Maximizing Tensile Strain in Germanium Nanomembranes for ...

Maximizing Tensile Strain in Germanium Nanomembranes for Enhanced

Optoelectronic Properties

By

José Roberto Sánchez Pérez

A dissertation submitted in partial fulfillment of

the requirements for the degree of

Doctor of Philosophy

(Materials Science)

at the

UNIVERSITY OF WISCONSIN-MADISON

2015

Date of final oral examination: 01/13/15

The dissertation is approved by the following members of the Final Oral Committee:

Max G. Lagally, Professor, Materials Science and Engineering

Donald S. Stone, Professor, Materials Science and Engineering

Mark A. Eriksson, Professor, Physics

Xudong Wang, Associate Professor, Materials Science and Engineering

Robert H. Blick, Professor, Head of the Institute of Applied Physics, and of the Center

for Hybrid Nanostructures University of Hamburg, Germany

i

Abstract

Maximizing Tensile Strain in Germanium Nanomembranes for Enhanced Optoelectronic

Properties

José R. Sánchez Pérez

Under the supervision of Professor Max G. Lagally

At the University of Wisconsin Madison

Silicon, germanium, and their alloys, which provide the leading materials platform of mi-

croelectronics, are extremely inefficient light emitters because of their indirect fundamental en-

ergy band gap. This basic materials property has so far hindered the development of group-IV

photonic-active devices, including light emitters and diode lasers, thereby significantly limiting

our ability to integrate electronic and photonic functionalities at the chip level. Theoretical stud-

ies have predicted that tensile strain in Ge lowers the direct energy band gap relative to the indi-

rect one, and that, with sufficient strain, Ge becomes direct-band gap, thus enabling facile inter-

band light emission and the fabrication of Group IV lasers. It has, however, not been possible to

impart sufficient strain to Ge to reach the direct-band gap goal, because bulk Ge fractures at

much lower strains. Here it is shown that very thin sheets of Ge(001), called nanomembranes

(NMs), can be used to overcome this materials limitation.

Germanium nanomembranes (NMs) in the range of thicknesses from 20nm to 100nm

were fabricated and then transferred and mounted to a flexible substrate [a polyimide (PI) sheet].

An apparatus was developed to stress the PI/NM combination and provide for in-situ Raman

measurements of the strain as a function of applied stress. This arrangement allowed for the in-

troduction of sufficient biaxial tensile strain (>1.7%) to transform Ge to a direct-band gap mate-

ii

rial, as determined by photoluminescence (PL) measurements and theory. Appropriate shifts in

the emission spectrum and increases in PL intensities were observed.

The advance in this work was nanomembrane fabrication technology; i.e., making thin

enough Ge sheets to accept sufficiently high levels of strain without fracture. It was of interest to

determine if the strain at which fracture ultimately does occur can be raised, by evaluating fac-

tors that initiate fracture. Attempts to assess the effect of free edges (enchant access holes) on

the NM were made and an increase of 35% in the strain to at which crack first formed was found

on NMs that lack etchant access holes. Ge NMs were used as a platform to investigate the rela-

tionships between surface passivation / functionalization and the physical properties of the mate-

rial. Furthermore, attempts to investigate the relationship between these surface treatments and

the formation of cracks under biaxial strain were made, but no convincing increases in maximum

achievable strain were found with the passivation approaches that were evaluated.

iii

Acknowledgements

First of all I would like to thank Professor Max Lagally for all the support and knowledge

imparted professionally and personally. He gave me independence to do my work while creating

an encouraging work environment that helped me hone my skills as a researcher. Thank you Pro-

fessor Roberto Paiella, Cicek Boztug, Faisal Sudrajat and Jian Yin from Boston University for

collaborating with me on this work, providing the photoluminescence measurements. Your ex-

pertise in the field of optoelectronics was invaluable. I will also like to acknowledge my commit-

tee members Professors Donald Stone, Mark Eriksson, Xudong Wang, and Robert Blick for tak-

ing the time to review my work.

Thanks to all of the Lagally group members past and present that helped with experiments

and gave feedback on research, talks, and journal submissions. I would especially like to

acknowledge Frank Flack for his invaluable feedback on preparing this thesis and ideas on

strengthening my work. Thank you RB Jacobson for all the help designing the pressure cell use

in this work, for always being there when I needed help either fixing or redesigning the whole

system, and for doing it all with a smile on your face and encouraging words. WeiWei Hu,

Pornsatit Sookchoo, and Xiaorui Cui, thank you for all the conversations, research and non- re-

search related, that made my day better. Thank you Deborah Paskiewicz for all the lessons from

how to grow and fixing the MBE to how to improve Raman measurements. Don Savage, Fran-

cesca Cavallo, and Shelley Scott, thank you for all the support and lessons that you imparted

over the last few years.

Thank you to all of the staff members and scientists who assisted me with the experimental

work in this thesis. In particular, the staff at the Wisconsin Center for Applied Microelectronics

iv

(WCAM) for cleanroom training, and the staff at the Materials Science Center (MSC) for help-

ing with the material characterization (XRD, XPS, and Raman) needed for this work..

The support from the Graduate Engineering Research Scholars (GERS) helped tremen-

dously, both financially and personally. Thank you Prof. Douglass Henderson and Kelly Burton

for creating a supporting community where I made friends that will last a lifetime. Thanks to Di-

ana Rhoads for her expertise in student affairs and her commitment to the students in the Materi-

al Science Program. Without her, my experience in Madison would not have been as good.

Lastly, I want to thank my family and friends for all the encouragement and support

through the years. Richard Rojas and Damaris Bezares treated me like family through our highs

and lows in Madison. Richard thank you for making me laugh even when the outlook was glum,

and for making our work space a little bit more like home. Thank you Danielle for meeting me.

Marrying you was the highlight of my time in Madison, your support and patience during these

years has been amazing. Thank you to my in-laws Chuck and Sue Broeren; I couldn’t ask for a

better extended family. A special thank you to my mother Ana Mercedes Pérez Reyes, the wom-

an that singly raised the man everyone knows today. Thank you for all the kind words and all the

strict ones too. Thank you for instilling in me the desire for knowledge and teaching me that hard

work is always worth it in the end.

v

Table of Contents

Abstract ............................................................................................................................................ i

Acknowledgements ........................................................................................................................ iii

Introduction ..................................................................................................................................... 1

Chapter 1: Strain and optical properties in semiconductors ........................................................... 6

1.1 Advantages of germanium .................................................................................................... 7

1.2 Properties of Germanium under biaxial tensile strain ........................................................... 9

1.3 Straining techniques for germanium ................................................................................... 11

1.4 Heteroepitaxial growth........................................................................................................ 14

1.5 Stressor layers ..................................................................................................................... 16

1.6 Mechanical Stress ............................................................................................................... 19

1.7 Mechanically stressed nanomembranes .............................................................................. 22

1.8 Chapter summary ................................................................................................................ 23

1.9 References ........................................................................................................................... 24

Chapter 2 Nanomembranes and fabrication of tensilely strained germanium .............................. 35

2.1 Germanium NM fabrication ................................................................................................ 36

2.2 Mechanically strained NMs ................................................................................................ 39

2.3 Strain characterization ........................................................................................................ 42

2.3.1 X-ray diffraction........................................................................................................... 42

2.3.2 Raman spectroscopy .................................................................................................... 44

2.4 Relationship between thickness and strain threshold.......................................................... 47

2.5 Crack formation and distribution of strain in the NMs ....................................................... 49

2.5.1 Crack formation under pressure .................................................................................. 49

2.5.2 Strain around an etchant access hole .......................................................................... 52

2.5.3 Comparisons of strain behavior of unstrained and previously strained NMs ............. 52

2.6 Effect of etch holes on NM strain distribution.................................................................... 55

2.7 Chapter summary ................................................................................................................ 57

2.8 References ........................................................................................................................... 58

Chapter 3 Light emission from tensilely strained Ge(001) ........................................................... 62

3.1 Photoluminescence and strain in Ge(001) NMs ................................................................. 62

3.2 Grating coupled light emission ........................................................................................... 75

3.3 Chapter summary ................................................................................................................ 78

3.4 References ........................................................................................................................... 79

Chapter 4 Nanomembrane surface passivation: Can we reduce cracking? ............................ 82

vi

4.1 Surface energy and reconstruction ...................................................................................... 84

4.2 Passivation of the germanium surface ................................................................................ 86

4.3 Organic functionalization of germanium surfaces. ............................................................. 88

4.4 Experiments on passivation and functionalization of bulk germanium .............................. 91

4.4.1 Characterization of surface chemistry of Ge (001) ......................................................... 92

4.4.2 Effect of treatments on surface roughness ................................................................... 95

4.5 Passivation of Ge(001) NMs ............................................................................................... 96

4.6 Strain comparison for functionalized and non-functionalized Ge(001) NMs .................... 98

4.7 Chapter summary .............................................................................................................. 100

4.8 References ......................................................................................................................... 103

Chapter 5 Conclusions ................................................................................................................ 107

5.1 Dissertation summary ....................................................................................................... 107

5.2 Outlook ............................................................................................................................. 109

5.2.1 Ge MEMS ................................................................................................................... 109

5.2.2 Study of crack formation in germanium NMs ............................................................ 110

5.2.3 Germanium tunable photodiode ................................................................................ 110

5.3 References ......................................................................................................................... 111

1

Introduction

Motivation

Strain in a material changes the lattice constant and crystalline symmetry, and thereby cre-

ates a material with new properties relative to the unstrained, but chemically identical, material.

The ability to alter the strain (its magnitude, direction, extent, periodicity, symmetry, and nature)

allows tunability of these new properties. In Si, SiGe, and Ge the electronic band structure,(1,

2)electronic transport,(3,4) optoelectronic properties,(5,6) phonon structure,(7) and kinetics and

thermodynamics of atom motion and structure (8) are all affected by strain. Recent interest in

tuning the germanium band structure, was created when theories predicted Ge(001) can be

changed into direct band gap semiconductor by biaxially straining it to 1.7-2%. (9-14).The re-

sulting band gap corresponds to light emission that encompasses the 2.1-2.5 μm mid-infrared

atmospheric transmission window. This spectral region is technologically important for use in

biochemical sensing and spectroscopy, where the distinctive absorption features of many molec-

ular species can be exploited. Specific applications include environmental monitoring, bio-agent

detection for security screening, medical diagnostics, and industrial process control.

It has, however, been difficult to attain the desired strain values. Attempts from heteroepi-

taxial growth (15-18) to applying mechanical stress (19,20) have not achieved the strain values

required to tune the band structure from direct to indirect. In the one case that claimed to reach

the required strain, no enhancement in the photoluminescence was observed.(15) In each of these

approaches, the amount of strain that can be introduced before a form of irreversible (plastic)

structural relaxation occurs is limited. Plastic relaxation, primarily through dislocation formation

or through cracking, occurs when the strain energy built up in the material exceeds the thermo-

dynamic and kinetic barriers to make strain relief favorable.(21)

2

Nanomembranes offer a novel way to tackle this problem, as they can be readily transferred

to different substrates. This transferability to any host and the thinness to accept larger strains

allows the development of stressing techniques that can achieve the desired levels of strain. This

dissertation describes such a method and the resulting photonic results. The dissertation also ex-

plores the materials science of stress and strain in very thin sheets, with the goal of eventually

finding ways to reach even higher levels of strain without materials failure.

Structure of dissertation

In Chapter 1, I provide background information on band structure and the difference be-

tween direct and indirect band gap. The theory of what happens to the Ge band structure when

biaxial strain is induced in the material is discussed. I review the work done on straining germa-

nium and make my case as to why nanomembranes are a better option.

Chapter 2 includes the fabrication of Ge NMs and the different ways to transferred to it to a

flexible substrate. These NMs on a flexible substrate are used with a pressure cell designed to

allow for in-situ Raman measurements while stressing the NM. The thickness and strain thresh-

old dependence are investigated. Crack formation in NMs is explored.

The dependence of photoluminescence (PL) on biaxial strain in Ge(001) is shown in Chap-

ter 4. Equivalent NMs and the same straining protocol were used by our collaborators in Boston

University, using an identical pressure cell I provided. A discussion on the results and how to

proceed in the future are shown in this chapter as well.

In Chapter 4 I discuss various passivation schemes for Ge in an effort to investigate the

effect of surface passivation in crack formation or inhibition. X-ray photoelectron spectroscopy

(XPS) was used to study the stability of these chemical treatments at atmospheric conditions.

3

Atomic force microscopy was used to evaluate the effect of the surface roughness. Attempts to

transfer these chemical treatments to a NM/film structure were made and the results are shown in

this chapter.

Chapter 5 is a summary of the work presented in this dissertation and of future directions

for straining Ge NMs. Specific suggestions of pathways to take to extend this work on Ge NMs

are provided.

References

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tors and Metal-Oxide-Semiconductor Field-Effect Transistors. J. Appl. Phys. 101:104503.

2. Fischetti, M.V., Ren, Z., Solomon, P.M., Yang M., & Rim, K. (2005). Six-Band KP Calcu-

lation of the Hole Mobility in Silicon Inversion Layers: Dependence on Surface Orienta-

tion, Strain, and Silicon Thickness. J. Appl. Phys. 94:1079-1095.

3. Schäffler, F. (1997). High-Mobility Si and Ge Structures. Semicond. Sci. Technol. 12:1515-

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4. Chu, M., Sun, Y., Aghoram, U., &Thompson, S.E. (2009). Strain: A Solution for Higher

Carrier Mobility in Nanoscale MOSFETs. Annu. Rev. Mater. Res. 39 :203-209.

5. Sun, Y., Thompson, S.E., & Nishida, T. (2010). Strain Effect in Semiconductors: Theory

and Device Applications Springer: New York.

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Strained Silicon as a New Electro-Optic Material. Nature 441: 199-202.

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45: 9447-9450.

4

8. Liu, F., Wu, F., & Lagally, M.G. (1997). Effect of Strain on Structure and Morphology of

Ultrathin Ge on Si(001). Chem. Rev. 97: 1045-1061.

9. Fischetti, M. V. & Laux, S. E. (1996). Band Structure, Deformation Potentials, and Carrier

Mobility in Strained Si, Ge, and SiGe Alloys. J. Appl. Phys. 80: 2234-2252.

10. Menéndez, J.; Kouvetakis, J. (2004). Type-I Ge/Ge1-x-ySixSny Strained- Layer Heterostruc-

tures with a Direct Ge Bandgap. Appl. Phys. Lett. 85: 1175-1177.

11. Liu, J., Sun, X., Pan, D., Wang, X., Kimerling, L. C., Koch, T. L., & Michel, J. (2007)

Tensile-Strained, n-Type Ge as a Gain Medium for Monolithic Laser Integration on Si.

Opt. Express. 15: 11272-11277.

12. Lim, P. H., Park, S., Ishikawa, Y., & Wada, K. (2009). Enhanced Direct Bandgap Emis-

sion in Germanium by Micromechanical Strain Engineering. Opt. Express 17: 16358-

16365.

13. Zhang, F., Crespi, V. H., & Zhang, P. (2009). Prediction that Uniaxial Tension along

<111> Produces a Direct Band Gap in Germanium. Phys. Rev. Lett. 102: 156401.

14. El Kurdi, M., Fishman, G., Sauvage, S., & Boucaud, J. (2010). Band Structure and Optical

Gain of Tensile-Strained Germanium Based on a 30 Band k.p Formalism. J. Appl. Phys.

107: 013710.

15. Huo, Y., Lin, H., Chen, R., Makarova, M., Rong, Y., Li, M., Kamins, T. I., Vuckovic, J., &

Harris, J. S. (2011), Strong Enhancement of Direct Transition Photoluminescence with

Highly Tensile-Strained Ge Grown by Molecular Beam Epitaxy. Appl. Phys. Lett. 98:

011111.

16. Jakomin, R., de Kersauson, M., El Kurdi, M., Largeau, L., Mauguin, O., Beaudoin, G.,

Sauvage, S., Ossikovski, R., Ndong, G., Chaigneau, M., Sagnes, I., & Boucaud, P. (2011)

5

High Quality Tensile-Strained n-Doped Germanium Thin Films Grown on InGaAs Buffer

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L., Mauguin, O., Jakomin, R., Sagnes, I., Ndong, G., Chaigneau, M., Ossikovski, R., &

Boucaud, P. (2013). Effect of Increasing Thickness on Tensile-Strained Germanium Grown

on InGaAs Buffer Layers. J. Appl. Phys. 113: 183508.

18. Fang, Y. Y., Tolle, J., Roucka, R., Chizmeshya, A. V. G., Kouvetakis, J., D’Costa, V. R., &

Menéndez, J. (2007). Perfectly Tetragonal, Tensile-Strained Ge on Ge1-ySny Buffered

Si(100). Appl. Phys. Lett. 90: 061915.

19. El Kurdi, M., Bertin, H., Martincic, E., de Kersauson, M., Fishman, G., Sauvage, S.,

Bosseboeuf, A., & Boucaud, P. (2010). Control of Direct Band Gap Emission of Bulk

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20. Cheng, T. H., Peng, K. L., Ko, C. Y., Chen, C. Y., Lan, H. S., Wu, Y. R., Liu, C. W., &

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Phys. Lett. 96: 211108.

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face Evolution. Cambridge University Press: Cambridge, UK.

6

Chapter 1: Strain and optical properties in semiconductors

The band structure of a solid describes the ranges of energy that an electron within the solid

may have (energy bands) and ranges of energy that are forbidden (band gaps). Band theory de-

rives these bands and band gaps by examining the allowed quantum mechanical wave functions

for an electron in a large, periodic lattice of atoms or molecules. Band theory has been success-

fully used to explain many physical properties of solids, such as electrical resistivity and optical

absorption, and forms the foundation of the understanding of all solid-state devices.

The band gap of a semiconductor is either direct or indirect. The minimum-energy state in

the conduction band and the maximum-energy state in the valence band are each characterized

by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are the same, the

band gap is direct. If they are different, the gap in indirect. These cases are illustrated schemati-

cally in Fig 1.1. If the band gap is direct, a conduction band electron can transition directly to a

hole state in the valence band and emit a photon (radiative recombination). If the gap is indirect,

a photon can be emitted only with the generation of a phonon of the correct momentum. For ra-

diative recombination in an indirect-band gap material like Si or Ge, the involvement of the pho-

non makes this process much less likely to occur. Therefore radiative recombination is far

weaker in indirect-band gap materials than direct-band gap ones. Light-emitting and laser diodes

are therefore almost always made of direct-band gap materials.

7

Figure 1.1 (A) Photon emission in a direct-band gap semiconductor (e.g., GaAs); recombination occurs at zero mo-

mentum (k-vector) where the maxima of the valence band and the minima of the conduction are located. (B) Photon

absorption in an indirect-band gap semiconductor (e.g., Si); phonon emission or absorption occurs to conserve mo-

mentum, in these materials the highest available state in the valance band and the lowest state of the conduction

band have different k-vectors.

Strain in a material changes the lattice constant and crystalline symmetry, and thereby cre-

ates a material with new properties relative to the unstrained, but chemically identical, material.

The ability to alter the strain (its magnitude, direction, extent, periodicity, symmetry, and nature)

allows tunability of these new properties. In Si, SiGe, and Ge the electronic band structure, (1,2)

electronic transport, (3,4) optoelectronic properties,(5,6) phonon structure, (7) and kinetics and

thermodynamics of atom motion and structure (8) are all affected by strain. Here I will review

how this strain can be used to alter optical and electronic properties in Ge.

1.1 Advantages of germanium

Germanium, a group-IV semiconductor, offers a wide range of established and potential

technological applications of high relevance and impact. In microelectronics, the large mobility

of both electrons and holes in bulk Ge is attractive for the purpose of increasing the speed and

8

drive current of CMOS-based logic devices. (9) The widespread development of Ge metal-oxide-

semiconductor field effect transistors (MOSFETs) has been limited by the lack of a stable native

oxide for gate insulation (in contrast to SiO2 on Si). The recent focus on high-k dielectrics as a

means to enable continued device miniaturization has, however, opened the door to potential

high-mobility replacements for Si as the channel material, and among these Ge has the advantage

of direct CMOS compatibility. In optoelectronics, Ge is already a well-established photodetector

material for use in on-chip data distribution, thanks to its strong interband absorption at near-

infrared optical communication wavelengths and, again, to its direct compatibility with the Si

microelectronics platform. (10) Additional applications within the emerging field of group-IV

photonics, including light emitters, (11) lasers, (12) and solar cells,(13) are being widely inves-

tigated.

As in other crystalline semiconductors, the transport and optical properties of Ge can be

engineered to enhance device performance through the controlled introduction of strain. The un-

derlying idea is that the electronic band structure of a semiconductor crystal, which determines

many of its key measurable properties, depends not only on the chemical nature of the constitu-

ent atoms but also on their spatial arrangement, which in turn is directly modified by the pres-

ence of strain. Strain can be used to lift degeneracies in the band structure at high-symmetry

points of reciprocal space, thereby suppressing intervalley and interband scattering, and to modi-

fy the curvature of energy bands near their extrema, and therefore the effective masses relevant

to electronic transport. These ideas have already been widely applied to group-IV semiconduc-

tors (including Ge as well as Si and SiGe) to produce significant carrier mobility enhancements,

leading to improved MOSFET performance. (14,15)

9

1.2 Properties of Germanium under biaxial tensile strain

Particularly remarkable for Ge (and not possible for Si) is that strain can be used to modify

its fundamental energy band gap, making a direct band gap and leading to a potentially dramatic

change in its optical radiative properties. As is well known, unstrained Ge is an indirect-band

gap semiconductor, with the valence-band maxima occurring at the Γ point of reciprocal space

(where the crystal wave vector k is zero), whereas the conduction band has four degenerate abso-

lute minima at the L points (i.e., on the boundaries of the first Brillouin zone along the 111 di-

rections). Electron-hole recombination between these band extrema involves a very large change

in the electronic momentum ћk that cannot be simply transferred to a photon, as photons carry

negligible momentum compared to carriers in a semiconductor. As a result, unstrained Ge is an

extremely inefficient light emitter. At the same time, a local conduction band minimum also ex-

ists at the Γ point, which can be lowered in energy relative to the L valleys through the applica-

tion of tensile strain until (around 2% biaxial strain) Ge becomes a direct-band gap material.

(15)This behavior is illustrated in Figs. 1.2(A) and 1.2(B), which show schematically the band

structures of unstrained Ge and Ge under 1.9% biaxial tensile strain, respectively. In other

words, the band structure of Ge is so sensitive to the interatomic separation that if the lattice is

made about 2% larger, the band edges move sufficiently (and differentially) so that the minimum

at the Γ point becomes the absolute conduction-band minimum. Under these conditions, a large

fraction of the electrons in the conduction band resides near the Γ point, where they can efficient-

ly recombine with the holes in the corresponding k=0 valence band maxima via light emission.

10

Figure 1.2. Strain-induced modifications of the Ge band structure. (A) Schematic band structure of unstrained Ge.

(B) Schematic band structure of Ge under 1.9% biaxial tensile strain in a {100} plane. From Ref. 16

The promise of tensilely strained Ge as a direct-band gap Group IV semiconductor has

been known for several years, based on extensive theoretical studies. (17-25) Direct-band gap Ge

represents a particularly striking manifestation of the potential power of strain engineering in sol-

id-state science and technology. From an application standpoint, it has important potential im-

plications in the ongoing search for a practical Si-compatible laser technology that can be inte-

grated seamlessly with CMOS microelectronics. (26) Such a technology, combined with the al-

ready existing suite of group-IV optoelectronic devices, would allow for the complete integration

of electronic and photonic functionalities on the same chip, for applications ranging from clock

and signal distribution in microprocessors to lab-on-a-chip systems for biochemical sensing, im-

aging, and LIDAR (“Laser Interferometry Detection and Ranging”).

The difficulty, of course, is that a bulk piece of Ge cannot be strained nearly that much

without fracturing. It has been realized, from strain energy considerations, that thin sheets of Ge

11

could be strained more than a bulk piece of Ge. Nevertheless, no one has been able to reach the

required levels of tensile strain to demonstrate direct-band gap behavior in Ge. My research has

focused on processing methods to create structures that enable the introduction of the required

strain to make Ge direct-band gap. Using Group IV nanomembrane technology I have been suc-

cessful in doing so. In particular, Ge(001) is the most favorable orientation and sheets as thin as

24 nm have been fabricated and strained.

1.3 Straining techniques for germanium

There are different approaches to create strain in Ge. Stress can be applied by heteroepitax-

ial growth, by the use of deposited stressor materials, and by mechanical means. In each of these

approaches, the amount of strain that can be introduced before a form of irreversible (plastic)

structural relaxation occurs is limited. Plastic relaxation, primarily through dislocation formation

or through cracking, occurs when the strain energy built up in the material exceeds the thermo-

dynamic and kinetic barriers to make strain relief favorable. The strain energy increases accord-

ing to the relation (27)

, 1.1

where U is the strain energy, σ is the normal stress on the material, ε is the corresponding strain,

and V is the sample volume. This equation shows two important relationships: 1) For a given

film area, the strain energy increases with thickness; and 2) a given strain energy is reached at

higher stress for a thinner sheet than for a thicker sheet.

For heteroepitaxial growth, where a thin film is grown on a host substrate having a differ-

ent lattice constant, in general the formation of dislocations limits the achievable strain. The me-

chanics of dislocation formation are well understood. (28) The thermodynamics of strain buildup

dVdU xx21

12

in growth of lattice-mismatched films and the transition to dislocation formation is expressed

through the concept of a critical thickness. (29) The transition to dislocation formation is also

dependent on the nature of the substrate. Thus for growth on thin substrates, either supported on

a release layer like an oxide or free-standing, the barriers for dislocation formation are lower and

the critical thickness for dislocation formation is consequently also lower. (30) Whereas dislo-

cated films can still contain strain, the strain will be laterally non-uniform because of plastic re-

laxation in the vicinity of dislocations. In terms of tensilely strained Ge, dislocations are undesir-

able, as they can act as nonradiative recombination sites, limiting the light emission efficiency.

Additionally, dislocations can degrade the transport characteristics in electrically injected devic-

es. Laterally non-uniform strain causes in-plane variations of the band structure. Under these

conditions, the emission will arise primarily from the high-strain regions, where the band gap

energy is smaller and the density of electrons and holes correspondingly higher. Importantly,

this behavior may also mitigate the deleterious effect of dislocations as nonradiative recombina-

tion centers, as the relatively higher band gap energy in the immediate surroundings of disloca-

tions may act as a potential-energy barrier that limits the number of carriers that can recombine

there.

For sheets or ribbons that are mechanically stressed via the application of an external ten-

sion, the likely mechanism for plastic relaxation is crack formation and fracture. Equation (1)

applies for the buildup of strain; except now we have a given volume and the stress is increased,

until a critical stress is reached. The key quantity is the strain energy release rate, which is de-

fined as the energy dissipated during fracture per unit of newly created fracture surface area. The

energy that must be supplied to a crack tip for it to grow must be balanced by the amount of en-

http://en.wikipedia.org/wiki/Fracture

13

ergy required for the formation of new surfaces and for plastic deformation. The energy release

rate is given by (31)

𝐺 ≡ −𝜕(𝑈−𝑊)

𝜕𝐴, 1.2

where U is the potential energy available for crack growth (the strain energy in the materi-

al), W is the work associated with any external forces present, and A is the crack area (crack

length for two-dimensional problems).

A crack will grow when the energy release rate G is greater than or equal to a critical val-

ue, Gc, called the fracture energy, which is a materials property independent of the applied loads

and the geometry of the body. (27,31) For a thin sheet, the potential energy U for a fixed value

of strain is lower at a lower thickness [see Eq. (1.1)]. Therefore the value of the energy release

rate G reaches the critical value Gc at higher strain levels for a thinner sheet. The effect of cracks

on achievable strain is similar to that of dislocations, but more severe. At and near cracks the

material will relax strain [for caveats, see later], and thus strain non-uniformities result, and the

average maximum strain is limited. For tensilely strained Ge, again, light emission will arise

primarily from the high-strain regions, where the band gap energy is smaller and the density of

electrons and holes correspondingly higher. Cracks will limit the light emission efficiency and

degrade the lateral charge transport characteristics in electrically injected devices.

For the group of techniques that use deposited stressor layers, the high levels of strain re-

quired to obtain direct-band gap Ge frequently are not achievable because the stressor layer can-

not generate a high enough level of stress for the thickness of the Ge layer used. Thus defect

formation may not even be an issue in some of these methods. Thinner Ge layers would be more

highly strained [see Eq. (1)], and may be subject to dislocation formation as described above. If

14

stressor layers that bend the Ge sheet are used, the strain varies through the thickness of the

sheet, and so will the band gap and shape of bands.

1.4 Heteroepitaxial growth

Strain engineering in electronic and optoelectronic device fabrication is generally based on

heteroepitaxy. As long as the film thickness is kept below the critical value for plastic defor-

mation, the growth proceeds in a pseudomorphic fashion and the film is strained as it adjusts to

the substrate in-plane crystal structure. The tensile strain required to make Ge direct-band gap is,

however, significant and it is no easy matter to a) find substrates with appropriate lattice con-

stants to serve as templates, and b) to grow a sufficiently thick film without the introduction of

massive numbers of dislocations, which, of course, relax the strain. Very thin layers of Ge can

be grown pseudomorphically on SiGe substrates that are formed via compositionally graded

deposition of SiGe on Si. (32)This procedure, used routinely for growing tensilely strained Si,

results in compressively rather than tensilely strained Ge, because Ge has a larger lattice constant

than SiGe, and thus this approach does not suit the purpose of creating direct-band gap Ge. Ten-

sile strain in Si does not achieve the same end, as the conduction-band minima of Si are too far

apart in energy and do not move appropriately with strain. (33) In any case, compositionally

graded SiGe substrates contain mosaic features (microcrystalline tilts) and strain inhomogenei-

ties, both caused by dislocation formation during the compositional grading, that ultimately cre-

ate defects in the strained Si or Ge films grown on top of these substrates. (34-36)

A small amount of tensile strain can be induced in Ge if it is grown on Si and allowed to re-

lax plastically (i.e., via formation of dislocations) at high growth temperatures (~900 ºC), and

subsequently cooled, because of the large difference in thermal expansion coefficients between

Ge and Si. Annealing at these high temperatures also somewhat reduces the density of disloca-

15

tions. The maximum tensile strain that can be obtained in this manner is limited to ~0.3%. (37)

This amount of strain is nevertheless useful, even with the induced dislocations: in fact, the com-

bination of this approach with highly degenerate n doping has led to the recent demonstration of

an electrically pumped Ge diode laser. (38)

Alternative growth template materials with lattice constant close to but somewhat larger

than that of Ge, such as InGaAs (39-41) and GeSn, (42) have also been investigated. For exam-

ple, a biaxial tensile strain of up to ~ 0.25% was obtained in Ge grown on a GeSn buffer layer

deposited on a Si substrate by chemical vapor deposition, with the Ge strain depending on the

buffer thickness and composition. (42) 0.5% biaxial tensile strain was introduced in Ge grown

on an InGaAs template layer on GaAs with In concentration of 9.8%. (20) Room-temperature

photoluminescence (PL) measured from this Ge film red-shifts with increasing In concentration

of the substrate, consistent with the increase in tensile strain in the Ge film. The classical ap-

proach of using a compositionally graded substrate, here InGaAs layers with increasing In con-

centration deposited on GaAs and annealed at each step to reduce dislocations, produced much

higher biaxial tensile strain values in Ge. (39) For a 10-nm thick Ge film pseudomorphically

grown on a graded In0.4Ga0.6As substrate, a biaxial tensile strain of 2.33% (as measured via x-ray

diffraction and Raman spectroscopy) was reported. This value is well above the expected thresh-

old for direct-band gap behavior (1.9%). Note that the Ge film is very thin, as otherwise it would

exceed its critical thickness. Even below its critical thickness, this Ge film would be expected to

have threading dislocations throughout it, as well as a mosaic (microtilt) structure and lateral

strain inhomogeneities, emanating from the strain graded substrate (similar to those found in ten-

silely strained Si epitaxially grown on compositionally graded SiGe substrates). (34) A large in-

crease in the overall PL peak intensity relative to a similar unstrained Ge sample was reported

16

(greater than 20), but only at cryogenic temperatures and without the large red shift expected

from theoretical considerations of the change in band gap accompanying the increasing strain.

The authors did not persuasively comment on the lack of a red shift or the rapid extinction of the

PL with increasing temperature. The causes may be related to the extended defects in the grown

film that one would expect from the compositionally graded substrate that was used.

1.5 Stressor layers

Tensile strain in Ge can also be obtained via the use of suitable stressor layers. Illustrative

examples are shown in Figure 2. Typically, these layers consist of material under large compres-

sive strain, which is then allowed to relax partially via elastic strain sharing with the Ge film. As

a result, tensile strain is introduced in the Ge. An example of a suitable geometry that allows for

such elastic strain relaxation to take place is illustrated schematically in the cross-sectional image

of Figure 1.3(a). This geometry has been demonstrated recently using tungsten (which can be

deposited with a compressive stress of approximately 4GPa) as the stressor layer. (43,44) A 1.6-

μm-thick Ge film was deposited on a Si substrate, and then suspended inside a window by etch-

ing away the Si through a patterned layer of SiO2 on the substrate backside. Because Ge does not

grow epitaxially on Si, this film will be highly dislocated. The tungsten stressor layer (up to

900nm in thickness), deposited on the bottom surface of the edge-clamped suspended Ge film,

introduces an average biaxial tensile strain of about 1.1% in the Ge, through a bending of the

overall suspended layer. Because the Ge layer is curved, the strain will vary through its thick-

ness, an effect that is not considered. An increase in integrated PL intensity by a factor of ap-

proximately two was measured, together with a 130-nm red shift in peak emission wavelength.

A similar geometry was employed to strain a layered Ge p-n junction patterned in the shape

of a mesa with top-side contacts to the n and p regions, before deposition of the tungsten stressor

17

layer underneath the mesa. (43,44) Strained-Ge photodiodes and light emitting diodes (LEDs)

were fabricated; their responsivity and emission spectra, respectively, could be red-shifted

through the deposition of stressor layers of increasing thickness. The LED forward current was

also found to increase with increasing tensile strain, a behavior that was attributed to the ex-

pected increased intrinsic carrier concentration and enhanced carrier mobility caused by the

strain-induced band gap reduction. (14)

Figure 1.3. Schematic illustrations of the use of stressor layers to introduce tensile strain in Ge. (a) Cross-sectional

image of the geometry used in Ref. 29 to obtain nominally biaxial tensile strain in an edge-clamped suspended Ge

film. (b) Three-dimensional view of the uniaxially strained Ge photonic wires described in Ref.45. (c) Uniaxially

strained Ge microbridge geometry demonstrated in Ref.46 In all figures, the arrows pointing outwards (inwards)

indicate tensile (compressive) strain. The solid, dashed, and dotted arrows in (b) indicate regions of progressively

weaker tensile strain.

Tensilely strained Ge has also been obtained using Si3N4 as the stressor material. In the

work of Ref. 45, a compressively strained Si3N4 layer was deposited on a highly n-doped Ge film

that had been epitaxially grown on GaAs [Ge and GaAs(001) are closely lattice matched, so the

Ge was initially unstrained]. When this Si3N4 layer, the underlying Ge film, and part of the GaAs

substrate are patterned in the shape of a ribbon, as illustrated in Fig.1.3(b), the compressive strain

Ge stressor layer

substrate partially etched underlayer

(a)

(b)

(c)

18

in the Si3N4 layer relaxes as its flanks become free to move. Uniaxial tensile strain is correspond-

ingly introduced in the Ge along the direction perpendicular to the long axis of the ribbon. The

strain is non-uniform in the direction out of the plane, reaching maximally 0.6% at the Si3N4/Ge

interface and falling off rapidly with depth into the Ge layer. With this approach, net optical

gain was reported for light propagating along the ribbon. Similar to the laser demonstration of

Ref.38, this measured gain was enabled primarily by degenerate n doping of the Ge film. As

discussed in the next section, distinct advantages in terms of creating Ge light sources are ob-

tained with undoped Ge, but substantially larger strain levels are needed to allow for a population

inversion in the absence of high n doping.

In a somewhat different approach,(47) uniaxial tensile strain of approximately 1 % in sus-

pended Ge microbridges (ribbons) was obtained, using the deposition of tensilely strained Si3N4

stressor layers on both ends of the bridge [Si3N4 films can be either compressively or tensilely

strained depending on the evaporation conditions]. The same approach was also applied to a

cross-shaped bridge to obtain biaxial tensile strain near the cross center. Unexpectedly large PL

enhancements (by factors of over 100) were reported with these samples; it is likely, however,

that heating of the suspended membranes by the high-power cw pump light used in the PL meas-

urements played a role in these findings. (48)

Highly uniaxially strained Ge layers have been fabricated by taking advantage of the ther-

mal mismatch between Si and Ge, which allows using Si as the stressor material. (46) Ge is

grown directly on a Si-on-insulator (SOI) or bulk-Si substrate using low-energy plasma-

enhanced chemical vapor deposition. After growth, a series of annealing cycles is performed in

situ to reduce the density of threading dislocations, while at the same time introducing a small

amount of biaxial tensile strain in the Ge (about 0.15 %). As discussed earlier, this strain is

19

caused by the mismatch between the thermal expansion coefficients of Si and Ge and the result-

ing hindered relaxation of the Ge layer upon cooling. Constricted Ge structures [in the shape of

suspended microbridges, as shown in Figure 1.3(c)] were then patterned using electron-beam li-

thography, dry etching of the Ge layer, and a selective wet etch of the material underneath (either

Si or the SOI buried oxide). Because stress is inversely proportional to cross-sectional area, the

constricted regions in this geometry experience much larger tensile strain compared to the rest of

the Ge film. In fact, uniaxial-strain values up to 3.1% were measured in these regions using Ra-

man microscopy. A 210-meV (5.9 μm) peak-energy shift in the emission with respect to bulk Ge

and a strong increase (25) in the spectrally integrated micro-PL intensity were also observed.

No claim of a transition to direct-gap Ge was made; in fact a threshold of 4.7% tensile strain was

cited. (46)

Nam et al. followed the same concept but used the small (about 0.2 %) pre-existing tensile

strain in the Ge template layer of a Ge-on-insulator (GOI) substrate. (49 ) They obtained Ge

wires uniaxially strained up to 2.8 %. Furthermore, they showed that the strain (and therefore

the band gap energy) in the patterned Ge film could be modulated as a function of in-plane posi-

tion by varying the wire width, effectively producing strain-induced pseudo-heterostructures,

which had earlier been demonstrated for Si nanowires. (50) A large enhancement in micro-PL

intensity was observed, and attributed mostly to carrier confinement in the high-strain regions.

1.6 Mechanical Stress

Ge can be strained through the application of external mechanical stress. In general, this

approach is quite flexible, and in fact historically has provided the first means used to investigate

strain engineering of semiconductors. (51) Furthermore, it allows tailoring the materials proper-

ties after sample preparation (by varying the applied stress), a feature that is attractive for basic

20

studies as well as device applications. Recently, the same general approach has also been ap-

plied to nanostructures based on III-V semiconductors, such as GaAs nanowires. (52, 53) In the

context of Ge, the use of mechanical stress to enable optical gain has been investigated numeri-

cally in Ref. 20. The specific geometry considered in that study consists of a cross-shaped sus-

pended Si platform supporting a Ge disk at its center, in the presence of a vertical force of 330

mN applied at the platform center. This force may be obtained using an L-shape hook in the ex-

ternal chip package or an electrostatic actuator based on micro-electro-mechanical system

(MEMS) technology. The resulting stress field distribution, computed by finite element analysis,

is shown in Figure 1.4. At the platform center, where the Ge active layer resides, a maximum

biaxial tensile stress of 5 GPa is obtained, corresponding to a strain level of about 2.7 %. This

geometry should therefore be suitable for the development of direct-band gap Ge light-emitting

devices.

At the same time, straining via the application of mechanical stress has the important limi-

tation that, when bulk samples are employed, only small amounts of tensile strain can be intro-

duced before the onset of plastic relaxation via defect formation. The reason is that the strain

energy for a given stress increases with thickness (volume) as discussed earlier [Eqs. (1) and

(2)].This limitation is clearly illustrated in the initial attempts to study direct-band gap light

emission from mechanically stressed Ge. (54,55) In particular, in the work described in Ref. 54,

a maximum biaxial tensile strain of only 0.6 % [limited by sample debonding or fracture] could

be introduced in a 28-μm-thick Ge film mounted on a bulge/blister test apparatus, leading to a

red shift in emission wavelength (by about 125 nm) but no concomitant increase in output inten-

sity. In the work described in Ref. 55 a n-doped Ge wafer was used, featuring an even smaller

21

fracture limit of less than 0.4 % strain, and leading to a small (1.8) increase in measured PL in-

tensity.

Figure 1.4. Calculated in-plane stress distribution on a cross-shaped suspended Si platform supporting a Ge disk at

its center. From Ref. 13.

Much larger PL enhancements (almost 100) were observed using tensilely strained Ge

nanocrystals. (56) These samples were fabricated by mortar grinding of undoped (100) bulk Ge

wafers and the lattice constants measured from several electron diffraction patterns suggest a 2.2

± 1.1% strain. The emission wavelength was not red-shifted compared to unstrained bulk Ge, a

result that was attributed to quantum confinement effects, something that seems unlikely. (57)

There been also work in bending Ge nanowires. The mechanical strength of individual Ge

nanowires with <111> growth direction and diameters ranging from 23 to 97 nm was measured

by bending each with a robotic nanomanipulator. It is claimed that the nanowires tolerate bend-

ing strain of up to 17%, with a corresponding strength of 18 GPa prior to fracture. (58) The

strength is close to the ideal strength of Ge, 14-20 GPa. (59) This almost ideal measured strength

is presumably due to the limited size and cross-sectional area of the nanowires and the fact that

surfaces of whiskers (and the typically much smaller nanowires) can be very smooth without

22

crack initiation sites. Antipov et al. explain that such high strain in Si and Ge nanowires could

be due to microplasticity (parts of the wires becoming polycrystal), (60) which will affect the

electrical and optical properties of the material. Pearson et al. found an elastic strain of 2.6% for

a 20μm dia., >1mm long Si whisker. A value of strain of 1.75% for bending of a 4μm dia. Ge

whisker is quoted as a “private communication” between colleagues. (61) No PL experiments

were attempted with these nanowires.

1.7 Mechanically stressed nanomembranes

For samples with planar geometries, which are more directly compatible with device appli-

cations, nanoscale thicknesses are essential to enable large biaxial strains. Traditionally, single-

crystal semiconductor films with thicknesses of only a few tens of nanometers or less have been

the exclusive domain of heteroepitaxial systems, but, as already discussed above, such systems

have so far not been able to achieve the requisite strains in Ge (or if such strains were nominally

achieved, the light emission did not support the achievement of direct-band gap Ge). The emer-

gence of NM technology has created significant new opportunities for thin-film materials science

and applications. (33,35,36,62-72) This technology is based on the complete or partial release of

a thin semiconductor layer from its original substrate via the selective etch of an underlying sac-

rificial layer. The resulting membranes can be single-crystal while at the same time exhibiting

exceptional flexibility, with the capability of folding and unfolding many times without damage.

When completely released from their handle wafer, they can be transferred (using one of several

techniques such as wet transfer or dry printing) and strongly adhered onto a variety of host sub-

strates. Because of their extreme geometrical aspect ratios and the resulting unique mechanical

properties, NMs offer novel opportunities for strain engineering, both through spontaneous elas-

tic strain sharing in multi-layer NMs and through the external application of mechanical stress.

23

For the same reasons, they have been shown to provide an attractive high-performance alterna-

tive to organic semiconductors for applications in flexible electronics and optoelectronics. For

example, electronic devices can be fabricated on the NMs prior to the release step, followed by

transfer onto a new host substrate. This approach is highly desirable, particularly when the new

substrate cannot withstand the high-temperature processing necessary for electronic-device fab-

rication, as is the case for most organic materials. By performing the high-temperature pro-

cessing steps on the NM before release, it is thus possible to make extremely fast flexible elec-

tronics, using organic films as host substrates. (72,73)

In my work, (74-76) a simple straining technique involving the use of air to pressurize a

cell covered with a round sheet of compliant material has been applied to Ge(001) NMs to

demonstrate biaxial tensile strain sufficiently large to create a direct band gap. In order to illus-

trate the advantages of using NMs over other approaches to create highly strained Ge and thus to

put Ge photonics into reach, I describe the procedures and results for this approach in Chapters 2

and 3.

1.8 Chapter summary

In this chapter I have explained the modification of the Ge band structure from indirect-

band gap to direct-band gap under biaxial strain. I have highlighted the importance of a mid-

infrared optically active Ge that could be enabled with such strain. Recent work aimed at intro-

ducing large tensile strain levels in Ge was reviewed. Although considerable effort has been de-

voted to achieving high tensile strain in Ge using heteroepitaxy, a lack of optimally suited

growth templates has resulted in limited success. More recent work has involved the use of me-

chanically stretched thin sheets of Ge and nanowires, either via strain sharing with a stressor lay-

er or through the application of an external force. I explained why using ultrathin single-crystal

24

Ge NMs bonded to a compliant substrate and mechanically stressed can enable the measurement

of well-defined luminescence spectra at strain levels close to or beyond the threshold where Ge

becomes a direct-band gap semiconductor.

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35

Chapter 2 Nanomembranes and fabrication of tensilely strained germanium

Nanomembranes (NMs) are crystalline sheets of material that can be transferred, deformed,

and manipulated into 3D objects. NM technology allows the fabrication of electronic devices or

other structures, their release with patterned structures, and reattachment to a new substrate. This

approach is highly desirable, particularly when the new substrate cannot withstand the high-

temperature processing necessary for electronic-device fabrication, as is the case for plastics or

other organic substrates. Completely released NMs can be transferred and bonded to a new

host material using both wet and dry transfer techniques.

Semiconductor nanomembranes have emerged as a novel materials platform offering

unique opportunities for strain engineering, (1-4) both through spontaneous elastic strain sharing

upon NM release and through the external application of mechanical stress. In the present work,

this basic platform is applied to a major challenge of semiconductor optoelectronics, namely the

demonstration of practical silicon-compatible light sources. In particular, we show that biaxial

tensile strain in mechanically stressed Ge NMs can be used to transform Ge into a direct-band

gap material, with strongly enhanced radiative efficiency, which is capable of supporting popula-

tion inversion, as required for laser action. Importantly, these strained Ge NMs luminesce al-

ready at room temperature, are in principle suitable for light emission via electrical injection, and

should be fully integratable with complementary-metal-oxide-semiconductor (CMOS) electronic

devices using micro-electro-mechanical-systems (MEMS) technology. Therefore, unlike exist-

ing approaches, they meet all the key requirements of group-IV photonics-active materials. In

this chapter I will show how to fabricate these NMs and how to apply mechanical strain. I will

demonstrate the importance of NM thickness in this procedure and explore the potential im-

36

portance of edges and defects in limiting the achievable strain, and speculate on ways to limit

crack formation by changing the boundary conditions on the NMs.

2.1 Germanium NM fabrication

Ge NMs are fabricated, based on a methodology that has been developed in recent years for

a wide range of applications, (1-11) by releasing the Ge template layers of commercial GOI(001)

(Soitec SSA). Figure 2.1 illustrates the procedure. The GOI substrates are cleaned with acetone

and isopropyl alcohol and patterned with standard UV lithography to define the membrane

boundaries and small etchant access holes, as needed. For areas greater than 1mm2 etchant access

holes are needed for a complete release of the NMs in a reasonable time using standard photore-

sist. In those cases, etchant access holes of 5μm x 5μm area that are spaced 100μm apart are

used. Reactive ion etching is employed to define the Ge NM shape (Fig.2.1B), followed by a wet

etch in a solution of 49 % hydrofluoric-acid further diluted 1:10 in water to dissolve the under-

lying SiO2 layer (Fig. 2.1C) in around 12-13hrs, allowing the Ge NM to settle back onto the Si

handle wafer, where it is weakly bound. The NMs are subsequently transferred and bonded onto

125-µm thick, flexible polyimide (PI) films (Kapton©, Du Pont), by using spin-on liquid PI as a

glue layer and pressing the membrane onto the PI film (Fig. 2.1D). After transfer, the spin-on PI

is cured at 350 °C and the Ge NM is thinned from its original thickness (140-160 ± 5nm) to the

desired thickness using a wet etch with dilute hydrogen peroxide (H2O2) in water at 80 °C (etch

rate ~0.9 nm/sec). I used thicknesses ranging from ~80 nm to 20nm to investigate the amount of

biaxial strain I could introduce into the NM before cracking.

37

Figure 2.1. Schematic illustration of the Ge NM fabrication process used in my studies. From Refs.12 and 13

As an alternative method, the NMs can be transferred using wet transfer, see Fig.2.2. In-

stead of removing the photoresist used for patterning (Fig 2.2C), we can use this layer as an extra

stressor to help release the NM (Fig. 2.2D and E). For thick (>100nm) Ge template layers with

etch holes the photoresist can be removed before release but for thin (<100) Ge template layers

with or without etch holes the photoresist is required for release. Using a wet etch in a 49% HF

solution to dissolve the underlying SiO2 layer and quickly submerging the remaining system in

deionized (DI) water before the NM attaches to the Si host wafer, Ge NMs freely floating in wa-

ter can be achieved. As a higher concentration of acid can be used here, etching of the SiO2 and

release in water can be done in less than 30mins. The Ge NMs can be harvested by using a wire

loop to “fish” the NMs out. Because the NM will bond to the wire if they touch, the loop must

be small enough for the water to form a film within it and the NM is carried by the water film for

transfer to a new substrate or “host”. NMs can also be directly harvested by any host not rapidly

soluble in water by inserting the host underneath the NM and picking it up.

38

The NM will be bound to the host via hydrogen and van der Waals bonding, as shown in

Fig. 2.2F. The transferred NM is annealed at low temperatures (e.g., 30 min at 60–200 °C) to

evaporate any water. This procedure creates an oxide at the interface between the Ge and host.

The bond is so strong that it is not possible to remove the nanomembrane, irrespective of the host

(i.e., glass, polyimide (PI), polyethylene terephthalate (PET), or polydimethylsiloxane (PDMS)).

After annealing, the photoresist can be removed with acetone and isopropyl alcohol or by using a

low-power oxygen plasma.

The wet and dry transfer methods each have advantages that can be exploited for specific

applications. Dry-transfer methods are preferable when the new host substrate is soluble in wa-

ter or when higher-precision alignment is demanded for a particular application. Both techniques

allow for a NM to be transferred to a flexible substrate, i.e., a PI film. The transferred NMs can

be further processed as long as the new substrate can survive the required steps. NMs transferred

to flexible substrates can be distorted to introduce strain to a much greater degree than is possible

with bulk materials.

39

Figure 2.2. Schematic illustration of release and wet transfer of a Ge NM.(14)Wet transfer is a powerful technique

to transfer patterned or partially processed NMs to essentially any host substrate.

2.2 Mechanically strained NMs

The external application of mechanical stress historically provided the first means to inves-

tigate the effect of strain on the electronic and optical properties of semiconductors. (15) An im-

portant limitation of strain application is that, as long as bulk samples are employed, only very

small amounts (of the order of several tenths of a percent) of strain can be produced before the

onset of significant extended-defect formation. (16) This limitation is clearly illustrated in at-

tempts to study direct-band gap light emission from mechanically stressed bulk Ge, (17,18)

where maximum tensile strains of only 0.6% or less could be introduced, limited by sample de-

lamination or fracture.

40

Ge NMs offer a new perspective. With this technology, Ge NMs transferred and bonded to

a flexible host substrate are biaxially stretched. The characteristic NM thicknesses of only a few

tens of nanometers lead to substantially larger strain thresholds for plastic deformation and for

cracking than does the use of bulk materials. Specifically, because the amount of strain energy

stored in the NM is directly proportional to its thickness, the NM contains insufficient strain en-

ergy to drive defect formation (see discussion in Ch. 1). (9) NMs therefore represent the ideal

materials platform for strain engineering studies and applications in which a large strain is neces-

sary or desired.

To achieve the relative conduction band valley motion required to make Ge direct-band gap

with the least amount of strain, the Ge NM must be biaxially stretched. In order to do so, the 125

μm PI film on which the NM has been transferred is used to seal an otherwise rigid cavity that is

then filled with gas whose pressure can be reliably and reproducibly increased (from 0 to 900

kPa, higher values were not possible with this arrangement). A schematic illustration of the sam-

ple mount is shown in Fig. 2.3, together with an optical micrograph of a Ge NM bonded onto a

PI film and a photo of the actual pressure cell. The pressure cell allows for in-situ Raman meas-

urements but measurements using x –ray diffraction or interferometry were not possible because

of size constrains. In this arrangement the NM lies on the surface of an expanding sphere of PI,

so that the resulting strains are biaxial. The spherical expansion of the PI is effectively a bending

mode, in which maximum tensile strain is created at the top surface, where the NM resides. The

Ge NM on top of the pressurized PI film acts like a thin outer coating on an expanding sphere.

The strain in an expanding sphere increases radially, with the largest tensile values on the outer

surface, i.e., the NM. The NM is, however, much thinner than the PI film, so we can assume a

constant radial strain, i.e., the NM is uniformly strained. I will be using pressure and stress inter-

41

changeably during our discussion. I understand that the stress (pressure) I use to expand the PI

film may not represent the actual value of the stress the NM is feeling. We would need to meas-

ure the deformation of the NM to establish the nature of the stress in the film, but this cannot be

done in our current setup. From the basic relationship, 𝜎 = 𝜀𝐸, (16) we know the stress if we

know the strain. For example, for Ge at a 2% strain, the stress that the material might be experi-

encing is around 2GPa. However, this simple relationship assumes no shear stress in the materi-

al.

Figure 2.3 Ge NMs and sample mount. (A) Optical micrograph of a Ge NM bonded on a PI film. The array of

etchant access holes used in the release process is clearly visible. (B) Diagram showing the sample mount and the

location of the NM. (C) Pressure cell used for stressing the NM and for in-situ Raman spectroscopy measurements.

(D) Pressure cell with PI film. The black circle shows where the NM is located during the experiment.

42

2.3 Strain characterization

In this section I describe the two major methods I used to characterize NM strain – x-ray

diffraction and Raman spectroscopy.

2.3.1 X-ray diffraction

X-ray diffraction (XRD) is widely used to measure lattice constants and film thicknesses in

single-crystal thin films. Diffraction of x-rays from atomic planes in a crystalline lattice gives a

measurement of the plane spacing, d, according to Bragg’s law:

, 2.1

where θ is half of the scattering angle of the x-rays and λ is the wavelength (λ=1.5406Ǻ for the

PANalytical X’Pert PRO XRD system used in this project). For planes parallel to the surface, the

incident-x-ray angle is equal to half of the diffracted-x-ray angle (Fig. 2.4A). For thin films (t <

500nm), the x-rays will also diffract off the surfaces and interfaces of the film. These scans are

fit to simulations to extract lattice constants and thicknesses of individual layers or a

homogeneous thin film. Figure 2.4B shows an example of an XRD scan in which thickness

fringes can be observed. As films become thinner the x-ray intensity is reduced and the x-ray

fringe spacing becomes greater. The thinner the film the lower the number of fringes that can be

observed. For this project we used XRD to determine the thickness of our Ge layers before and

after etching. XRD was also use to investigate the initial strain condition of the Ge NM

transferred to PI and to compare the value with what was calculated from Raman spectroscopy.

43

Figure 2.4 (A) Schematic diagram of Bragg’s Law relationship. By varying the incident angle we can obtain (B) a

curve showing the spacing between the planes and subsidiary peaks, called fringes. From the spacing of these

fringes, we can extract the thickness of the film.

Figure 2.5 compares XRD from the GOI substrate (blue curve) and a transferred Ge NM

(red curve). The template layer in the GOI is thicker than the etched and transferred GeNM, as

seen by the fringe spacing. A reason to characterize the transferred NM is to detect any residual

strain resulting from the transfer process. The results show an equally good structural quality,

with a small compressive strain (<0.4%) induced by the polyimide as it finishes polymerizing (it

shrinks in the process). The value is calculated assuming the Ge template in the GOI is com-

pletely strain-free. Using Eq. 2.1 we can calculate the d spacing for strained and unstrained mate-

rials using the following equation:

, 2.2

where C11 and C12 are elastic constants for Ge.

44

Figure 2.5. XRD scan of Ge NM before release from the host GOI substrate (blue line) and after release and transfer

onto a polyimide film (red line). The shift in the peaks indicates a small net compressive strain in the transferred

NM (~0.4%).

Measurements of this kind for a NM mounted in our pressurizing rig could not be done in

the diffractometer because of size constraints. We use Raman spectroscopy as a more robust and

rapid way of getting information on the strain state of our system.

2.3.2 Raman spectroscopy

Raman spectroscopy is used to observe vibrational, rotational, and other low-frequency

modes in materials. (19) In the Raman effect, monochromatic light (Fig 2.6A), usually from a

laser in the visible, near infrared, or near ultraviolet range, interacts with molecular vibrations,

phonons, or other excitations in the system, resulting in the energy of the incident photons being

shifted up or down. The shift in energy gives information about the vibrational modes in the sys-

tem. Because these vibrations are dependent on the lattice constant, this information can be used

to calculate strain in the system.

45

The energy shift is caused by the excitation or deexcitation of a vibrational mode. The in-

cident light interacts with an electron from a filled state (valence band), exciting it to a higher-

energy empty state (Fig 2.6B-1). The excited electron interacts with a phonon, reducing its ener-

gy by the amount needed to excite the phonon mode [ωj] (or increasing in energy by the amount

needed to de-excite the phonon mode) (Fig 2.6B-2). The excited electron then recombines with

the hole and emits light at a new frequency, ωs = ωi ± ωj, where ωj is the phonon energy (Fig

2.6B-3). The scattered radiation one vibration quantum higher in energy is known as anti-Stokes

scattering and one vibration quantum lower in energy is known as Stokes scattering.

Micro-Raman spectroscopy uses a microscope objective to focus the laser light onto a

small area of the sample. The spot size is set by the numerical aperture and magnification of the

objective lens.

Figure 2.6 Raman effect. (A) Monochromatic light interacts with the sample and scatters inelastically by the energy

of a vibrational phonon. (B) Schematic diagram of the energetics of the Raman scattering process.

46

When crystalline materials are strained, the phonon modes shift in energy to reflect a

change in the lattice constant; a higher energy is required to excite phonon modes in compres-

sively strained material and a lower energy is required for tensilely strained material. This behav-

ior can be seen in Figure 2.7, where the spectrum for relaxed bulk Ge (blue peak) is compared

with that of a 40nm Ge NM under compressive strain (black curve) and the same NM under ten-

sile strain (red curve). The wavenumber is directly proportional to energy.

Figure 2.7 Example of Raman spectra for relaxed (blue curve), compressively strained (black curve), and tensilely

strained (red curve) Ge(001). The amount of strain here is 0.13% for compressively and 1.78% for tensilely strained

Ge. This latter degree of strain is possible only in NMs.

The change in energy needed to excite each phonon mode is determined by the magnitude

and direction of strain. Biaxial strain in the plane of the NMs can be measured as a function of

applied stress (i.e., gas pressure) via Raman spectroscopy. Raman spectroscopy is extremely

47

sensitive to strain in Ge when using the line associated with Ge-Ge stretch vibrations. The shift

of this line, Δω, can be related to strain, ε, using Equation 2.3:

ε = -B Δω , 2.3

where the coefficient B depends on known, experimentally determined, values of the Ge defor-

mation potentials. (20)

The strain in the plane of the NMs is determined as a function of applied stress (i.e., gas

pressure) using a LabRAM ARAMIS (HORIBA Scientific) Raman microscope equipped with a

633-nm-wavelength excitation laser. In these measurements, the laser beam is passed through a

filter to attenuate its incident power from 6 mW to ~ 1 mW and then focused onto the NM with a

50× objective lens, producing a spot size of about 2 μm. Because of the low thermal conductivi-

ty of the PI film supporting the NM, the use of sufficiently low incident power is required to

avoid heating the NM, which would affect the Raman shifts and therefore the inferred strain val-

ues. Ten random sites on each NM are measured for each value of the applied stress, and each

site is probed three times with a 15-sec exposure time. The peak position of the Raman signal is

determined from a Gauss-Lorentz fit of the measured spectra after background subtraction

(which is done real time by the instrument’s software), using the fitting tool available in the in-

strument’s software, LabSpec 5©

. The biaxial strain values are then calculated from the Raman

shifts (21) using Equation 2.3.

2.4 Relationship between thickness and strain threshold

The pressure/strain curves of four Ge NMs, 24-nm, 44-nm, 60-nm, and 84-nm thick, are

plotted in Fig.2.8. The small amount of compressive strain observed at zero pressure is attribut-

ed to PI-substrate curing effects, as I have already mentioned. As the sample mount is pressur-

48

ized, the measured biaxial tensile strain (averaged over several random sites on the NM) increas-

es linearly with the applied stress. Beyond a certain stress, the stress/strain relationship is no

longer linear, owing to the formation of cracks in the NM, which are visible in the Raman micro-

scope images, and which produce local strain relaxation. As the pressure is further increased,

rather than the strain increasing, more cracks form, leading to a saturation of the average strain.

Figure 2.8. Pressure/strain curves for four Ge NMs of different thicknesses. NM strain versus gas pressure in the

sample mount (Fig. 2.3B), as measured via Raman spectroscopy for (A) 24-nm, (B) 44-nm, (C) 60-nm, and (D) 84-

nm thick Ge NMs. The Ge NM after mounting on PI contains a small compressive strain, causing the offset at zero

pressure. Increasing error bars at higher pressures are due to the stochastic nature of the crack formation.

As mentioned earlier, for the same reasons that less strain can be induced in bulk samples, the

probability of crack formation at a given stress increases with membrane thickness. Cracks ulti-

Pressure (kPa)

24nm

44nm

60nm

84nm

0

1

2

0

1

2

0

1

2

0

1

2

0 200 400 600 800

Str

ain

(%

)

A

B

C

D

49

mately limit the maximum average strain. When the Ge NM initially shows cracks they are wide-

ly separated. As the stress is increased the density of cracks increases and no increase in strain

any longer occurs. That is quite evident in the strain/pressure curves. Specifically, for the 84-nm

and 60-nm-thick NMs the measured area-averaged strain saturates at ~1.4 % at a critical pressure

of ~500 kPa, as shown in Fig. 2.8C. A micrograph of a 60nm Ge NM at ~500 kPa is shown in

Figure 2.9 B.3; the extent of cracking in this NM can be seen. For the 24-nm-thick NM (Fig

2.8A), the area-averaged tensile strain continues to increase linearly with pressure up to a value

of 2.0% at 700 to 800 kPa, with no evidence of leveling off. Results for the 44-nm-thick NM are

consistent, with the area-averaged strain reaching a peak value of ~2.0 % at a stress of ~700 kPa

and then leveling off. The comparison between the traces in Fig. 2.8 therefore highlights the im-

portance of nanoscale thicknesses to obtain the desired large amounts of tensile strain.

2.5 Crack formation and distribution of strain in the NMs

2.5.1 Crack formation under pressure

In Fig. 2.9 I compare optical micrographs of two NMs with similar thicknesses. Sample A

is 53nm and Sample B is 60nm. At low pressure, e.g., 100 kPa, corresponding roughly to .08%

strain (Figs. 2.9 A.1 and B.1) we can see the NM without cracks. The first signs of cracks can be

seen in Fig. 2.9 A.2 and B.2 at 310 kPa (roughly 0.75% strain for these thicknesses). As seen at

this pressure the cracks are few and spread out. As the pressure increases the number of cracks

will increase as the critical energy release rate value (Gc explained in Ch.1) is reached. The NM

releases the strain by cracking. The dramatic change in cracks density can be seen in Figs. 2.9

A.3 and B.3, where the pressure is 517 kPa and the average strain is ~1.30%. An important ob-

servation at this point is the obvious difference between A.3 and B.3 in terms of crack density.

The only difference in the NMs is the spacing between etch holes, which would suggest that the

50

etch holes have an effect on crack formation, possibly acting as stress concentrators (discussed in

2.5.2). For sample b the number of cracks keeps increasing with increasing stress. A micrograph

of this sample at 620 kPa is shown in Figure 2.10.

Figure 2.9 Comparison of NMs at 100kPa (1), 310kPa (2) and 517kPa (3). Sample A is a 53nm NM with etch hole

spacing of 80μm. Sample B is a 60nm NM with 10μm x 10μm etchant access holes spaced 120μm apart. These im-

ages would suggest that the spacing between free edges might have an effect on crack formation. The cracks occur

principally along the orthogonal low-index <110> directions, which mark the {110} cleavage planes for Ge(001).

Scale bar is a 100μm.

Crack formation and propagation in such NMs is confusing and not understood. The mi-

crograph in Fig. 2.10 shows that NMs crack both close to and away from etch holes. It is not

possible to say if the cracks originate from the etch holes, if some of them do, or if none of them

51

does. Some of the cracks seem to start from previous cracks and will stop at another crack. The

majority of the cracks are oriented in <110> directions, which mark the {110} cleavage planes

for Ge (001). Also interesting is the observation that, while some areas are completely traversed

by cracks, other areas of up to 120μm by 120μm seem to be fully strained at values close to

1.6% (taking into consideration the error bars in Figure2.8C). This result suggests that making

the area being strained smaller for a given thickness can delay the formation of cracks. I discuss

this idea in Section 2.6.

Figure 2.10 Micrograph of 60nm Ge NM at a pressure of 620kPa. Cracks can be observed in the direction, <110>,

that marks the cleavage planes. Some cracks seem to originate from etch hole edges. Cracks stop when interrupted

by other cracks or when they reach a free edge (e.g., etch holes). Scale bar is a 100μm.

52

2.5.2 Strain around an etchant access hole

As seen in Figs. 2.9 and 2.10, many of the cracks seem to start at the edge of an etchant ac-

cess hole. One might assume that strain buildup near etchant holes and away from any edge

might occur differently. Certainly for a freestanding NM that is stretched, one can imagine some

strain relaxation to occur around the etch holes. For a NM that is glued everywhere onto the PI,

that seems less possible, unless local delamination occurs. Because of space constraints cause by

the pressure cell, the necessary measurement could not be made on my samples to examine this

issue.

Another study in this group has relevance here. Silicon NM windows tethered at their edges

like a window and with silicon nitride grown on one side to introduce strain were investigated,

using a Raman spectrometer with a spot size of 700nm, to explore how far laterally a strain gra-

dient extends. By mapping the Si peak shift on a 22nm Si NM with 100nm of SiNx deposited (a

strain in the Si of 0.4%), it was determined that the strain relaxation at etch holes varied only by

10% of the total strain and extended about 700-1000nm before reaching the average val-

ue.(22,23) In a free edge, the strain would in any case be less. In a bonded NM, as we have in my

work, there should certainly be no increase in strain. It is therefore not likely that a higher strain

exists at the etch holes that would drive crack formation. But the etch holes do present edges at

which cracks can initiate. Any time you have step, kink, jog, etc. there is a lower energy barrier

to dislocation formation, which would in turn lead to crack formation.

2.5.3 Comparisons of strain behavior of unstrained and previously strained NMs

An important question for potential applications of mechanical straining technology is the

repeatability of achieving the same strain at the same applied stress. In our experimental setup,

the PI support (a sheet 125μm thick) appears to be plastically deforming throughout the entire

53

experiment, and stays visibly deformed after ~300 kPa. The PI never visibly cracks, but it can

flow and stretch. We never reach the point where the PI film breaks (it would then not hold pres-

sure any longer). We are only concerned with the Ge NM being elastically or plastically de-

formed, and that the Ge NM stays bonded to the deforming PI film. We do not see signs of de-

lamination of the Ge NM from the PI film at any pressure. The picture then is that the NM ad-

heres everywhere and is locally elastically strained. Around the cracks there may be some relax-

ation, but no delamination. Any such relaxation must be countered by the PI to which the NM is

bonded, by atomic distortion in the bonds of the PI. A future experiment would be to design a

stress ing system that would allow us to measure the degree and lateral extension of relaxation

away from a crack in the NM.

We can say that the Ge (at least locally) is elastically deforming because I obtain consistent

stress-strain data from Ge NM samples of similar thickness, before and after cracking com-

menced. For example, I strained a 40-nm Ge NM to 620 kPa and brought it back to zero and then

re-strained it by repressurizing the sample mount up to 620 kPa. I use this range to see if strain is

linearly elastic up to the strain of interest for photoluminescence measurements (See Chapter 3

for PL data on this exact NM). The Raman measurement for the re-strained NM is shown in

black in Fig.2.11B. Some cracks were observable in the NM before re-straining it. These results

are compared to those for a fresh 44 nm thick sample with no cracks or previous strain (red graph

in Fig.2.11B). The two samples have the same strain at similar pressures within error. The error

bars for the re-strained NM are larger, possibly because the already existing cracks cause a larger

strain distribution over the Raman sampling area. The important point here is that the cracks that

form at the pressures I show here (0-620kPa) do not significantly affect the average amount of

strain in the Ge NM.

54

Figure 2.11 Raman measurements of the strain in two Ge NMs. (A) Optical micrograph of a NM after being

strained to 620kPa, cracks can be seen in this NM at 0kPa as shown in this picture. (B) Raman measurements. The

40 nm NM (black) was cycled to ~620kPa and down prior to re-straining and measurement while the 44 nm NM

(red) had never been strained. The strain behavior with stress is the same in both NMs. Scale bar is a 100μm.

I do not have data at pressures > 620 kPa to compare a new NM and one that has been cy-

cled and thus developed cracks, but one may expect the strain shown in Fig. 2.11 to diverge at

higher pressures. Intuitively many small NMs, with more edge length per area to initiate cracks,

should crack at lower stresses, especially as the edges are rough. Assuming there is no delamina-

tion of the cracked NMs at the edges, the strain in a large NM and a small one should be the

same at the same pressure. Of course, other factors may affect crack formation, such as the PI

substrate, surface roughness, and defects in the NM itself. But, as the same wafer and procedure

was used for these two NMs, most of those factors are the same.

55

2.6 Effect of etch holes on NM strain distribution

In order to establish if the cracks on our previous samples were being driven by strain con-

centrators at the square etch holes, I developed a study in which many smaller circular NMs of

the same size and same thickness, but without etch holes, could be observed at the same time.

Each such disk is larger than the separation of the etch holes in the NMs( disk diameter is

~300μm). The disks show the same stress/strain behavior and, within uncertainty, the same strain

values, see Figure 2.13.

Figure 2.13. Strain in NMs without etch holes. A) Optical micrograph showing Ge NMs ~300µm in diameter and

84nm thick. .B) Graph showing the strain behavior of this pattern compared to a 84nm Ge NM with etch holes

100µm apart.

We observe the first formation of cracks in these circular NMs at a somewhat higher gas

pressure compared to the NMs with etch holes. For an 84-nm-thick round NM without etch

holes, the first fracture lines were observed at 1.1% strain (~400kPa) compared to a NM with

etch holes, for which first fracture lines could be observed at 0.72% strain (~300kPa), a

0 200 400 600

0

1

2S

tra

in[%

]

Pressure [kPa]

No Etch Holes NM

Etch Holes NM

100 m

A B

56

35%increase in the value of strain at which the first cracks are observed, suggesting that etch

holes do act somewhat as crack initiators.

Figure 2.14 Comparison of Ge(001) NMs at ~100kPa (1), and ~520kPa (2). Sample A is a 84nm NM with etch hole

spacing of 100μm. Sample B is 84nm thick NM disk with a 300μm diameter. Qualitatively the density of cracks in

the NM with etch holes is higher than that of the circular NMs. The cracks occur principally along the orthogonal

low-index <110> directions, which mark the {110} cleavage planes for Ge(001)The darken area around the etch

holes are due to the image processing on a bright field image to enhanced the contrast of the cracks. Scale bar is

100μm

Comparisons of the cracks in the NM with etch holes and cracks in the circular NMs are

shown in Figure 2.14. When the Ge NM initially shows cracks they are widely separated (see

Figure 2.9) and then they keep growing with increase in stress. At 520-550 kPa, the NM with

57

etch holes (Fig 2.14 A.2) appears to have more cracks per area than the circular NM (Fig 2.14

B.2). The fact that the circular NM does eventually crack suggests that etch holes are not the on-

ly factor initiating cracks, but may be the limiting factor. I have not performed sufficient experi-

ments with the round NMs to make a firm determination.

Because etch holes appear to be deleterious, it would be an advantage to eliminate them.

Ideally we would fabricate a large NM without etch holes, but there are limits in the size that can

be fabricated. Alternative choices may be an array of long strips or of closely spaced disks. .

For photoluminescence, these approaches could enable a wider range of band gap engineering

and thus wavelength manipulation in light emission. For electroluminescence, which requires

charge flow, end connection of the strips or a grid of contact wires embedded in the compliant

substrate or added to the top of the circular NMs could supply charge.

2.7 Chapter summary

In this chapter I have described the use of GeNMs to increase the biaxial strain in Ge suffi-

ciently to obtain a direct band gap. I designed a pressure cell that also allows access to Raman

spectroscopy so one can measure strain in-situ using a Ge-Ge Raman line. Biaxial tensile strain

increases linearly with the applied stress (as expected in the elastic region of the stress-strain

curve in the absence of delamination), up to the maximum measured value of 2 % for a 24nm Ge

NM. Similar measurements with other NMs indicate that, as the gas pressure is further in-

creased, the average strain eventually saturates. We do not fully understand this phenomenon but

believe the formation of cracks in the NM produces strain relaxation in their immediate vicinity

(which we do not think is important), by relaxation due to delamination from the PI (which we

also do not think is important), or by phenomena in the PI at the cracks. The maximum achieva-

ble average strain increases with decreasing NM thickness. Specifically, because the amount of

58

strain energy stored in the NM is directly proportional to its thickness, when very thin compared

to the substrate, the NM contains insufficient strain energy to drive defect formation.(9) These

considerations underscore the importance of nanoscale thicknesses in the present context.

Free edges and the concentration on etch holes seem to affect the amount of cracks formed

at a given strain. These cracks do not affect the reproducibility of the same strain values at lower

pressures. By changing the shape of the NM and eliminating etch holes I found an increase in the

stress needed to crack the NM, with an increase at which the cracks begin to form by ~35%. The

NMs do eventually crack, suggesting that etch holes are not the only factors initiating cracks.

The theoretical fracture strengths of Ge are large: for the crystalline <100> direction, Ruoff (24)

has computed the maximum Ge uniaxial tensile strain and stress to be 18.3% and 14.7 GPa re-

spectively. We expect maximum biaxial strain might be much lower. Using the relationship

𝜀 =(1−2𝜐)𝜎

𝐸 , where ε is the biaxial strain, υ is the Poisson’s ratio, and σ is the stress, gives a val-

ue for the theoretical maximum biaxial strain closer to 7%. We so far have achieved the highest

values of strain in Ge sheets, but appear to be far from the theoretical limit. Thus there is value

in more research in this area.

2.8 References

1. Roberts, M. M., Klein, L. J., Savage, D. E., Slinker, K. A., Friesen, M., Celler, G., Eriks-

son, M.A.,& Lagally, M. G. (2006). Elastically Relaxed Free-Standing Strained-Silicon

Nanomembranes. Nature Mater. 5:388-393.

2. Scott S.A. & Lagally, M.G. (2007). Elastically Strain-Sharing Nanomembranes: Flexible

and Transferable Strained Silicon and Silicon-Germanium Alloys. J Phys D. 40:R75-R92.

59

3. Euaruksakul, C., Li, Z. W., Zheng, F., Himpsel, F. J., Ritz, C. S., Tanto, B., Savage, D.E.,

Liu, X.S., & Lagally, M. G. (2008). Influence of Strain on the Conduction Band Structure

of Strained Silicon Nanomembranes. Phys Rev Lett. 101:147403.

4. Huang, M., Ritz, C. S., Novakovic, B., Yu, D., Zhang, Y., Flack, F., Savage, D.E., &

Lagally, M. G. (2009). Mechano-electronic Superlattices in Silicon Nanoribbons. ACS

Nano. 3:721-727.

5. Rogers J.A., Lagally M.G., & Nuzzo R.G. (2011). Synthesis, Assembly, and Applications

of Semiconductor Nanomembranes. Nature. 477:45-53.

6. Yoon, J., Baca, A. J., Park, S. I., Elvikis, P., Geddes, J. B., Li, L., Kim, R.H., Xiao, J.,

Wang, S., Kim, T., Motala, M.J., Ahn, B.Y., Duoss, E.B., Lewis, J.A., Nuzzo, R.G., Fer-

reira, P.M., Huang, Y., Rockett, A, & Rogers, J. A (2008). Ultrathin Silicon Solar Micro-

cells for Semitransparent, Mechanically Flexible and Microconcentrator Module Designs.

Nature Mater. 7:907-915.

7. Ko, H. C., Stoykovich, M. P., Song, J., Malyarchuk, V., Choi, W. M., Yu, C. J., Geddes,

J.B., Xiao, J., Wang, S., Huang, Y, & Rogers, J. A. (2008). A Hemispherical Electronic

Eye Camera based on Compressible Silicon Optoelectronics. Nature. 454:748-753.

8. Kim D.H., Kim, D. H., Ahn, J. H., Choi, W. M., Kim, H. S., Kim, T. H., Song, J., Huang,

Y.Y., Liu, Z., Lu, C., & Rogers, J. A. (2008). Stretchable and Foldable Silicon Integrated

Circuits. Science. 320:507-511.

9. Yuan, H. C., Shin, J., Qin, G., Sun, L., Bhattacharya, P., Lagally, M. G., Celler, G.K., &

Ma, Z. (2009). Flexible Photodetectors on Plastic Substrates by use of Printing Transferred

Single-Crystal Germanium Membranes. Appl Phys Lett. 94:013102.

60

10. Thurmer D.J., Bof Bufon C.C., Deneke C., & Schmidt O.G. (2010). Nanomembrane-based

Mesoscopic Superconducting Hybrid Junctions. Nano Lett. 10:3704-3709.

11. Feng, P., Mönch, I., Huang, G., Harazim, S., Smith, E. J., Mei, Y., & Schmidt, O. G.

(2010). Local-Illuminated Ultrathin Silicon Nanomembranes with Photovoltaic Effect and

Negative Transconductance. Adv Mater. 22:3667-3671.

12. Sanchez-Perez, J. R., Boztug, C., Chen, F, Sudradjat, F. F., Paskiewicz, D.M., Jacobson,

RB, Lagally, M.G., & Paiella, R. (2011). Direct-Bandgap Light-Emitting Germanium in

Tensilely Strained Nanomembranes. Proc. Natl. Acad. Sci. 108:18893–18898.


Lagally, M. G., &Paiella, R. (2013). Tensilely Strained Germanium Nanomembranes as In-

frared Optical Gain Media. Small. 9:622-630.

14. Boztug, C., Sánchez-Pérez, J. R., Yin, J., Lagally, M. G., & Paiella R. (2013). Grating-



15. Jayaraman, A. (1983). Diamond Anvil Cell and High-Pressure Physical Investigations. Rev

Mod Phys. 55:65-108.

16. Freund, L.B. & Suresh, S. (2003). Thin Film Materials: Stress, Defect Formation and Sur-

face Evolution. Cambridge University Press, Cambridge, UK.

17. El Kurdi, M., Bertin, H., Martincic, E., De Kersauson, M., Fishman, G., Sauvage, S.,


Germanium by Mechanical Tensile Strain. Appl Phys Lett. 96:041909.

61

18. Cheng, T. H., Peng, K. L., Ko, C. Y., Chen, C. Y., Lan, H. S., Wu, Y. R., Liu, C.W., &

Tseng, H. H (2010). Strain-Enhanced Photoluminescence from Ge Direct Transition. Appl

Phys Lett. 96:211108.

19. Gardiner, D.J. (1989). Practical Raman Spectroscopy. Springer-Verlag. ISBN 978-0-387-

50254-0.

20. Cerdeira F, Buchenauer C, Pollak F.H., & Cardona M. (1972). Stress-induced Shifts of

First-order Raman Frequencies of Diamond-and Zinc-Blende-type Semiconductors. Physi-

cal Review. 5(2):580.

21. Fang, Y. Y., Tolle, J., Roucka, R., Chizmeshya, A. V. G., Kouvetakis, J., DCosta, V. R., &

Menendez, J. (2007). Perfectly Tetragonal, Tensile-strained Ge on Ge1-ySny Buffered

Si(100). Appl Phys Lett. 90:061915.

22. Clausen, A.M. (2012). Using Silicon Nanomembranes to Evaluated Stress in Deposited

Thin Films.( Doctoral dissertation). University of Wisconsin, Madison, WI.

23. Clausen, A.M., Paskiewicz, D.M., Sadeghirad, A., Jakes, J. ,Savage, D.E., Stone, D.S., Liu,

F., & Lagally M.G.(2014). Silicon Nanomembranes as a Means to Evaluate Stress Evolu-

tion in Deposited Thin Films, Extreme Mechanics Letters. ISSN 2352-4316.

24. Ruoff, A.L. (1978). On the Ultimate Yield Strength of Solids. J. Appl. Phys. 49(1):197-

200.

62

Chapter 3 Light emission from tensilely strained Ge(001)

Si, Ge, and their alloys are not suitable for light emitting diodes and lasers based on tradi-

tional approaches, because their indirect energy band gap (as discussed in Ch.1) results in ex-

ceedingly low radiative recombination efficiency (10-5

-10-6

efficiency at low excitation rate).

This issue represents the key limiting factor in the development of Group IV photonics. Howev-

er, in Ge(001) (also in Ge(111), but not in Si for any orientation) tensile strain is predicted to

lower the conduction band edge at the direct (Γ) point relative to the indirect L-valley minima,

while the overall band gap energy correspondingly decreases. (1-6) In the presence of electrical

or optical pumping, a substantial population of electrons at the Γ minimum can therefore be es-

tablished in sufficiently tensilely strained Ge(001), thereby increasing the light emission effi-

ciency. The fundamental band gap becomes direct for biaxial strain in excess of approximately

1.7%. (1-6)

In this chapter I demonstrate that mechanically stressed nanomembranes allow for the in-

troduction of sufficient biaxial tensile strain to transform Ge(001) into a direct-band gap material

with strongly enhanced light-emission efficiency.

3.1 Photoluminescence and strain in Ge(001) NMs

The light emission properties of strained Ge(001) NMs are investigated via room-

temperature PL studies, in a collaboration with the research group of Roberto Paiella at Boston

University. The pump light is provided by a tunable optical parametric oscillator (OPO), and

consists of a train of pulses having 5-ns width, 20-Hz repetition rate, 960-nm wavelength, and 3-

mW average power (0.15-mJ pulse energy), focused onto the NM with a spot size of about 1

mm. The emitted light is dispersed through a monochromator and measured using a room-

temperature extended-range InGaAs photodetector with 1200–2600 nm spectral response and 45

63

MHz bandwidth. The measured PL spectra are normalized to the spectral response of the setup

by dividing them by the system response curve (Fig. 3.1D), which is determined by the reflec-

tivity of the monochromator grating and the responsivity of the photodiode.

Figure 3.1 Photoluminescence experiment. (A) Schematic diagram. (B) Photo of the physical setup at Boston Uni-

versity. (C) Close-up photo of the pressure cell designed for this experiment. (D) The system response, combining

the reflectivity of the monochromator and the responsivity of the photodiode.

Room temperature PL spectra obtained from a 40-nm-thick Ge(001) NM at different strains

are shown in Fig. 3.2. Figure 3.2A shows a schematic diagram of the expected valley movement

in Ge(001) due to strain. [The schematic diagram of the NM deformation is misleading: as I in-

dicated in Ch.2, the radius of curvature is so large that the NM effectively only expands and

bends only negligibly]. As described in Ch. 2, there is no significant difference in the strain

achieved in a fresh NM and one that had been “cycled” to high strain and back.

As the strain is increased, the emission wavelength undergoes a pronounced red shift while

the integrated PL intensity increases, indicating enhanced light emission. Although it does not

64

establish it, this behavior is at least consistent with the expected lowering of the Γ-point conduc-

tion-band edge relative to the L-valley minima with increasing tensile strain.

Figure 3.2 Behavior of band edges with tensile strain in Ge(001) and corresponding PL data. (A) Schematic dia-

gram showing the movement of the Γ and L valleys in Ge(001) as the tensile strain increases. (B) PL spectra of a 40-

nm-thick Ge(001) NM at different levels of biaxial tensile strain, for incident 960nm radiation . The vertical axis is

in arbitrary units. The different spectra are shifted vertically relative to one another for the sake of illustration clari-

ty. The small narrow bumps near 1900 nm are the result of second-order diffraction of spurious pump light by the

monochromator grating. From Refs. 7, 8 and 9

As a second example, Figure 3.3 shows room temperature PL spectra of a 57 nm thick

Ge(001) NM, approximately 50% thicker than the one shown in Fig.3.2, at different strains.

Again, as the strain is increased, the emission peak is significantly red-shifted. The curves de-

velop a long-wavelength shoulder, more pronounced than in the spectra in Fig. 3.2. As ex-

plained in the following, the main peak and the shoulder are associated, respectively, with gam-

ma-to-heavy-hole (c-HH) and gamma-to-light-hole (c-LH) emission, with the latter contribu-

tion extending into the 2.1–2.5 m atmospheric transmission window (any of the wavelengths at

which electromagnetic radiation from space can penetrate the earth's atmosphere) at high strain.

At the same time, the integrated PL intensity significantly increases with increasing strain, indi-

65

cating enhanced light emission efficiency. The two sets of data illustrate that even sheets as thin

as 40nm produce significant light emission. The penetration of the 960nm incident light is much

greater, ~ 520nm as calculated using 𝑑𝑝 ≈2.3

2𝛼 where dp is the penetration depth and α is the ab-

sorption coefficient in Ge, (10) so that uniform emission throughout the GeNM, but only from

the NM, can be assumed. Separately it has been shown that the PI host luminesces at wave-

lengths below the ones observed in our experiment. (11)

Figure 3.3. Room temperature PL vs. strain. (A) PL spectra of a 57nm-thick Ge NM at different strains. The spectra

are shifted vertically relative to one another for the sake of illustration clarity. The dashed arrows are drawn to illus-

trate the red-shift of the cΓ-LH and cΓ-HH PL peak positions with increasing strain. (B-D.) Examples of date nor-

malized to the equipment’s response, with the corresponding Gaussian fits indicated by solid lines; for a 44nm Ge

NM. From Refs. 7and 8

Figure 3.4A shows several PL spectra measured with an even thinner (24 nm) Ge NM at

different strains. The emitted-power levels in this case are substantially lower than those in Figs.

3.2B and 3.3A, attributable, we estimate, to smaller pump light absorption and increased nonra-

diative surface recombination in thinner samples. As a result, the weaker, longer-wavelength

66

emission peaks due to cΓ-LH transitions cannot be unambiguously resolved in these lumines-

cence spectra. At the same time, the smaller NM thickness allows reaching strain values up to

2% (above the predicted threshold for turning Ge into a direct-band gap material) with improved

structural integrity across the NM area. The normalized PL spectrum measured at 2% strain is

plotted in the inset of Fig. 3.4B together with a single-peak numerical fit. The emission wave-

length inferred from this fit is 1950 nm, longer than the calculated cΓ-HH band gap wavelength

at the indirect-to-direct transition point. Therefore, both strain and PL measurements here indi-

cate the formation of direct-band gap Ge. This conclusion is supported in Fig. 3.4B, where the

peak emission energies from Fig. 3.4A are plotted as a function of strain together with the theo-

retical band gap energies. The agreement between theory and experiments is quite good.

67

Figure 3.4 Strain-dependent luminescence properties of a 24-nm-thick Ge NM. (A) PL spectra of a 24-nm-thick Ge

NM at different levels of biaxial tensile strain (shifted vertically relative to one another for the sake of illustration

clarity). The vertical axis is in arbitrary units. A small degree of smoothing (three-adjacent-points averaging) has

been applied to these data. (B) Symbols: peak emission energies obtained from the PL spectra of (A), plotted as a

function of strain. Lines: calculated band gap energies between the Γ or L conduction-band minima and the HH or

LH valence band maxima. Inset: normalized PL spectrum of the NM of (A), measured at a tensile strain of 2%

(symbols) and corresponding Gaussian fit (solid line). From Ref. 7

The optical-gain spectrum (range of frequencies where optical amplification can occur) of

tensilely strained Ge due to electronic transitions between the conduction band minimum and

either the heavy-hole (HH) or the light-hole (LH) valence band is calculated as follows:(12)

212101221

2

210

0 dEEhffEEMh

Chg r

TETM

. 3.1

In this equation, 0 is the optical frequency, 21EMTETM is the polarization-dependent mo-

mentum matrix element, r(E21) is the reduced density of states, f1 and f2 are the occupation

68

probabilities of, respectively, the valence band and conduction band states of equal momentum

and energy difference E21, and (h0 – E21) is the lineshape function that describes gain broaden-

ing (the increase in the linewidth of an atomic transition caused by effects that act differently on

different radiating or absorbing atoms). Finally, the constant C is given by 200

2

2 cmn

hqC

, where n

is the refractive index of Ge, q the electron charge, h Planck’s constant, 0 the permittivity of free

space, c the speed of light in vacuum, and m0 the free electron mass. The momentum matrix el-

ement is different for transverse electric (TE) and transverse magnetic (TM) polarizations, which

are defined, respectively, as linear in the directions parallel and perpendicular to the plane of the

NM. The total gain spectrum for either polarization is computed by evaluating Equation 3.1 for

both direct conduction-to-light-hole band (cΓ-LH) and direct conduction-to-heavy-hole band

(cΓ-HH) transitions and then adding the results.

In the following we assume parabolic energy bands, so that the expression in Equation 3.1

only depends on a few well established materials parameters, namely the band gap energies, the

effective masses, and the momentum matrix elements. These parameters vary as a function of

biaxial strain (defined as the fractional change of the in-plane lattice constant from its equilib-

rium value), and their strain dependence can be determined using data from the literature. In par-

ticular, the band gap energies are calculated from standard formulas (13,14) in terms of the de-

formation potentials (values used in deformation potential theory to calculate strain effects on the

band structure) av, ac, 3/ud , and b (which describe, respectively, the strain-induced shift of

the average valence-band maximum, the conduction band minimum at Γ, the conduction band

minima at L, and the splitting of the valence bands at Γ). The specific values of the deformation

potentials used in the simulations were chosen in accordance with available theoretical and ex-

69

perimental data (1,2,14-17) and are listed in Table I, together with the values of the unstrained

direct and indirect band gap energies (Eg and EgL), spin-orbit splitting (), and elastic moduli

(C11 and C12).

b [eV] -2.16

a [eV] 1.24

ca [eV] -8.24

3/ud

[eV]

-2.34

gE [eV] 0.802

gLE [eV] 0.661

[eV] 0.290

11C [GPa] 128.53

12C [GPa] 48.26

Table I: Materials parameters used to compute the strain-dependent band gap energies of Ge. (1,2,14-17)

Figure 3.5. (A) Calculated band gap energies between the Γ or L conduction-band minima and the HH or LH

valence-band maxima, plotted as a function of strain. (B) Schematic band structure of unstrained Ge. (c) Sche-

matic band structure of Ge under 2% biaxial tensile strain. In (B) and (C), the relative positions of all band edges

correspond to their calculated values. From Ref. 8

70

In order to compare these PL data with theoretical predictions, the measured spectra were

normalized to the spectral response of the experimental setup, and then numerically fitted with

multiple (maximum four, minimum two) Gaussian peaks, Fig. 3.6. The peak photon energies of

the resulting fitting curves are plotted as a function of strain in Fig. 3.6A (symbols) together with

the calculated band gap energies from Figure 3.5A (solid lines). In general, all four transitions

shown in the figure (i.e., direct and indirect transitions involving HHs and LHs) contribute to the

luminescence spectra. However, depending on their relative strengths and spectral positions,

some of these contributions could not always be resolved in the data analysis, so that the meas-

ured spectra could only be fitted with two or three peaks. Some of the fits were already shown in

Fig. 3.3; they are repeated here as Figs. 3.6 B-D. The peak emission energies of all the fitting

curves obtained with this procedure are shown by the symbols in Fig. 3.6A. Overall, the agree-

ment between the experimental peak emission energies and the theoretical band gap energies in

Figure 3.6A is quite good.

71

Figure 3.6 Emission photon energy and PL intensity versus strain for a 44nm NM. (A) Symbols: peak emission en-

ergies obtained from the PL spectra of Fig. 3.1, plotted as a function of strain. Lines: calculated band gap energies

between the Γ or L conduction-band minima and the HH or LH valence-band maxima, same as Fig. 3.5. (B-D)

Symbols: normalized PL spectra shown in Fig. 3 at strains of -0.13% (B), 0.75 % (C), and 1.78 % (D). The corre-

sponding Gaussian fits are indicated by the solid lines. (E) Measured TE component of the direct-band gap PL in-

tensity and its individual cΓ-HH and cΓ-LH contributions (where distinguishable), plotted in arbitrary units as a

function of strain. From Ref.7

Near zero strain, the HH and LH band edges are nearly degenerate, and therefore in the

numerical fits we can resolve only two peaks, the direct and indirect transitions. At high strain,

indirect transitions are suppressed because of the decreasing number of electrons in the L val-

leys, in addition to their inherent weakness. Correspondingly, the high-strain (> 1%) spectra

could also only be fitted with two peaks, due to direct conduction-to-heavy-hole (c-HH) and

conduction-to-light-hole (c-LH) transitions. At intermediate strain values, convergence of the

numerical fits could be obtained with more than two peaks, indicating the simultaneous presence

of both direct and indirect transitions into both valence bands (HH and LH). With these assign-

ments, the agreement between experimental peak emission energies and theoretical band gap en-

ergies is quite good. Possible sources of discrepancy include heating of the NM by the strong PL

pump pulses, leading to lattice thermal lattice expansion (equivalent to more thermal strain) and

0.0 0.5 1.0 1.5 2.0

0.5

0.6

0.7

0.8

Strain [%]

Ene

rgy [e

V]

c-LH cL-LH

c-HH cL-HH

A-0.13%

D

C

1.78%

0.75%

1500 2000 2500

Wavelength [nm]

B

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

2.0

PL in

tensity

Strain [%]

TE, LH+HH

TE, HH

TE, LH

E

72

therefore reduced band gap energies, (2, 3) but we took considerable care to investigate this con-

tribution and assure that the effect would be minor (see below).

The numerical-fit results shown in Fig. 3.6A demonstrate a large strain-induced red shift of

the c-LH transition, from 1535 to 2227 nm (0.81eV to 0.56 eV) as the strain increases to

1.78%. Figure 3.7 shows the strain-induced red shift of the cΓ-LH transition, from 1526 to 2166

nm (0.81 eV to 0.57eV) as the strain is increased to 1.42 % for a 57nm Ge NM. The agreement

between the experimental peak emission energies and the theoretical transition energies in Fig.

3.7A is again good, but we can reach only (slightly) lower strains.

In Fig.3.6E, we show the strain dependence of the measured direct-band gap PL intensity,

together with its individual c-HH and c-LH contributions where distinguishable, as obtained

from the integrated areas under the corresponding fitting peaks. In Fig. 3.7B we do the same for

a 57 nm NM. We believe the small but non-negligible signal observed near zero applied strain is

caused by the relatively high-power pump pulses used in this experiment. As both NMs (44nm

and 57nm) are strained, the PL intensity increases as expected, with the cΓ-HH transitions

providing the dominant contribution, despite the larger hole occupancy of the LH band under

tensile strain.

It should be noted that these PL signals are collected along the sample surface normal, and

therefore only correspond to the TE (i.e., in-plane polarized) emission. In contrast, most of the

photons created via electron/LH recombination under biaxial strain have TM polarization (12,13)

(i.e., linear along the axis perpendicular to the surface), and therefore propagate on the plane of

the NM and cannot be detected in our geometry. This selection rule is particularly strong under

high tensile strain. (6) We expand on the discussion of these plots below.

73

Figure 3.7 PL from a strained 57nm Ge(001) NM. A Peak emission energies for a 57 nm GeNM obtained by fitting

the PL spectra of Figure 3.3 (symbols) and calculated band gap energies (lines), plotted as a function of strain. (B)

Measured PL intensities due to cΓ-LH and cΓ-HH transitions and their sum (obtained by fitting the PL spectra of

Figure 3.3A), plotted as a function of strain. From Ref. 8

The theoretical framework presented in Ref. 8 is used to fit the experimental PL spectra in

order to infer the quasi-equilibrium carrier density N produced by the pump pulses in the NM.

This procedure was applied to the spectrum measured at the highest strain tested (1.42 % and

1.78%), where the cΓ-LH and cΓ-HH emission peaks can be clearly resolved. As a result, N can

be uniquely determined based on the relative strength of these two contributions, which are cal-

culated using the following general expression for the TE-polarized spontaneous emission spec-

trum: (12)

212101221

2

2100 1 dEEhffEEMKhhR rTEsp . 3.2

In this equation, K is a constant that in practice depends on the collection efficiency of the

PL measurement setup, among other factors, and all other symbols are as defined in Equation

(1). Once again, parabolic energy bands are assumed, and the relevant materials parameters are

calculated as discussed previously. For a more realistic description of the actual experimental

74

sample, the spectrum of Equation3.2 is initially computed [with a Lorentzian lineshape function

(h0 – E21) accounting for lifetime broadening] as a function of strain, and then convoluted

with a Gaussian strain distribution with mean value and standard deviation based on the Raman

spectroscopy results. The only fitting parameters used in these simulations are the prefactor K

and the carrier density N.

The calculated room temperature emission spectrum including both cΓ-LH and cΓ-HH con-

tributions is plotted in Figure 3.8A (solid line) together with the normalized PL data at 1.42%

strain (symbols) and the double-Gaussian fit used in Fig. 3.8 (dashed lines). The agreement with

the data is reasonably good, except for the dip between the two peaks in the theoretical spectrum,

which can be attributed to the assumption of parabolic valence bands. In reality, as we move

down in energy from the top of the LH band towards the top of the HH band, the LH band be-

comes increasingly nonparabolic, (5) as illustrated in the schematic band diagram of Fig. 3.5c; as

a result, its curvature decreases, leading to an increased joint density of states r and therefore

increased light emission. The specific value of N inferred from the fit of Fig. 3.8a is 3.0×1018

cm-3

.

75

Figure 3.8 Normalized PL spectra for two NMs at two strains. (A) Normalized PL spectrum of the 57nm Ge NM

at a strain of 1.42 % (symbols) and calculated TE-polarized spontaneous emission spectrum (solid red line). (B)

Normalized PL spectrum of a 44-nm Ge NM at a strain of 1.78 % (symbols) and calculated TE-polarized sponta-

neous emission spectrum (solid red line). The dashed green lines are the Gaussian fits to the experimental data.

From Ref. 8

3.2 Grating coupled light emission

Under biaxial tensile strain, light emission near the direct-band gap edge involves transi-

tions between the conduction band and the LH valence band, due to the aforementioned strain-

induced splitting of the valence bands. The resulting luminescence is predominantly transverse-

magnetic (TM), i.e., linearly polarized in the direction perpendicular to the strained layer. This

light propagates on the plane of the NM and therefore cannot be collected in our measurement

setup. As a result, the experimental spectra are dominated by conduction-to-heavy-hole (c-HH)

transitions that produce transverse-electric (TE) light at shorter wavelengths, despite the smaller

hole population of the HH band caused by its lower energy. Evidence of conduction-to-light-

hole (c-LH) emission under high tensile strain was observed, but only in the form of a relative-

ly weak long-wavelength shoulder in the predominantly c-HH emission spectra, as shown in

76

Figures 3.6 and 3.7. Furthermore, the measured increase in luminescence efficiency brought

about by the applied stress was limited to values of about 4. This observation can be ascribed

to the same unfavorable polarization selection rules, as most of the strain-enhanced emission is

TM polarized and therefore could not be detected.

To measure the emission involving the LH band, a two-dimensional grating structure that

allows for efficient extraction of the in-plane-emitted light via first-order diffraction was added

the strained Ge(001) NM, see Fig. 3.9. With this geometry, emission spectra featuring two well

resolved peaks are obtained under sufficiently high tensile strain, associated with c-LH and c-

HH transitions. Depending on the strain and pumping conditions, the former feature can provide

the largest contribution to the overall luminescence spectrum and extend to mid-infrared wave-

lengths as long as 2.4 m. A maximum strain-induced PL efficiency enhancement of about 11

is measured with these samples (see Fig. 3.9B). These results confirm the aforementioned ex-

pectations regarding the radiative properties of tensilely strained Ge, and directly highlight the

promise of this materials system for mid-infrared optoelectronics applications.

To fabricate these structures, Ge NMs transferred to polyimide as explained in Chapter 2

were used. Poly(methyl-methacrylate) (PMMA) resist is then spun on the NM and electron-beam

lithography is used to pattern a square-periodic array of cylindrical holes. Amorphous Ge is then

deposited on the patterned PMMA, followed by lift-off. The end result is a regular array of cy-

lindrical Ge pillars with sloped sidewalls, as illustrated in the scanning electron microscopy

(SEM) image of Fig. 3.9A. Finally, a relatively thick (about 3 μm) PI coating is spun over the

array in order to produce a symmetric dielectric environment around the high-index NM/array

layer, which improves the vertical optical confinement of the emitted light and its overlap with

77

the grating. A schematic cross-sectional view of the resulting device structure is shown in the

inset of Fig. 3.9A.

Figure 3.9.(A) SEM image of a periodic array of amorphous Ge (a-Ge) pillars fabricated on a Ge NM on PI. The

scale bar is 1 μm. Inset: schematic cross-sectional view of the same sample. (B) Normalized PL spectrum of a simi-

lar sample under 1.9 % tensile strain. From Ref. 18

Strain is induced in the same manner as explained in Chapter 2. The PL measurements

were done in the same manner as explained in Section 3.1.The measured PL spectra are finally

normalized to the spectral response of the setup, which is determined by the reflectivity of the

monochromator grating and the responsivity of the photodiode. One might ask how these extra

layers on top of the Ge(001) NM affect our ability to strain the NM. We tested this and found no

effect. A simple calculation shows that the thin coating of PI, even though it is much thicker

than the GeNM, has negligible effect, because its modulus is so much lower. The Ge columns

also have negligible effect (we calculate 3%) because they are disconnected and narrow, and can

thus effectively relieve stress.

Altogether, these results indicate that the NM/array geometry provides a suitable platform

for the development of optical cavities compatible with the flexibility requirements of mechani-

cally stressed active layers.(18)

78

3.3 Chapter summary

Ge NMs under large biaxial tensile strain therefore represent a very promising materials

platform for the development of infrared optoelectronic devices based on Ge, including lasers.

Importantly, such lasers could be developed without the need for degenerate n doping, as neces-

sitated in prior work. (19) In this context, the key remaining challenge is the development of a

laser cavity that can provide strong optical confinement and feedback in a NM with highly sub-

wavelength thickness. Photonic-crystal cavities consisting of dielectric pillars directly fabricat-

ed on the NMs, such as the structure shown in Figure 3.9A, can provide an optically thick layer

for the confinement of the in-plane-propagating emitted light, while at the same time preserving

the NM flexibility.

An additional challenge is the development of electrically injected devices. This issue can

be addressed with the fabrication of lateral P-I-N junctions in the active NM via ion implantation

and surface passivation, an approach that has already been demonstrated for the development of

flexible (unstrained) Ge NM photodiodes. (20)

From the strain dependence of the Ge direct-band gap energy (Figure 3.5A), one expects

that the emission wavelength of these tensilely strained Ge lasers could be tuned across the 2.1-

2.5 μm mid-infrared atmospheric transmission window. This spectral region is technologically

important for use in biochemical sensing and spectroscopy, where the distinctive absorption fea-

tures of many molecular species can be exploited to detect them sensitively. Specific applica-

tions include environmental monitoring, bio-agent detection for security screening, medical di-

agnostics (e.g., via breath analysis), and industrial process control. It should be noted that the

2.1-2.5 μm spectrum lies at the boundary of what is presently covered by mature semiconductor

laser technologies, i.e., GaAs- and InP-based diode lasers on the short-wavelength side and III-V

79

quantum cascade lasers at longer wavelengths. (21) Thus, sufficiently tensilely strained Ge is

also attractive for the purpose of extending the overall spectral reach of mid-infrared optoelec-

tronics.

3.4 References

1. Fischetti M.V. & Laux S.E. (1996). Band Structure, Deformation Potentials, and Carrier

Mobility in Strained Si, Ge, and SiGe Alloys. J Appl Phys. 80:2234-2252.

2. Menéndez J. & Kouvetakis J. (2004). Type-I Ge/Ge1-x-ySixSny Strained-Layer Heterostruc-

tures with a Direct Ge Bandgap. Appl Phys Lett. 85:1175-1177.

3. Liu, J., Sun, X., Pan, D., Wang, X., Kimerling, L. C., Koch, T. L., & Michel, J. (2007).

Tensile-Strained, N-type Ge as a Gain Medium for Monolithic Laser Integration on Si. Opt

Express. 15:11272-11277.

4. Lim P.H., Park S., Ishikawa Y., & Wada, K. (2009). Enhanced Direct Bandgap Emission in

Germanium by Micromechanical Strain Engineering. Opt Express. 17:16358-16365.

5. El Kurdi M., Fishman G., Sauvage S., & Boucaud, P. (2010). Band Structure and Optical

Gain of Tensile-Strained Germanium Based on a 30 band k · p Formalism. J Appl Phys.

107:013710.

6. Pizzi G., Virgilio M., & Grosso G. (2010). Tight-binding Calculation of Optical Gain in

Tensile Strained [001]-Ge/SiGe Quantum Wells. Nanotechnology. 21:055202.

7. Sánchez-Pérez, J.R., Boztug, C., Chen, F., Sudradjat, F.F., Paskiewicz, D.M., Jacobson,

RB, Lagally, M.G., & Paiella, R. (2011). Direct-Bandgap Light-Emitting Germanium in

Tensilely Strained Nanomembranes, PNAS.108(47):18893-18898.

80


Lagally, M. G., & Paiella, R. (2013).Tensilely Strained Germanium Nanomembranes as In-

frared Optical Gain Media. Small. 9:622-630.

9. Boztug, C., Sánchez‐Pérez, J.R., Lagally, M.G., & Paiella, R. (2014). Strained-Germanium

Nanomembranes for Infrared Photonics, ACS Nano. 8(4):3136-3151.

10. Philipp H. P. & Taft, E.A. (1959). Optical Constant of Germanium in the Region 1 to 10

eV, Phys. Rev. 113 (4):1002-1005.

11. Yen, H., Wu, J., Wang, W., & Liou, G. (2013). High-Efficiency Photoluminescence Whol-

ly Aromatic Triarylamine-based Polyimide Nanofiber with Aggregation-Induced Emission

Enhancement. Advanced Optical Materials. 1(9):668-676.

12. Coldren, L.A. & Corzine, S.W. (1995). Diode Lasers and Photonic Integrated Circuits.

Wiley, New York,

13. Chuang, S.L. (2009). Physics of Photonic Devices. Wiley, Hoboken, NJ.

14. Van de Walle, C.G. (1989). Band Lineups and Deformation Potentials in the Model-Solid

Theory. Physical Review B, 39(3):1871.

15. Ahmad, C. N. & Adams, A. R. (1986). Electron Transport and Pressure Coefficients Asso-

ciated with the L 1 C and Δ 1 C Minima of Germanium. Physical Review B. 34(4):2319.

16. Goi, A. R., Syassen, K., & Cardona, M. (1989). Direct-Band-Gap Absorption in Germani-

um Under Pressure. Physical Review B. 39(17):12921.

17. NSM Archive- Physical Properties of Semiconductors,

www.ioffe.rssi.ru/SVA/NSM/Semicond/ Last accessed 2015-01-03.

81

18. Boztug, C., Sánchez-Pérez, J.R., Yin, J., Lagally, M.G., & Paiella R. (2013). Grating-



19. Camacho-Aguilera, R.E., Cai, Y., Patel, N., Bessette, J.T., Romagnoli, M., Kimerling, L.

C., & Michel, J. (2012). An Electrically Pumped Germanium Laser. Opt. Express.

20:11316-11302.

20. Yuan, H. C., Shin, J. H., Qin, G. X., Sun, L., Bhattacharya, P., Lagally, M. G., Celler, G.

K., & Ma, Z. (2009). Flexible Photodetectors on Plastic Substrates by use of Printing

Transferred Single-Crystal Germanium Membranes. Appl. Phys. Lett. 94:013102.

21. Paiella, R. (2011). Quantum Cascade Lasers. In Comprehensive Semiconductor Science &

Technology, Volume 5: Devices and Applications. Bhattacharya, R., Fornari, R., Kami-

mura, H., Eds., Elsevier.

82

Chapter 4 Nanomembrane surface passivation: Can we reduce cracking?

As discussed in Chapter 2, the measured biaxial tensile strain in a Ge(001) NM initially in-

creases linearly with the applied stress. This result is expected in the elastic region of the

stress/strain curve in the absence of delamination. Beyond a certain stress, the stress/strain rela-

tionship is no longer linear. This deviation from linearity is correlated with the observation of

cracks in the NM. One can stress a NM until cracks begin to form (e.g., 620kPa for a 40nm NM)

and then cycle it up to ~600kPa and obtain the same strain as for the initially uncracked one, as

determined from a Raman signal averaged over 10 random regions on the NM, with each region

~2um dia. Such a result is in contrast with the textbook stress-strain curve taken beyond the elas-

tic limit, in which the plastically deformed material returns via a different path.

We also know that thinner NMs begin to crack at higher values of applied stress. We know

that as we increase the stress beyond the point where cracks first form, more cracks form. The

standard deviation of measurements of the strain broadens, as presumably more areas in which

there is no strain are included in a Raman measurement. We know that elimination of stress con-

centrators, such as etch holes, allows reaching higher values of stress at which crack first begin

to form. The stress-strain curves fall on top of each other in the linear region. We also know, cir-

cumstantially, that elastic relaxation at etch holes in even a free-standing strained NM is negligi-

ble.(1)

These results are currently not fully understood. It must be remembered that we do not

have a simple one-component system here, but rather a composite of a rather thick, but highly

compliant, low-modulus substrate and a very thin, stiff, high-modulus sheet bonded to it. From

other studies we know that in composite systems the properties of a thin stiff sheet can be modi-

fied by a compliant substrate.(2) We can observe that the PI sheet is distorted and remains dis-

83

torted after we reach pressures where the NMs crack; i.e., some form of plastic deformation takes

place in this polymer. It may be undergoing viscoelastic creep. Yet we do not see any preferen-

tial bulging or deformation in the PI areas not covered by the Ge NM. Here we have 150 μm of

PI with a modulus of 2.5GPa (3) and a ~50nm sheet with modulus of 103GPa (4). The strain in

NM and PI at the same stress therefore differs by a factor of ~40.

One might expect dislocation formation in the NM before cracking. We do not see signa-

tures of dislocations in the usual manner seen in step graded SiGe alloys of orthogonal steps at

the surface. In thin sheets, the stability of dislocations is quite different from that in bulk materi-

als. But we cannot exclude dislocation formation. We have not done the proper experiments to

observe them.

Although we presently do not understand these results completely, at minimum suggest that

decreasing the number of cracks formed in the Ge NM during the introduction of stress will yield

higher average strain and thus a narrower, stronger PL signal shifted to higher wavelengths. It

would be valuable to prove that the broadening of the PL signal is caused by the formation of

cracks. Elimination of factors that serve to initiate the formation of cracks may allow reaching

these higher strains. These factors may include defects in the material, edge roughness, PI sub-

strate/NM interaction and the surface energy. The purpose of this chapter is to describe efforts in

this regard.

Any means that prevents the NM system from reducing its free energy by forming

cracks, or that raises the kinetic barrier for forming cracks would accomplish our aim of in-

creasing the strain. For example, surface passivation may prevent or reduce crack formation.

(5,6) Reducing surface or edge roughness, or functionalizing the surface may accomplish

these goals. Multiple factors are in play in crack formation. The stress in the material tends

84

to cause crack growth while the characteristic strength (the ability to withstand an applied

force without failure) of the material tends to resist crack growth. The growth of cracks re-

sults in the creation of new material surface. Griffith postulated that a certain amount of

work per unit area of crack formation (material property) must be expended in creating that

area. The Griffith argument also applies to crack shortening by healing. (5,6) The growth of

cracks requires the creation of two surfaces, and requires an associated increase in total sur-

face free energy. Crack initiation occurs when the surface free energy plus the strain energy

achieve a peak critical energy. Beyond the peak, the total energy decreases with increased

crack length. I have investigated several of these topics, as described below. However, my

efforts so far have not been successful in increasing the strain at which cracking occurs.

4.1 Surface energy and reconstruction

Surface energy quantifies the disruption of intermolecular bonds that occur when a surface

is created. Surfaces are intrinsically less energetically favorable than the bulk of a material (sur-

face energy is positive; atoms on the surface have broken bonds); otherwise, there would be a

driving force for surfaces to be created, removing the bulk of the material. Therefore, surface en-

ergy may be defined as the excess energy at the surface of a material compared to the bulk. Cut-

ting a solid body into pieces disrupts its bonds, requiring formation energy. However, surfaces

are often more complex than this simple “cleaved bond” model. Surfaces are highly dynamic re-

gions that have the ability to readily rearrange or react to reduce energy at the surface through

such processes as passivation or adsorption.

A clean surface will modify its structure to lower surface energy. In an infinite bulk crystal

the equilibrium positions of atoms are determined by the criterion that the net force on them is

zero. When a surface is created this equilibrium is disturbed because broken bonds are created.

85

The free energy of the system increases by the energy associated with the broken bonds. The sys-

tem attempts to minimize this surface energy by shifting the positions of atoms, a process called

surface recombination. There are two types of recombination: relaxation and reconstruction.(7)

In surface relaxation, the atoms in the surface will change their plane spacing, relative to

the bulk spacing, to lower the surface free energy. The surface layers may move in a direction

normal or lateral to the surface plane, resulting in a smaller-than-usual or larger-than-usual inter-

layer distance. Most metals experience the normal-to-the-bulk type of relaxation. (7) When look-

ing at a relaxed-only surface, we would not see a change in periodicity as we would see in sur-

face reconstruction.

Reconstruction refers to the motion of atoms with dangling bonds to lower the surface en-

ergy. Reconstruction results in a change in periodicity of the surface structure. For example, in a

cubic material the surface layer might restructure itself to assume smaller two-dimensional spac-

ing between the atoms as lateral forces from adjacent layers are reduced.(7) The Ge (100) surface

reconstructs to form germanium dimers, thereby reducing the number of dangling bonds per sur-

face Ge atom from two to one. These dimers are arranged in rows separated by trenches, with the

row direction changing by 90° at an atomic step. The nature of the bonding of the dimers on the

Ge(100) surface strongly influences the reactivity of this surface toward gas-phase reactants. Lo-

cally, the surface structure of reconstructed Ge (100) is similar to that of Si (100)-2×1; e.g., both

exhibit dimer rows with similar geometrical spacing. (8)

86

Figure 4.1 Models of the Ge(100) surface: (left) p(2×1) dimer reconstruction involving symmetric dimers; (middle)

c(4×2) dimer reconstruction with buckled dimers; and (right) p(2×2) dimer reconstruction with buckled dimers.

Larger circles are raised above the (100) plane, smaller ones are beneath the plane. From Ref. 9

Any surface functionalization or passivation of Ge must take into account how the sur-

face atoms and bonds respond to the functionalizing or passivating material. I describe a few

possible situations below.

4.2 Passivation of the germanium surface

Germanium oxide - Native silicon oxide (SiO2) is a remarkably stable passivating layer,

acts as a good electrical insulator, and forms an excellent interface with Si. In contrast, native

germanium oxide (GeO2) has less desirable properties. GeO2 is water soluble and forms a poor

interface with Ge, which results in easy removal of the oxide layer and a high density of elec-

tronic defects.(10) Another major difference between Si and Ge oxides is that thermal oxide

growth is readily achieved for silicon, but not for germanium. Oxidation of Ge by O2 results in

growth of the Ge 1+, 2+, and 3+ oxidation states, but little or no growth of the desired 4+ state

(GeO2). GeO2 disappears with a high-temperature anneal.(11,12) GeO desorbs from the surface

at 450°C, and thus annealing above this temperature results in the oxide-free surface.(12)

Sulfide Passivation - Sulfide termination of Ge leads to a remarkably well passivated inter-

face. Sulfur makes two bonds with the surface. Because each of the surface atoms on the

Ge(100)-2×1 surface has two dangling bonds, sulfur may occupy the germanium lattice sites

leading to a 1×1 surface structure.

Such a 1×1 structure was demonstrated by Weser et al. (13,14) in the formation of a

S/Ge(100)-1×1 surface by chemisorption of elemental sulfur on the Ge(100)-2×1 surface under

ultrahigh vacuum (UHV) conditions. In a different approach, elemental deposition of S, by

87

treatment of a cleaned, hydrogen-terminated Ge(100) surface with aqueous (NH4)2S, produced a

S/Ge(100)-1×1 surface with 1 monolayer (ML) coverage of sulfur atoms, consistent with the ad-

sorption of elemental sulfur in vacuum.(10) Lyman et al. (11) attempted to repeat the aqueous

passivation and deposited up to 3ML of sulfur, finding an amorphous GeSx layer over a partially

ordered bridge-bonded S/Ge interface, rather than the 1-ML well-ordered sulfur bridge-bonded

surface previously observed. We should note that even though the same chemical was used, the

process of passivation was different. Additionally, even though sulfur overlayers obtained by the

aqueous treatment differ, all cases resulted in a self-limiting overlayer that was resistant to oxida-

tion in air for days. (15-18)

Chloride Passivation - Chloride passivation can be used as a precursor for wet organic

functionalization. Cl adsorption on the Ge (100) surface changes the low-energy electron diffrac-

tion (LEED) pattern from c(4x2) to (2x1), indicating monochloride saturation (19)This recon-

struction is possible because of the addition of a chlorine atom to one dangling bond on each sur-

face atom. Cl terminated surfaces were prepared by immersing Ge(111) in dilute HCl.(20) Klesse

et al.(21) demonstrated the preparation of a clean Ge(001) surface with minimal roughness (RMS

~0.6 Å), low defect densities (~0.2% ML) and wide monatomic terraces (~80-100 nm) using

HCl. The chloride-terminated surface shows stability against oxidation on the scale of hours in

ambient air.

Hydrogen Passivation - Wet chemical methods for hydrogen termination of Ge evolved

from the surface cleaning processes. In the cleaning process, oxide is repeatedly formed and

etched away. During the etch step, use of hydrofluoric acid (HF) produces a hydrogen-

terminated surface for both the Ge(100) and Ge(111) surfaces. (22)IR data from hydride-

terminated Ge(100) show a broad Ge-H peak arising from mono-, di-, and trihydride termina-

88

tion.(23). After the HF etch, the surface is not atomically flat, and the surface roughness of 1 nm

likely stabilizes the formation of the dihydride and trihydride products that are observed.(24)

Despite the range of hydrides present, termination by HF etching stabilizes the surface

against oxidation and maintains surface ordering for further wet-chemistry treatment. Hydride-

terminated Ge shows no oxidation after exposure to ambient atmosphere for at least 1 h

(17,23,24)and little oxidation after 1 week.(24) Although the surface has multiple hydride phas-

es, subsequent hydrogermylation and alkanethiol reactions with the surface yield densely packed

organic monolayers. (24-26)When compared with chloride termination, the wet hydride termina-

tion seems less desirable, because it lacks a well-ordered, atomically flat surface. The hydride-

terminated surface is sufficiently passivated to withstand oxidation in ambient atmosphere on a

timescale of hours and can be used as a reactive precursor for subsequent surface reactions.

4.3 Organic functionalization of germanium surfaces.

The motivation for depositing organic layers on a semiconductor stems from a desire to

impart new functionality by tapping into different properties of the organic material. Organic ma-

terials offer great flexibility in designing and creating unique molecular properties that can then

be exploited to provide new capabilities in optical, electronic, and mechanical function as well as

in chemical and biological activity. For example, the organic layer may be designed to provide

surface passivation, (27-29) providing an alternative approach to the oxide, sulfide, chloride, or

hydride layers discussed above. Other organic groups can be chosen to respond to different

chemical or biological stimuli to form chip-based sensors. Research using the Ge surface is still

quite limited.

Organic functionalization has been carried out both in solution phase (wet) and in vacuum

(dry) conditions. In vacuum, Ge(100)-2×1 has been the principal surface investigated. On the

89

Ge(100)-2×1 surface the Ge dimers exhibit a double bond–like character, owing to the weak π

bond between the atoms, as well as a dipolar character, in which the up atom is nucleophilic

(electron donor) and the down atom is electrophilic (electron acceptor). Both of these descrip-

tions have close counterparts in organic chemistry, and in fact many of the reactions of organic

species at the Ge(100)-2×1 surface can be categorized into one of two types of reactions—

cycloadditions (two unsaturated molecules react to form a cyclic compound; the π electrons are

used to form two new σ bonds ) and nucleophilic/electrophilic reactions (substitution reactions in

which the nucleophile/electrophile molecule wins or loses an electron while bonding to another

molecule)—or combinations of both. Under solution conditions, the functionalization reactions

have been initiated at a hydride- or chloride-terminated germanium surface [either (100) or

(111)]. Wet chemical functionalization involves replacement of the terminal atoms with the de-

sired organic groups. Gringnard and hydrogermanilation (Ge-C) are two types of functionaliza-

tion that have been studied for the Ge surface but the processing required for these types of func-

tionalizations aren’t compatible with the platform (PI film) that we will use in this study. Our

work will focus on the wet chemical functionalization known as an alkanethiol reaction (Ge-S-

C), which can be done at relatively low temperatures and involves only simple processing.

Alkanethiol reaction (Ge-S-C) - The alkanethiol [a compound in which a sufanyl bond –SH

is attached to an alkyl (CnH2n-1) group] reaction at a Ge surface creates a Ge-S-C bond configura-

tion. The reaction at the surface happens through the sufanyl bond in which the H bond is re-

placed by the Ge bond. Research into the reaction of 1-alkanethiols with the hydride-terminated

Ge(111) surface [no results are available on Ge(001)] at room temperature demonstrated a well-

ordered monolayer after 1 day of exposure to a solution of alkanethiol in isopropyl alcohol

(IPA).(25) Kosuri et al. (26)speculate that the reaction proceeds by the creation of H2 after the

90

surface H reacts with the sufanyl bond. The times for both monolayer deposition and saturation

coverage are concentration dependent, reaching a maximum coverage of 80% of the Ge surface

at 1-M(monolayer) alkanethiol. (26)X-ray photoelectron spectroscopy measurements indicate

that an alkanethiolate monolayer is formed at the Ge surface, with no GeOx observed after

“short” exposure to air. Vibrational measurements using high resolution electron loss spectros-

copy show similar alkyl modes to alkanethiolated Au and alkylated Si, but the Ge-S stretch is not

observed. This observation means that a claim that the alkyl modes are from the surface can’t be

made, because the Ge-S is what attaches the chain to the surface, but this could be due to the sig-

nal from the peak being attenuated by the monolayer.(25) Contact angle measurements match

those of the Grignard-alkylated Ge(111) surface, corresponding to a well-ordered alkane mono-

layer;(26) however, the surface is less stable (oxidizes faster) than the corresponding direct sur-

face alkylation through direct Ge-C bond formation. For example, although no change in the sur-

face coverage is observed upon annealing to 350 K, after a 450 K anneal, the surface coverage is

significantly reduced, owing to desorption.(25) Although a 12-h exposure to ambient tempera-

ture resulted in no change in the contact angles, after 24 h a decrease is observed.(25) Finally,

decreases are also observed upon immersion into boiling water and boiling chloroform.(25) This

decreased surface stability likely results from the presence of the Ge-S bond, which is weaker

than the Ge-C bond. Han et al. (25) suggest that the weaker bond allows water to attack at the Ge

interface, leading to oxidation and subsequent desorption of the monolayer upon oxide dissolu-

tion. Robust alkanethiolate self-assembled monolayers (SAMs) on germanium substrates have

been reported by Hohman et al. (30) and Yuan et al. (31) Direct self-assembly of alkanethiols

on Ge is impeded by the presence of the native germanium oxide, but if the oxide is removed

before the reaction takes place a robust layer can be achieved. A SAM was produced on Ge nan-

91

owires (31) and Ge(001) surfaces (30) using 1-dodecanethiol. Yuan et al. (31) reported that be-

cause these molecular assemblies formed spontaneously on surfaces by adsorption and organized

into more or less large ordered domains, cracking during thermal expansion of the devices was

reduced. An increase in the life of the devices was seen, but no physical model was provided.

In my work, described below, I used Ge NMs as a platform to investigate the relationship

between surface passivation / functionalization and the physical properties of the material. I in-

vestigated the relationship between these surface treatments and the formation of cracks under

biaxial strain. We hoped for a lower probability of crack formation. Using chemical treatments

briefly explained in the sections above, I compared crack formation and strain behavior between

treated and untreated surfaces. The idea is that if a surface is passivated and all the bonds are sat-

isfied the surface free energy will be lower and crack formation will be more difficult.

There are a few key points that need to be considered. 1. Our goal is to have a passivation

process that doesn’t increase surface roughness, as surface roughness likely would increase the

probability of crack formation 2. Quantifying the etch rate of each surface functionalization

treatment is important so the resulting thickness of the NM can be known with certainty. 3. The

stability of chemical treatments should be understood in order to determine the time available for

strain investigation using Raman spectroscopy.

4.4 Experiments on passivation and functionalization of bulk germanium

Epitaxial-quality Ge wafers were used to test passivations and functionalization, to under-

stand the quality and stability of the final surface. Samples were treated using well-known pas-

sivation schemes. X-ray photoelectron spectroscopy (XPS) was used to evaluate the surface and

the stability of the passivation under atmospheric conditions. I completed two sulfide passivation

procedures, utilizing concentrated (24%) (16) and diluted (4%) (18) ammonium sulfide (NH4)2S.

92

These specific chemicals were selected because they provide good coverage, stability in air, and

a known reconstruction (1x1). Additionally, these passivation procedures could provide insight

into the building blocks of alkanethiol functionalization.

Following the procedure described in Klesse et al.,(21) I performed a chloride passivation

using hydrochloric acid (HCl). This process has shown good surface coverage results for the

(001) surface using wet chemistry at ambient pressure, consistent with previous work. (20,21) I

performed hydrogen passivation using a dilute (1%) hydrogen peroxide solution to dissolve the

native oxide, followed by concentrated HF(49%) to provide a H terminated surface.

Functionalization of Ge was performed using the alkanethiol reaction described in Yuan et

al., (31) which shows a simple procedure for SAM growth on Ge.

4.4.1 Characterization of surface chemistry of Ge (001)

The bulk samples were characterized before and after treatment using x-ray photoelectron

spectroscopy (XPS) with an Mg source. The experiments for sulfide, chloride, and hydrogen

were conducted immediately (at 0 hours), at 48 hours, and 1 week after passivation. Collecting

characterization data from the samples across multiple time points provides insight on the pas-

sivation stability when exposed to atmospheric conditions. Table 1 details the XPS peaks of in-

terest and binding energy, which will change due to passivation. The GeOx peak disappears after

the chemical treatment is complete, and the C and O peaks are lower in intensity. However, we

note here that the GeOx reappeared at 48 hours (Fig. 4.2), meaning part or the entire surface has

started to oxidize. Similar trends were observed for all passivations I investigated. Peaks for the

sulfide S2p (140eV) and chloride Cl2p (200eV) are also present for their respective passivations.

The XPS study concentrates on the Ge 3d5 and GeOx peaks, Fig. 4.2. Preliminary data show

93

passivations and Raman analyses need to be completed in a 48 hr. window, as after this time any

benefits from the adsorbates will be lost due to oxidation.

Peak of Interest Binding Energy

O1s

C1s

Ge3d5

GeOx

530 eV

285 eV

30 eV

33 eV

Table 1. XPS peaks of interest and their binding energies of unpassivated bulk Ge.

28 30 32 34

GeOx

N(E

)

Binding Energy (eV)

Ge 3d5

Figure 4.2. XPS spectra of the Ge3d5 and GeOx peaks. We see this type of spectrum on an oxidized Ge surface.

Similar to the passivation process explained above, the alkanethiol functionalization was

also characterized with XPS. The main difference between the two methods is an increased

number of measurement time points with the alkanethiol characterization. Measurements were

taken at 0 hours, 24 hours, 1, 2, and 3 weeks. The XPS spectra of C 1s peak in Ge before and af-

ter dodecanethiol passivation shows a change in form and intensity, meaning a well ordered

change has occurred. A sulfide peak, the building block for the SAM, can also be identified in

94

the spectra and the absence of a GeOx peak shows a surface free of oxygen. This treatment has

the ability to keep the surface free of oxide for a minimum of 2 weeks, as shown in Figure 4.3.

Figure 4.3. (a) Ge3d5 peak for SAM functionalization of bulk Ge(001) from no functionalization up to 3 weeks. At

0 hrs. the GeOx peak disappears as we remove the oxide from the surface. After we deposit the SAM, the spectrum

stays the same for the first 2 weeks. (b) At week 3 the GeOx can be seen, indicating that the surface has started to

oxidize.

Figure 4.4 shows a comparison of all the treatments described so far, up to a week after

treatment; we can see that the functionalized sample is not oxidized compared with the other

treatments. The stability of SAMs on bulk Ge(001) potentially provides a larger window of time

to investigate the response of NMs to strain for this specific surface modification.

95

Figure 4.4. Comparison of the Ge3d5 and GeOx XPS peaks for all treatments. (A) Before treatment: all samples

were oxidized, as shown by the peak at 33eV. (B) Immediately after treatment: the GeOx peak has disappeared, i.e.,

the oxide is replaced by the passivating element (e.g., Cl or S). (C) After a week at ambient conditions: the 1-

dodecanethiol passivation still shows no oxide formation, but all the other passivations show some oxide has formed

on the surface.

4.4.2 Effect of treatments on surface roughness

Atomic Force Microscopy (AFM) images were taken before and after treatment of bulk

Ge(001) for all the elemental terminations described above.. Between two and three areas of

1x1μm2 were selected at random places for this roughness analysis. Figure 4.5 shows the change

in roughness pre- and post-passivation for all treatments. Preliminary data indicate that chloride

treatment does not affect surface roughness as much as sulfide treatment. The results for H-

termination using our current recipe (1% H2O2 solution) are not presented here; we provide the

results in which we lower the concentration of the hydrogen peroxide (H2O2) solution before

submerging the sample in 49%HF solution. The concentration of hydrogen peroxide used for the

96

H-termination has been lowered because of the drastic change in roughness post passivation and

because at high concentrations H2O2 has a high etching rate for germanium. As seen in Figure

4.5 as we lower the concentration of H2O2 the roughness post passivation decreases. Data on the

organic functionalization is not provided here, but, as the sample preparation requires a H termi-

nated surface, one can assume their roughness to be close to the ones shown in Fig.4.5.

Figure 4.5. Change in RMS roughness after surface treatments of bulk Ge(001). The values of the pretreatment

samples are below 0.3nm. All increase after treatment. Hydrogen termination shows the highest values of roughness,

but these decrease with lower concentrations of H2O2 used in the passivation.

4.5 Passivation of Ge(001) NMs

The work described above was also performed on Ge NMs after transfer and bonding to a

PI film, in which case only the top NM surface is passivated. Because HF and HCl only passiv-

ated bulk Ge for a few hours I decided to try (NH4)2S and 1-dodecanethiol passivation on the Ge

NM/PI structure. During the course of my investigation I discovered that when using (NH4)2S,

transferred NMs will debond and break off from the PI, probably due to a reaction with the glue

or to etching of the Ge NM. The 1-dodecanethiol trials reveal that when the NMs were placed in

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Hydrogen(20%)Sulfide(4%) Hydrogen(50%)Sulfide(21%)

Rm

s(n

m)

Before passivation

After passivation

Chloride

97

this solution the sample would wrinkle and in other parts debond from the PI films at 80°C (the

process temperature) and at room temperature.

Because wet chemistry for these passivating chemistries did not work, I tried a different

approach for SAMs. I coated the NMs using a “dry” process with a reagent called hex-

amethydisilazane (HMDS). HMDS is used in photolithography as an adhesion promoter for pho-

toresist. Best results are obtained by applying HMDS from the gas phase on heated substrates.

(32) Functionalization with this reagent requires an OH terminated surface on the Ge NM. On Ge

this surface can be obtained by first cleaning the surface by rinsing with acetone, then isopropa-

nol and finally methanol; then rinsing the surface with DI water. The functionalizations of the

samples are done at room temperature. A beaker is filled with HMDS and the sample is placed

on top of a raised platform. The beaker is then sealed with a glass lid for 30 mins (Fig 4.6).

Figure4.6 Schematic diagram for functionalization of Ge using HMDS. The glass lid helps to concentrate the

amount of reagent reacting on the surface.

HDMS is volatile at room temperature and will react with the OH terminated surface and

attach to the surface via a Si-O bond. XPS spectra of bulk germanium samples were measured

and can be seen in Figure 4.7. Before any processing on the surface and after cleaning and func-

tionalization, XPS shows a sharp carbon peak consistent with an assembled carbon chain. Com-

98

parison of the spectrum 3 weeks after treatment shows that the functionalization is stable. The

process can be used with Ge NMs on PI, as there is no wet chemistry to destroy the NM/PI

bonds.

284 286 288

N(E

)

Binding Energy (eV)

As received

24 hrs

3 weeks

Figure 4.7 XPS spectra of the C1s peak for untreated Ge(001) (black curve), 24 hours after HDMS treatment (red

curve) and 3 weeks after (blue curve). The observed shift to low binding energy is consistent with stable carbon

chains.

4.6 Strain comparison for functionalized and non-functionalized Ge(001) NMs

The strain in the plane of the NMs is determined as a function of applied stress (i.e., gas

pressure) via Raman spectroscopy using the same setup described in Chapter 2. The biaxial

strain values are then calculated from the Raman shifts using Equation 2.1. Raman spectra and

pictures for samples with and without passivation or functionalization were taken at each pres-

sure to compare strain values and visual information about crack formation. Figure 5.8 shows the

comparison between two 111nm Ge NMs transferred to PI. One was functionalized using the

method described above for HMDS and the other was untreated and used as a control. As seen in

this comparison, no concrete difference in strain can be detected as both lines follow a similar

99

trend and show similar error values. These measurements, however, did not extend to high

enough pressures to make a clear determination: the strain in the functionalized NM seems still

to be in the linear range, albeit with high uncertainty. In any case, from these data no conclusions

can be reached about the effect of this functionalization, other than that it had neither beneficial

nor deleterious effect.

0 100 200 300 400

-0.5

0.0

0.5

1.0

1.5

2.0

Str

ain

[%

]

Pressure [kPa]

Control(no HMDS)

HMDS Functionalized

Figure 4.8 Strain vs pressure/ for two 111nm Ge(001) NMs on PI substrates with different surface terminations.

To get an impression of any differences in cracking or cracking mechanisms, I compare, in

Fig.4.9, optical micrographs of two NMs with the same thickness, 111nm. The thickness is arbi-

trary; from Chapter 2 we know that thinner NMs can achieve higher strain, but crack formation

can be investigated at any thickness. Sample A is the control, with no chemical treatment other

than the process explained in Chapter 2, and Sample B is a NM with a HMDS treatment. At zero

pressure, e.g., 100 kPa, corresponding roughly to 0.40% strain (Figs. 4.9 A.1 and B.1) we can see

the NM without cracks. The first signs of cracks can be seen in Fig. 4.9 A.2 and B.2 at 207 kPa

(roughly 0.81% strain for these thicknesses). As seen at this pressure there are many cracks, rela-

100

tive to the lower thicknesses shown in Chapter 2. As the pressure increases the density of cracks

for both samples increases. Figures 4.9 A.3 and B.3 show no discernible differences between

treating the sample with HMDS or leaving the samples oxide terminated. Thus I am forced to

conclude that surface treatment, as far as I have explored it, does not provide any increase in ki-

netic barrier or energetic benefit to reducing crack formation.

Figure 4.9 Comparison of functionalized and unfunctionalized NMs at 0kPa (1), 207 kPa (2) and 414 kPa (3). Sam-

ple A is a 111nm Ge NM without any chemical treatment, Sample B is a 111nm Ge NM with an HMDS treatment.

Both samples have etch hole spacing of 100μm. Scale bar is 200μm.

4.7 Chapter summary

In this chapter I discussed my experiments to explore means to inhibit crack formation in

order to increase the strain produced in Ge(001) NMs. I focused on surface modifications, as

presumably these would also influence the edges or any free surface of a NM. We hypothesized

that lowering the surface energy by way of chemical treatment should lower the probability of

crack formation and the driving force for crack propagation. The Ge surface when not chemical-

101

ly treated has an oxide layer that is soluble in water at room temperature. We can assume that

any treatment that stabilizes that surface will do so by lowering the surface free energy either by

relaxation or by reconstruction. Surface free energy is an important factor on crack formation, as

shown by Griffith. (5)

I described several chemical treatments for the Ge surface that I felt might be useful to ac-

complish this task. My effort is not exhaustive; there are many chemical treatments one could

try. I investigated sulfide, chloride, and hydrogen termination on bulk Ge (100). Results show

that these elemental terminations, when done with wet chemistry, only last an average of 48 hrs.,

not enough time to complete a strain test. I showed that self-assembled monolayers (SAMs) are

more robust and can stay on the Ge surface for weeks before signs of oxide can be observed. I

used 1-dodecanethiol and HMDS.

Ge NMs were used as a platform to investigate the relationships between surface pas-

sivation / functionalization and the physical properties of the material. Specifically I made at-

tempts to investigate the relationship between these surface treatments and the formation of

cracks under biaxial strain.

Transferring these chemical treatments to our NMs was difficult. Wet chemistry proved to

be a challenge when using the NM/PI structure, as some samples debonded while others etched

away. I changed the process to a dry functionalization. We used HMDS to functionalize Ge(001)

with a SAM using an OH terminated surface, but no changes in the behavior of the strain with

pressure or in crack formation was observed.

Of course, other factors may affect crack formation, such as the PI substrate, surface

roughness, and defects in the NM itself. These factors may need to be dealt with so that the sur-

face effect can be observed. PI has a Young’s modulus of 2.5 GPa (3) when compared with the

102

103 GPa (4) modulus of Ge. A very thin sheet bonded to a thicker compliant one takes on some

of the “softness” of the compliant one.(2) We see deformation of the PI film, which begs the

question what the PI deformation does to the interface with the NM and if the PI is driving crack

formation (micro cracks starting from the film). This topic should be explored in future efforts

to increase the strain without cracking. Possibly TEM can be used in such investigations. Also a

change to even more flexible substrate material can be explored. Polydimethylsiloxane has a

Young’s modulus of 360-870 kPa (33) (depending on processing), more than three orders of

magnitude lower than our current PI support. A more compliant support could give us more de-

flection without substrate plastic deformation. The required thickness will depend on the modu-

lus. It would need to be sufficiently cross-linked to avoid viscoeleastic creep.

One should also investigate the possibility of eliminating the current pressurizing cell by

using a MEMs approach and creating a cavity seal with a free standing NM without etch holes or

edges that can be strained from the back with an air channel. Lim et al. (34) has shown fabrica-

tion cross shaped cantilevers in Ge that could be extended for this type of work. This approach

will only leave us with the innate materials defects. Their effect may be mitigated by making the

study area smaller. For example, Ge nanowires grown in the [111] direction were able to support

a bending strain of around 17% (for the smallest nanowire disk 23nm) and 18 GPa stress before

fracture.(35) With the MEMs approach we can envision doing dry functionalization of both sides

of the NM and have stable surfaces on both sides. One such passivation could be graphene,

which has been proven to grow on (001) Ge(36,37) and is stronger than Ge and flexible at the

same time. All these approaches will illuminate the question whether a higher strain might be

achievable in Ge NMs.

103

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35. Smith D.A., Holmberg, V.C., & Korgel, B.A. (2010). Flexible Germanium Nanowires:

Ideal Strength, Room Temperature Plasticity, and Bendable Semiconductor Fabric. ACS

Nano. 4 (4):2356–2362

36. Wang, G., Zhang, M., Zhu, Y., Ding, G., Jiang, D., Guo, Q., & Wang, X. (2013). Direct

Growth of Graphene Film on Germanium Substrate. Scientific reports. 3.

37. Lee J.H., Lee E.K., Joo W.J., Jang Y., Kim B.S., Lim J.Y., Choi S.H., Ahn S.J., Ahn J.R.,

Park M.H., Yang C.W., Choi B.L., Hwang S.H., & Whang D. (2014). Wafer-Scale Growth

of Single-Crystal Monolayer Graphene on Reusable Hydrogen-Terminated Germanium,

Science. 344 (6181):286-289.

107

Chapter 5 Conclusions

5.1 Dissertation summary

In this dissertation I have shown that nanomembranes can be used to extend the range of

strain values that can be achieved in a material. Specifically for Ge(001), the ability to introduce

sufficiently tensile large strain is very valuable, because the relative motion in energy of the elec-

tronic bands are such that Ge(001) becomes direct-band gap. This feature makes Group IV pho-

tonics viable, as now light sources and lasers can be envisioned. Using a pressure cell, I was

able to measure strain in-situ via Raman spectroscopy. Biaxial tensile strain increases linearly

with the applied stress (as expected in the elastic region of the stress-strain curve in the absence

of delamination), up to the maximum measured value of 2 % for a 24nm Ge NM. Similar meas-

urements with other NMs indicate that, as the gas pressure is further increased, the average strain

eventually saturates. Although we do not fully understand this result, we believe the formation of

cracks in the NM produces strain relaxation in their immediate vicinity. As expected, the maxi-

mum achievable average strain increases with decreasing NM thickness. Specifically, because

the amount of strain energy stored in the NM is directly proportional to its thickness, when very

thin compared to the substrate, the NM contains insufficient strain energy to drive defect for-

mation.(1) These considerations underscore the importance of nanoscale thicknesses in the pre-

sent context.

Free edges and the concentration on etch holes seem to affect the level of cracks formed at

a given strain. These cracks do not affect the reproducibility of the same strain values at lower

pressures. By changing the shape of the NM and eliminating etch holes I found an increase in the

stress needed to crack the NM, with an increase in the strain at which cracks are first observed by

35%. The NMs do eventually crack, suggesting that etch holes are not the only factors initiating

108

cracks. The theoretical fracture strengths of Ge are large: for the crystalline <100> direction, Ru-

off et al. (2) has computed the maximum Ge uniaxial tensile strain and stress to be 18.3% and

14.7 GPa respectively. Using the relationship 𝜀 =(1−2𝜐)𝜎

𝐸 , where ε is the biaxial strain, υ is the

Poisson’s ratio, and σ is the stress, gives a value for the theoretical maximum biaxial strain closer

to 7%. We so far have achieved the highest values of strain in mechanically stressed Ge sheets,

but are far from the theoretical limit. Thus there is value in more research in this area.

Ge NMs under large biaxial tensile strain represent a very promising materials platform for

the development of infrared optoelectronic devices based on Ge, including light sources and la-

sers. Importantly, interband lasers at wavelengths in the mid-infrared could be developed with-

out the need for degenerate n doping, as necessitated in prior work,(3) and thus they would not

suffer from the resulting large free-carrier absorption losses and fast nonradiative Auger recom-

bination that are byproducts of high doping. In this context, the key remaining challenge is the

development of a laser cavity that can provide strong optical confinement and feedback in a NM

with highly sub-wavelength thickness. Photonic-crystal cavities consisting of dielectric pillars

directly fabricated on the NMs, such as the structure shown in Figure 3.9(A), can provide an op-

tically thick layer for the confinement of the in-plane-propagating emitted light, while at the

same time preserving the NM flexibility.

From the strain dependence of the Ge direct-band gap energy (Figure 3.5A), one expects

that the emission wavelength of these tensilely strained Ge lasers could be tuned across the 2.1-

2.5 μm mid-infrared atmospheric transmission window. This spectral region is technologically

important for use in biochemical sensing and spectroscopy, where the optical features of mole-

cules can be used for detection and identification. Specific applications include environmental

monitoring, bio-agent detection for security screening, medical diagnostics, and industrial pro-

109

cess control. It should be noted that the 2.1-2.5 μm spectrum lies at the boundary of what is

presently covered by mature semiconductor laser technologies, i.e., GaAs- and InP-based diode

lasers on the short-wavelength side and III-V quantum cascade lasers at longer wavelengths. (4)

Thus, sufficiently tensilely strained Ge is also attractive for the purpose of extending the overall

spectral reach of mid-infrared optoelectronics.

Finally in this dissertation Ge NMs were used as a platform to investigate the relationships

between surface passivation / functionalization and the physical properties of the material. At-

tempts were made to investigate the relationship between these surface treatments and the for-

mation of cracks under biaxial strain. I showed some options for dry and wet surface passivations

and studied their stability. Although much work remains to be done in this area, I believe I have

shown a feasible path, with some changes in stressor cell design, to increase biaxial strain in Ge

beyond the levels I was able to achieve here.

5.2 Outlook

The results of my work suggest several future research opportunities that would aid in the devel-

opment of Ge lasing diodes. I briefly describe these here.

5.2.1 Ge MEMS

While in the present work the NMs are mechanically strained using high-pressure gas, we

expect that similar results can be obtained on integrated silicon chips using suspended platforms

loaded with suitable stressor layers or electrostatic actuators, as are commonly fabricated with

MEMS technology. A possible implementation, based on a cross-shaped cantilever with all four

sides attached on rigid supports (so as to allow for the introduction of biaxial strain), is proposed

in the theoretical work of Ref. 5. Alternatively, creating a cavity seal with free-standing NM

without etch holes that can be strained from the back using a microfluidic channel should allow

110

reaching higher strains. Making smaller NMs may prove to be a better idea when trying to reach

the limits of fracture stress. As shown with Ge nanowires, 17% bending strain can be achieved

before fracture.(6)

5.2.2 Study of crack formation in germanium NMs

In my work I tried to explain the effect of cracks on the strain in the NM and tried to de-

termine what caused them and how to prevent them from forming. There still is a lot to work to

be done here, including understanding the interface of the NM/support film and its role in NM

cracking failure. The effect of etchant holes and free edges on crack formation needs to be better

understood. To gain such understanding, changes in the pressure cell need to be effected to allow

for multiple characterizations. Its size needs to be made smaller to allow access to XRD, to the

high resolution feature of the Raman, and possibly even plan-view TEM. One can conceive mak-

ing all-MEMS devices or other alternatives, such as PDMS stamps that can be fabricated to have

an air cavity.

One cannot ignore the likelihood that the materials quality represents a large factor in crack

formation. GOI is not readily available in high crystal quality like their silicon counterpart. The

growth of germanium on a matching substrate like GaAs and the in-house fabrication of GOI

needs to be investigated to create high-quality samples for this studies. Such studies have begun.

5.2.3 Germanium tunable photodiode

Epitaxially grown Ge P-I-N junctions with contacts for charge injection represent a device

structure that will allow the use of biaxially strained Ge as a light emitter that is tunable over a

range of wavelengths in the technologically important 2.1-2.5-µm spectral region. Such strain

tunable light emitting diodes may have multiple applications. An alternative, but likely more dif-

ficult approach is a lateral P-I-N junction in a strainable NM, where the P and N regions are de-

111

fined by ion implantation, an approach that has already been demonstrated for the development

of flexible (unstrained) Ge NM photodiodes.(7). The development of tunable-wavelength Ge

LEDs could also be approached using the growth of Ge on a lattice matched III-V material, such

as GaAs, AlAs, or InGaP, allows for the integration of III-V heterostructures with well-defined

electronic, optical, and piezoelectric properties into the structure within a release and transfer

technology. Early efforts by others along these lines, but without release and transfer were not

very successful, but much work can be envisioned to improve results. (8) Ge NMs produced in

this manner could be then transferred to flexible substrates that can be mechanically strained. For

this project to be successful, advances in preventing cracks and obtaining defect-free large-area

NMs need to be achieved first.

5.3 References

1. Freund, L.B. & Suresh, S. (2003). Thin Film Materials: Stress, Defect Formation and Sur-

face Evolution. Cambridge University Press, Cambridge, UK.

2. Ruoff, A.L. (1978). On the Ultimate Yield Strength of Solids, J. Appl. Phys. 49(1):197-

200.

3. Camacho-Aguilera, R.E., Cai, Y., Patel, N., Bessette, J.T., Romagnoli, M., Kimerling, L.

C., & Michel, J. (2012). An Electrically Pumped Germanium Laser. Opt. Express

20:11316-11302.

4. Paiella, R. (2011). Quantum Cascade Lasers. In Comprehensive Semiconductor Science &

Technology, Volume 5: Devices and Applications. Bhattacharya, R., Fornari, R., Kami-

mura, H., Eds.; Elsevier.

5. Lim P.H., Park S., Ishikawa Y., & Wada K. (2009). Enhanced Direct Band gap Emission in

Germanium by Micromechanical Strain Engineering. Opt Express. 17:16358-16365.

112

6. Smith D.A., Holmberg, V.C., & Korgel , B.A. (2010). Flexible Germanium Nanowires:

Ideal Strength, Room Temperature Plasticity, and Bendable Semiconductor Fabric. ACS

Nano. 4(4):2356–2362.

7. Yuan, H.C., Shin, J. H., Qin, G. X., Sun, L., Bhattacharya, P., Lagally, M. G., Celler, G. K.,

& Ma, Z. (2009). Flexible Photodetectors on Plastic Substrates by use of Printing Trans-

ferred Single-Crystal Germanium Membranes. Appl. Phys. Lett. 94:013102.


Harris, J. S. (2011). Strong Enhancement of Direct Transition Photoluminescence with

Highly Tensile-Strained Ge Grown by Molecular Beam Epitaxy. Appl. Phys. Lett.

98:011111.

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