and final state. For quantitative description of stimulated emission we use the gain coefficient g(A) which stands for the negative absorption coefficient a of the material. It can be expressed by

g = —a = <7 N, (2.16)

where a is the cross-section of stimulated emission and N is the population inversion in the material; for non-degenerate energy levels it is the difference of the populations of the

CHAPTER 2. LUMINESCENCE OF SEMICONDUCTORS

Figure 2.4 : Sketch of (a) the VSL technique, sample is excited with a stripe, (b) the SES technique, sample is excited with a moving spot.

where /o(A) is the intensity of incident beam. Because material gain depends on the wavelength the spectrum of amplified light is narrower than its initial spectrum.

Furthermore, when a strong electromagnetic wave is present in the material the wave tends to deplete population inversion and to equalize the populations of the upper and the lower level. This process results in a decrease of gain coefficient with increasing intensity of light. It is known as saturation and is fully described in [21].

2.3.2 Variable Stripe Length TechniqueOptical gain in semiconductors can be measured by a Variable Stripe Length (VSL) technique proposed by K. L. Shaklee in 1971 [22]. In this method a sample is excited with a homogeneous narrow stripe made of a laser beam that passed through a cylindrical lens (Fig. 2.4(a)). The length of the excitation stripe can be varied by a moving shield, The stripe provides a pump of the sample and can build up population inversion. Then the light emitted by spontaneous emission in the sample can be amplified by acts of stimulated emission when passing through the pumped stripe. At the output the amplified spontaneous emission (ASE) from the sample edge is measured as a function of the stripe length 1. For a theoretical description of this model we assume that the width of the stripe is infinitely small. From the measurement we can extract the net modai gain g which is defined as a relative change of light intensity I(x. A) on a distance d.r along the stripe [23]

18

upper and the lower level involved in the process. Generally, gain coefficient depends on wavelength.

When the gain is present in the material and a probe beam from an external source passes through the material, its intensity rises exponentially with the distance x travelled by the wave in the material following the formula


This formula can be used to evaluate the gain spectrum by measuring I a s e for two stripe lengths.

However, measurement of optical gain with the VSL method is not straightforward and, in particular, in case of low values of the gain coefficient g(X), it can be accompanied by several artifacts (which will be discussed in the next paragraph). It is desirable to provide complementary Shifting Excitation Spot (SES) measurement (paragraph 2.3.4) to take control over some of them.

2.3.3 Artifacts of the VSL TechniqueOriginally the VSL method was proposed to measure optical gain in high-gain semiconductors. For example, net gain of 105 cm- 1 was reported in GaN using this method [24]. However, when the VSL method is applied to a system with low gain such as silicon nanocrystals, the interpretation of the measured spectra becomes rather uncertain and a special attention must be paid to distinguish several unwanted effects from real gain.

Firstly, the quality o f the excitation stripe must be perfect. It means that the distribution of light intensity along the stripe must be homogeneous (which can be a problem for Gaussian beams) and the stripe has to be theoretically ‘infinitely’ narrow. Even when the profile of the laser beam is homogeneous (e.g. for fin excimer laser or a gaussian beam passed through a homogenizer) the Fresnel diffraction occurs at the edge of the moving shield yielding creation of maxima and minima in the intensity profile of the excitation stripe [25]. The increase of intensity of the pumping beam due to diffraction results in

where gm is the material gain (negative absorption coefficient) and 7 stands for the total propagation losses. We assume that g does not depend on the position x along the stripe. The change of light intensity on an infinitesimal distance d i is then

where /o is the intensity of spontaneous emission per unit length that does not depend on x. By solving equation (2.19) we obtain the measured amplified spontaneous emission signal Iase as a function of the stripe length I [23]

This equation enables us to obtain the value of g by fitting the measured ASE signal. But when increasing I above certain value the saturation of gain appears and equation (2 .2 0 ) is not applicable any more. Therefore only the onset of the ASE signal can be fitted. We can also calculate the gain spectrum g{A) by applying the equation (2.20) for two stripe lengths I and 21. After dividing I a s e [20 by I a s e (I) and performing simple calculation we get


an increase of the ASE intensity which is not due to presence of a gain in the material. The Fresnel diffraction can be detected directly by measuring the intensity at the pump wavelength instead of the ASE wavelength. The region of the sharp increase of the signal due to diffraction has to be discarded from the data for further processing.

Requirement of homogeneity is also imposed on the sample to ensure the constant pumping density. Sample also has to be perpendicular to the pumping beam.

Second very important demand for the adequate performing of the VSL method is the constant coupling of light emitted from the sample (ASE) to the detection system, i.e.the coupling efficiency must not depend on the length of the excitation stripe. When the focal point of the detection lens is not at the edge of the sample but inside the sample the light is coupled more effectively when the stripe reaches the focal plane. This may result in a false-gain increase of the measured signal. The effect of non-constant coupling can be revealed by the SES technique (see next paragraph).

The matter of constant coupling is especially important in samples that form planar waveguides, e.g. Si-nc layers on the silica substrate prepared by ion implantation or chemical vapour deposition. The waveguiding properties of the planar waveguides (whichwill be discussed in detail in Chapter 3) strongly influence the spectral shape of emitted light and the observed gain behaviour. When the light is guided inside the layer it has certain directional properties and it is emitted from the sample edge at a certain solid angle. Therefore, how much of the light will be coupled to the detection system depends on the numerical aperture of the collecting lens. In order to get correct data one has to ensure the constant coupling or introduce a coupling coefficient [26] and involve it in the VSL data processing. In this case performing the SES measurement is essential.

Another important feature of some waveguide samples is leaking of the light into the substrate (see section 3.3). Apart from the amount of light guided in the waveguide there is also a fraction of light that can escape from the Si-nc layer after severed reflections. This leaked light further propagates in the substrate and is not amplified any more. However, it is not clear whether it has been amplified when it was inside the Si-nc core and how the leaky modes influence the VSL data. Some numerical calculation on this phenomenon have been made [27] showing that fitting the data by equation (2.20) may not be accurate and rather complicated fitting procedure is needed to obtain valid results. This phenomenon still needs both experimental and theoretical investigation.

2.3.4 Shifting Excitation Spot TechniqueIn order to reveal the artifacts caused by inhomogeneity of the stripe intensity profile and non-constant coupling to the detection system a complementary method called Shifting Excitation Spot (SES) method has been proposed [26]. The SES method is a modification of the VSL method in which the moving shield is replaced by a moving narrow slit and thus only a small rectangular spot of the sample is excited (Fig. 2.4(b)). The excitation spot moves along the x axis. Since there is no pumping (except the small spot) the signalemitted from Si-ncs will be attenuated when propagating through the sample and the measured output intensity I s e s { x ) decays with increasing the distance x from the sample


where α(λ) stands for residual attenuation that is surmounted by gain in the VSL setup. Thus for a homogeneous sample with homogeneous pumping density and with constant coupling to the detection system the SES signal should be decreasing exponentially. The fluctuation of the SES signal reveals the fluctuation of the pumping intensity or the sample properties. Even an increase in the SES signal is possible when the coupling is not constant.

To compare the SES and VSL results the SES data have to be numerically integrated for x from 0 to I. Integration of equation (2.22) from 0 to Z yields

Thus, for a situation without artifacts, the integrated SES curve should have a slightly concave shape. If there is no net gain present in the material also the VSL curve should be the same as the integrated SES curve. However, in case where some artifacts are present, a superlinear increase both in the VSL and in integrated SES curve can be observed. But it means no gain, only an unwanted effect. For net gain to be present the integrated SES curve must lie under the VSL curve.

In order to confirm the presence of optical gain in a certain material it is necessary to provide sufficient number of measurements under different conditions, e.g. with increasing pumping intensity, for different detection wavelengths, time-resolved measurements. It is desirable to observe threshold behaviour of the dependence of the output intensity on the pumping intensity, and narrowing of the measured spectrum with increasing either the length of the stripe or the excitation intensity. The second can be a challenging problem for inhomogeneously broadened systems such as Si-ncs.

2.3.5 Optical Gain in Silicon NanocrystalsAs it has already been shown the quantum efficiency of luminescence of silicon nanocrystals is appreciably higher than that of bulk silicon. Luminescence from silicon nanocrystals can be observed at room temperature, however, providing stimulated emission on nanocrystals is a big challenge. Competing non-radiative processes, particularly the Auger processes, are present in Si-nc systems and may deplete the population inversion and thus prevent the system from laser action. In order to achieve optical amplification the process of stimulated emission must be fast enough to take place before the Auger processes. Despite many complications the values of net optical gain of the order of 10 cm-1 have been reported by several groups in different types of Si-nc samples using the VSL method. Net gain has been measured in porous silicon embedded in a sol-gel matrix [28, 29], in Si-ncs prepared by high energy Si+ ion implantation into fused silica [7, 29], in plasma-enhanced chemical vapour deposited Si-ncs [18, 30], in Si-ncs prepared by reactive Si deposition [31].


From these measurements it is evident that the process of stimulated emission in Sines is fast, it is present in the material on a nanosecond time scale after the excitation. Furthermore, the gain spectrum is shifted to shorter wavelengths with respect to the photoluminescence spectrum. The maximum gain values were obtained for wavelengths in the range of 600 — 800 nm [7, 18, 28, 29, 30]. The observation of optical gain depends on the balance between gain cross-section in Si-ncs, propagation losses and the rate of non-radiative Auger processes.

Chapter 3

Asymmetrical Planar Optical Waveguide

Many samples containing silicon nanocrystals are made - sometimes intentionally, sometimes unintentionally - in the form of optical planar waveguides. The waveguiding properties of the samples are important in measurements in which signal is detected from the sample edge (e.g. VSL technique [22]). Modes of the waveguide can create artifacts in measurements so fully understanding of their origin is necessary for correct interpretation of measured results. Moreover, such modes are interesting themselves in view of their potential applications in silicon photonics.

In the samples made in form of planar waveguides a surprising spectral shape was observed when the luminescence spectrum was detected from the sample edge [32]. This spectrum is plotted with a red line in Fig. 3.1. In comparison with the non-guided broad spectrum (black line in Fig. 3.1) the spectrum from the edge contains two narrow peaks. In order to explain the origin of the peaks we invoke modes of planar asymmetrical waveguides in this Chapter. We illustrate the standard model of guided modes and we introduce a model of leaky modes which are usually treated as parasitic phenomenon but in our case they play an important role.

3.1 Guided M odesLet us consider an asymmetrical planar optical waveguide made of core of width d with refractive index nc, prepared on a substrate with refractive index na (Fig. 3.2). The refractive index of the cladding layer is n„. We will describe the guided modes of the waveguide assuming plane uniform waves proportional to e‘(*r-wt) that experience total internal reflections on core-substrate and core-cladding boundaries. It means, that conditions

23

must be fulfilled. In order to create a self-consistent field distribution inside the core, the phase-shift that the wave undertakes when travelling from point A to C (see Fig. 3.2)

CHAPTER 3. ASYMMETRICAL PLANAR OPTICAL WAVEGUIDE 24

w avelength (n m )

Figure 3.1 : Upper panel - a sketch of a sample and PL detection from the sample edge and non-guided PL. Lower panel PL spectra of the sample prepared by ion implantation with the fluence of 5 x 1017 cm- 2 . Black line is non-guided spectrum, red line is detected from the sample edge.

where ω is the angular frequency of the wave, and are the phase-shifts obtained by total internal reflection on the core-cladding and the core-substrate boundaries, respectively. They depend on the polarization of the wave. We distinguish two types of guided modes: T£-modes for which the vector of electric field is perpendicular to the plane of incidence, and T M-modes for which the vector of magnetic field is perpendicular to the plane of incidence. The phase-shifts and are related to reflection coefficients

Figure 3.2: Asymmetrical planar optical waveguide.

must be an integer multiple of 2π. This reflects the phase-matching condition


In the substrate and cladding layers the wave of guided modes is an evanescent wave and the transverse components (ka±) of the wave vectors are complex. We denote the real quantities — ik,± and —ikax as attenuation constants. We introduce quantities v and w as products of the core thickness d and the transverse attenuation constants in the substrate and the cladding layers, respectively

by Tea = e llfica and ra = e '*et. From Fresnel equations we have for the core-cladding boundary

analogically for the core-substrate boundary. To solve equation (3.2) we introduce dimen- sionless quantity u as a product of the core thickness d and the transverse component kcX of the wave vector in the core

for TM modes. Equations (3.7) and (3.8) are transcendental equations, thus they cannot be solved analytically and their solution is rather complicated. To demonstrate the character of the solution we will focus on weakly guiding waveguide for which the equations become simpler [33].

In a weakly guiding waveguide the refractive index of the core is only slightly larger than the refractive index of the substrate. They both are much larger than the refractive index n0 of the cladding which is mostly equal to 1. For a guided mode of a weakly guiding waveguide the angle Θ remains quite large because it has to be greater than the critical angle on the core-substrate boundary. It means that the transverse constant u remains quite small (u kcd). The longitudinal component of the wave vector k\\ = kc sin 6 which is the same in the core, substrate and cladding layers may have values between kt and kc. Since kt is only slightly smaller than kc, the attenuation constant v in the substrate layer must also remain small. But the wave vector in the cladding layer is considerably smaller than /sy, hence transverse attenuation parameter w is large compared to u and v. The inequality


Figure 3.3: Graphical solution of equation for guided modes in weakly guiding waveguide.

is, so called, generalized frequency parameter of the asymmetrical waveguide. The condition (3.11) is plotted as a circle in Fig. 3.3. The intersections of this circle with curves displaying the equation (3.10) represent the mode solutions for weakly guiding waveguide. Since T E and T M modes axe degenerate, each intersection represents two polarization resolved modes. From Fig. 3.3 it is clear, that for V < π/2 there are no guided modes in the asymmetrical waveguide. When the value of V is increased (e.g. by increasing frequency) the number of modes increases. When the generalized frequency exceeds values

reflects the relations between refractive indices in a weakly guiding asymmetrical planar waveguide.

Taking the tangent of equations (3.7) and (3.8) and taking into consideration inequality (3.9) we get a simplified phase-matching condition

Two equations (3.7) and (3.8) reduced to only one equation (3.10), it means that the T E and T M modes are degenerate for weakly guiding waveguides. Equation (3.10) can be solved graphically, υ as a function of u is plotted in Fig. 3.3. Note that from equations (3.4) and (3.5), u and v must also satisfy a condition

where

two more modes TEm and TM m appear (m has the same value as in equation (3.2)). The situation described by equation (3.13) is called cut-off. When a new mode originates at the cut-off, the wave propagates with longitudinal wave vector k\\ = k„, therefore t; = 0 and the wave extends infinitely wide into the substrate [33]. The angle Θ is equal to the


critical angle on the core-substrate boundary. When increasing parameter V, the mode becomes more localized, it means v > 0, k\\ increases from ka to kc and angle Θ gets larger.

Let us return to the general planar waveguide (not weakly guiding). In this case equations (3.7) and (3.8) for TE and TM have to be solved. The degeneracy is broken and we get two values V£E and V ™ for cut-off. The cut-off is characterized by v = 0, sin0 = ns/nc and Vm = u. Using these conditions we get from equations (3.7) and (3.8) the values of V for cut-off:

Note that because n\/n\ > 1 the condition V£E < V ™ is valid for every m. When we increase frequency from zero to the cut-off frequency so that V achieves Vq E the first mode TEq starts to propagate and the waveguide is in a single-mode regime. Further increasing of V leads to building up of the other modes (TMq, TE\, TM\...). The waveguide guides all wavelengths that are shorter than the cut-off wavelength.

3.2 High-Loss WaveguideTo explain the spectral shape in Fig. 3.1 Khriachtchev et al. [34, 35] introduced a theory of wavelength-selective guiding in high-loss asymmetrical waveguide. According to this theory the spectrum of guided light contains narrow peaks because of the change of mode localization as a function of the generalized frequency (3.12). An essential condition of this theory is that the losses in the core are much larger than in the substrate. Modes that start to propagate at the cut-off when V = V£E (V£M) are most delocalized. They propagate mostly in the optically transparent substrate, thus they experience smaller losses. Modes far away above cut-off are more localized in the core and thus suffer higher losses. This model supposes that only the modes just above cut-off are transmitted by the waveguide. They propagate at the angle Θ close to but higher than the critical angle on the core-substrate boundary. The modes are TE/TM split because the waveguide is not weakly-guiding.

However, this model cannot describe the narrow shape of the modes.

3.3 Leaky ModesSecond model proposed to explain the narrow shape of measured spectra has been the model of leaky modes proposed by our Prague group [36]. Leaky modes can occur only in asymmetrical waveguides and they are not guided modes. They suffer total internal reflection at the core-cladding boundary but at the core-substrate boundary they are


Figure 3.4: Left panel - leaky modes and guided modes in asymmetrical planar waveguide. Right panel - amplitude reflection coefficients r and phase-shifts φ on a planar boundary in dependence on the angle of incidence 0, arrow G labels the position of angle Θ of the guided modes just above cut-off, arrow L labels the position of angle Θ of the leaky modes.

incident at angle Θ close to but smaller than the critical angle, thus they leak into the substrate (see left panel of Fig. 3.4). This is expressed by a condition

In the right panel of Fig. 3.4 reflection coefficients and phase-shifts on a planar boundary according to the Fresnel equations are plotted. The difference between the guided and the leaky modes is depicted by arrows G (for guided modes) and L (for leaky modes).

In order to calculate the spectral shape of leaky modes a model based on wave optics was developed [37]. This model assumes a light emitting nanocrystal inside the waveguide core coupled to the electro-magnetic field in the waveguide. Light inside the core suffers losses by scattering and absorption which are described by coefficient of losses 7 . The calculation of the leaky mode intensity is similar to the calculation of the Fabry-Perot resonator with the source of light inside the core. The intensity of the leaky modes depending on the propagation angle Θ is given by

where r m , r „ are reflection coefficients on the core-cladding and the core-substrate boundary and / o ( A ) is the intrinsic spectrum of nanocrystal radiation. For a given angle Θ equation (3.17) has maxima for certain wavelengths and since τα is close to unity (see right panel of Fig. 3.4), the spectrum contains narrow peaks. The peaks are polarization resolved because the reflection coefficients (their phase φ) depend on the polarization of the wave ( T E or T M ) .

When the modes leave the core they propagate along the core-substrate boundary where they suffer considerably smaller losses and they are not coupled to the field in the core any more. They leave the waveguide a t nonzero but small angle a (with respect to the waveguide plane, Fig. 4.4(b)) which is related to the angle Θ inside the core by


valid for angles Θ < arcsin (na/ nc). The spectral position of the peaks depends on the angle a.

3.4 M atrix FormulationThe profile of the refractive index in many samples is not a step-like function but it is a continuous function (e.g. a gaussian curve). To compute leaky modes in this structure transfer matrix method (described in detail in [38]) was used by T. Ostatnický et al. [37].

Using this method the waveguide core is cut into layers with constant refractive index inside each layer and the core is treated like a multilayer structure bounded by two homogeneous semiinfinite layers (cladding and substrate layer, see Fig. 3.5). Similarly like in planar waveguides we have two independent waves - T E and T M - propagating in the multilayer. We denote the axis perpendicular to the layers as the y axis and the axis parallel to the direction of propagation of light in the waveguide as z axis (Fig. 3.5). Each layer of width h and with refractive index n< (i = 1 ,2 , . . . , N) is characterized by an unimodular 2 x 2 transfer matrix M,(/i) that connects the amplitudes Q< of the electric and the magnetic field of the wave at the bottom border (y, = ih) of the layer with the amplitudes Qv_i of the field at the upper border (y,-\ = (i — l)/i) of the layer:

Both Mi and Q, depend on the polarization of the wave. For T E wave U(y) is the amplitude of the electric field (which has only one component for T E wave) and V(y) is the amplitude of the «-component of the magnetic field. For T M wave U(y) is the amplitude of the only one component of the magnetic field and V(y) is the amplitude of the «-component of the electric field.

Transfer matrix of a homogeneous layer with refractive index Uj and thickness h is

where ko is the wave vector in vacuum, 0, is the angle between the ray and the y axis in the i-th layer (Fig. 3.5) and p* is a parameter that depends on the polarization of the wave, its values are


Figure 3.5: Multilayer structure of N layers between two semiinfinite layers with refractive indices na and ne, a ray propagating through the layers is indicated.

where and μ* are the relative dielectric constant and the relative magnetic permeability of the i-th layer, respectively.

To compute spectrum of the leaky modes from equation (3.17) we need to determine from the transfer matrix formalism the reflection coefficients rm at y = 0 and rM at y = d. To compute Γω we assume a plane wave propagating from the M -th layer with the highest refractive index n « to the core-cladding boundary. The transfer matrix M of M layers is

Knowing the transfer matrix M the reflection coefficient can be calculated according

where pa and Pm are parameters determined by equation (3.22) with εΓ and μ,, taken for the cladding layer and for the M th layer, respectively. Calculation of the reflection coefficient r „ is similar to the calculation of rm.

to [38]

KNIHOVNA MAT -FYZ. FAKULTY Knihovna Fr lavisky ttyz. odd.)

Ke Kartovú 3 121 16 Praha 2

Chapter 4

Results: Planar Waveguides withSi-ncs

4.1 SamplesIn this work we study samples (waveguides made from luminescent Si nanocrystals) prepared by two different methods: ion implantation and reactive Si deposition.

4.1.1 Samples Prepared by Si+ Ion ImplantationOur samples were prepared at Australian National University in Camberra by implantation of Si+ ions into 1 mm thick synthetic silica slab (Infrasil) with polished edges [32]. The energy of ions was 400 keV and four implantation fluences of 3, 4, 5 and 6 x 1017 cm-2 were performed. For future usage we label these samples as sample 3 x 1017 cm-2 , sample4 x 1017 cm-2, sample 5 x 1017 cm-2 and sample 6 x 1017 cm-2. Peak excess Si concentration was up to 26 at.% Si. After implantation samples were annealed for 1 hour in N2 atmosphere at temperature of 1100 °C to form Si nanocrystals. Further annealing for 1 hour in forming gas (95% N2l 5% H2) at 500 °C was performed to passivate the nanocrystal surface, and thus enhance photoluminescence intensity. The presence of nanocrystals in samples was determined by Raman scattering [39]. From position and half-width of the Raman peak the sizes of nanocrystals were estimated to be in the range of 4 — 6 nm.

The Si nanocrystals have larger refractive index than the substrate and so they form a planar optical waveguide. The profile of the refractive index can be extracted from fitting the transmission spectra [40]. For our samples the transmission spectra were measured by K. Kusová and fitted by T. Ostatnický with asymmetric Gaussian curves. The refractive index profiles are plotted in Fig. 4.1. The position of the maximum refractive index is 0.63 μτα below the surface for all samples and the width of the gaussian curves is between0.12 and 0.29 μπι. The refractive index of the substrate is 1.455 and the maximum refractive index is 1.732 for the sample 3 x 1017 cm-2, 1.801 for the sample 4 x 1017 cm“ 2, 1.867 for the sample 5 x 1017 cm-2 and 1.975 for the sample 6 x 1017 cm-2.

31

CHAPTER 4. RESULTS: PLANAR WAVEGUIDES WITH SI-NCS 32

Figure 4.1: Profiles of refractive index for samples 3, 4, 5 and 6 x 1017 cm 2.

4.1.2 Samples Prepared by Reactive DepositionSecond type of samples was prepared at Helsinki University of Technology by reactive Si deposition onto 1 mm thick silica plate [34, 35]. As Si and O sources electron beam evaporation and radio frequency plasma cells were used. After deposition the samples were annealed in N2 ambient at 1100 °C for 1 hour to form nanocrystals. The presence of nanocrystals was demonstrated by Raman scattering and the nanocrystal diameters were estimated to be 3 — 4 nm [35].

The deposition conditions were asymmetrical (there was a 30° angle between the Si beam and the substrate) which formed a gradient of concentration of Si along one direction in the sample. For future usage we label this sample as a gradient sample. The photograph of the gradient sample is in the left panel of Fig. 4.2. From the preparation conditions of the sample we suppose that the Si nanocrystals form a layer of thickness d on the substrate with a constant refractive index nc. However, both d and nc depend on the position x on the sample along the direction of the gradient. Measurements were performed on different positions on the sample and for each measurement we recorded the position x of the excitation spot on the sample from line perpendicular to gradient. With increasing x the concentration of Si and the thickness of the nanocrystlal layer get larger.

The optical thickness ncd of the sample can be extracted from the spacing between the interference maxima in the transmission spectra. The interference maximum in the transmission spectrum occurs when the phase-shift φ = 4nncd / \ obtained by the wave after passing through the nanocrystal layer forth and back is an integer multiple of 2tt. From this condition of constructive interference we get for the optical thickness

where Δ(1/λ) is the spacing between two adjacent maxima in the transmission spectrum.


100

Figure 4.2: Left panel photograph of the gradient sample, gradient of the sample properties is along the x axis, positive and negative values of x are indicated in the figure. Right panel - transmission spectra of the gradient sample for x = — 3 mm, 3 mm and 10 mm, inset shows the optical thickness ncd.

Transmission spectra of the gradient sample at different positions x on the sample were measured with spectrometer Shirnadzu UV3101 (PC). They are plotted in the right panel of Fig. 4.2. Inset shows optical thickness at different positions on the gradient sample calculated using equation (4.1).

4.2 Experimental SetupThe experimental setup for photoluminescence measurements is sketched in the left panel of Fig. 4.3.

Photoluminescence of the samples was excited by the 442 nm line of cw HeCd laser. The profile of the laser beam is in the right panel of Fig. 4.3. The diameter of the excitation spot was approximately 2 mm and the power density of the excitation beam at the sample was ~ 0.5 W.cm-2. In most measurements the laser beam was not focused. Samples were excited on their surface and to facilitate the collection of luminescence light, an optical cable Oriel (thickness of 2 nun, numerical aperture of 0.22) was placed close to the sample. Luminescence signal was detected in two geometries: transverse geometry - signal detected from the surface of the sample, and waveguiding geometry - signal detected from the sample edge (Fig. 4.4). A glass filter was placed in front of the cable to suppress scattered light from the laser beam. In some measurements also polarization filter was used. Luminescence signal was further analysed with monochromator Jobin Yvon (concave holographic grating. 600 grooves/mm, focal length 20 cm, linear dispersion 8 nm/mm) and detected with CCD (Andor, cooled to —40 °C). All measurements were performed at room temperature.

The measuring system (e.g. the transmission of the optical cable, the efficiency of the


Figure 4.3: Left panel experimental setup for the phot.oluminescence measurement. Right panel - profile of the HeCd laser beam.

Figure 4.4: Sketch of the detection geometry, (a) transverse geometry, (b) waveguiding geometry.

grating and of CCD) affects the shape of measured spectra. Therefore we had measured spectrum of a known source ( “blackbody radiation” ) and compared it with its theoretical shape; in this way we obtained correction curves which we have been using to correct measured spectra. All experimental results presented in this work were thus corrected for the system response.

4.3 Light Emission from the Samples Prepared by Si+ Ion Im plantation

4.3.1 M ode Structure of the EmissionNon-guided photoluminescence spectra of the samples measured in the transverse geometry are plotted in Fig. 4.5. The full width at half maximum (FWHM) of the spectra is large (~ 200 nm) due to inhomogeneous broadening (there are nanocrystals of different sizes in the sample). Spectra are fitted by Gaussian curves, parameters of the curves are presented in the figure. The maximum of photoluminescence signal is at 850 — 860 nm and no structures in the spectra are observed.

The shape of measured spectra changes dramatically when the signal is detected in the waveguiding geometry (Fig. 4.6). Except the sample 3 x 1017 cm-2, we observe two narrow polarization resolved peaks (TE and T M peak). Their FWHM is ~ 15 nm only


Figure 4.5: PL spectra measured from the surface of samples 3, 4, 5 and 6 x 1017 cm-2, red lines are gaussian fits, xq is the centre of gaussian curve, a is the standard deviation.

and their spectral position changes depending on the implantation fluence of the samples. The spectra were measured at angle a > 0 from the sample edge.

In order to interpret the spectral shape Khriachtchev et al. [34] proposed a theory of delocalized modes in a high-loss waveguide (section 3.2). The cut-off wavelength for our samples is ~ 2 μιη (from equations (3.12) and (3.13) with m = 0). It means that the waveguide should transmit the whole spectrum of nanocrystals inside the core because it lies below the cut-off wavelength. The structure of the guided spectrum then may arise, according to [34], from the fact that the most delocalized (but still guided) modes suffer the smallest losses, thus they proceed nonattenuated in the core.

Second theory suggested to explain the spectral shape is the theory of leaky modes [36] (section 3.3). The fact that the spectra were measured at the angle a > 0 suggests that the theory of leaky modes is valid but we have to study the mode emission in detail to manifest reliably the origin of the modes.

Spectral position of the modes itself cannot bring decision since it is roughly the same within both theories: According to the guided modes theory the observed modes lie just above but close to the cut-off frequency. On the contrary, leaky modes lie below but close to the cut-off frequency. Therefore we cannot distinguish between these theories from the spectral position of the modes. Both theories also predict TE/TM mode splitting due to polarization dependent boundary conditions for guided modes as well as for leaky modes.

One way to confirm the origin of the modes is to compare the measured spectra with numerical calculation. Ostatnický et al. [37] provided numerical calculation of leaky modes in planar waveguides. The calculations were performed for asymmetric Gaussian refractive index profile using transfer matrix formalism. The results of calculations com-


wavelength (nm)

Figure 4.6: Measured spectra in the waveguiding geometry, red lines - TE polarization, green lines - TM polarization, black lines - without polarizer

wavelength (nm)

Figure 4.7: PL spectra of the samples 3, 4, 5 and 6 x 1017 cm-2 measured in the waveguiding geometry (left column), numerical calculated spectra of leaky modes for the same samples (right column), calculations were performed using the code written by T. Ostat- nický.


pared with measured spectra are plotted in Fig. 4.7. The computed spectra contain two narrow T E and T M modes which are in good agreement with measured spectra. In measured spectra (mainly in samples 3 and 4 X 1017 cm-2) also broad-band guided modes are observed. In the PL spectrum of the sample 3 x 1017 cm-2 no leaky modes are observed because in spectral position where they are expected to be the Si-ncs do not emit light. In calculated spectra the broad band is not present because the model does not include guided inodes. However, as it has already been said, the spectral position of the modes is approximately the same within both theories, so we cannot consider the spectra in Fig. 4.7 as the final approval of the theory of leaky modes.

4.3.2 M odes under Different Ambient ConditionsSecond way how to distinguish between guided and leaky modes is to locally change refractive index of the cladding. This approach is one of the main goals of this thesis [39, 41]. Both guided and leaky modes depend on the refractive index na of the cladding and we expect that the spectra should change when changing na. However, leaky modes leave the core after several reflections and propagate further in the substrate. When propagating in the substrate the change of refractive index of the cladding does not affect leaky modes any more. Therefore, when we change refractive index of the cladding by dropping a liquid exactly on the excitation spot, spectral position of the modes should change no matter whether they are leaky modes or guided modes. On the other hand, when we change the refractive index of the cladding layer between the excitation spot and the sample edge, guided modes should be modified but leaky modes not. Local change of refractive index of the cladding was experimentally performed by putting a drop of various liquids on the sample surface (Fig. 4.8). The drops were hold on a black bar with a pit to keep them on a specific place and not to spill out on the surface.

Figure 4.8: Sketch of the experimental setup for changing refractive index of the cladding, (a) liquid drop on the excitation spot, (b) liquid drop between the excitation spot and the sample edge.


In Fig. 4.9 measured spectra with ethanol (n = 1.361) are presented. When the drop was put on (or it is better to say below, see Fig. 4.8(a)) the excitation spot, the modes shifted to longer wavelengths. When the drop was put between the excitation spot and the sample edge (Fig. 4.8(b)) no spectral change was observed. This fact strongly indicates that the observed modes are leaky modes.

Further measurements with different liquids were performed to confirm the nature of the modes. When any liquid drop was put between the excitation spot and the sample edge no change in spectra resulted as shown in Fig. 4.10 which contains measured spectra for the sample 5 x 1017 cm-2 with different liquid drops between the excitation spot and the sample edge.

When the same liquid drop was put on the excitation spot the spectral position of the modes changed. Also a numerical calculation with different refractive indices of the cladding layer was provided (using the code written by T. Ostatnický). In Fig. 4.11 measured and calculated spectra for different refractive indices na on the excitation spot for the sample 5 x 1017 cm-2 are plotted. Systematic mode red-shift with increasing liquid refractive index can be seen and when ne reaches the refractive index of the substrate (na = n, = 1.455) the leaky modes disappear. At this point (when na = na) the asymmetry of the waveguide is broken and total internal reflection on the core-cladding boundary does not occur. When na is further increased the waveguide is inversed (na > n„), therefore no leaky modes propagating in the substrate are observed.

The dependence of the position of leaky modes on the refractive index of the liquid was obtained both theoretically and experimentally (Fig. 4.12). Red-shift of the modes is observed in both cases when na increases from 1 to n„. When crossing n„ no peaks are observed experimentally but the theory predicts blue-shift of the peaks. That is because asymmetrical waveguide is inversed for na > nt and new leaky modes should appear in the liquid. However, these modes were not observed experimentally because of outcoming light scattering in the liquid and the irregular shape of the liquid drops.

Measurements and calculations were performed also for the sample 4 x 1017 cm-2 (Fig. 4.13, 4.14). They all are coherent with results presented above and confirm validity of the leaky-mode model.


wavelength (nm) wavelength (nm)

Figure 4.9: Measured spectra in the waveguiding geometry for (a) sample 5 x 1017 cm' 2 and (b) 3 x 101T cm 2, measurements were performed with ethanol (n = 1.361) drop on the excitation spot (red lines) and between the excitation spot and the sample edge (green lines), black lines were measured without ethanol.

700 750 800 wavelength (nm)

Figure 4.10: PL spectra of the sample 5 x 101' cm 2 measured in the waveguiding geometry with different liquid drops between the excitation spot, and the sample edge.


wavelength (nm)

Figure 4.11: Modes emitted from the sample 5 x 1017 cm '2 with different liquids on the excitation spot, (a) measured spectra, (b) numerically calculated spectra using the code written by T. Ostatnický, part of these results have been published in [41].

Figure 4.12: Positions of the PL maxima in the spectrum of the sample 5 x 1017 cm-2, dots are extracted from the measurement, lines are numerically calculated using the code written by T. Ostatnický.


Figure 4.13: Modes emitted from the sample 4 * 1017 cm"2 with different liquid drops on the excitation spot, (a) measured spectra, (b) numerically calculated spectra using the code written by T. Ostatnický.

Figure 4.14: Positions of the PL maxima in the spectrum of the sample 4 x 1017 cm-2 , dots are extracted from the measurement, lines are numerically calculated using the code written by T. Ostatnický.


Figure 4.15: (a) Non-guided PL spectrum of gradient sample, position of the excitation spot was 5 mm, black line - measured spectrum, red line - gaussian fit, xo - centre of the gaussian curve, a - standard deviation, (b) Non-guided PL spectra of the gradient sample measured at three different positions of the excitation spot. Spectra were smoothed using Fourier transform and cutting higher frequencies in order to clearly see the positions of the maxima. Inset shows the position of the PL maximum as a function of the position x of the excitation spot.

4.4 Light Emission from the Sample Prepared by Reactive D eposition

4.4.1 Mode Structure of the Emission and the Physical Properties of the Sample

Sample prepared by reactive deposition (gradient sample) shows modal structure of emission from the edge similarly as the samples prepared by ion implantation. There is a gradient of the optical properties along one direction of the sample, therefore detailed measurements were performed on different positions x of the excitation spot on the sample. The determination of x is sketched in the left panel of Fig. 4.2.

Non-guided photoluminescence spectrum measured in the transverse geometry for the position x = 5 mm of the excitation spot is plotted in Fig. 4.15(a). Spectrum is fitted by a gaussian curve peaked at 877 nm with FWHM ~ 200 nm. The spectrum is inhomogeneously broadened. Because the physical properties change with x there is a slight shift of the photoluminescence maxima with increasing x (Fig. 4.15(b)). The spectral position of the maximum of the photoluminescence as a function of the position x is plotted in the inset of Fig. 4.15(b).

When measured in the waveguiding geometry narrow modes (FWHM ~ 20 nm) are observed (Fig. 4.16). The spectral position of the modes shifts to longer wavelengths with increasing position x of the excitation spot. Contrary to the samples prepared by ion implantation we observe more than two modes in some spectra (Fig. 4.16(c, d)). The modes at shorter wavelengths (around 700 — 750 nm in Fig. 4.16(c, d)) are modes of one


order higher than the modes at longer wavelengths (around 800 — 900 mu).The modes are polarization resolved, they appear as doublets with T E inodes at

shorter wavelengths and T M modes at longer wavelengths. However, for a step-like refractive index profile the theory predicts inversed spectral positions of the cut-off T E and T M wavelengths. Equations (3.14) and (3.15) imply that V ^E < V ™ for every order m and since Vm ~ 1/λ,„ we have > λ ™ . Because the spectral positions of leaky modes and also the spectral positions of weakly guided modes lie in the vicinity of the cut-off wavelengths there should be T M modes for shorter wavelengths and T E modes for longer wavelengths in the measured spectra no matter the modes are guided or leaked. This discrepancy between the measurement and the theory can be overcome by introducing birefringence of the nanocrystal layer [42], When we suppose that there is a mechanical strain in the direction perpendicular to the sample surface then the material is anisotropic and its index ellipsoid is a spheroid with the optical axis perpendicular to the sample surface. Under this condition the T E wave experiences the ordinary refractive index nc and the T M wave the extraordinary refractive index ne. The difference between the refractive indices for the TE and T M wave implies the different mutual spacing between adjacent modes of the same polarization and this may result in the inversion of the spectral positions of the T E and T M modes.

To study the anisotropy of the gradient sample we put this sample between two crossed polarizers and measured the amount of light from helium-neon laser transmitted through this setup. The HeNe laser line with wavelength of 633 nm was used because the Si- nc sample practically does not absorb light at this wavelength, Although the polarizers

Figure 4.16: PL spectra of the gradient sample in the waveguiding geometry, position of the excitation spot is indicated in each part of the figure, red lines - TE polarization, green lines TM polarization, black lines without polarizer.


Figure 4.17: Photograph of the gradient sample between two crossed polarizers. One polarizer can be seen behind the sample, the second one was in front of the camera.

were crossed some proportion of laser light was transmitted through the setup when the sample was placed between the polarizers. The amount of transmitted light depends on the angle of rotation of the sample and, surprisingly, on the position on the sample. This measurement showed that the sample produces ellipt icaily polarized light from the linearly polarized light and rotates the plane of polarization. This property depends on the position on the sample. We ascribe this observation to the mechanical strain along the gradient in the sample. To demonstrate the anisotropic properties of the sample we replaced the HeNe laser with a standard electric bulb and took a photograph of the sample between two crossed polarizers (see Fig. 4.17). It can be seen that the sample rotates the plane of polarization and the angle of rotation depends on the position on the sample (the right corner of the sample is brighter than the left corner). This observation implies that the index ellipsoid of the nanocrystal layer is either an inclined spheroid or a scalene ellipsoid.

Knowing the fact that the sample is anisotropic we now introduce a simplified model to extract the sample thickness d and the refractive indices n0 and ne from the photoluminescence measurement in the waveguiding conditions and from transmission measurement. We suppose that the sample is made of an uniaxial material with the optical axis perpendicular to the sample surface. Under this assumption the TE wave experiences the ordinary refractive index n0 and, therefore, in the transmittance measurement the quantity n0d was measured (see inset in the right panel of Fig. 4.2). Furthermore, we suppose that the measured spectral position of the modes is very close to the cut-off position. Then we can substitute the measured spectral position of the TE mode and the optical thickness n0d from the transmittance measurement to the equation (3.14) for the cut-off frequency of the TE modes. This transcendental equation has been solved numerically using the bisection method and the values of d and n0 were obtained. After that from equation (3.15) for the spectral positions of the TM modes we have obtained the extraordinary index ne. Equations (3.14) and (3.15) have an infinite number of solutions corresponding to the particular orders of the modes. We chose the order of the modes in the way to get the best correspondence of relative spacing between the modes of the same


x (mm) -3 1.5 3 7 10ά{μαή 1.718 1.721 1.746 1.753 1.796

n0 1.819 1.863 1.859 1.889 1.894Tie 1.896 1.942 1.943 1.983 1.991

Table 4.1: Thickness d, ordinary n0 and extraordinary ne refractive indices of the gradient sample on different positions x on the sample, the estimated relative deviation of the values is 20%.

polarization for x = 10 mm where two of the modes of each polarization were observed. The inaccuracy of this calculation is caused mainly by the uncertainty in determination of the position x on the sample in transmission and PL measurements, in approximation of the spectral positions of the modes by cut-off positions and in the assumption of the uniaxial material. The estimated relative deviation for the values of d, n0 and ne is 20%. Properties of the sample obtained by the procedure described above are summarized in Table 4.1. These properties are coherent with the properties of samples prepared by the same procedure and measured in the laboratory of their origin [35, 42].

4.4.2 Modes under Different Ambient ConditionsSimilarly as for the samples prepared by Si+ ion implantation, measurements with different liquids on different positions of the excitation spot were performed in order to demonstrate the nature of the modes. Measured spectra with different liquid drops on the excitation spot are presented in Figs. 4.18 - 4.22(a), measured spectra with the saune liquid drops between the excitation spot and the sample edge are in Figs. 4.18 - 4.22(b). In order to compare the measured spectra with the leaky mode theory, the leaky modes of the gradient sample were also calculated numerically. Because of the step-like refractive index profile the transfer matrix method did not need to be used and a code based on equation(3.17) was written. The properties of the sample (d, n0 and ne) needed for the numerical calculation were taken from Table 4.1. The calculated leaky mode spectra were multiplied by the measured non-guided photoluminescence spectrum in order to get a more realistic result. The results of numerical calculation on different positions on the sample and for different refractive indices of the cladding layer are presented in Figs. 4.18 - 4.22(c).

The modes behave in the same way as the modes of the samples prepared by ion implantation. They shift to longer wavelengths when refractive index na of the cladding layer on the excitation spot is increased and they disappear when na = n„. This behaviour is observed both in the measured and in the calculated spectra. No spectral change in the measured spectra is observed when the liquid drop is put between the excitation spot and the sample edge.

The spectral positions of the modes as a function of the refractive index of the cladding layer on the excitation spot are shown in Fig. 4.23. The solid circles are taken from measurement and the open circles are from numerical calculation. Both theoretical and


experimental points show a gradual red-shift of the modes with increasing the refractive index of the cladding layer. In the spectral region around 800 — 850 nm there is a very good agreement between the theoretical and the experimental values. However, for longer wavelengths the difference between theory and experiment becomes larger and the theory predicts higher number of modes. This discrepancy may be due to the fact that the theoretical calculation is rather simplified and neglects the complicated anisotropic properties of the sample. Moreover, the intensity of Si-nc photoluminescence at longer wavelengths is rather low which may complicate the formation of leaky modes. The good matching of calculated and measured mode spectral positions at shorter wavelengths (around 800 nm) is expectable because the input data (n0, ne and d) for numerical calculation of leaky modes were obtained using the experimental values from measured PL spectra.

Polarization properties of the modes measured with different liquid drops on the excitation spot are presented in Fig. 4.24. Modes at shorter wavelengths (~ 750 nm) are linearly polarized (T E and T M polarization), but modes at ~ 950 nm are not. This observation can be attributed to the complicated anisotropic properties of the sample.

Figure 4.18: Modes emitted from the gradient sample, position of the excitation spot was- —3 rnm, (a) measured spectra with different liquid drops on the excitation spot, (b) measured spectra with different liquid drops between the excitation spot and the sample edge, (c) numerically calculated spectra for corresponding refractive indices of the cladding layer.


Figure 4.19: Modes emitted from the gradient sample, position of the excitation spot was 1.5 mm, (a) measured spectra with different liquid drops on the excitation spot, (b) measured spectra with different liquid drops between the excitation spot and the sample edge, (c) numerically calculated spectra for corresponding refractive indices of the cladding layer.

Figure 4.20: Modes emitted from the gradient sample, position of the excitation spot was 3 mm, (a) measured spectra with different liquid drops on the excitation spot, (b) measured spectra with different liquid drops between the excitation spot and the sample edge, (c) numerically calculated spectra for corresponding refractive indices of the cladding layer.


Figure 4.22: Modes emitted from the gradient sample, position of the excitation spot was 10 mm. (a) measured spectra with different liquid drops on the excitation spot, spectrum measured with n-hexane is missing, because n-hexane evaporated during the measurement and the measurement is not repeatable in exactly the same conditions, (b) measured spectra with different liquid drops between the excitation spot and the sample edge, (c) numerically calculated spectra for corresponding refractive indices of the cladding layer.

Figure 4.21: Modes emitted from the gradient sample, position of the excitation spot was 7 mm, (a) measured spectra with different liquid drops on the excitation spot, (b) measured spectra with different liquid drops between the excitation spot and thr sample edge, (c) numerically calculated spectra for corresponding refractive indices of the cladding layer.


Figure 4.23: Spectral positions of the leaky modes as a function of the refractive index na of the cladding layer on the excitation spot taken from measurement (solid circles) and from numerical calculation (open circles).

Figure 4.24: PL spectra of the gradient sample measured in the waveguiding geometry with different liquid drops on the excitation spot, position of the spot was —1.5 mm. red lines - TE polarization, green lines TM polarization, black lines no polarizer


Figure 4.25: PL spectra of the gradient sample measured in the waveguiding geometry at different detection angles a, (a) position of the excitation spot x = 3 nm, (b) position of the excitation spot x = 9 nm.

4.4.3 Angular Dependence of the M odesFurther measurements with goniometer were performed in order to study in detail the angular dependence of the modes. Detection angle n between the horizontal axis of the sample and detection optical cable is taken positive when the cable is tilted to the substrate (Fig. 4.4(b)) and negative when the cable is tilted to the opposite side.

In Fig. 4.25 spectra measured for angles a = 0°, +4° and —4° are plotted. When ot — 0° we observe leaky modes because the detection optical cable has a finite numerical aperture ( N A = 0.22) and thus light emitted in small interval of angles a around zero is detected. When the detection angle is increased to positive values, modes become more expressed, whereas when the detection angle has a negative value the modes disappear and we observe only a part of guided light diffracted on the waveguide edge.

To characterize the angular dependence of the modes in detail measurement and also numerical calculation of leaky modes for different values of angle a were performed (Fig. 4.26, calculated spectrum for o = 0° is not present because the expression (3.17) for intensity of leaky modes diverges). In the measured spectra when angle o is increased above ~ 10° the modes disappear and a broad-band emission is observed. In the calculated spectra the modes are present for all values of a , however, for higher » their intensity is lower and their width gets larger This difference is caused by the fact that the numerical model computes only leaky modes and does not involve the broad-band emission. The finest mode structure from the numerical model is obtained for a ~ 4C which is in good agreement with experimental observation.

The fact that the modes are most expressed at a small angle n and disappear at higher values of a (both in measured and calculated spectra) is due to the dependence of the finesse of the peaks on the number of interfering beams. Correspondingly to the Fabry-Perot interferometer the peaks are sharper when the number of interfering beams is larger. For small values of a the angle Θ of the ray inside the waveguide core is close to the critical angle on the core-substrate boundary (see equation (3.18)) and according to

CHAPTER 4 RESULTS: PLANAR WAVEGUIDES WITH SI-NCS 51

Figure 4.26: (a) PL spectra of the gradient sample measured in the waveguiding geometry, position of the excitation spot was 3 mm, detection angles a are indicated at each spectrum, (b) numerically calculated leaky mode spectra.

Fresnel equations (right panel of Fig. 3.4, arrow L) the corresponding reflection coefficient

is close to unity. In this rase the number of interfering beams leaving the core is high

yielding formation of a fine mode structure. For large values of tv the angle ft of the ray

inside the corc is much smaller than the critical angle and the reflection coefficient is far

below unity. Therefore the number of reflections, thus the number of interfering beams,

is smaller and a fine mode structure is not observed.

Spectral position of the modes slightly shifts to longer wavelengths with increasing

angle a as it demonstrates Fig. 4.27(b) in which both measured and calculated spectral

positions of the peaks are plotted. Labels of the peaks 1. 2. 3. 4 are indicated in the

measured spectrum in Fig. 4.27(a). Peak 3 is the most intensive one and remains in the

measured spectrum when o is increased to higher values. For higher values of a (a > 20°).

however, the observed spectrum consists mainly of the non-guided light and it is arguable

to differentiate whether the observed mode is still a leaky mode or just a part of a normal

luminescence from the sample. The other peaks disappear for a ~ 15° —20° as the broad

band emission begins to dominate. The qualitative agreement between the experiment

and theory is good, both predict a gradual increase of the peak spectral position with

increasing a The small difference in the absolute spectral position of the modes between

experiment and theory is due to the simplification of the numerical model (that computes

only leaky modes and other phenomena are neglected), the error in the input data for

the calculation (sample height d and refractive indices n„ and ne) and the problematic

anisotropy properties of the sample.


4.5 Summary on the M ode EmissionWe now summarize the observed properties of the modes emitted from the planar waveguides with Si-ncs:

• The modes are observed in the waveguiding geometry a t detection angles a > 0 (detection geometry in Fig. 4.4)

• The mode spectra do not change when the refractive index of the cladding layer between the excitation spot and the sample edge is modified.

• When the refractive index of the cladding layer on the excitation spot is increased the modes shift to longer wavelengths.

• The modes disappear when the refractive index of the cladding layer on the excitation spot exceeds the refractive index of the substrate.

• The observed behaviour of the modes is in a good agreement with numerical calculations for leaky modes.

These observations have definitely proved that the luminescence filtering properties of the planar waveguides with Si-ncs are due to losses of intensity of guided modes in the waveguide core and the presence of the leaky modes. The propagation losses in the planar waveguides with Si-ncs are caused by absorption and Mie scattering of light due to composite nature of the Si-nc layer [43]. Now the question arises whether the leaky modes are a positive or a negative phenomenon.

For the measurement of optical gain with the VSL technique the presence of leaky modes is a rather negative effect because the energy that should be amplified inside the core leaks out to the substrate. However, it turns out that the leaky modes do not make the light amplification by stimulated emission completely impossible [27].

Figure 4.27: (a) Measured PL spectrum of the gradient sample in waveguiding geometry for x = 9 mm and a = 6°, labels of 4 peaks are indicated, (b) spectral positions of the peaks from (a) as a function of angle a, red points measured, black points calculated.


On the other hand, there are several indications to practical exploitation of the leaky

modes. They could be used for wavelength division multiplexing (WDM) [l]. WDM is

a technology used in communications for transporting large quantities of data. The idea

of WDM is in multiplexing of signals with different wavelengths at the transmitter and,

at the end of the optical fiber, their splitting apart by a WDM demultiplexer. For WDM

components mainly planar waveguide diffraction gratings and arrayed waveguide gratings

[1] are used. Leaky modes can be used to demultiplex the signal consisting of a manifold

of wavelengths. The spectral position of the leaky modes can be tuned by (i) changing

the refractive index of the cladding layer on the excitation spot, (ii) changing the physical

properties (thickness, refractive index) of the core layer, (ii) changing the observation

angle. This wavelengths tuning allows appropriate setting of the transmitted wavelength.

Further possibility of exploitation of leaky modes are optical sensors in optoelectronic

circuits. When an unknown liquid is placed on the Si-nc layer then its refractive index

can be determined from the spectral position of the leaky modes provided that a former

calibration of leaky modes wavelengths was done. Such a detector would be small and

portable thus suitable for sensing of the liquids.

Chapter 5 Results: Rib Optical WaveguideProm the point of view of light confinement, one-dimensional (rib) waveguide intuitively

seems to be better candidate for the occurence of positive optical gain compared to a

two-dimensional (planar) waveguide. To this end we get first samples of rib waveguides

containing Si-ncs fabricated and we performed first optical characterization of such waveg

uides, both theoretically and experimentally. In this Chapter we present the results of

experimental observation of the light emission from the edge of the rib sample. We further

introduce a simplified theoretical model of leaky modes in a rib waveguide and we present

the results of numerical calculation.

5.1 Rib W aveguide SampleSamples in the form of rib waveguides were prepared by the following procedure. Firstly,

a rib pattern was chemically etched by optical litography onto the Si0 2 matrix with

dimensions approximately 39 x 8 x 1 mm at the Institute of Physics of the Academy of

Sciences in Prague. The rib width w changes from 2 μπι to 5 μπι. The rib height d is

approximately 1 μια and the separation between the ribs is ~ 100 μπι or 200 μιη (Fig. 5.1).

After the etching ion implantation was provided at Australian National University in

Canberra in a similar way as in the samples studied in section 4.3. The implantation

energy was 400 keV and ion fluences of 3, 4, 5 and 6 x 1017 cm- 2 were implanted on different

positions of the slab. After that, samples were annealed for 1 hour in N2 atmosphere at

temperature of 1100 °C to form Si nanocrystals. Further annealing for 1 hour in forming

gas (95% N2, 5% H2) at 500 °C was performed to passivate the nanocrystal surface.

Finally, the edges of the sample were polished out to let the rib structure reach the

sample edge. The photograph of the rib sample is in Fig. 5.2. Unfortunately, the quality

of the ribs is not very high, there are many defects and fluctuations of rib widths.

Experimental setup was the same as in section 4.2 (left panel of Fig. 4.3) but in some

measurements the laser beam was focused with a cylindrical lens (/ = 15 cm) to form an

excitation stripe along the rib.

54

CHAPTER 5. RESULTS: RIB OPTICAL WAVEGUIDE 55

Figure 5.2: Photographs of the rib sample, (a) Microscopical reflection image of the quality part of the rib sample taken by J . Valenta [44], (b) photograph of another part of the rib sample taken by V. Jurka.

5.2 Experimental Observation of Light EmissionNon-guided photoluminescence spectra of the rib sample measured in the transverse geometry are presented in Fig. 5.3. The excitation spot was not focused. The spectra are s i m i l a r

to that of samples without etched structure. They are broad with FWHM « 200 nm and peaked at ~ 880 nm. There is a small red-shift in comparison with the no-rib samples. This shift is due to differences in fabrication process (nanocrystal size, surface passivation). The rib structure does not affect the non-guided spectrum.

5.2.1 Excitation with a StripeMany measurements on the rib sample in waveguiding geometry were provided attempting to observe mode structure from the ribs. Because the unfocused excitation spot has the


Figure 5.3: PL spectra of the rib waveguide sample measured in transverse geometry. Red lines are gaussian Sts, xq is the centre of gaussian curve, σ is the standard deviation.

diameter of ~ 2 mm, it excites ~ 20 ribs and also the planar layer with Si-ncs between the ribs. Thus, measured spectra are inhomogeneously broadened and contain light not only from ribs but also from the planar structure. In order to avoid this broadening and to enhance the emission from a single rib the laser beam was focused with a cylindrical lens to form an excitation stripe ~ 35 μια wide parallel to the ribs. The profile of the focused laser beam is in the left panel of Fig. 5.5 and a sketch of the excitation and detection geometry is in the inset of the right panel of Fig. 5.5. The excitation stripe was moved across the sample and light emission from the sample edge was measured. Spectra measured on parts of the sample with fluences of 3 x 1017 cm-2 and 5 x 1017 cm-2 are shown in Fig. 5.4. The modes that appear in the part with the fluence of 5 x 1017 cm-2 are the planar waveguide leaky modes because they do not change when the excitation stripe is displaced across the sample. The observation angles and the position of excitation stripe were varied but no mode structure from the ribs was observed.

For further investigation of the ribs we provided a measurement in which the intensity of emission from the sample edge was measured as a function of the position of the excitation stripe. The measurement was done on the rib sample 3 x 1017 cm-2 where no leaky modes from the planar layer occur and therefore we expect more evident emission from the ribs. Results are plotted in the right panel of Fig. 5.5. It can be seen that the intensity has maxima for certain positions of the excitation stripe. These maxima occur when the excitation stripe is on the rib and therefore the observed intensity is higher due to confinement of the light in the ribs. The broadening of the maxima arises from the width of the ribs and the width of the excitation stripe. Since the ribs are not high-quality not all of them appear in the measured graph.

KNIHOVNA MAT.-FYZ. FAKULTYKnihovna Fr Závisný iiyz odo.)

Ke Kariovu 3 121 16 Praha 2

CHAPTER 5. RESULTS: RID OPTICAL WAVEGUIDE 57

Figure 5.4: PL spectra measured from the edge of the rib sample.Black line - sample 3 x 1017 cm“2, red line sample 5 x 1017 cm- 2 , blue line - gaussian fit to the spectrum of the sample 3 x 1017 cm -2 .

5.2.2 Evanescent Wave ExcitationSecond achievement provided to enhance the emission from the ribs was excitation by an evanescent wave from the light totally reflected from the prism as depicted in the upper panel of Fig. 5.6. When the prism is put on the ribs and laser light is totally reflected from the prism then the evanescent wave should excite the ribs but it should not reach the layer between the ribs. The penetration depth is estimated to be of the order of 0.1 μιη. However, in practise, layer between the ribs is also partially excited mainly due to scattered laser hght. Results of this measurement are plotted in the lower panel of Fig. 5.6. Black lines are spectra measured with standard excitation, red lines are obtained by excitation with an evanescent wave. The laser beam was not focused. All spectra are normalized to unity. In the measured spectra of the rib samples 3 and 4 x 1017 cm-2 only broad-band emission is observed and it is only slightly changed when excited with or without the prism. In the spectra of the rib samples 5 and 6 x 1017 cm-2 leaky modes at shorter wavelengths and a broad-band emission at longer wavelengths are observed. From Fig. 5.6 it is seen that when the sample is excited using the prism the leaky modes are suppressed and the intensity of broad-band emission is increased in comparison with the spectra measured without prism. This observation confirms that the leaky modes originate in the planar layer of Si-ncs and the broad-band emission is guided more effectively in the ribs.

5.2.3 Summary on Experimental ObservationTo sum up the experimental observation on the rib sample, mode structure from the ribs was not observed. The modes that appear in the spectra originate in the planar part of the sample between the ribs. However, the ribs confine light and have some small effect


displacement (μίτι)

F i g u r e 5 .5 : Left panel profile of the HeCd laser beam focused with a cylindrical lens. Right panel - PL intensity at 900 nm from the edge of the rib sample 3 χ 1017 cm-2 as a function of the position of the excitation stripe, inset shows the geometry of the experiment.

Figure 5.6: Upper panel sketch of the excitation of the ribs with an evanescent wave. Lower panel - PL spectra of the rib samples measured in waveguiding geometry, black lines - standard excitation, red Unes evanescent wave excitation.


on the guided spectra. We ascribe the absence of the modes in the ribs to the bad quality

of the ribs. The etching procedure was not performed perfectly and ribs with defects were

created. There are fluctuations in rib width and even interruptions of the ribs. Therefore

no modes were able to develop in them.

5.3 Theoretical M odelIn this section we introduce a simple scalar wave model of leaking modes in a rib waveg

uide. Tracing an individual ray inside the core of the rib waveguide is a complicated

procedure since the path of the ray in the cross-section of the waveguide is not a closed

curve but it has an irregular zigzag shape. Therefore, the intensity of modes that leak

out of the core is calculated in the framework of wave optics. The problem of the rib

waveguide is much complicated than that of the planar waveguide and the solution can

not be divided to the TE and TM solution. To simplify this model, the polarization of

waves is neglected and they are treated as scalar waves. The core of this model are planar

waves propagating inside the rib that must fulfill boundary conditions. Leaking modes

are computed as the part of light transmitted from the core to the substrate, further

propagating in the substrate and finally leaving the substrate at the edge of the sample.

5.3.1 Labeling and Useful Geometric RelationsWe assume a rib waveguide which cross-section is depicted in Fig. 5.7. Refractive indices

of the core, cladding and substrate layers are nc, nQ and na, respectively. We label the

rib width w and height d. We introduce a cartesian coordinate system as indicated in

Fig. 5.7: 2 axis is along the rib (parallel to the direction of propagation of light in the rib),

x and y axes are horizontal and vertical axes, respectively, in the plane perpendicular to

z. The origin of the coordinate system is in the left lower corner of the rib (Fig. 5.7).

To describe a direction of the planar wave inside the core we introduce angles Θ and

a as follows: angle Θ € (0, π/2) is between the ray and the z axis, angle a is between the

projection of the ray to the xy plane and the x axis (Fig. 5.7). Because of the symmetry

of the rib waveguide it is sufficient to take a € (0,7r/2 ). The reflection coefficients on

the boundaries are: Γα on the core-substrate boundary, ry ^ on the upper core-cladding

boundary, rmv on the left and right core-cladding boundaries, and finally rea on the

substrate-air boundary for the light that is leaving the waveguide. Note that rr„-r φ because the reflection coefficients depend not only on the refractive indices of the layers

but also on the angle of incidence on the boundary and that is different for a wave

impinging on the upper core-cladding boundary and a wave impinging on the left or right

core-cladding boundaries.

Now we assume a wave propagating in the core at the direction given by angles Θ and a. From geometrical considerations it follows that the angles of incidence θχζ on the

upper core-cladding boundary and the core-substrate boundary, and 6yz on the left and


Figure 5.7: Cross-section of a rib optical waveguide, four waves inside the core are indicated, RH and RV are projections of the ray leaving the sample to horizontal plane (xz) and to vertical plane (yz), respectively.

Reflection coefficients on the boundaries between the z-th and the j -th layer are calculated from Fresnel equations for T E waves

where n, and r i j are refractive indices of the z-th and the j -th layer and is the angle of incidence determined by equations (5.1) or (5.2).

To calculate the intensity of the modes when they finally leave the substrate (and thus can be observed experimentally) we need to know the transmission coefficients Uj on the core-substrate and substrate-air boundaries. They are also calculated from Fresnel equations for T E waves

To describe the direction of leaking modes leaving the waveguide we introduce angle a h between the projection RH of the ray that leaves the sample to the horizontal plane (xz) and the z axis, and angle a v between the projection RV of the ray to the vertical plane (yz) and the z axis (Fig. 5.7). The relation between angles and a v of the ray leaving


the waveguide and angles Θ and a inside the core has been calculated using geometric optics and Snell law on core-substrate and substrate-air boundaries:

Angles a/, and a u can be determined experimentally.

5.3.2 Wave Model of Leaking ModesAs a source of light in the waveguide we assume a silicon nanocrystal placed in the rib at point (xc, yc) that emits light with amplitude E0 in all directions coupled to the field inside the rib.

For a given direction of propagation of the mode determined by angles Θ and a inside the core we assume four infinite planar waves E\, E2, E3 and £ 4 inside the core (Fig. 5.7). The waves are proportional to the factor e’(fcr-u,i), where k = (kx, ky, kz) is the wave vector in the core and ω is the angular frequency of the wave.

At first we will assume that the nanocrystal is a source of light in the direction of the wave E\. Contributions to other directions will be added later. The wave i? i(0 ,0) at the point (0 ,0) is a sum of an infinite geometric series £ i ( 0 ,0) = i?o(0,0) -I- £ľó(0,0) + i?o(0,0) + . . . , where £q(0,0) = Eo(0, exp 2i(kxw + kyd) is the wave fromnanocrystal after one round-trip through the rib at the point (0 ,0), ^ ' ( 0 ,0) is the wave after two round-trips, etc. The final equation for E\ is

where the phase term el(' lXc~ yVc' originates in the fact that we do not take the field Eq at the point (xc, yc) but at (0,0). At this point the phase term could be included in the initial phase of Eo, however, later when we assume field Eq in other directions we will need the phase term explicitly.

When we assume the waves Εγ, £ľ2, E3 and Et propagate clockwise in the rib they must fulfill boundary conditions

Furthermore, since the waves are infinite planar waves they also have to fulfill set of boundary conditions for counter-clockwise propagation:


The denominators of these equations are the same and they reflect the necessity of fulfillment of the phase-matching condition of the waves in the core in order to obtain consistent field distribution. The spectral position of the modes depends mainly on the value of the denominator. Conversely, numerators only modify the value of the modes. This modification depends on the position of the light-emitting nanocrystal. We can perceive this phenomenon in the way that for every mode a specific field distribution exists inside the

Simultaneous fulfillment of the conditions (5.8) and (5.9) is necessary for the wave theory to be coherent with the ray approach where the rays can circulate in both directions and multiple reflections from the sidewalls occur. Hence the wave EL transmitted to the substrate can be written in the form

where £<(0,0) is the wave from the clockwise round-trip (satisfying conditions (5.8)) and ££(0,0) is the wave from the counter-clockwise round-trip (satisfying conditions (5.9)). Therefore, for calculating the amplitude of the leaking modes quantities £ 4 (0,0) and £ 4 (0 ,0) need to be known. They can be expressed in terms of £ i(0 ,0) using sets of equations (5.8) for £ 4 (0,0) and (5.9) for £ 4 (0 ,0), respectively, and £7i(0,0) is given by equation (5.7). The sum of £ 4 (0,0) and £J(0,0) is then given by

where index I in Ei means that the nanocrystal emits light in direction of the wave E\.Now we will assume that the nanocrystal emits light in directions of waves £ 2 , £ 3 and

£4, respectively. The procedure of computing amplitudes of waves £ 4 before they leak to the substrate is the same as the one of computing £ /. The difference is in the phase factors of the wave £ o( 0 , 0 ) which arise from different directions of the waves £ j , £ 2 , £ 3

and £ 4 and depend on the position (zc, yc) of the nanocrystal. The amplitudes £ // , E m and E jv of waves before they leak to the substrate are


where T = Ta Taa is the total transmittance involving refraction on the core-substrate and substrate-air boundaries. Transmittance T can be calculated using well-known relations and geometric considerations

As it has already been mentioned above the intensity I depends on the position of the nanocrystal that is the source of light. Therefore, averaging of the intensity through the position of nanocrystals was provided. We assume that the nanocrystals radiate independently so we average the intensities not the field amplitudes. Furthermore, we suppose a uniform distribution of nanocrystals in the rib core. The final averaged intensity is

core and the light emitting nanocrystal may be in a node of this distribution or in an antinode. When the nanocrystal is in the node it does not contribute to the given mode. On the contrary when it is in the anti-node it contributes appreciably to the mode. Therefore the intensity of leaking modes depends on the position of the nanocrystal inside the core.

The final amplitude of the field E4 is the sum of (5.11), (5.12), (5.13) and (5.14) and the total intensity I of leaking modes leaving the sample is

Finally, the intensity of leaking modes is calculated using equations (5.15), (5.16) and (5.17).

5.3.3 Results of Numerical CalculationIn the framework of this thesis a code in Fortran77 was written which for a given wavelength calculates the intensity of leaking modes leaving the rib sample using the procedure described in the previous paragraph. The dimensions of the rib waveguide were taken from the parameters of the etching procedure and from photographs of the rib sample (Fig. 5.2), in most calculations the values d — l μτη and w = 2 μτη were used. The value of the refractive index nc of the Si-nc core was estimated to be 1.7 using values obtained for the planar waveguide samples (section 4.3). In all calculations the values of na = 1.455 and n„ = 1 were used. Calculations were provided for different values of input parameters (dimensions d and w, angles a/, and a„, refractive index nc) in order to characterize how the spectral position and intensity of the modes are dependent on selected properties of the rib waveguide.

Calculated spectra for different values of observation angles »/, and a„ are plotted in Fig. 5.8. In Fig. 5.8(a, b) angle a„ is held at the constant value of 5° or 20°, respectively. It is clearly seen that the spectral positions of the modes strongly depend on the angle Oh and for αυ = 20° the intensity of the modes is approximately four times smaller than

CHAPTER 5. RESULTS: RID OPTICAL WAVEGUIDE 64

wavelength (nm ) wavelength (nm )

Figure 5.8: Calculated leaking mode spectra for different observation angles o/, and a„, the values of the angles and other parameters axe indicated in each part of the figure. Inset in panel (c) shows angle a as a function of angles and r»„, respectively (the latter angle was 5°).

for a„ = 5°. On the other hand, the dependence of the mode spectral position on the angle av is not very strong as can be seen from Fig. 5.8(c, d). This observation can be understood in terms of multiple beam interference. The spectral position of the modes strongly depends on the phase-shift obtained by the wave by total reflection on the core- cladding boundary and this phase-shift depends on the angle of incidence. The angles of incidence θχζ and θν. depend on the angles Θ and a of the ray inside the core (equations (5.1)) and they depend on the angles ah and av of the ray leaving the sample. However, the relation between angle Θ and angles a/, and a„ is symmetrical with respect to α Λ and av (equation (5.5)) but the formula for angle a (5.6) is not. Thus when considering the phase-shift as a function of the angles a/, and a t,, respectively, it is sufficient to be interested only in how the angle a is dependent on the angles ah and a„, respectively. This function is plotted in the inset of Fig. 5.8(c). From this plot it is evident that the angle o declines quite rapidly with the increase of angle o* while it changes very slowly when changing angle a u. This fact explains the observed rapid change of leaking mode spectral positions with varying angle a/, and their slow change when angle n„ is varied.

CHAPTER 5. RESULTS: RJD OPTICAL WAVEGUIDE 65

Figure 5.9: Spectral position of the leaking modes as a function of (a) angle ah, (b) angle a„, dimensions and refractive index of the rib waveguide were the same as in Fig. 5.8.

To show the observed variances more clearly the spectral positions of the modes as a function of angles r*/, and a„. respectively, are plotted in Fig. 5.9.

Second parameters to be changed are dimensions of the rib. The leaking mode spectra for different values of rib height d and rib width w, respectively, are shown in Fig. 5.10 and the spectral positions of the modes as functions of the rib dimensions are in Fig. 5.11. With increasing rib height d at constant w = 2 μηι the number of modes within the studied spectral region gets higher. One can imagine that rising the rib height lengthens the path of the ray inside the core before it leaks out. For observation angles ah = av = 5° we get q = 84° which is large enough to conceive the zigzag path of the ray only in the vertical plane, i.e. neglecting the reflections from the vertical core-cladding boundaries. This concept is made only for imaginary purposes. In this situation when d is increased the relative spacing of the modes decreases in a similar way as in optical resonators when their lengths is increased. On the other hand, when the rib width w is increased the relative spacing between the modes does not change considerably because the path of the ray inside the core does not lengthen much. Only a gradual red-shift of the mode spectral positions is observed (Figs. 5.10(b) and 5.11(b)).

Lastly, the leaking mode spectra in the rib waveguide were calculated for different values of the core refractive index nc (Fig. 5.12). With increasing nc the modes become narrower and shift to longer wavelengths.

Unfortunately, mediocre quality of our rib samples prevents us from comparing the theoretical calculations with experimental data for the present.

CHAPTER 5. RESULTS: RID OPTICAL WAVEGUIDE 6 6

wavelength (nm) wavelength (nm)

Figure 5.10: Calculated leaking mode spectra for different values of (a) rib height d, (b)

rib width w.

Figure 5.11: Spectral position of the leaking modes as a function of (a) rib height d, (b)

rib width w, the input parameters were the same as in Fig. 5.10.

Figure 5.12: (a) Calculated leaking mode spectra of a rib sample with different refractive indices nc, (b) spectral peak positions as a function of nc, input parameters are the same as

in (a).

Chapter 6Results: Pulsed ExcitationIn addition to the measurements under cw excitation, results of which are presented in

previous two Chapters, we have also performed measurements on Si-nc samples under

pulsed excitation (pulse duration ~ 8 ns). In this Chapter we present results of the

time-resolved PL measurements on a sample with Si-ncs prepared by reactive deposition

and VSL/SES measurements both on well-known laser active materials (laser dye Rho

damine 610 and ruby) - as a test of performance of the experimental setup - and on

samples with Si-ncs.

6.1 Tim e Resolved Photolum inescence6.1.1 Experimental SetupThe time resolved photoluminescence was measured on the sample prepared by reactive

deposition (preparation and properties described in paragraph 4.1.2). The sample was

excited by the third harmonic (wavelength 355 nm) of a Q-switched NdrYAG laser. The

pulse duration was ~ 8 ns and the repetition rate 10 Hz. The experimental setup was

similar to that of VSL measurement (see next section, Fig. 6.3) where the optics forming

the stripe was removed and a third harmonic generator was added to the laser head. We

used a dispersion prism to spatially separate the three wavelengths from the laser (the first,

second and the third harmonic). The excitation spot was not focused, its diameter on the

sample was ~ 1 cm. The PL signal was measured in transverse geometry (Fig. 4.4(a)).

The photoluminescence signal from the sample was collected by two lenses ( / = 7 cm

and / = 10 cm, entrance numerical aperture 0.41), spectrally resolved by a spectrograph

(Andor Shamrock SR-163Í) with Czerny-Turner optical design, wavelengths resolution of

0.17 nm and a diffraction grating with 300 lines per mm. After that signal was detected

with a CCD camera Andor iStar equipped with microchannel plate for amplification of

the signal and a digital delay generator for time-resolved measurements. Triggering was

provided by TTL signal from the laser to the CCD. To minimize thermal noise the CCD

was water cooled to —30°C- All measurements were performed at room temperature. All

the detected spectra were corrected for the system spectral response.

67

CHAPTER 6. RESULTS: PULSED EXCITATION 6 8

Figure 6.1: (a) PL spectra of the gradient sample in different times after excitation, gate width 2 μκ, excitation wavelength 35.5 nm, (b) PL decay at 750 and 820 nm, respectively, red and green lines are fits by the stretched exponential function to measured data.

6.1.2 Slow (microsecond) PL ComponentThe results of tirne-resolved PL of the gradient sample on a microsecond time scale are shown in Fig. 6.1. In panel (a) of the figure the spectra acquired in different times after excitation are presented. The gate was opened for 2 /xs (gate width) to detect signal, the pumping fluence was 6 mJ.cm-2 . Unlike the photoluminescence under cw excitation (Fig. 4.15) where the observed spectrum does not have any structure, in the time-resolved measurement two components peaked at 750 nm and 820 nm, respectively, appear The decay of the component at the shorter wavelength is faster while the longer wavelength component remains in the measured signal for a longer time. The observed spectral shape of PL suggests that there are many mechanisms involved in the luminescence process of the sample. The time decay of the PL signal at 750 and 820 nm is plotted in Fig. 6.1(b). From this plot it is evident that the luminescence decays faster at shorter wavelengths. The experimental data cannot be fitted well by a single exponential function but they can be fitted by the stretched exponential function (equation (2.15)). This fact indicates the possibility of the presence of exciton migration between the nanocrystals in the S1O2 matrix [20]. The decay times from the fit are r = (5.39 ± 0.07) //s for λ = 750 nm and t = (8.9 ± 0.2) ßs for A = 820 nm. the Q parameters are 0.625 ± 0.006 for λ = 750 ηιη and 0.573 ± 0.006 for λ = 820 nm, respectively.

6.1.3 Fast (nanosecond) PL ComponentMeasurements on the gradient sample on a nanosecond time scale were performed 111 order to observe the fast dynamics of the PL and the luminescence rise within and short after the excitation pulse. In these measurements the gate was opened for 5 ns and the excitation fluence was 2 m J .cm 2. The measured PL spectra are in Fig. 6.2. The shorter wavelength part of the spectra (below ~ 580 nm) was measured without any filter in

CHAPTER 6. RESULTS: PULSED EXCITATION 69

wavelength (n m )

F ig u r e 6.2: PL spectra of the gradient sample in different times with respect to the excitation pulse, excitation wavelength 355 nm. gate width 5 ns, the right part of the spectrum was measured with filter OG590, the line at ~ 710 nm is the second diffraction order of the laser beam.

front of the spectrograph while the longer wavelength part was measured with edge filter

OG590 placed in front of the entrance slit of the spectrograph in order to suppress the

second diffraction order of the detected light. A very fast blue band emission peaked at

~ 450 nm with relatively high intensity (note that the intensity of shorter wavelength

part of the spectra is 10-times decreased in Fig. 6.2) is observed. A similar emission

from samples with Si-ncs in SiOo matrix has been reported by other groups [45 and also

in Si0 2 deposited layer before and after Si+ implantation before annealing (i.e. before

forming nanocrystals) [46]. Therefore we interpret the observed blue band emission as

the photoluminescence of states related to defects in the SÍO2 matrix.

On the other hand, we suppose that the weak luminescence signal at the longer wave

lengths part of the spectra (~ 700 nm) originates in nanocrystals. Because the edge

filter OG590 was placed in front of the spectrograph no weak second order diffraction of

the blue signal is present in this spectral region, except extremely strong pump line at

~ 710 nm. The luminescence signal from Si-ncs is rather weak and slower than the emis

sion from the defects in the Si0 2 matrix. It is possible that the energy from the matrix is

transfered to the nanocrystals and after that they emit light. It is worth noting that the

maximum intensity at ~ 450 nm occurs in temporal coincidence with the excitation pulse

(within the 5 ns gate) but the maximum PL at ~ 700 nm is observed after a 5 ns delay.

The near-infrared emission band at ~ 800 nm that is present in the slow PL component

(Fig. 6.1(a)) is not observed in the fast PL component. This component is present on a

microsecond time scale and when the gate is opened for 5 ns only the signal is too low to

be detected.


Figure 6.3: Experimental setup for the VSL and SES measurements.

6.2 R esults o f the VSL M easurem ents6.2.1 Experimental SetupDuring my master’s thesis I have been participating in building a new experimental setup

for the Variable Stripe Length (VSL) and Shifting Excitation Spot (SES) methods (see

paragraphs 2.3.2 and 2.3.4) at the Institute of Physics of the Academy of Sciences in

Prague. A sketch of the setup is in Fig. 6.3. We used the second harmonic (532 nm) of

the Nd:YAG laser for excitation because of better beam properties than those of the third

harmonic and the fact that we needed to use a glass beam expander (that cannot be used

for UV beam) to improve the excitation beam properties (to achieve a flat profile of the

beam cross-section). The pulse duration was ~ 8 ns and the repetition rate 10 Hz. The

excitation wavelength of 532 nm provides nearly resonant excitation of the Si-ncs and it is

supposed not to excite all the states that the third harmonic of Nd:YAG (355 nm) excites.

The photoluminescence dynamics strongly depends on the excitation wavelength [45].

Furthermore, the absorption of the sample at 532 nm is smaller than in the UV spectral

region. The lower absorption may result in lower pumping rate of population inversion.

On the other hand, excitation of only a part of the energy states in nanocrystals may be

feasible for occurrence of the stimulated emission, e.g. because of expected suppression

of the Auger effect.

Turning back to our experimental setup, we separated the first and the second har

monic using a dispersion prism. After that the second harmonic passed through a dielec

tric rotational filter to decrease its intensity to the desired value. Since the profile of the

laser beam emanating from the laser is not Gaussian and there are fluctuations in its in

tensity we used the beam expander to improve the homogeneity of the excitation intensity

along the stripe. Because the entrance aperture of the beam expander is smaller than the

dimension of the laser beam we selected a suitable part of the beam by the expander and


Figure 6.4: Horizontal sum profile of the excitation stripe.

expanded it. Further, the stripe from the excitation beam was formed by a cylindrical

lens (/ = 15 cm). In the image plane of the lens a moving shield (or a moving narrow

slit for the SES method) was placed to change the length of the stripe (or the position

of moving spot, respectively). Then the stripe was imaged with two plan-convex lenses

(magnification 0.5) onto the sample. The profile of the excitation stripe was measured

with a BeamStar detector, the horizontal sum profile of the stripe is shown in Fig. 6.4.

The transversal width of the stripe was ~ 30 μιη.

Light emission from the sample edge was detected with two lenses (entrance numerical

aperture NA « 0.41) and sent to a spectrograph. Signal was spectrally resolved and

detected by the same system as in the time-resolved PL (section 6.1). Triggering was

provided by a TTL signal from the laser to the CCD. Signal was acquired in temporal

coincidence with the excitation pulse with the gate width of 100 μβ. All spectra presented

hereafter are corrected for the system spectral response.

6.2.2 VSL on Rhodamine 610Firstly, to demonstrate the method and to test the performance of our new experimental

setup, we measured VSL and SES on a laser dye Rhodamine 610 dissolved in methyl

alcohol (concentration 4 g/1). This organic dye has been known for decades as a reliable

laser active medium, having net optical gain (dependent on dye concentration in the

solution, pump power density, etc.) in the range of 10 — 100 cm-1. The pumping fiuence

was 70 mJ.cm-2. Measured ASE spectra of Rhodamine 610 are presented in Fig. 6.5(a,

b). The emission is peaked at ~ 600 nm and a nonlinear increase of the intensity with

increasing stripe length is evident. Besides, the emission spectra are narrowing for longer I

(see normalized spectra in Fig. 6.5(b)) which suggests the presence of stimulated emission.

In Fig. 6.5(c) the SES signal is shown. For small values of excitation spot position

( i < 0.075 mm) the signal is increasing because at the beginning the excitation spot is

next to the edge of the cuvette with Rhodamine and is slowly merging into the dye. For

x > 0.1 mm the SES signal shows exponential decay and can be fitted well by equation

(2.22). The fit yields the value of the coefficient of total losses of (71 ± 5) cm-1. The data

are quite noisy due to the low intensity of the signal. When the SES signal is integrated we


Figure 6.5: (a) ASE spectra of Rhodamine 610 for different stripe lengths, (b) normalized ASE spectra for stripe lengths of 0.1 mm and 0.8 mm, (c) SES curve at 596 nm, red line

fit by equation (2.22), inset integrated SES, (d) VSL (red circles) and integrated SES (black squares) curves at 596 nm, red line - fit by equation (2.20), inset gain spectrum.

get a curve with sublinear increase (see inset in Fig. 6.5(c)) coherent with the theoretical predictions. Next, in Fig. 6.5(d) both the VSL and integrated SES curves are plotted. The SES curve lies under the VSL curve (note the intensity scale in the inset of Fig. 6.5(c) and Fig. 6.5(d) are much different) and the VSL shows a superlinear increase. Fit by equation (2.20) to the VSL data yields net optical gain of (52 ± 2) cm-1 , inset in this figure shows the gain spectrum of Rhodamine 610 calculated using equation (2.21 ) for stripe lengths of 0.8 mm and 0.4 mm. The maximum gain is located approximately at 597 nm. All these observations confirm good performance of our VSL/SES setup in case of relatively high value of optical gain.

6.2.3 VSL on a Ruby SampleOur next step in testing the performance of the VSL/SES setup consisted in measurements on a ruby sample (AI2O3 doped with Cr3+) which has a considerable smaller gain coefficient (g « 0.2 cm -1 depending on the doping concentration of Cr3+ ions [47]). In


Figure 6.6: (a) VSL (red circles) and integrated SES (black squares) curves for a ruby sample, inset - the normalized ASE spectra for two different stripe lengths, (b) difference between the VSL and integrated SES curves, lines are fits by equation (6.1) with different parameters g and Iq.

contrast to this small value ruby is the first material on which the laser action has been

achieved. Therefore, wc cxpected to report positive gain coefficient from our VSL/SES

measurements on the ruby sample.

The results of the measurements are plotted in Fig. 6.6, the pumping fluence was

50 mJ.cm-2. Contrary to the results on the high-gain laser dye (Fig. 6.5) the VSL curve

for ruby in Fig. 6.6(a) does not show a superlinear increase and the integrated SES curve

matches the VSL curve for shorter stripe lengths (Z < 1.5 mm) very well. Furthermore,

spectral narrowing with increasing stripe length is not observed (see inset in Fig. 6.6(a)).

Nevertheless, the presence of small net optical gain seems to be indicated due to a small

difference between the VSL and integrated SES curves for longer stripe lengths. In order

to determine the value of net optical gain we analyzed the difference between the VSL and

integrated SES data. According to the theory (equations (2.20) and (2.23)) this difference

should be described by

where a tot stands here for total losses. The intensity /0 of spontaneous emission per unit

length and the coefficient of total losses a tot were determined from the SES measurement:

Jo = 0.76 a.u. and u to, = (4.0±0.2) cm-1 Then the difference of VSL and integrated SES

(Fig. 6.6(b)) was fitted by equation (6.1) with 70 and o tot from the SES data in order to

obtain the value of net optical gain. The fit (red line in Fig. 6.6(b)) yields small negative

value of net optical gain (g = —2.8 cm-1) which is in contrast with our expectations.

However, the difference of VSL and integrated SES data can be fitted well by equation

(6.1) with small, either positive or negative, values of g and slightly changed intensity I0

(green and blue lines in Fig. 6.1(b)). A large fluctuation in the difference curve of VSL

and integrated SES data is caused by the fact that we have subtracted two close values.


From the fitting procedure we conclude that the VSL/SES method is not sufficient for

determination of small values of optical gain.

6.2.4 VSL on Silicon NanocrystalsMeasuring amplified spontaneous emission on samples with Si-ncs is a rather complicated

process because their absorption at 532 nm is not high, they are inhomogeneously broad

ened systems with a complexity of energy levels and they exhibit considerable losses due

to absorption and fight scattering [43]. The experimental performance is very sensitive to

the adjustment of the sample and the optical components. We have performed first VSL

and SES measurements on the gradient sample using our new experimental setup.

Firstly, we measured non-guided PL spectrum of the gradient sample under 532 nm

excitation (Fig. 6.7). The excitation spot was not focused (diameter on the sample was

~ 1 cm) and the excitation fiuence was ~ 0.1 mJ.cm-2. The PL spectrum is broad with

no structure. Compared to the PL spectrum measured under UV (355 nm) excitation

(Fig. 6.1(a)) with similar gate width (microsecond range) the spectrum excited by 532 nm

laser line is red-shifted showing no component at ~ 750 nm. This observation suggests

that the 532 nm laser line does not excite all the states in Si-ncs that the UV excites.

The very difference between the emission spectra displayed in Figs. 4.15, 6.1 and 6.7 is

quite remarkable and perhaps will deserve more attention in the future.

wavelength (nm)

Figure 6.7: Non-guided PL spectrum of the gradient sample under 532 nm pulsed excitation, gate width 1 0 0 μβ.

The first experimental results of the VSL/SES measurements on the gradient sample

with a stripe of maximum length of 1 mm and step 0.025 mm are plotted in Fig. 6 .8 .

The step was chosen to be approximately the same as the length of the excitation spot

on the sample in the SES measurement. This adjustment ensures that the whole area

of the sample that is excited with a stripe in the VSL method is covered by the spots

in the SES method but the adjacent spots do not to overlap. The pumping fiuence was

1 0 0 mJ.cm-2. Owing to the fact that the emission from the sample is detected from the

edge, the measured spectra contain leaky modes (see Fig. 6 .8 (a) with spectra for different

stripe lengths). These mode spectra are qualitatively the same as the PL spectra measured


Figure 6.8: (a) Spectra taken from the edge of the gradient sample for different stripe lengths, (b) SES curves for 750 and 800 nm, respectively, (c - h) VSL (red circles) and integrated SES (black squares) curves for wavelengths indicated in panel (a).

KNIHOVNA MAT -FYZ. FAKULTY Knihovna Ft lavisKy (fyz odd.)

Ke Karlovu 3 121 16 Praha 2


Figure 6.9: VSL (red circles) and integrated SES (black squares) for the gradient sample at different wavelengths, excitation fluence 58 mJ.cm-2.

in the waveguiding geometry under cw excitation (section 4.4, Fig. 4.16), The entrance

numerical aperture of the detection lens (NA fa 0.41) is high enough to detect leaky

modes that propagate under certain angle from the Si-nc layer even when the sample is

in the axis of the detection system.

The results of the SES measurements are in Fig. 6.8(b). Because of the fluctua

tions of the intensity of pumping stripe and the low measured signal, the measured SES

curves show the variation in the pumping intensity (which can arise either from spatial or

temporal fluctuations) rather than the exponential decay according to the theory (equa

tion (2.22)). Therefore, we were not able to fit them to obtain coefficient of losses. The

increasing part of the SES curves for small values of x arises from the fact that at the

beginning the excitation spot is next to the sample edge and starts to penetrate into the

sample. It is interesting to note that while the SES curve at 750 nm (between leaky

modes) has the maximum at x = 0.75 mm, the SES curve at the wavelength of the leaky

mode (800 nm) has maximum at x = 0.2 mm. This difference occurs because of the fact

that the leaky modes need certain travel length in the sample to develop. The theory

of leaky modes presented in section 3.3 assumes infinite number of reflections before the

modes leak out to the substrate. When the excitation spot is too close to the sample edge

only a finite number of reflections occurs yielding smaller proportion of light leaking to

the substrate. This effect can also be seen from the spectra in Fig. 6.8(a) where a fine

mode structure is observed for I — 1 mm but for I — 0.1 mm the modes are not much

expressed. The narrowing of the spectra is due to formation of the leaky modes, in this

case, not due to presence of net optical gain.

The VSL and integrated SES curves for different wavelengths indicated in Fig. 6.8(a)

are presented in Fig. 6.8(c - h). This experiment revealed one surprising difference be-


Figure 6.10: VSL (red circles) and integrated SES (black squares) for the gradient sample at different wavelengths, excitation fluence 115 mJ.cm-2.

tween the shape of the curves for leaky mode wavelengths and the curves for guided light at wavelengths between the leaky modes. Both the integrated SES and VSL curves

for leaky inodes (Fig. 6.8(c, f, h )) are approximately lines while the curves on the other

wavelengths show variation in their slope (F ig 6.8(d, e, g )) This observation clearly

demonstrates the different origin of the leaky modes and the fact that they suffer different losses. The lowering of the slope for the stripe length of about 0.2 mm may be due

to the decrease of the pumping intensity which can be seen from the decrease of the SES signal (Fig. 6 .8 (b )). Unfortunately, a detailed theoretical understanding of the shape of the measured curves is missing at present.

For analyzing the process of light amplification we have to compare the V SL and integrated SES curves. At the longer wavelength region (Fig. 6.8(f, g, h )) the integrated

SES curves match the VSL curves almost perfectly showing no presence o f optical gain. On the contrary Fig. 6.8(c. d, e) for shorter wavelengths show a slight difference between

these curves for stripe lengths longer than ~ 0.5 mm suggesting perhaps the presence of light amplification. However, to confirm it surely, additional measurements with different excitation intensities were required to be done.

Because of that, we have performed two more measurements on the same position on

the gradient sample; one with lower pumping fluence (58 mJ.cm-2 , results presented in

Fig. 6.9), and the second with higher pumping fluence (115 mJ.cm-2 , results in Fig. 6.10). The other experimental conditions were kept the same as in the former experiment (gate width 100 μ8, maximum stripe length 1 mm, step 0.025 mm). From the graphs in Figs. 6.9

and 6.10 it is evident that the integrated SES and VSL curves match perfectly each other indicating no net optical gain in the sample. This observation proves that the small difference between the integrated SES and V S L curves in the previous measurement with


pumping fluence of 100 mJ.cm- 2 (Fig. 6 .8 ) was caused by an artifact, probably by the

fluctuation of pumping intensity during the measurement. Interpreting it as an optical

gain would be misleading. On the other hand, the feature that repeats in all measurements

is the shape of VSL and integrated SES curves for leaky modes and for guided light

confirming that it is not caused by some artifacts but by the nature of the leaky modes.

Chapter 7ConclusionsIn this work we studied light emission from planar and rib optical waveguides with silicon

nanocrystals prepared by Si+ ion implantation and reactive Si deposition. Firstly, we

focused our attention on the mode emission from planar waveguides with Si-ncs under cw

excitation. A peculiar mode structure from the edge of the samples has been observed and

a number of experiments were performed in order to reveal the origin of the modes. The

experimental data, in particular those with different liquid drops placed on the excitation

spot and between the excitation spot and the sample edge, have clearly manifested that

the observed modes are those that leak out of the Si-nc layer and propagate further in

the substrate. It is interesting to note that the two types of samples studied in this work

were prepared by two different methods (Si+ ion implantation and reactive Si deposition)

in two different laboratories (in Canberra and in Helsinki). In spite of that, both the

samples show surprising but similar PL waveguiding properties. The common properties

of the samples are the asymmetry of the waveguide layer and the loss mechanisms due to

absorption and light scattering [43]. Also the spectral ordering of the TE/TM ‘doublets’

has been found the same in the both types of samples, even if this was expected to

be in a reverse order. Plausible explanation has been proposed in terms of mechanical

strain (induced birefringence) occurring in the sample prepared by reactive deposition but

missing in the sample prepared by Si+ ion implantation.

In order to study further light emission from Si-ncs in waveguide structures we per

formed measurements on a rib waveguide with Si-ncs. Measurements with excitation

stripe along the ribs and with excitation by sin evanescent wave were realized. We ob

served an increase of the proportion of guided light in the ribs with respect to the planar

layer, but no mode structure from the ribs similar to the mode structure of planar waveg

uides was observed. We developed a theoretical model of waves leaking out of the rib

core to the substrate and computed leaky mode spectra for various parameters of the rib

but mediocre quality of the rib samples did not enable us to compare the model with

experimental data. For further experimental investigation of the mode structure in ribs

with Si-ncs new high quality rib samples have to be fabricated.

In addition to the investigation of light emission under cw excitation, we studied time-

resolved photoluminescence under pulsed excitation. We observed photoluminescence

79

CHAPTER 7. CONCLUSIONS 80

decay on the sample prepared by reactive Si deposition on microsecond and nanosecond

time scale. On the microsecond time scale the decay shape can be fitted well by the

stretched exponential function with shorter decay times for shorter wavelengths. On the

nanosecond time scale a fast excitation of the defect luminescence in the S1O2 matrix was

observed.

I have participated in building of a new experimental setup for VSL and SES tech

niques. We performed first measurements of amplified spontaneous emission on a laser dye

Rhodamine 610 with relatively high gain coefficient to confirm good performance of our

experimental setup. We have shown on a ruby sample which is a well-known laser mate

rial, however, with low gain coefficient, that for low values of gain coefficient (g < 1 cm-1)

the VSL method, even combined with the SES method, is not sufficient to determine the

gain coefficient. The VSL/SES measurements on the sample with Si-ncs in S1O2 prepared

by reactive Si deposition did not show presence of optical gain. This our observation is in

contrast with the results of Khriachtchev et al. [31] who observed stimulated emission on

samples prepared by the same procedure. However, in their experiments the excitation

wavelength was shorter (308 nm) and temporal resolution was higher (of the order of

nanoseconds). We intend to proceed with our experiments in this way.

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Published Articles

Appi. Phys. b 83.87-91 (2006)___________________________________________________________ Applied Physics B ___DOI: 10 .1007/s00340-005-2118-5 | Uwtw and Optta |

I. PELANT1 Waveguide cores containingjT silicon nanocrystals as active spectral filters* — , for silicon-based photonicsT. MATES I in s ti tu te 0f Physics, Academy o f Sciences o f the Czech Republic, 16253 Prague 6, Czech RepublicR.G. ELLIMAN 2 Department of Chemical Physics & Optics, Faculty of Mathematics & Physics. Charles University.

121 16 Prague 2, Czech Republic 3 Electronic Materials Engineering Department, Research School o f Physical Sciences and Engineering,

Australian National University, Canberra ACT 0200, Australia

Received: 20 October 2005Published online: 17 January 2006 · © Springer·Verlag 2005ABSTRACT Layers of densely packed luminescent Si nanocrystals embedded in fused silica act as wavelength-specific planar waveguides that filter the wide-band spontaneous emission. The waveguides' light output consists of two spectrally narrow (~ 10 nm), orthogonally polarized, and spatially directed bands. This effect is shown to result from leaky modes of the lossy waveguides. The results have general applicability to lossy, asymmetric waveguides and show the way to produce spectrally narrow emission without the use of optical cavities.

PACS 78.67.Bf; 42.79.Gn; 81.07.Bc

1 IntroductionSilicon-based photonics is an exciting new area

of research that aims to produce integrated electronic and photonic functionality in a single silicon chip. Silicon quantum dots or nanocrystals (Si-NCs) are efficient light emitters [1 -3 ], unlike bulk silicon, and have been used to Iemonstrate silicon-based light-emitting diodes [4,5], The Si-NCs can also be employed to fabricate active optical waveguides [6-12]. Some o f these Si-NC waveguides, with aroperly designed refractive-index profile, exhibit spectral iltering of the Si-NC photoluminescence emission. The fil- ered emission consists o f narrow ( ~ lOnm), polarization- lependent emission lines [7,8 ,12). This unexpected effect, vhich holds promise for potential applications in silicon pho- onics, was reported by Khriachtchev et al. [7] for Si/SiO? vaveguides and by our group [12-14] (probably also by vanda et al. [15]) for samples containing Si-NC prepared by !i+ implantation into silica slabs. Full understanding o f the rfienomenon is, however, still missing. Here we study this iltering effect in more detail and demonstrate, both experi- nentally and using theoretical modeling, that the origin o f the iltering is based, contrary to intuition, on leaky modes o f the assy planar waveguides.

9 Fax: +420-2-21911249, E-mail: [email protected] at: IPCMS. Groupe d'O ptique Nonlineaire et d'Optoelectronique,IMR 7504 CNRS-ULP, 67037 Strasbourg Cede*. France

2 Methods

The Si-NC thin-film waveguides were prepared by 400-keV Si+-ion implantation into optically polished Infrasil slabs. Samples were subsequently annealed for 1 h at 1100 °C in a N2 ambient to form Si-NCs and further annealed for 1 h at 500 °C in forming gas (N2/H 2) to enhance the luminescence emission. The presence o f Si-NCs and an estimate o f their size was determined by Raman scattering, as shown in Fig. lc. A simple approach, exploiting the shift and half-width o f the Raman peak [16], provided an estimation o f the Si-NC sizes from 4.4 nm to 5.9 nm.

Photoluminescence was measured at room temperature using a cw He-Cd laser (325 or 442 nm) and detected with a spectrograph coupled to a CCD camera. All spectra were corrected for the system response. Emitted light was coupled to the detection system either using a quartz optical fiber (collection angle ~ 1°) or by a microscope objective lens (magnification x2.5, NA = 0.075, collection angle ~ 8.6°). To measure a polar radiation diagram, the input o f the optical fiber was rotated around the sample by a goniometer.

Phase-shift interferometry and atomic force microscopy (AFM) were used to characterize the surface morphology of the samples.

Neither spectral profiles nor spectral positions of substrate radiation modes can be calculated analytically. Numerical calculations were therefore performed using the formula for the cavity enhancement factor [17]. The relevant reflectivity coefficients on the boundaries were calculated using the transfer matrix method, taking into account the continuous profile of the refractive index. We also considered both the numerical aperture of the given experimental set-up and the loss coefficient in the Si-NC films. Details of this procedure will be published elsewhere.

3 Results and discussion

The visual appearance of our samples is shown in Fig. la. The refractive-index change for different implant fluences leads to variations in the color o f the implanted regions under ambient (white) light. The resulting Si-NCs are embedded in the silica slabs as a thin ( ~ 1 μιπ) buried layer that


88 Applied Physics B - Lasers and Optics

Photon Energy (eV)2 18 1.6 1.4 2 18 1.6 1.4

700 800 900 700 800 900 b Wavelength (nm)

Moreover, each of these peaks has a distinct linear polarization: the electnc vector E of the short-wavelength peak lies in the Si-NC film (red curves, TE polarization) while the long- wavelength peak is characterized by E perpendicular to the film (green curves, TM polarization). The right-hand column in Fig. lb represents theoretically calculated spectra, the basis o f which will be discussed later.

The strong directionality of the TE/TM peak emission is highlighted in Fig. 2. which shows a polar radiation diagram of the spectrally integrated emission for the sample implanted to a fluence o f 5 x 1017 cm 2. The emission contains surface Lambertian photoluminescence emission peaked at

90° (brownish areas in Fig. 2a), as well as two distinct lobes due to emission emanating from the sample edge (the left- hand lobe) and the internal reflection (the right-hand lobe). The well-developed TE/TM peaks occur within the left-hand lobe, close to the angle ~ 0° only (yellow region in Fig. 2a). This is more clearly seen in Fig. 2b, where the photoluminescence emission was collected using a microscope objec

400 420 440 460 480 500 520 540 c Raman Shift [cm'1]

FIGURE I Planar optical waveguides formed by Si-NC thin layers embedded in silica slabs, (a) Edge view of a silica sheet (Infrasil) S.O x 1.0 x 0 .1 cm3 under diffused white light, with colored regions formed by Si-NC 61ms. Ccwresponding implant fluences. ranging from 3 to S x 1017 cm*2 are indicated, (b) Dolled curves: conventional broad photolummescence spectra from Si-NCs measured at normal incidence Full lines room-temperature photoluminescence spectra taken from the sample facet, in the direction indicated by arrows in (a). Left-hand plots - experimental, right-hand plots - calculated, (c) Examples of Raman spectra evidencing the presence of Si-NCs (red and brown curves). Blue curve - Raman spectrum of unimplanted Infrasil. black curve reference spectrum of crystalline Si wafer

forms the high- refractive-index core of the waveguide structure Because the refractive index of the Si-NC film is higher than that o f the SiO? substrate and extends to the surface, the film acts as a planar asymmctnc optical waveguide.

The effect of photoluminescence spectral filtering is highlighted in Fig. lb. The left-hand column in this figure shows measured room-temperature photoluminescence spectra for four different Si-NC waveguides under UV excitation. The dotted curves represent emission from Si-NCs embedded within the waveguide core, measured from the sample surface, i.e. perpendicular to the Si-NC layer. Such broadband spectra are typical of the inhomogeneously broadened emission from Si-NCs but are undesirable for many optical applications. The solid curves represent spectra taken parallel to the surface, i.e. from the edge (facet) o f the waveguide (arrows in Fig. la). The two sets o f spectra are clearly quite different, the latter being composed of two distinct peaks separated by about 30 nm.

FIGURE 2 Directionality of edge emission (the sample was implanted to a fluence o f 5 x !017 cm J). (a) Spectrally integrated photolummescence emission as a funcuon of the polar angle, measured with the «ample fixed at the center of a goniometer. (b> Micro-photoluminescence spectra for six directions (±5°, ± I0 C. ± 1 5 ') ; the direct emission from the excited spot is plotted by blue lines, the edge emission by black lines, and the polarization resolved TE and TM modes by red and green lines, respectively. (The collection angle of the objective lens is ~ 8.6° ) Note different intensity scales for upper and lower plots

b Wavelength [nm]

pelant et al Waveguide cores containing silicon nanocrystals as active spectral filters for silicon-based photonics 89

tive (with numerical aperture of 0.075, i.e. collection angle

of ~ 8,6°), The nucro-imaging-spectroscopic set-up enabled

us to detect separately photoluminescence leaving the excited

spot directly (blue lines) and that coming from the edge of the

implanted layer (black lines).

With regard to the physical processes that give rise to this

novel spectral structure, we consider two distinct mechanisms

(summarized in Fig. 3a and b):

(i) The two linearly polarized peaks could simply re

sult from standard guided modes of the planar Si-NC wave

guide (Fig. 3a). However, an ideal transparent planar wave

guide should transmit a continuous spectrum of guided modes

up to a cut-off wavelength [18J. The cut-off wavelength for

the firsl-ordcr modes of our waveguides can be estimated to

lie above ~ !500nm. Consequently, the Si-NC films should

transmit the entire 600-900 nm band emitted by the nanocrys

tals, which obviously is not the case. Nevertheless, some

structure might arise from wavelength-dependent losses, with

those modes (wavelengths) that undergo the smallest loss be

ing guided to the edge of the sample. These are likely those

modes that are ‘weakly guided’, i.e. the modes whose electric

field is strongly delocalized, and the modes propagate basi

cally as a planar wave in the substrate [18]. Their effective

guide thickness tends to infinity [19], Ray optics describes

these modes by an angle of incidence Θ that is greater than but

very close to the critical angle 0C for total internal reflection'.

The situation is depicted in Fig. 3c, which displays schemati

cally the reflectance R and phase shift Φ of TE and TM waves

on the boundary between two dielectric media as a function

1 Here the lower boundary is of importance only since the refraclive-

mdex contrast al the upper boundary is high enough lo assure total

internal reflection at angles H safely higher than 0C

FIGURE 3 Schematics of spectral filtering processes, (a l Guided modes of

an asymmemc waveguide Unset shows implanted Si* -ion distribution across

Ihe Si-NC film as calculated by SR1M (the Stopping and Range of Ions in

Mailer), which determines (he refracdve-index profile), (b ) Substrate radia

tion (leaky) modes from the Si-NC core, (c) Reflectance and phase shifts on

the planar boundary between two dielectric media plotted for TE and TM

modes versus incident angle H

of Θ. In our case the boundaries are either the core/air (upper

boundary) or the core/SiO? substrate (lower boundary). The

arrow G labels the angle Θ for the strongly delocalized guided

modes, which were invoked [20,21) to be responsible for the

filtration effect. The salient feature of the filtering, namely, the

separation between TE and TM modes, is then a direct con

sequence of the asymmetric guide. It is due to different phase

shifts Φ for the TE and TM modes under total reflection at

both boundaries. In order to fulfill the phase condition that

after two successive reflections the phase difference can only

be equal to an integral multiple of 2π, suitable wavelengths

from the (continuous) emission band are combined with avail

able (continuous) values of Φ. The latter is slightly different

for TE and TM polarizations at a given angle of incidence

(Fig. 3c) and results in mode wavelengths that are also slightly

different.

(ii) The second possible mechanism involves substrate

leaky or radiation modes of the Si-NC waveguide (Fig. 3b).

These propagate at an angle ft situated close to but below

ftc (arrow S in Fig. 3c). These modes undergo total reflec

tion at the upper boundary (larger index difference) but are

only partially reflected on the lower boundary (smaller index

difference). Consequently, a small fraction of their power is

radiated into the substrate at each bottom reflection. These

leaky modes are usually considered undesirable parasitic ra

diation [18) and thus do not normally receive much attention.

If, however, the angle Θ is only slightly less than the leaky

modes propagate near-parallel to the Si-NC plane. Moreover,

the number of reflections is very high (R is close to unity ), re

sulting in a narrow spectral width for the modes. The mechan

ism of spectral filtering in this case remains basically the same

as discussed above, the only difference being that a phase shift

Φ at the upper boundary only comes to play during the initial

stages of propagation.

After a finite number of internal reflections all the radiant

power escapes into leaky modes and emerges from the sample

facet in a well-defined direction, basically parallel with the Si-

NC film (see [14] and Fig. 2). This makes such leaky substrate

modes virtually indistinguishable from the guided modes.

The fact that the two mechanisms have a different depen

dence on the refractive-index difference at the surface pro

vides the basis for testing their validity. The principle is to

change locally the cladding layer refractive index between

a photoexcitation spot and the sample facet - which can be

achieved by putting drops of various liquids on the sample

surface close to the sample edge (Fig. 3a and b). If the ef

fect of spectral filtering is due lo weakly guided modes, then

the edge-emission spectrum should be strongly distorted by

such changes in index, since reflections on the upper boundary

(now with modified refractive index) control the phase condi

tion for mode creation all along the ray trajectory. If. on the

other hand, the filtering is due to the substrate leaky modes,

no change in the spectrum is expected since, after propagat

ing < I mm from the excitation source, all energy flux in the

modes has leaked into the substrate and is no longer influ

enced by the upper boundary (Fig. 3b).

Results of this experiment are displayed in Fig. 4a and

show no change in emission spectrum for liquid refractive

indices in the range from 1.359 to 1.657 - clear evidence

that the effect is due to leaky substrate modes. (This ob-

90 Applied Physics B - Lasers and Optics

Distanc· (μτη)

'Súí&ižÍÍS

WBvetength (nm)FIGURE 4 Orthogonal polarization emission 'doublet' in Ihe sample implanted to a fluence of 5 * I017 cm -2 , (a l Drops of various liquids located on the upper boundary between excitation spot and sample facet, as sketched by (he liquid drops on the nghi in Fig. 3a and b. Black curve - blank upper boundary. (b> The same liquids as in (al but located above the excitation spot (the doited drops on the left in Fig. 3a and b)

servation contrasts with a similar experiment performed by shifting the same liquid drops just above the excitation spot - dotted drops in Fig. 3a and b - where reflections o f the leaky modes on the upper boundary still occur. The results are shown in Fig. 4b: drastic spectral modifications, scaling with liquid refractive index [22].) As further confirmation of this model, the right-hand column in Fig. lb shows theoretically calculated edge-emission spectra o f the substrate radiation modes for all samples. In calculating these curves the graded index profile o f each sample [14] was employed as extracted from interference-modulated optical transmission curves, measured in normal incidence2. It is evident that the calculated curves reproduce the measured spectra very well.

Importantly, the dominance o f the leaky substrate mode emission implies the suppression of the broadband emission from the Si-NCs. (This latter emission is partly ob-

FIG l Kt. $ Morphology of the sample surface (upper waveguide boundary). (ai t.ine profile measured with a ZYGO phase-shifung interferometer over a range of 180 nm. (b) AFM normal force image over an area of 500 x 500 nm2 A selected line profile of the local height is also shown, giving the vertical distance between the points marked by arrows of about 1.7 nm. in good agreement with the mterferometnc data (c) Three-dimensional image of the local height in a 500 * 500 nm2 area The ;-range of the surface (minimum to maximum) is 3.9 nm, yielding a RMS roughness of 0.5 nm

2 We take this opportunity to correct the original version o f the calculated curves quoted in |I 4 |. where a numerical error made worse the agreement with experiment

served in samples implanted to fluences of 3 x 1017 c m '2 and 4 x 10,7cm - - Fig. lb.) The attenuation o f these guided modes is attributed to waveguide losses. Surface and side-wall roughness is often invoked to explain waveguide losses; however. this is not a likely cause in the present case. Indeed, in the present case the waveguide surface morphology (Fig. 5) is very flat with a RMS roughness of ~ 0.5 nm only. This value is substantially lower than typical side-wall roughness in e.g. etched semiconductor waveguides [23] or in typical silica waveguides [24], The loss is therefore likely due to self-absorption and/or Mie scattering in the waveguide core (Diffraction of the guided modes at the output facet may also play a role.) The exact nature o f the observed waveguide attenuation remains unsolved at present.

PELANT et al. Waveguide cores containing silicon nanocrystals as active spectral Alters Tor silicon-based photonics

4 Conclusions

To summarize, using a combination o f experimental and theoretical results we have elucidated the principal role of substrate radiation modes in the spectral filtration effect of thin-film Si-NC waveguides. It is noteworthy that the narrow spectral width of both orthogonal polarization modes is comparable with the emission o f Si-NCs in an optical microcavity [25 ,26J, without fabricating any Bragg reflectors. In a certain sense the investigated waveguides act as a microscopic Lummer-Gehreke plate. The possibility o f selecting the output wavelength via modification o f waveguide parameters can be applicable in silicon photonics for Si-laser wavelength tuning, optical signal multiplexing, and optical sensing.

ACKNOWLEDGEMENTS Financial support through Research Grants Nos. 202/03/0789 and 202/01/0030 of GACR, Project No. ΙΑΛΙ0Ι0316 of GAAVCR, LC5I0 Centrum, ind the Australian Research Council is greatly acknowledged. The research work at the Institute of Physics is supported by Institutional Research Plan No. AV0Z 10100521. The authors thank F. Trojánek for help with calculations and A. Poruba, A. Fejfar. and K. Kusova for experimental assistance.

REFERENCES

1 G. Amato, C. Delenie. H.-J. von Bardeleben (eds.). Structural and Optical Properties o f Porous Silicon Nanostructures (Gordon and Breach, Amsterdam 1997)

2 D J. Lockwood (ed.). Light Emission in Silicon. From Physics to Devices (Semicond. Semimet. 49) (Academic, San Diego. CA 1998)

3 S. Ossicini, L. Pavesi, F. Priolo (eds.). Light Emitting Silicon fo r Microelectronics (Springer Tracts Mod. Phys. 194) (Springer, Berlin 2003)

4 A. Irrera, D. Pacifici, M. Miritello. G. Franzo, F. Priolo, F. Iacona. D. Sanfilippo. G Di Stefano. P.G. Fallica. Appl. Phys. Leu. 81, 1866(2002)

5 R J. Walters, G.l. Bourianoff. H.A. Atwater. Nat. Mater. 4, 143 (200S)

6 L. Dal Negro, M. Cazzanclli, N. Daldosso, Z. Gaburno, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, F. Iacona, Physica E 16,297 (2003)

7 L. Khriachtchev, M. Räsänen, S. Novikov, J. Sinkkonen, Appl. Phys. Lett. 79. 1249(2001)

8 L. Khriachtchev, M. Räsänen, S. Novikov, J. Lahtinen. J. Appl. Phys. 95, 7592(2004)

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10 M. Cazzanclli, D. Navarro-Urrios, F. Riboli, N. Daldosso, L. Pavesi, J. Heitmann. L.X. Yi, R. Scholz, M. Zacharias, U. Gösele. J. Appl. Phys. 96,3164(2004)

11 L. Pavesi. L. Dal Negro, C. Mazzoleni, G. Franzo. F. Priolo, Nature 408, 440(2000)

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13 J. Valenta, I. Pelant, J. Linnros. Appl. Phys. Lett. 81, 1396 (2002)14 J. Valenta, T. Ostatnický, I. Pelant, R.G. Elliman, J. Linnros, B. Höner

lage. J. Appl. Phys. 96, 5222 (2004)15 M. Ivanda, U.V. Desnica, C.W. White, W. Kiefer, in Towards the First

Silicon Laser, ed. by L. Pavesi, S. Gaponenko, L. Da) Negro (NATO Sei. Ser. I I 93) (Kluwer. Dordrecht 2003) pp. 191-196

16 G. Viera, S. Huet, L- Boufendi. J. Appl. Phys. 90.4175 (2001)17 R. Baets, P. Bienstman, R. Bockstaele. in Confined Photon Systems. Fun

damentals and Applications, ed. by H. Benisty, J.-M. Gerard, R. Houdre. J. Rarity, C. Weisbuch (Springer, Berlin 1999) pp. 39-79

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(2003)21 L. Khriachtchev. S. Novikov, J. Lahtinen. M. Räsänen, J. Phys.: Con-

dens. Matter 16,3219 (2004)22 K. Luterova, E. Skopalova. I. Pelant, M. Rejman, T. Ostatnický, J. Va

lenta. in preparation23 J.H. Jang, W. Zhao, J.W. Bae. D. Selvanathan. S.L. Rommel. I. Adesida.

A. Lepore, M. Kwakemaak. J.H. Abeles, Appl. Phys. Lett. 83, 4116(2003)

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(2001)

91

JO U R N A L O F APPLIED PH YSICS 100 074307 (2006)

Active planar optical waveguides with silicon nanocrystals: Leaky modes under different ambient conditions

K. Luterová, E. Skopalová, and I. Pelant®Institute o f Physics, Academy ofScieiu.es o f the Czech Republh , Cukrovarnícku 10, CZ-162 53 Prague 6. Czech Republic

M Rejman, T Ostatnický, and J. ValentaDepartment o f Chemical Physics and Optics, Fm ulty o f Mathematics anil Physics, Charle s University,Ke Karlovu 3. CZ-121 16 Prague 2. Czech Republic

(Received 9 Februar) 2006; accepted 8 June 2006; published online 6 October 2006)

We study both experimentally and theoretically the propagation o f light emitted from silicon nanocrystals forming planar waveguides buried in S i0 2. Photoluminescence spectra detected from the sample facet show significant spectral narrowing— leaky modes— with respect to the spectra measured in standard photoluminescence configuration. The spectral position o f the leaky modes responds strongly to a local change o f refractive index (liquid drop) on the sample surface. Higher refractive index o f the liquid induces higher redshift o f the mode position. Experimental data agree with the previously proposed leaky mode model. © 2006 American Institute of Physics.[D O l: 10.1063/1.2356781]

INTRODUCTION

Luminescent layers containing silicon nanocrystals are

very promising materials for potential all-silicon optoelec

tronics. Strong effort is aimed nowadays towards successful

demonstration o f silicon-based laser. Several laboratories reported positive optical gain in systems with silicon

nanocrystals.1*8 Most o f these samples are designed in a

form o f active planar waveguides, A significant narrowing o f the photoluminescence (P L ) emission spectrum measured in

the direction o f the waveguide plane (from the sample facet)

is, among others, often used as an indication o f the presence of stimulated emission in such waveguide structures. H ow

ever, some recent works showed that in appropriate cases the

significant PL spectrum narrowing does not result from stimulated emission, but from the development o f a wave

guide mode structure in the close vicinity o f the waveguide cutoff frequency.9' 1 Such mode structure in PL spectra has

so far been interpreted either as substrate leaky modes13' 1,1 or las a kind o f delocalized guided modes near the cutoff

frequency.' 1' The question o f which o f the two models is

■valid deserves more detailed discussion.

In the present work, we study behavior o f the panocystalline-waveguide PL spectra at different ambient

bonditions and give further evidence in favor o f the leaky

fnode model, developed previously by our group.1* 13 We

fhange locally the refractive index (by dropping vanous liq

uids) on the sample surface above the excited luminescing

fcpot and monitor subsequently spectral change o f the PL. We compare the results with the theoretical spectra calculated

(ising the leaky mode model. Excellent agreement o f the ex

perimental and theoretical data affirms the validity o f the hode I.

Electronic mail: [email protected]

»21 -8979/2006/100(71/074307/4/523.00

E X P E R IM E N T

The samples used m this study were prepared by implanting 400 keV Si* ions into I mm thick silica slab (Infrasil, refractive index ns- 1.455) with optically polished surface and edges. Implant fluences o f 3, 4, 5. and 6 X I0 r cm-2 were applied in four different regions o f the slab. They produced different levels o f refractive index contrast (with asymmetric graded index profiles12) between the core and cladding/substrate layers. Peak excess Si concentrations were up to 26 at. % Si. Implanted samples were subsequently annealed for I h in N 2 ambient at 1100 °C and for 1 h in forming gas (5% H2 in N 2) at 500 °C , Raman scattering confirmed the presence o f Si nanocrystals in the annealed layers, with diameter between 3 and 6 nm.lř

The PL properties o f the samples were investigated using a continuous wave He-Cd laser (442 nm) as an excitation source. A silica optical cable collected the PL radiation. The output o f the cable was connected to an /=20 cm spectrograph equipped with a cooled charge-coupled device (CCD ) camera. A ll measurements were performed at room temperature and all PL spectra were corrected for the system spectral response.

RESULTS AND DISCUSSION

Figure I recalls the peculiar waveguiding properties in our S i' ion implanted samples, The spectrum recorded in the standard 45° PL geometry [see thin solid line in Fig 1(c) for the sample implanted to a fluence o f 5 X 1017 cm '2] consists o f one broad peak (full width at half maximum o f — 150 nm) centered at —860 nm. However, the P L spectra detected from the cleaved facet o f the sample— in the waveguide geometry— show, besides the broad peak due to ordinary guided modes, a fundamentally different feature: doublet o f two narrow [full width at half maximum (FW H M ) o f —20 nm] peaks. Here, the short-wavelength peak is TE po-

© 2006 American Institute ot Physics100. 074307-1

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074307-2 Luterová e t al. J. Appl. Phys. 100, 074307 (2006)

HG. I. Room-temperature PL spectra from the sample facet (in the waveguiding geometry schematically depicted in the inset) for layers implanted to a fluence of (a) 3 X I0 1’ cm '2, (b) 4 X 1 0 ” cm"2, (c) 5 X 10IT cm"2, and (d) 6 X I01’ cm '2, compared to the conventional 45° PL geometry spectrum [curve “nonguided" in panel (c)]. Thick lines—PL without polarizer and thin lines— measurement with a polarizer TE polarization (vector E parallel to the waveguiding layer) and TM polarization (£ perpendicular to the layer).

larized (vector E parallel to the sample plane) while the peak on the long-wavelength side is TM polarized (vector E perpendicular to the sample plane). The position of this doublet shifts with increasing implant fluence (increasing refractive index contrast between substrate and the waveguiding layer) towards longer wavelengths.

We interpret the narrow modes in the edge PL spectra using the leaky mode model12,13 schematically depicted in Fig. 2. The waveguide refractive index profile can be approximated by nonsymmetrical Gaussian or Gaussian- Lorentzian curves (similar to the implanted Si-ions distribution) with FWHM of about 0.3 μτη}2 The trajectory of relevant optical waves emitted by a chosen Si nanocrystal is shown. In case of ordinary guided modes, the optical wave undergoes total reflections both on the sample surface and at the interface waveguide core/substrate and the wave propagates inside the waveguide core. The leaky modes, on the contrary, are developing in a different way: optical wave, emitted by a silicon nanocrystal to the suitable direction (close to the boundary for the total reflection on the sample surface), undergoes the total reflection on the sample surface only. On the interface between the waveguide core and the substrate, where the refractive index contrast is lower than on the sample surface, the condition for the total reflection is not

fulfilled. The light partially reflects and partially refracts at the angle very close to 90°; the refracted part then propagates outside the waveguide core (leaky or radiation mode) but almost parallel to it. The reflected part of light reflects again on the sample surface and interferes with the original refracted wave. The constructive interference arises only for a narrow range of wavelengths. Therefore, only narrow spectral range fulfilling the condition for the constructive interference is selected from the broad PL spectrum and these leaky modes manifest themselves in the PL spectra as very narrow peaks. Different spectral positions of the TE and TM polarized peaks can be then explained by different phase shifts for both polarizations, which are induced during the optical wave total reflection at the sample surface.

The question arises as whether ordinary waveguided light mode propagation within the implanted layer core can also occur in our samples. The answer is yes; this kind of emission can be noticed in samples implanted to fluences of 3 X 1 0 17 and 4 X 1 0 l7 cm"2 as a wide band peaked at ~ 8 5 0 -9 0 0 nm [Figs. 1(a) and 1(b)]. However, these guided modes are strongly attenuated in samples implanted to higher total fluences due to waveguide losses. The exact nature of this attenuation is not known at present.14

From the point o f view of the waveguide optics, we expect the leaky modes to be spectrally situated at slightly lower frequencies than the cutoff frequencies o f the waveguide. This is the main observable difference between our leaky mode theory and the approach based on delocalized ordinary waveguide modes as proposed by Khriachtchev et al.,1 17 where these modes approach the cutoff frequency from the higher frequency side. Because values of theoretical cutoff frequencies are not easy to calculate, in particular, for graded index profile, neither is easy to distinguish between the two above models on the basis of spectral PL measure- mens themselves. However, we have recently proposed and realized a simple experimental approach of how to do it, which takes advantage of local change of refractive index on the sample surface.14 In what follows we apply this method in a modified form to investigate further the properties of the TE/TM doublets.

Figure 2(a) depicts the principle of our experiment, based on dropping various liquids onto the excited spot on the sample. By dropping a selected liquid, we change locally the refractive index of the surrounding media on the sample surface (air, formerly). The optical conditions for developing leaky modes will thus be changed on the sample surface. The optical wave travels different distances and undergoes different phase shifts during total reflection. Therefore, also the conditions for constructive interference forming the leaky modes change, which should manifest directly in the PL spectra as a shift o f the observed modes. Indeed, the left column in Fig. 2(b) shows the change of the PL spectra in our quartet of the samples upon dropping ethanol onto the sample surface. In all cases, the observed narrow modes undergo a significant redshift.

The right column of Fig. 2(b) demonstrates clearly that the above-mentioned leaky mode model is able to describe the observed redshift of the modes with high fidelity. This column presents the results of theoretical calculations of the

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074307-3 Luterova et al

FIG 2 (C olor) (a) Schem atic cross section o f the asym m etric p lanar w aveguide show ing propagation o f the gu ided m odes as w ell as form ation o f the substrate leaky m odes Surface refrac tive index change (induced hy a liquid drop p laced directly above the excited region) influences the developm ent o f the leakv m odes (b) C om parison o f the PL spectra in the w aveguiding geom etry for the sam ples in am bient atm osphere (full lines) and upon d rop ping ethanol (refractive index n - I 361. do tted lines) on the sam ple surfaceIm plant fluences arc m dicaicd for each sam ple Left co lum n expenm enta l data and right colum n: theory o f leaky m odes

leaky mode model developed in ihe framework of wave optics. In calculating these curves the above mentioned graded index profile of each sample, as determined by fitting interference-modulated optical transmission spectra of the implanted layers, was taken into account, together with refractive index values of applied liquids. Neither spectral profiles nor spectral positions of the substrate leaky modes can be calculated analytically. Numerical calculations were performed using the formula for cavity enhancement factor’11 (for more details, see Refs. 12 and 13) for the whole set of the samples. Taking in account that the theoretical model calculates only the leaky mode pan of the PL spectra but not the ordinary, spectrally broad guided modes, both experimental data and the model correspond very well, which pro vides strong support for the validity of the model.

In order to further support the model, we investigate both experimentally and theoretically the effect of different liquids (different refractive indices) dropped onto the sample implanted to a fluence of 5 X I017 cm": . The results are drawn in Fig. 3(a) and again, the measured and the simulated data agree very well. With increasing refractive index of the liquid, we initially observe increasing redshift of the modes. At some point, however, the “doublet" mode structure disappears and a broad PL spectrum can be seen. Actually, this happens when the refractive index of the liquid reaches the

J Appl Phys 100. 074307 (2006)

FIG. 3. (C olor) (a) PL spectra in the w aveguiding geom etry show ing leaky m odes in the layer im planted to a fluence o f 5 X I 0 1’ cm * D rops o f various liquids above the exc ited spot lead to a redshift o f both T E and TM m odes. S pectra correspond ing to various liquids have been vertically sh ifted (h) PL peak position as a function o f the refrac tive index o f the liquid. Sym bols experim ental da ta and lines: theory. For liquid refrac tive index h igher than refrac tive index o f the silica substrate in , = I 455) the theory predicts hoth d isappearance o f the d istinct double t s tructure and a back shift o f the broad em ission band to shorter w avelengths [see a lso the right panel in (a)].

refractive index of the sample substrate (n, = 1.455). i.e.. the point where the waveguide loses its asymmetry, total reflection on the upper boundary is canceled, and the condition for developing narrow TE/TM resolved leaky modes is not ful filled anymore.

Figure 3(b) plots the PL peak position versus the refractive index of the applied liquids. Further refractive index increase above n, still keeps the broad spectrum Theoret. cally calculated shift goes, somewhat surprisingly, back to shorter wavelengths. However, this can be intuitively understood. since with further increasing refractive index of the liquid above the refractive index of the sample substrate, the role of the substrate and of the capping medium will interchange and (another type of) leaky modes should appear again. Such a back shift is. however, difficult to trace expen- mentally because of the large spectral bandwidth and possible admixture of normal incidence PL emission,

In calculating the theoretical curves in Figs. 3(a) and

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074307-4 Luterová et al. J . Appl. Phys. 100, 074307 (2006)

3(b) we considered the liquid droplet thickness infinite, since its real thickness (~1 mm) is much larger than the waveguide core thickness as determined by the refractive index profile (FWHM of —0.3 /Am).

CONCLUSIONS

In conclusion, by comparing the experimental and theoretical PL spectra under different ambient conditions, we further verified the validity of the leaky mode PL model in the samples containing silicon nanocrystals embedded in a S i0 2 matrix. This phenomenon can find practical applications, for example, as an optical sensor of the refractive index of the media surrounding the sample.

ACKNOWLEDGMENTS

Financial support through Project No. IAA1010316 of GAAV CR and LC5I0 Research Centrum is greatly acknowledged. Institutional Research Plan No. AV0Z 10100521 supports the research work at the Institute of Physics. The authors thank R. G. Elliman from the Australian National University, Canberra, for providing the samples and V. Kohlová and J. Pšenčík for experimental assistance.

' ľ . Pavesi, L. Dal Negro. C. Mazzoleni. G. Franzo. and F. Priolo. Nature(London) 408. 440 (2000).

2L. Dal Negro el al.. Physica E (Amsterdam) 16, 297 (2003).

3L. Dal Negro. M. Cazzanelli. L. Pavesi, D. Pacifici. G. Franzo. F. Priolo. and F. Iacona. Appl. Phys. Lcii. 82. 4636 (2003).

*l_. Khriachtchev. M. Räsänen. S. Novikov, and J. Sinkkonen, Appl. Ptiys. Lett. 79. 1249 (2001).

JJ. Ruan, P. M. Fauchet, L. Dal Negro, M. Cazzanelli. and L Pavesi. Appl. Phys. Leu. 83. 5479 (2003).

6K. Luterová, K. Dohnalová, V. Svitek, I. Pelant, J.-P. Likforman, O. Crrgut, P. Gilliot. and B. Hönerlage. Appl. Phys. Lett. 84, 3280 (2004).

7M. H. Nayfeh, N. Barry, J. Themen, O. Aksakir, E. Gratton. and G. Bclomoin, Appl. Phys. Lett. 78, 1131 (2001).

*K. Luterová. I. Pelant, 1. Mikulskas, R. Tomasiunas, G. Muller. J.-J. Grob. J.-L. Rehspringer, and B. Hönerlage. J. Appl. Phys. 91. 2896 (2002).

’j. Valenta, I. Pelant, and J. Linnros. Appl. Phys. Lett. 81, 1396 (2002). I0K. Luterová, D. Navarro, M. Cazzanelli, T. Ostatnický, J. Valenta, S.

Cheylan. I. Pelant. and L. Pavesi. Phys. Status Solidi C 2. 3429 (2005). MK. Luterová el a l, Opt. Mater. (Amsterdam. Nelh.) 27. 750 (2005).>2J. Valenta, T. Ostatnický, I. Pelant, R. G. Elliman, i. Linnros, and B.

Hönerlage. J. Appl. Phys. 96. 5222 (2004).IJT. Ostatnický, J. Valenta. I. Pelant, K. Luterová, R. G. Elliman. S. Chey

lan. and B. Hönerlage. Opt. Mater. (Amsterdam, Neth.) 27. 781 (2005). I4I. Pelant. T. Ostatnický, J. Valenta. K. Luterová. E. Skopalová. T. Males.

and R. G. Elliman. Appl. Phys. B: Lasers Opt. 83. 87 (2006).IJL. Khriachtchev, M. Räsänen. and S. Novikov. Appl. Phys. Lett. 83. 3018

(2003).“ L. Khriachtchev, M. Räsänen. S. Novikov, and J. Lahtinen, J. Appl. Phys.

95, 7592 (2004).>TL. Khriachtchev, M. Räsänen, and S. Novikov, Appl. Phys. Lett. 86.

141911 (2005)."G . Viera. S. Huet. and L. Boufendi. i. Appl. Phys. 90. 4175 (2001).'*R. Baets, P. Bienstman, and R. Bockstaele. in Confined řholun Systems.

Lecture Notes in Physics Vbl. 531, edited by H. Benisty. J.-M. Gérard. R. Houdrí. J. Rarity, and C. Weisbuch (Springer. Berlin. 1999). p. 38.

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Available online at www.sciencedirect.com

• · * r * · r \ · i JOURNAL OF

·· ScienceDirect LUMINESCENCEELSEVIER Journal o f Luminescence 121 (2006) 267-273 ----- —

www.elsevier.com/locate/jlumin

Silicon nanocrystals in silica—Novel active waveguides for nanophotonics

P. Janda“, J. Valenta3’*, T. Ostatnický3, E. Skopalová6, I. Pelantb,R.G. Elliman0, R. Tomasiunasd

“Department o f Chemical Physics <£ Optics, Faculty o f Mathematics and Physics, Charles University. Prague, Czech Republic ''Institute o f Physics, Academy o f Sciences o f the Czech Republic, Prague. Czech Republic

cElectronic Materials Engineering Department, Research School o f Physical Sciences and Engineering. Australian National University. Canberra. Australia Λ Institute o f Materials Science and Applied Physics, Vilnius University, Vilnius. Lithuania

Available online 7 Septem ber 2006

Abstract

Nanophotonic structures combining electronic confinement in nanocrystals with photon confinement in photonic structures are potential building blocks οΓ future Si-based photonic devices. Here, we present a detailed optical investigation o f active planar waveguides fabricated by S i+-ion im plantation (400keV, fluences from 3 to 6 x 10l7cm~2) o f fused silica and thermally oxidized Si wafers. Si nanocrystals formed after annealing emit red-IR photoluminescence (PL) (under UV-blue excitation) and define a layer o f high refractive index that guides part o f the PL emission. Light from external sources can also be coupled into the waveguides (directly to the polished edge facet o r from the surface by applying a quartz prism coupler). In both cases the optical emission from the sample facet exhibits narrow polarization-resolved transverse electric and transverse magnetic modes instead o f the usual broad spectra characteristic o f Si nanocrystals. This effect is explained by a theoretical model which identifies the microcavity-like peaks as leaking modes propagating below the waveguide/substrate boundary. We present also perm anent changes induced by intense femtosecond laser exposure, which can be applied to write structures like gratings into the Si-nanocrystalline waveguides. Finally, we discuss the potential for application of these unconventional and relatively simple all-silicon nanostructures in future photonic devices.© 2006 Elsevier B.V. All rights reserved.

PACS: 78.67.Bf; 42.79.gn; 8l.07.Bc

Keywords: Nanocryslals; Waveguide: Silicon: Photonics

I. Introduction

Research on silicon-based photonics is m otivated by the aim to com bine integrated electronic and photonic structures on a single silicon chip. Silicon quantum dots or nanocryslals (Si-NCs) have attracted much atten tion due to their strong photolum inescence (PL) [I] and have been used to dem onstrate silicon-based light-em itting diodes [2,3]. Ensembles o f Si-NCs can also be employed lo fabricate active optical waveguides [4-8] tha t exhibit spectral filtering o f the Si-N C PL em ission, if the refractive

‘ Corresponding author. Tel.: +420221911272; fax: +420221911249. E-mail address: [email protected] (J. Valenta).

0022-2313/S-see front m atter © 2006 Elsevier B.V. All rights reserved, doi: 10.1016/j.jlumin.2006.08.004

index profile is properly designed. The occurrence of narrow (~ 1 0 n m ), polarization-dependent emission lines was reported by K hriachtchev et al. [4] for S i/S i0 2 waveguides and by our group [5,9] for sam ples containing Si-N C prepared by S i+ -im plantation into silica slabs. In o u r previous papers we explained the unexpected waveguiding properties using a model based on substrate leaking m odes o f a lossy waveguide [10,11].

In this w ork we com pare the propagation o f the intrinsic luminescence from Si-NCs with th a t o f external light coupled into the waveguides. This knowledge is crucial for pum p-and-probe m easurem ents (e.g. optical gain) and potential application as photonic devices (m odulators, am plifiers etc.). In addition we show perm anent changes

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P. Janda el al. / Journal o f Luminescence 121 (2006) 267-273

induced by fem tosecond laser exposure which can be applied to w rite 2D structures (gratings etc.) into the Si- nanocrystalline waveguides with sub-m icron resolution.

2. Experimental methods

Sam ples used in this study were prepared by S i+ -ionim plan ta tion in to 1 mm thick Infrasil (refractive index n, = 1.455) slabs with polished surfaces and edges, and into SiC>2 layers (about 5 μτη thick) prepared by therm al oxidation o f Si wafers. A n im plan ta tion energy o f 400 keV and ion fluences ranging between 3.0 and 6.0 x 10l7cm -2 were used to fabricate the slab waveguides. In order to form Si nanocrystals the sam ples were annealed for I h at 1100 °C in an N 2 am bien t and then passivated for I h a t 500 eC in form ing gas (5% H 2 in N j).

The im planted layer acts as an asym m etric planar waveguide. The profile o f the refraction index depends no t only on the im plantation energy and fluence but also on the annealing conditions. A lthough the annealing tem peratures, am bients and durations were nom inally the sam e, various sets o f sam ples were annealed in different laboratories and furnaces. Possible variations in the therm al history and levels o f oxidation lead to apparent differences in refraction index fo r nom inally identical sam ples (here, Figs. 2 -4 present results from one set o f sam ples and another set with lower refraction index is show n in Figs. 5-7). In o rder to num erically model the optical properties o f particu lar sam ples the refraction index profiles were m easured separately for each im planted sam ple. This was done by m easuring infrared transm ission spectra (see Fig. 2B) and fitting the interference fringes assum ing an asym m etric doublc-G aussian refraction index profile. T he maxim um o f the profile is typically abou t 600 nm below surface with a half w idth o f ab o u t 300 nm. T he peak refraction index has a value as high as 2 for the highest im plantation fluence [11]. T he d iam eter o f n ano crystals in the samples is estim ated to be between 4 and 6 n m using Ram an scattering (no t show n here) [I I].

PL was excited by a continuous wave H e-C d laser (325 nm, excitation intensity ~0 .3 W /cm2). The sample was placed on a rotatable x -y -z stage. A microscope with numerical aperture (NA) o f 0.075 (i.e. an angular resolution o f about 8.6°) was used to collect light and send it to a detection system consisting o f an imaging spectrograph (Jobin Yvon Triax 190) with a CC D camera (Ham am atsu C4880) [9]. All measurements were performed at room tem perature and all PL spectra were corrected for the system response.

T he coupling o f external light in to the waveguides was achieved in two ways (Fig. I):

(a) Prism coupling o f light from the upper surface o f the sample. Light from the Xe o r halogen lam p was collim ated into a q u artz prism. F or better optical con tact between the prism and sam ple an immerse liquid (index o f refraction n = 1.515) was dropped between the contact surfaces.

(B)

Fig. I. Two experimental arrangements for coupling o f external light into a waveguide sample: (A) coupling through a quartz prism on the upper sample surface. The second prism below sample is used to inhibit the back reflection o f light not coupled into the waveguide; (B) focused light directed on the truncated edge o f a sample. In both cases light leaving the opposite edge o f sample is collected with an optical fiber and sent to a spectrometer. Sketches not to scale.

(b) D irect coupling into the truncated facet (Fig. IB). The edge o f the sam ple was polished a t angle o f abou t 70° in o rder to separate light refracted to the higher-index waveguide from light entering lower-index substrate. H ere a warm -white L ED was used as a convenient light source. The angle o f incidence γ was between 15° and 30° with respect to the plane o f im planted layer. The divergence o f incident light was abou t 10°.

In both external-light-coupling set-ups the signal is collected by an optical fiber (detection N A ~0.008) and guided to the entrance slit o f the imaging spectrom eter Jobin Y von T riax 320 (with the low-dispersion grating of 100 grooves/m m ). Spectra are detected with the PI-Max intensified C C D (Princeton Instrum ents).

3. Results and discussion

3.1. Transmission speclra o f Si-NC layers

T he color o f the Si-NC waveguide layers is yellow-brown with the optical density increasing with im plantation fluence. The corresponding absorbance spectra are plotted in Fig. 2A (they are measured in a direction perpendicular to the nanocrystal plane using a UV-VIS double beam spectrom eter (Hitachi U-3300), the non-im planted area of a silica slab being em ployed as a reference). The absorption edge has approxim ately exponential shape. In infrared spectral region several interference fringes arc observed (Fig. 2B) which are used to model refraction index profile (see above).

268

P Janda el ul. / Journal o f Luminescence 121 (2006) 267-273 269

Wavelength [nm]

200 300 400 500 600 700 BOO

Wavelength [nm ]

Fig. 2. (A) Absorption spectra o f the samples implanted with fluences

from 3 lo 6 x 10'7 cm-3. A non-implanted area of the fused silica slab was

used as a reference. (B) Infrared transmission spectra of the same samples.

Interference fringes are used lo calculate refraction index profiles.

3.2. PL of active planar waveguides

The PL spectra o f the active planar waveguides have

very different shape depending on the experiment geome

try. Two arrangements are used: (i) the light is collected in

a direction roughly perpendicular to the sample plane (this

is a conventional PL arrangement) or (ii) in the direction

close to parallel lo the waveguide plane (i.e. from the

sample facel-waveguide arrangement)— see inset in Fig. 3.

In the former geometry the PL spectra are always broad

with a peak around 830 nm, typical of oxide-passivated Si

NCs with mean diameter ~5nm . On the other hand, the

waveguide geometry reveals narrow (down to lOnm)

spectral features with a high degree of linear polarization.

Figs. 3A and B show PL spectra of implanted oxide

layers (on Si substrates) measured in directions perpendi

cular and parallel lo the layer, respectively. The conven

tional PL (Fig. 3A) is modulated by deep interference

fringes due to high reflectivity o f ihe Si substrate. The

facet-PL (Fig. 3B) is not affected by interference; instead

a relatively narrow band is observed, the position of

which depends on implantation fluence (i.e. refraction

index profile). This peak shows partial linear polarization

500 600 700 800 900

Wavelength [nm]

Fig. 3. PL spectra of SiO j layers on Si substrates implanted with fluences

o f 3, 4, and S x IO'7cm~J. (A) PL detected in direction perpendicular to

the layer. (B) PL detected in direction parallel to the layer (from the facet).

The inset illustrates the experimental arrangement.

Wavelength [nm]

Fig. 4. PL spcctra of 4 x I0 l7cm-i layers measured in edge geometry

without polarizer (solid line) or with a linear polarizer parallel (TE. dashed

line) or perpendicular to the waveguide plane (TM, dotted line). The upper

panel (A) concerns S i02 layers on Si substrate, while the lower panel (B) is

for implanted fused silica slab.

270 P. Janda et at. / Journal o f Luminescence 121 (2006) 267 273

(Fig. 4A). U nder identical conditions (o f bo th fabrication and PL-experim ent) the facet-PL features a re m uch better resolved in im planted silica slabs (Fig. 4B). H ere a clear splitting o f the narrow PL peak into two peaks with polarization parallel (transverse electric T E o r s m ode) and perpendicular (transverse m agnetic T M o r p m ode) to the Si-N C waveguide plane is observed. The following discussion is restricted to im planted fused silica slabs where the T E /T M splitted m odes are nicely resolved.

PL spectra o f o the r set o f five sam ples prepared by im plantation to fluences o f 4.0, 4.5, 5.0, 5.5, and 6.0 x 10l7cm -2 are p lotted in Fig. 5. T he upper spectra in Fig. 5A represent PL collected from the plane o f im planted layers, while the lower PL spectra with T E /T M double-peaks are collected from the facet a t angle + 5° (NA de, = 0.075). An angle-resolved facet PL spectra from the layer implanted with dose o f 6 x 1017 cm -2 are plotted in Fig. 5B and the polar representation o f their integrated intensity is shown in Fig. 5C. The T E /T M split doublets shift

to longer wavelength with increasing im plantation dose. The facet PL has a very narrow emission cone with the maximum slightly shifted closer to substrate (ot^O0) (Figs. IB and Q .

3.3. Theoretical model o f the mode structure—radiative substrate modes

The surprising PL observations reported above do not correspond to simple waveguiding in ideal transparent waveguide which should transm it a continuous spectrum of guided m odes up to a cu t-off wavelength [12]. The cut-ofT for the first o rder m odes o f ou r waveguides can be estim ated to lie above ~ 1500nm . Consequently, the waveguides should transm it the entire 600-900 nm band em itted by Si-NCs, which is clearly not the case. There are two possible explanations:

(i) Delocalized guided modes: Let us assume wavelength- dependent losses in the waveguide, then those modes

Fig. 5. PL spectra o f five fused silica slabs implanted to fluences o f 4 -6 x I0 l7cm -2 . (A) Upper curves (a single wide band) correspond to PL emitted in a direction perpendicular to the waveguide, while lower spectra with doublet peaks are facei-PL detected in a direction a = 5" (a sketch o f the experimental arrangement is shown in the inset). (B) Angle resolved facet PL spectra o f the sample 6 x I0 l7cm ~2. ( Q Polar representation o f integrated PL intensity of angle resolved facet spectra from the panel B. M ost o f the PL intensity is emitted in a direction close to 0".

P. Janda et at. / Journal o f Luminescence 121 (2006) 267-273

(wavelengths) that undergo the sm allest losses will be advantaged. These are likely those m odes tha t are “weakly guided” with a strongly delocalized electric field. Such m odes propagate basically as p lanar waves in the substrate [13]. Ray optics describes these m odes by an angle οΓ incidence 0 tha t is greater than but very close to the critical angle 0C for to ta l internal refection (here the lower co re /S i0 2-substrate boundary is o f im portance only since the refractive index con trast a t the upper core/air boundary is high enough to ensure total internal reflection a t angles 0 safely higher than 0C). This model was proposed by K hriachtchev et al. [14,15] to explain T E /T M m ode structure in Si-NC planar waveguides sim ilar to ours. T he spectral separation between TE and TM m odes, is then a direct consequence o f the asym m etric index profile with different phase shifts expected for the T E and TM modes under to tal reflection a t bo th boundaries.

(ii) Radiative substrate modes: We have previously p ro posed an alternative mechanism involving substrate leaking or radiation m odes o f the Si-N C waveguide [10,11]. These modes propagate a t angle 0 situated close to but below 0C and undergo total reflection a t the upper boundary (larger index difference) b u t are only partially reflected on the lower boundary (sm aller index difference). Consequently, a small fraction o f their power is radiated into the substra te a t each bottom reflection. If the angle 0 is only slightly less than 0C, the leaking modes propagate near-parallel to the Si-NC plane. M oreover, the num ber o f reflections is very high (R is close to unity), resulting in a narrow spectral width for the modes. The mechanism o f spectral filtering in this case rem ains the sam e as discussed above, the only difference being that a phase shift at the upper boundary only comes to play during the initial stages o f propagation. A fter a finite num ber o f internal reflections all the radiant power escapes in to leaking m odes and emerges from the sam ple facet in a well defined direction, basically parallel to the Si-N C film. This m akes such substrate modes virtually indistinguishable from the guided modes. T he substrate modes are usually considered undesirable parasitic radiation and thus do no t norm ally receive much attention. Indeed, only in cases where guided m odes undergo significant losses (absorption and scattering in the waveguide core and diffraction on the narrow output aperture) do the substrate leaking m odes play a dom inant role.

The fact that the two above proposed m echanism s have a different dependence on the refractive index difference at the surface provides the basis for testing their validity experimentally. The principle is to change locally the cladding layer refractive index. This was done by placing liquid drops on the waveguide/air surface [11,16]. If a d rop is above the excited PL spot, the T E /T M m odes gradually red-shift and broaden with increasing refraction index o f

applied liquid and eventually d isappear if the index con trast approaches zero. However, when the d ro p is placed some millimeters aw ay from the spo t (betw een the photo-excited spot and the ou tpu t facet), no changes in modes is observed, consistent with all the rad ian t pow er escaping into radiative substrate m odes. These experim ents are supported by num erical m odeling o f the PL spectra which show excellent agreem ent with experim ents and provide unam biguous validation o f the leaking m odes model [11].

3.4. Coupling and propagation o f external light in Si-Nc waveguides

The transm ission spectra o f the five samples (im plan tation fluence 4 -6 x I0 17cm -2 ) obtained by white-light coupling through a prism (Fig. 1A) are shown in Fig. 6. In the m easured spectral region two broad transm ission bands (blue and red) are observed for each sample. The positions o f both bands red-shifts with increasing fluence and the position o f long-wavelength bands coincides with tha t o f the PL leaking m odes (Fig. 5A). O ur calculation show that the red and blue bands correspond to second and third o rder leaking m odes (the first one being in infrared). Broadening o f the m ode structure m ay be a consequence of the very low num ber o f reflections undertaken by coupled light before escaping to the substrate [17].

C oupling o f external light (the w arm -w hite LED) through a truncated facet (Fig. IB) gives the best result for a coupling angle y~20°, as expected (Fig. 7). In this configuration we detect narrow and polarization-split peaks a t an ou tpu t angle a~ 2 ° . T he peaks are, however, not transm ission bu t absorp tion peaks. This can be understood if it is assum ed tha t the detected light is not from radiative substra te m odes (which represent a small portion o f transm itted light) but from filtered transm itted light propagating alm ost parallel to the Si-N C waveguide

Wavelength [nm]

Fig. 6. The transmission spectra o f prism-coupled light detected at angle a = 7° from samples presented in Fig. S.

271

272 P. Janda eI al. / Journal o f Luminescence 121 (2006) 267-273

Wavelength [nm]

Fig. 7. Com parison o f transmission spectra o f sample 5.5 x I0 l7cm ~2 obtained by the direct facet-coupling (upper curves, solid line— nopolarization, dashed and dotted lines correspond to TE and TM polarization, respectively) and by the prism-coupling (lower spectrum).

from which a part o f pow er escaped to the substrate modes. The blue th ird o rder m odes are m uch stronger com pared to second o rder because o f higher absorp tion in blue spectral region.

3.5. Leaking modes vs. optical gain

One o f the m ost interesting questions concerning nanocrystal waveguides is the interplay between radiative substra te m odes and optical am plification by stim ulated em ission. Since the first report on optical gain in Si-ion im planted Si-N C layers by Pavesi et al. [18] sim ilar samples have been investigated by o ther groups w ith both positive [4] and negative [19] results. Two aspects o f this problem are addressed here.

First, experim ental artefacts have been show n to play an im portan t role when m easuring optical gain close to leaking m odes m axim a by the com m only used variable- stripe-length (VSL) technique [20]. These artefacts are mainly due to unconventional propagation and coupling o f these m odes in the detection system, and their interplay with the N A o f detection. In order to correct m ost o f these artefacts it has previously been proposed tha t VSL m easurem ents be com bined with a shifting-excitation-spot (SES) technique [20]. Indeed, it should be stressed tha t the in terpretation o f VSL results w ithout associated SES m easurem ents can lead to erroneous results.

Secondly, the potential advantages o f leaking m odes for achieving optical gain are spectral narrow ing, low losses, and directionality o f propagation . On the o ther hand the propagation path o f radiative m odes th rough a pum ped active medium (Si-NCs form ing the waveguide) is limited by leakage into the substrate. A ttem pts to achieve optical

gain on leaking m odes was successful only under strong nanosecond pulsed pum ping (6 ns, 355 nm from THG- Nd:Y A G laser) w ith the gain threshold around 50m J/cm 2 and maximum gain a t TM m ode o f abou t 12 cm -1 for 100 m J/cm 2 excitation [21].

F urther theoretical investigation o f the radiative modes in the loss/gain m edium is in progress.

3.6. Permanent changes o f Si-NC waveguides induced by laser pulses

The Si-NC waveguides in silica m ay be dam aged by high-intensity laser excitation and apparen t differences in dam age are evident for nanosecond and femtosecond pulses. W hen irradiated with the 420-nm, 5 ns ou tpu t o f an optical param etric oscillator (O PO ) pum ped by THG- N d:Y A G (N L 303 + PG I22, Ekspla) the dam age threshold is very sharp a t around 800 m J/cm 2. T he dam age appears as micrometer-size granular aggregates in the Si-NC followed im m ediately by com plete ab lation o f the implanted layer. The mechanism is m ost probably related to heating and even melting o f Si-NCs [22] which leads to failure o f the silica m atrix. This is evidenced by the appearance o f cracks and surface ruptures which can lead to com plete rem oval o f the SiN C layer.

In contrast, fem tosecond laser excitation (400 fs, 400 nm from SH G -Ti:sapphire laser) sta rts to m odify sample at much lower pulse energies > 2 0 m J/cm 2. There are two distinct phases o f layer dam age. The initial stage appears as darkening (brow n coloration) o f the excited area. Micro- Ram an m easurem ents (no t presented here) show that it corresponds to am orphization o f the Si-NC layer

Fig. 8. (A) The diffraction grating (period o f about |2 μ ιη ) ablated in the Si-NC waveguide (implanted fluence 4 x I0 l7cm - J ) by an interfering laser pulses from femtosecond laser (SI-IG-Ti:sapphire laser, 400 fs, 400 nm). (B) A photograph o f the pattern produced by diffraction o f 633 nm Hc-Ne laser beam on tlie ablated grating.

P. Jandu et at. / Journal o f Luminescence 121 (2006) 267-273 273

(it appears similar to the implanted layer before annealing).

In the second step at higher excitation the layer is ablated.

Clearly, the damage mechanism for ultrashort laser pulses

(400 fs) is different to that of the longer (5 ns) pulses. The

advantage of fs-ablation is that the boundary between the

ablated and unchanged area can be very sharp, enabling

fs-laser-ablation to be used for lithography to create

microstructures in the planar waveguides. In Fig. 8 we

demonstrate a diffraction grating with 12 μπι period

written into 4 x l 0 l7cm-2 implanted layer by 400fs,

400 nm fs-pulses.

4. Conclusions

Si-ion implantation into silica slabs or oxide layers on Si

wafer followed by annealing is a relatively easy way to

fabricate active nanocrystalline planar waveguides. In spite

of their simplicity these waveguides show rich optical

phenomena which are mainly connected to peculiar

radiative substrate modes— so-called leaking modes. This

study has investigated the influence of these complex

propagation modes on PL, transmission, and gain spectra

both experimentally and theoretically. Similar anomalous

phenomena connected to the interplay between radiative

and guided modes are expected to take place in other types

of active waveguides. The possibility of spectral, polariza

tion, and spatial filtering reported for active Si-NC

waveguides ofTer interesting possibilities for application

in silicon-based photonic devices or sensors.

Acknowledgement

Financial support through the projects of Research plan

MSM0021620835 and Research centre LC510 o f MSM T

CR, Project no. IAA10I03I6 of GAAV CR , 202/0I/D030

ofGACR, the Australian Research Council, and a grant of

the Lithuanian State Foundation for Science and Studies

(R.T.) is greatly acknowledged. The research work at the

Institute of Physics is supported by Institutional Research

Plan no. AV0Z 10100521. One of the authors (I.P.) thanks

the Laserlab-Europe Integrated Initiative for financial

support (vulrcOOl 168).

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MASTER'S THESIS Mode Structure in the Light Emission from Planar Waveguides with Silicon

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