III-V Metamorphic Materials and Devices for Multijunction Solar

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III-V METAMORPHIC MATERIALS AND DEVICES FOR

MULTIJUNCTION SOLAR CELLS GROWN VIA MBE AND MOCVD

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree

Doctor of Philosophy in the Graduate School of The Ohio State University

Daniel Joseph Chmielewski, B.S., M.S.

Graduate Program of Electrical and Computer Engineering

The Ohio State University

2018

Dissertation Committee:

Professor Steven A. Ringel, Advisor

Professor Tyler J. Grassman

Professor Sanjay Krishna

Professor Lei Raymond Cao Copyright by

Daniel Joseph Chmielewski

2018

ABSTRACT

III-V multijunction solar cells (MJSC) are capable of the highest conversion

efficiencies among all solar cell classifications. These devices are thus of major interest

for both terrestrial and space applications. However, the economics of the terrestrial and

space markets leads to significantly different design requirements for III-V MJSCs to

become more economically viable in each market.

MJSCs with Si solar cells to demonstrate III-V/Si MJSCs. Such an approach

simultaneously takes advantage of the high conversion efficiency of III-V MJSCs and the low-cost manufacturing of Si.

In the space market, III-V MJSCs are already the dominant technology due to their high efficiency, radiation hardness, and reliability in extreme conditions. However, new III-V MJSC approaches must be developed if they are to push the boundary of conversion efficiency even further. An approach to improve the efficiency and thus economic viability is through the use of additional high-performance sub-cells at optimal bandgaps to more ideally partition the solar spectrum.

i Although the design requirements for improving the economic viability of III-V

MJSCs in the terrestrial and space markets differ drastically, the design of III-V MJSCs can be altered to meet the design requirements for both markets by using the versatile technique of III-V metamorphic epitaxy. This is the growth of relaxed (i.e. unstrained)

III-V compounds at a lattice constant that differs from that of the substrate. The major advantage of III-V metamorphic epitaxy is that it provides an additional degree of freedom for III-V MJSC device design. Traditional lattice-matched growth limits the number of materials that are available to integrate with the substrate material, which in turn limits the available bandgaps that can be achieved for a given III-V MJSC design.

This dissertation aims to leverage III-V metamorphic epitaxy to develop various critical components of III-V MJSCs grown by both molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD). This includes the development of metamorphic tunnel junctions to enable III-V/Si MJSC approaches for future terrestrial applications and the development of wide bandgap (AlzGa1-z)xIn1-xP top cells (lattice-

matched vs. metamorphic) to push the efficiency limits of III-V MJSC approaches for

future space applications.

Tunnel junctions serve as low-resistance, optically transparent interconnects between adjacent sub-cells within MJSCs. For III-V/Si MJSCs, these tunnel junctions are ideally grown at the same lattice constant as the metamorphic III-V sub-cells. Therefore, metamorphic tunnel junctions with relatively unexplored lattice constants are necessary.

Development of these metamorphic tunnel junctions initially began with MBE-grown materials and devices. At this early stage of research, the III-V/Si MJSC approach primarily focused on the MBE-grown triple-junction solar cell designed for operation

ii under high concentration. This in turn specified a variety of requirements for the necessary lower and upper tunnel junctions of the triple-junction including the necessary

peak tunneling current (JP), resistance-area product (RA), and bandgap to minimize parasitic losses within the tunnel junction.

After initial development of an MBE-grown metamorphic GaAs0.9P0.1

homojunction tunnel junction, efforts culminated in the demonstration of a high-

performance metamorphic double heterostructure tunnel junction. This device achieved

-2 -4 2 JP = 510 A·cm and RA = 2.0×10 Ω·cm ; due to these excellent electronic properties, as

well as its high optical transparency, this device is suitable for both the lower and upper

tunnel junction in the triple-junction. Upon integration into a Ga0.57In0.43P/GaAs0.9P0.1

dual-junction solar cell (a subset of the triple-junction containing only the III-V sub-cells

and upper tunnel junction) the tunnel junction operated successfully. Thus, such a design

is very promising for future III-V/Si triple-junction solar cells.

III-V metamorphic epitaxy was used to explore new III-V MJSC approaches for

future space applications. Current research trends are pushing to increase the efficiency

of III-V MJSCs via the use of more sub-cells compared to the traditional triple-junction

solar cell design. As the number of sub-cell increase from 4 to 6, the ideal bandgap profile of the MJSC shifts the bandgap of the top cell from ~2.05 eV to ~2.3 eV, respectively. Although the ideal bandgap required for the top cell can be achieved via lattice-matched (AlzGa1-z)0.52In0.48P, the necessary Al content tends to reduce device

performance due to increased oxygen content. Thus, an alternative solution was explored

for achieving a 2.05 eV top cell via the use of III-V metamorphic epitaxy.

iii Al content versus misfit was compared in MOCVD-grown lattice-matched

(Al0.32Ga0.68)0.52In0.48P and metamorphic Ga0.66In0.34P solar cells. Results demonstrated

that the metamorphic Ga0.66In0.34P solar cell possessed substantially higher short

wavelength current collection. This was due to the wider-bandgap, internally lattice-

matched window layer of the metamorphic Ga0.66In0.34P cell, as well as a longer emitter diffusion length. Device modeling and characterization results suggested similar base diffusion lengths in each cell, and ultimately merits to both approaches were demonstrated.

iv DEDICATION

To my Mom, Dad, Eric, and Callie

v ACKNOWLEDGEMENTS

The person that has had the greatest influence on my life has been my Mom. She has supported me unconditionally in more ways than I can possibly list here. She was the one who taught me to appreciate and pursue a higher education. I cannot be more thankful for everything that she has done for me. I would like to thank my Dad for always being there on the drop of a dime and for teaching me the importance of family. My brother Eric has taught me how to live in the present and enjoy life. The amount of love

and support that Callie has provided these past several years has been amazing. I am very

grateful for her patience as I completed graduate school and look forward to our future

adventures together.

Prior to graduate school, I received my B.S. in Materials Science and Engineering

at The Ohio State University. My undergraduate experience included a variety of

undergraduate research and I would like to thank Professor Robert Wagoner, Professor

Katharine Flores, and Professor Patricia Morris for supporting and preparing me for

graduate school. During my undergraduate experience, I became seriously interested in

semiconductors my junior year when taking a course on the processing of electronic

materials with Professor Roberto Myers. He sparked this interest, which cascaded into a

very eventful senior year taking as many electronic materials classes as I could. This

included a course on semiconductor devices with Professor Siddharth Rajan. After

vi expressing my interest to him about graduate school in Electrical and Computer

Engineering, he told me I should contact Steve Ringel due to his research group’s unique

blend of materials and device experience. I immediately stopped by his office to see if he

was available. He was. He was also free to talk for what seemed like half an hour.

Looking back and now knowing how often Steve is traveling, I feel like I was extremely

lucky that day!

After joining Steve’s group and transitioning from MSE to ECE, it did seem a bit

overwhelming at first – I went from feeling like I knew everything after graduating, to an environment that was very new to me. However, I learned quickly and am thankful for all

the support from the students in the group. Andrew Carlin was a great mentor and was

the one who taught me how to measure my first tunnel junction. I learned a wealth of

information from Chris Ratcliff and Javier Grandal in the MBE lab. Austin Speelman was

also very helpful with ECV.

As the years progressed, Drew Cardwell and Santino Carnevale joined the group

as postdoctoral students. I remember various conversations with Drew and appreciate his

ability to present ideas in new and refreshing ways. I had known Santino since working

on my senior design project, so I was glad to be working with him again. During my

transition from MBE to MOCVD, he played an instrumental role in operating the

MOCVD to realize my preliminary tunnel junction designs.

As I became one of the senior students in the group, I had the opportunity to

mentor various students including Nathan Vaughn, Jacob Boyer, and Daniel Lepkowski.

All were very helpful with assisting in the lab and I am glad to have worked with them.

The analytical IQE model that Jacob and Daniel created enabled a deeper understanding

vii of the AlGaInP top cell work. I also cannot thank Daniel enough for all the help during a month-long tunnel junction growth campaign last summer. After I completed a series of growths in the afternoon, he worked many late hours to provide one-day turnaround on processed and characterized devices. I would also like to thank all the DLTS/DLOS students in the group, and in particular Kevin Galiano, Pran Paul, and Christine Jackson for assisting with a variety of materials characterization. I am also thankful for all the words of wisdom Christine has provided over the years.

Mark Brenner has been very helpful keeping the MBE lab running and with training me on various processing tools in the ECE cleanroom. John Carlin taught me just about everything I needed to know to operate the MOCVD. All the staff at Nanotech

West have also been of great assistance with training me to process devices. Aaron Payne was tremendously helpful with keeping the MOCVD running. The ECE computing services team helped to ensure our labs ran smoothly. Don Gibb personally addressed

many concerns of mine.

Of course, through all these years in graduate school, Professor Tyler J. Grassman

has had one of the biggest impacts on me. I’ve known Tyler since he was a postdoctoral

researcher working under Steve. He has mentored me on just about every facet of our

group and has dedicated a tremendous amount of time with editing my proceedings and

papers. At a group meeting early on in my graduate career, I also remember Tyler making

a statement that we shouldn’t make knee-jerk reactions. I am pretty sure it was meant for me and has stuck with me ever since. I am glad to have continued working with Tyler after he became at professor at The Ohio State University.

viii That brings me back to Steve. Without his guidance and patience, none of this would have been possible. He has provided me with an opportunity that I could not have imagined prior to graduate school. Not only has Steve had many positive impacts within our research group, but also within a wide range of research communities. I am very proud to say that Steve has been my advisor.

I would also like to thank the agencies that have funded this research and continue to fund research at The Ohio State University. Metamorphic tunnel junction research was funded by the Department of Energy and the National Science Foundation under the

F-PACE program (SunShot award DE-EE0005398) and the PVRD program (SunShot award DE-EE-0007539-2), the Air Force Research Laboratory (contracts FA9453-08-C-

0172 and FA9453-11-C-0253), and The Ohio State University Institute for Materials

Research. Metamorphic (AlzGa1-z)xIn1-xP top cell research was funded by the Air Force

Research Laboratory (contract FA9453-14-C-0373).

ix VITA

October 11, 1988 ...... Born – Garfield Heights, Ohio

2011 ...... B.S. Materials Science and Engineering, The Ohio State University

2018 ...... M.S. Electrical & Computer Engineering, The Ohio State University

2017 to present ...... Ph.D. Candidate, The Ohio State University

PUBLICATIONS D. J. Chmielewski, C. M. Jackson, J. T. Boyer, D. L. Lepkowski, J. A. Carlin, A. A. Arehart, T. J. Grassman, and S. A. Ringel, “Comparative Study of >2 eV Lattice- Matched and Metamorphic (Al)GaInP Materials and Solar Cells Grown by MOCVD,” Proc. 44th Photovoltaic Spec. Conf., 2017. (accepted for publication)

D. J. Chmielewski, K. Galiano, P. Paul, D. Cardwell, S. Carnevale, J. A. Carlin, A. R. Arehart, T. J. Grassman, and S. A. Ringel, “Comparative study of 2.05 eV AlGaInP and metamorphic GaInP materials and solar cells grown by MBE and MOCVD,” Proc. 43rd IEEE Photovoltaic Spec. Conf., 2016. doi: 10.1109/PVSC.2016.7750300

D. J. Chmielewski, S. Carnevale, T. J. Grassman, J. A. Carlin and S. A. Ringel, "High- performance metamorphic tunnel junctions for III-V/Si multijunction solar cells," Proc. 42nd IEEE Photovoltaic Spec. Conf., pp. 1-4, 2015. doi: 10.1109/PVSC.2015.7356382

D. J. Chmielewski, T. J. Grassman, A. M. Carlin, J. A. Carlin, A. J. Speelman and S. A. Ringel, "Metamorphic GaAsP tunnel junctions for high-efficiency III-V/IV multijunction solar cell technology," IEEE Journal of Photovoltaics, vol. 4, pp. 1301- 1305, 2014. doi: 10.1109/JPHOTOV.2014.2328592

D. J. Chmielewski, T. J. Grassman, A. M. Carlin, J. Carlin, A. Speelman and S. A. Ringel, "Metamorphic tunnel junctions for high efficiency III-V/IV multi-junction

x solar cell technology," Proc. 39th IEEE Photovoltaic Spec. Conf., pp. 0882-0885, 2013. doi: 10.1109/PVSC.2013.6744285

J. T. Boyer, D. L. Lepkowski, D. J. Chmielewski, S. A. Ringel, and T. J. Grassman, “Graded (AlzGa1-z)xIn1-xP Window-Emitter Structures for Improved Short- Wavelength Response,” Proc. 44th Photovoltaic Spec. Conf., 2017. (accepted for publication)

T. J. Grassman, D. J. Chmielewski, S. D. Carnevale, J. A. Carlin and S. A. Ringel, "GaAs0.75P0.25/Si dual-junction solar cells grown by MBE and MOCVD," IEEE Journal of Photovoltaics, vol. 6, pp. 326-331, 2016. doi: 10.1109/JPHOTOV.2015.2493365

T. J. Grassman, D. J. Chmielewski, J. A. Carlin, and S. A. Ringel, “Development of epitaxial 2- and 3-junction III-V/Si solar cells,” Proc. 43rd IEEE Photovoltaic Spec. Conf., 2016. doi: 10.1109/PVSC.2016.7749986

D. W. Cardwell, N. Vaughn, P. Paul, C. Ratcliff, D. Chmielewski, S. Carnevale, A. Arehart, T. J. Grassman, and S. A. Ringel, "Investigations of metamorphic (Al)GaInP for III-V multijunction photovoltaics," Proc. 42nd Photovoltaic Spec. Conf., pp. 1-4, 2015. doi: 10.1109/PVSC.2015.7356437

T. J. Grassman, J. A. Carlin, C. Ratcliff, D. J. Chmielewski and S. A. Ringel, "Epitaxially-grown metamorphic GaAsP/Si dual-junction solar cells," Proc. 39th IEEE Photovoltaic Spec. Conf., pp. 0149-0153, 2013. doi: 10.1109/PVSC.2013.6744117

S. A. Ringel, J. A. Carlin, T. J. Grassman, B. Galiana, A. M. Carlin, C. Ratcliff, D. Chmielewski, L. Yang, M. J. Mills, Al Mansouri, S. P. Bremner, A. Ho-Baillie, X. Hao, H. Mehrvarz, G. Conibeer, and M. A. Green, "Ideal GaP/Si heterostructures grown by MOCVD: III-V/active-Si subcells, multijunctions, and MBE-to-MOCVD III-V/Si interface science," Proc. 39th IEEE Photovoltaic Spec. Conf., pp. 3383-3388, 2013. doi: 10.1109/PVSC.2013.6745175

C. Ratcliff, T. J. Grassman, J. A. Carlin, D. J. Chmielewski and S. A. Ringel, "Ga-rich GaxIn1-xP solar cells on Si with 1.95 eV bandgap for ideal III-V/Si photovoltaics," Proc. SPIE 8981, Physics, Simulation, and Photonic Engineering of Photovoltaic Devices III, pp. 898118, 2014. doi:10.1117/12.2042017

K. Swaminathan, T. J. Grassman, L. Yang, D. Chmielewski, M. Mills and S. A. Ringel, "Impact of threading dislocation density on metamorphic InxGa1-xAs and InzGa1-zP p- i-n photodetectors on GaAs," Proc. SPIE 8257, Optical Components and Materials IX, pp. 82571A, 2012. doi:10.1117/12.908581

FIELDS OF STUDY

MAJOR FIELD: Electrical & Computer Engineering

xi TABLE OF CONTENTS

Abstract ...... i Dedication ...... v Acknowledgements ...... vi Vita ...... x List of Tables ...... xvii List of Figures ...... xviii

CHAPTER 1: INTRODUCTION ...... 1 1.1. Background ...... 1 1.2. Terrestrial Solar ...... 4 1.3. Space Solar ...... 16 1.4. Dissertation Objectives ...... 21 1.4.1. Metamorphic Tunnel Junctions for III-V/Si MJSCs ...... 22

1.4.2. Wide Bandgap (AlzGa1-z)xIn1-xP Top Cells for III-V MJSCs ...... 23 1.5. Dissertation Layout ...... 23

CHAPTER 2: SOLAR CELL, MJSC, AND TUNNEL JUNCTION OPERATION ...... 25 2.1. Background ...... 25 2.2. The Solar Spectrum ...... 26 2.3. Solar Cell Fundamentals ...... 28 2.3.1. Photocurrent ...... 29 2.3.2. Dark I-V Characteristics of p-n Junctions ...... 35 2.3.3. Illuminated I-V Characteristics of p-n Junctions ...... 37 2.3.4. Solar Cell Design ...... 41 2.4. Detailed Balance Efficiency Limit ...... 47 2.4.1. Single Junction Solar Cells ...... 47 2.4.2. Multijunction Solar Cells ...... 50 2.5. Monolithic Multijunction Solar Cell Operation ...... 53 2.6. Tunnel Junction Operation ...... 57

xii 2.6.1. Tunnel Junction Theory ...... 58 2.6.2. III-V/Si MJSC Tunnel Junction Design Requirements ...... 61 2.6.2.1. MBE 3J Tunnel Junctions ...... 62 2.6.2.2. MOCVD 2J Tunnel Junction ...... 65

CHAPTER 3: EPITAXIAL GROWTH AND DEVICE FABRICATION ...... 66 3.1. Background ...... 66 3.2. Fundamental Aspects of Epitaxy ...... 67 3.2.1. Source Materials ...... 68 3.2.2. Mass Transport...... 69 3.2.3. Atomistic View of Epitaxy ...... 69 3.2.4. Epitaxial Growth Modes ...... 72 3.3. III-V Metamorphic Epitaxy ...... 75 3.3.1. Relevant III-V and IV Crystal Properties ...... 75 3.3.1.1. Crystal Structure ...... 75 3.3.1.2. Polarity ...... 76 3.3.1.3. Crystal Surfaces ...... 78 3.3.1.4. Crystal Defects ...... 79 3.3.1.5. Anti-Phase Domains ...... 79 3.3.1.6. Dislocations ...... 80 3.3.2. Polar-on-Nonpolar Heteroepitaxy ...... 82 3.3.3. Lattice-Mismatched Heteroepitaxy ...... 84 3.3.4. Metamorphic Buffer Design ...... 88 3.4. Epitaxial Growth Methods ...... 89 3.4.1. Molecular Beam Epitaxy ...... 89 3.4.1.1. Ultra-High Vacuum ...... 90 3.4.1.2. Molecular Beam Sources ...... 92 3.4.1.3. Substrate Temperature ...... 94 3.4.1.4. RHEED ...... 95 3.4.1.5. The Ohio State AsP/Si MBE ...... 97 3.4.2. Metal-organic Chemical Vapor Deposition ...... 98 xiii 3.4.2.1. Precursors ...... 100 3.4.2.2. Pyrolysis Reactions ...... 103 3.4.2.3. Mass Transport ...... 104 3.4.2.4. MOCVD Growth Regimes ...... 106 3.4.2.5. The Ohio State AsP/Si MOCVD ...... 108 3.5. Device Processing Techniques ...... 110 3.5.1. Electron Beam Evaporation ...... 110 3.5.2. Rapid Thermal Annealing ...... 111 3.5.3. Spin Coater...... 111 3.5.4. Photolithography ...... 112 3.5.5. Inductively Coupled Plasma Reactive-Ion Etching ...... 113 3.5.6. Supplemental Techniques ...... 114

CHAPTER 4: MATERIALS AND DEVICE CHARACTERIZATION TECHNIQUES ...... 115 4.1. Background ...... 115 4.2. Materials Characterization Techniques ...... 115 4.2.1. High Resolution X-ray Diffraction Reciprocal Space Mapping ...... 115 4.2.2. Photoluminescence ...... 120 4.2.3. Hall Effect ...... 121 4.2.4. Capacitance-Voltage ...... 123 4.2.5. Scanning Electron Microscopy Techniques ...... 126 4.2.6. Atomic Force Microscopy ...... 128 4.2.7. Nomarski Microscopy ...... 128 4.3. Device Characterization Techniques ...... 129 4.3.1. Current-Voltage ...... 129 4.3.1.1. Dark Current-Voltage ...... 129 4.3.1.2. Illuminated Current-Voltage ...... 130

4.3.1.3. JSC-VOC ...... 132 4.3.2. Quantum Efficiency ...... 132

CHAPTER 5: MBE-GROWN METAMORPHIC TUNNEL JUNCTIONS ...... 137

xiv 5.1. Background ...... 137 5.2. MBE 3J Lower Tunnel Junction ...... 139 5.2.1. Approach ...... 139 5.2.2. Results ...... 141 5.2.2.1. Doping Studies ...... 141 5.2.2.2. Tunnel Junction Characterization ...... 144 5.2.2.3. Device Simulations ...... 148 5.2.3. Discussion ...... 150 5.2.4. Conclusions ...... 151 5.3. MBE 3J Upper Tunnel Junction ...... 152 5.3.1. Motivation ...... 152 5.3.2. Results ...... 152 5.3.2.1. Double Heterostructure TJ Design ...... 152 5.3.2.2. Double Heterostructure TJ Characterization ...... 153 5.3.2.3. Towards Integration into the MBE 3J ...... 157 5.3.3. Conclusions ...... 158

CHAPTER 6: MOCVD-GROWN METAMORPHIC TUNNEL JUNCTIONS ...... 160 6.1. Background ...... 160 6.2. Approach ...... 163

6.3. Lattice-matched p-Type TJ Layer: AlxGa1-xAs Doping Study ...... 165 6.4. Lattice-matched n-Type TJ Layer: GaAs:Te Doping Study ...... 168 6.4.1. Bulk Doping Study ...... 168 6.4.2. Te Memory Effect: GaAs:Te Thickness Study ...... 172 6.4.3. Te Memory Effect: DETe Pre-dosing Study ...... 173 6.5. Metamorphic Doping Calibrations and TJ Devices ...... 176 6.5.1. Transition to Metamorphic Alloys ...... 177 6.5.2. Metamorphic Tunnel Junction Demonstration ...... 179 6.6. Conclusions ...... 183

CHAPTER 7: WIDE BANDGAP ALGAINP SOLAR CELLS ...... 184

xv 7.1. Background ...... 184 7.2. Approach ...... 187 7.3. Results and Discussion ...... 192 7.4. Conclusions ...... 201

CHAPTER 8: CONCLUSIONS AND FUTURE WORK ...... 203 8.1. Metamorphic Tunnel Junctions ...... 204 8.1.1. Summary ...... 204 8.1.2. Ongoing and Future Work ...... 208 8.2. AlGaInP Top Cells ...... 212 8.2.1. Summary ...... 212 8.2.2. Ongoing and Future Work ...... 213 8.3. Final Comments ...... 215

REFERENCES ...... 216

xvi LIST OF TABLES

Table 2.1. Target values of TJ figures of merit for the TJs within the MBE 3J operated at 500× AM1.5D...... 64

Table 2.2. Target values of TJ figures of merit for the TJ within the MOCVD 2J operated at various concentrations...... 65

Table 5.1. Target values of TJ figures of merit for the TJs within the MBE 3J operated at 500× AM1.5D...... 138

Table 5.2. GaAs and GaAs0.9P0.1 homojunction tunnel junction results...... 146

Table 5.3. Double heterostructure TJ figures of merit. GaAsP-B is the optimized homojunction TJ in the MBE 3J Lower Tunnel Junction section...... 157

Table 6.1. Target values of TJ figures of merit for the TJ within the MOCVD 2J operated at one sun, medium concentration, and high concentration...... 161

Table 6.2. Parameters of lattice-matched (LM) TJs grown for the GaAs:Te thickness study (devices A-D) and DETe pre-dosing study (devices C, E, F), as well as the metamorphic (MM) TJs...... 170

Table 6.3. Carrier concentrations determined via Hall in thick epilayers representative of the metamorphic tunnel junction layers under various anneal combinations...... 181

Table 7.1. Modeled emitter and base LD of each device using interpolated optical data...... 195

xvii LIST OF FIGURES

Figure 1.1. AM1.5G detailed balance isoefficiency contours of a monolithic, 2-terminal (a) dual-junction solar cell highlighting a maximum efficiency of 45.0% when using a 1.12 eV Si bottom cell and (b) triple-junction solar cell with a fixed 1.12 eV Si bottom cell indicating a global maximum of 49.1%. Calculated using a MATLAB script developed by our group...... 5

Figure 1.2. (a) 2-terminal, (b) mechanically-stacked 4-terminal, and (c) optically split 4- terminal configurations for a tandem solar cell...... 6

Figure 1.3. Bandgap vs. lattice constant chart of Si, Ge, and various relevant III-V arsenide and phosphide materials. This demonstrates a major challenge of III-V/Si integration; III-V materials with a direct bandgap have considerable lattice mismatch with Si...... 8

Figure 1.4. Approach to achieve a III-V/Active-Si triple junction solar cell via III-V metamorphic epitaxy...... 12

Figure 1.5. Schematic showing the typical current-voltage behavior of a p++/n++ tunnel junction. The resistance-area product, peak tunneling current, bandgap, as well as the lattice constant are key figures of merit of a metamorphic tunnel junction within a MJSC...... 15

Figure 1.6. Structure of the Ga0.50In0.50P/Ga0.99In0.01As/Ge upright lattice-matched triple-junction solar...... 17

Figure 2.1. The AM0, AM1.5G, and AM1.5D standard solar spectra (ASTM G173-03 standard [99])...... 27

Figure 2.2. Band diagram schematic of a p-n junction to define various features and to demonstrate asymmetry of built-in electric field...... 31

xviii Figure 2.3. Example of a collection probability curve of a p-n junction solar cell, demonstrating bulk and surface-limited cases in the QNRs and unity collection in the SCR due to the built-in electric field...... 33

Figure 2.4. Band diagrams of a p-n junction in the dark at (a) zero bias and (b) forward bias...... 36

Figure 2.5. Band diagrams of a p-n junction under illumination at (a) zero bias and (b) forward bias...... 38

Figure 2.6. Example of dark I-V and LIV curves of a solar cell that obeys the superposition principle...... 39

Figure 2.7. The LIV and power curves of a solar cell, highlighting various figures of merit of a solar cell including the short-circuit current (ISC), open-circuit voltage (VOC), and the maximum power point (PMAX)...... 40

Figure 2.8. (a) Schematic of a p+/n solar cell structure, including the top contact grid fingers and busbar, ARC, solar cell layer thicknesses appropriate for efficient absorption (based on G(x)), window and cladding layers, and the bottom contact. (b) Schematic of the band diagram of this solar cell, highlighting the minority carrier band offset at the window and BSF for carrier confinement and the SCR extending primarily into the base layer due to the asymmetric junction...... 46

Figure 2.9. AM1.5G detailed balance efficiency limit as a function of bandgap...... 49

Figure 2.10. Photon utilization efficiency of the Ga0.57In0.43P/GaAs0.9P0.1/Si triple junction solar cell...... 51

Figure 2.11. AM1.5G isoefficiency contour plot of an ideal triple-junction solar cell with the ideal 0.7 eV bandgap bottom sub-cell...... 52

Figure 2.12. Band diagrams of a GaAs0.75P0.25/Si 2J at a) at equilibrium, b) under illumination and at short-circuit conditions, and c) under illumination and at the maximum power point (structure in inset)...... 56

Figure 2.13. Example J-V curve of a 1.55 eV GaAs0.9P0.1 TJ. Labeled regions of interest include (a) equilibrium, (b) peak current, (c) excess current, and (d) thermal current...... 57

Figure 2.14. Band diagrams of the four regions of interest in a 1.55 eV TJ. The blue and red lines are the electron and hole quasi-Fermi levels, respectively...... 58

Figure 2.15. Semi-log plot of the 1.55 eV GaAs0.9P0.1 TJ J-V curve. Labeled regions of interest include (a) equilibrium, (b) peak current, (c) excess current, and (d)

xix thermal current. Dotted and dashed exponential curves with ideality factors of 8 and 2, respectively, are plotted as a visual aid...... 60

Figure 2.16. (a) The circuit diagram of a solar cell and TJ in series under illumination. The J-V curves in (b) and (c) are for a TJ (dotted), solar cell (dashed), and the circuit in (a) (solid). (b) When JP > JSC, the tunnel junction operates in the ohmic-like portion of the tunneling current regime and only introduces series resistance. (b) When JP < JSC, the TJ is the current limiter until the circuit is reverse biased enough to bias the TJ into the low-resistance regime of its thermal current component, at which point the solar cell becomes the current limiter. © 2006 IEEE (adapted from [119])...... 63

Figure 3.1. Simplified schematic demonstrating sequence to grow and process solar cell and tunnel junction devices (dimensions not to scale)...... 66

Figure 3.2. Steps of the general epitaxial process...... 67

Figure 3.3. The Kossel crystal, highlighting flat, stepped, and kinked surfaces...... 70

Figure 3.4. Possible atomic sites that an adatom can occupy and the associated number of atomic bonds; 1) embedded within flat surface (five bonds), 2) embedded within stepped surface (four bonds), 3) kink site (three bonds), 4) step site (two bonds), and 5) adsorbed to a flat surface (one bond)...... 71

Figure 3.5. Various atomistic processes that occur on the surface during epitaxial growth...... 71

Figure 3.6. The four primary growth modes at different levels of monolayer coverages...... 73

Figure 3.7. Atomic arrangement of (a) a (100) and (b) a vicinal (100) surface...... 73

Figure 3.8. The diamond cubic and zincblende crystal structures...... 76

Figure 3.9. Demonstration of the polarity of the zincblende structure...... 77

Figure 3.10. Schematic of surface reconstruction at a crystal surface...... 78

Figure 3.11. APD and APBs in GaP grown on single atomic-height stepped Si(100) resulting in incorrect P-P bonds along {111} directions. Reprinted from Thin Solid Films, vol. 517, B. Kunert, I. Németh, S. Reinhard, K. Volz, and W. Stolz, Si (001) surface preparation for the antiphase domain free heteroepitaxial growth of GaP on Si substrate, pp. 140-143, Copyright 2008, with permission from Elsevier...... 80

Figure 3.12. Atomic arrangement of (a) edge and (b) screw dislocations. © 2011 Fong Kwong Yam, Li Li Low, Sue Ann Oh, and Zainuriah Hassan. Adapted from xx Gallium Nitride: An Overview of Structural Defects, Optoelectronics Padmanabhan Predeep, IntechOpen; originally published under CC BY-NC- SA 3.0. Available from: 10.5772/19878 ...... 81

Figure 3.13. STM image of a vicinal Si (100) surface showing the two surface domains (dimer orientations) that alternate on adjacent terraces. Adapted by permission from Springer Nature Terms and Conditions for RightsLink Permissions Springer Nature Customer Service Centre GmbH: Springer Nature Applied Physics A: Materials Science & Processing “In vivo” STM studies of the growth of Germanium and Silicon on Silicon by B. Voigtländer and M. Kästner, 1996...... 84

Figure 3.14. Atomic arrangement during a) pseudomorphic lattice-mismatched heteroepitaxy where the epitaxial layer conforms to the substrate, and b) metamorphic lattice-mismatched heteroepitaxy with a misfit dislocation to relieve the bulk strain energy...... 85

Figure 3.15. Depiction of a dislocation half loop consisting of a misfit dislocation and two threading dislocations on a (111) plane...... 87

Figure 3.16. Dependence of GaAs minority carrier lifetime (τ) as a function of threading dislocation density. Reprinted from [22], with the permission of AIP Publishing...... 87

Figure 3.17. Schematic of a typical MBE reactor. “Molecular Beam Epitaxy” by Nikhil P. is licensed under CC BY-SA 3.0 ...... 90

Figure 3.18. Representative 2× and 4× RHEED patterns of GaAs(100) during a growth stop under an As overpressure. These patterns occur for both the 2×4 and 4×2 surface reconstructions of GaAs(100) in the orthogonal [011] and [011] directions, respectively...... 96

Figure 3.19. Schematic of a typical low pressure MOCVD reactor...... 99

Figure 3.20. Molecular structure of group II, III, and V precursors...... 101

Figure 3.21. Velocity profile of a boundary layer formed by a gas flowing at an initial velocity v0 over a surface...... 105

Figure 3.22. Primary MOCVD growth regimes...... 106

Figure 3.23. Schematic of a close-coupled showerhead MOCVD...... 108

Figure 3.24. Fully processed solar cells, diodes, and test structures...... 109

Figure 4.1. Bragg diffraction condition for X-rays incident upon a crystal...... 116

xxi Figure 4.2. Ewald sphere construction to determine diffraction conditions in reciprocal space...... 117

Figure 4.3. Schematic showing how reciprocal space is mapped by ω, 2θ, and ω-2θ scans (black arrows). The larger (red) and smaller (black) reciprocal lattice points represent two crystals that have slightly different lattice constants. An example of an RSM constructed using ω and ω-2θ scans is demonstrated. 119

Figure 4.4. Schematic of the Hall effect where the magnetic field is applied in the z direction (orthogonal to plane of image)...... 121

Figure 4.5. EBIC image of a metamorphic Ga0.63In0.37P solar cell. The dark circular spots occur due to recombination in the vicinity of threading dislocations...... 127

Figure 4.6. EQE and IQE of a GaAs0.9P0.1 solar cell...... 134

Figure 5.1. Structure of the MBE 3J, highlighting the need for lower and upper TJs. ..137

Figure 5.2. Comparison of actual Si concentration, measured by SIMS, and resultant n-type carrier concentration, measured by ECV, for a GaAs multilayered test structure designed to determine the effect of a) growth temperature while maintaining a V:III beam flux ratio of 24 and b) V:III beam flux ratio while maintaining a growth temperature of 500 °C on carrier concentration for a nominal n-type (Si) doping of 2×1019 cm-3. The SIMS profile in b) is taken from the sample in a), although is representative of the structure in b) as well...... 142

Figure 5.3. Current density-voltage measurements of GaAs and GaAs0.9P0.1 TJs for various doping conditions obtained at 300 K. Instability in the NDR is due to bias oscillations but does not significantly impact the extraction of the JP or RA values. The inset indicates the device structure. The structure for the GaAs TJ is identical except for the lack of a step-graded buffer...... 144

+ Figure 5.4. LIV data obtained for nominally-identical, non-optimized n /p GaAs0.9P0.1 solar cell structures on p-type (no TJ) and n-type (with TJ) metamorphic GaAsyP1-y/GaAs substrates. Measurements were made using a Class AAA AM1.5G simulator...... 147

Figure 5.5. Simulation of GaAsP-B TJ using a method that incorporates the Silvaco ATLAS model with the excess current component of the empirical model. Excellent agreement of peak tunneling current and voltage suggests the new optimized growth conditions indeed result in nearly-complete activation of dopants. The disagreement in the NDR region is due to bias oscillations. .148

xxii + + + Figure 5.6. EQE simulations of a n /p GaAs0.9P0.1 solar cell with a p /n -GaAs0.9P0.1 tunnel junction located above the solar cell. The GaAs0.9P0.1 middle cell spectral region of interest within the MBE 3J is indicated by the shaded region (λGaAsP)...... 153

Figure 5.7. Band diagram simulation of the Ga0.57In0.43P/GaAs0.9P0.1 double heterostructure TJ at zero bias condition...... 154

Figure 5.8. Performance of various double heterostructure TJs with respect to the optimized GaAs0.9P0.1 homojunction TJ (GaAsP-B in the MBE 3J Lower Tunnel Junction section)...... 155

Figure 5.9. QE and LIV of a Ga0.57In0.43P/GaAs0.9P0.1 dual-junction...... 158

Figure 6.1. Structure of the MOCVD 2J, highlighting the need for a metamorphic TJ...... 160

Figure 6.3. Hole concentration as a function of Al fraction in post-growth carbon activation annealed AlxGa1-xAs at various growth temperatures and CBrCl3 flows. The dotted lines aid in visualizing the trends and measurements were done at 300 K...... 167

Figure 6.4. Electron concentration as a function of DETe flow and growth temperature in GaAs:Te. A maximum electron concentration of 1.87×1019 cm-3 was obtained at a growth temperature of 600 °C. The V/III ratio for all samples was 110...... 169

Figure 6.5. Structures of tunnel junctions fabricated for the (a) GaAs:Te Thickness Study and (b) the DETe Pre-dosing Study to understand how the Te memory effect impacts device performance...... 171

Figure 6.6. JP of tunnel junctions from the GaAs:Te Thickness Study (devices A-D) and the DETe Pre-dosing Study (devices C, E, and F)...... 171

Figure 6.8. JP values for devices C, E, and F, highlighting the significant improvement in performance that the pulsed DETe pre-dosing used in device F has over the uniform pre-dosing used in device E...... 175 xxiii Figure 6.9. UID and C-doped GaAsyP1-y composition calibrations at a growth temperature of 525 °C. Compositions were determined via HRXRD RSM analysis...... 177

Figure 6.10. J-V results of the Al0.2Ga0.8As0.75P0.25:C/GaAs0.75P0.25:Te heterojunction metamorphic tunnel junction under various combinations of the C activation anneal to enhance performance and the MOCVD anneal to emulate the thermal load of the GaAs0.75P0.25 top cell...... 180

Figure 7.1. Lattice-matched (Al0.32Ga0.68)0.52In0.48P and metamorphic Ga0.66In0.34P approaches for achieving a direct bandgap of 2.05 eV. The filled circles indicate the cell/absorber material. The open circles indicate the direct bandgap of the internally lattice-matched AlxIn1-xP window, the dominant transition in the thin 20 nm window resulting in parasitic optical absorption of high energy photons...... 186

Figure 7.2. Device structures of the ~2.05 eV (a) LM-AlGaInP and (b) MM-GaInP cells...... 189

Figure 7.3. Modeled spectrally-resolved transmission through the 20 nm internally lattice-matched Al0.54In0.46P and Al0.69In0.31P windows on the LM-AlGaInP and MM-GaInP cells, respectively...... 193

Figure 7.4. IQE of LM-AlGaInP and MM-GaInP cells reveals the superior short wavelength response, as well as the slightly higher overall response, of MM-GaInP...... 195

Figure 7.5. (a) AM0 illuminated J-V and JSC-VOC (offset by JSC) of 2.06 eV LM-(Al0.32Ga0.68)0.52In0.48P and 2.02 eV MM-Ga0.66In0.34P cells without ARCs; the inset plots dJ/dV (with a running average to smooth data), showing equal slopes. (b) Dark J-V of corresponding diodes; values for the J02 and n2 parameters of each device are shown in the legend/inset...... 199

xxiv CHAPTER 1:

INTRODUCTION

1.1. BACKGROUND

III-V multijunction solar cells (MJSC) are capable of the highest conversion

efficiencies among all solar cell classifications [1], [2]. These devices are thus of major

interest for both terrestrial and space applications [3]. However, the economics of the

terrestrial and space markets leads to significantly different design requirements for III-V

MJSCs to become more economically viable in each market.

In the terrestrial market, despite their high efficiency, the high manufacturing cost of III-V MJSCs currently limits their applicability in a market that is currently dominated by crystalline silicon [4]–[6]. Thus, lower cost III-V MJSC approaches must be developed for them to become more competitive. This intuitively leads to the concept of merging III-V MJSCs with Si solar cells to demonstrate III-V/Active-Si MJSCs. Such an approach simultaneously takes advantage of the high conversion efficiency of III-V

MJSCs and the low-cost manufacturing of Si.

1 In the space market, III-V MJSCs are already the dominant technology due to

their high efficiency, radiation hardness, and reliability in extreme conditions [7].

However, new III-V MJSC approaches must be developed if they are to push the

boundary of conversion efficiency even further. An approach to improve the efficiency

and thus economic viability is through the use of additional high-performance sub-cells at

optimal bandgaps to more ideally partition the solar spectrum.

Although the design requirements for improving the economic viability of III-V

If III-V/Active-Si MJSCs are to be realized for terrestrial applications, III-V metamorphic epitaxy is necessary since no III-V compounds exist that are both lattice-

matched to Si and possess the required bandgaps to achieve high efficiency. For space

applications, III-V metamorphic epitaxy is already used for the lower bandgap sub-cells

of commercial III-V MJSCs [8]. However, the top cell of III-V MJSCs with 4+ sub-cells is typically achieved using lattice-matched (AlzGa1-z)0.51In0.49P (z ≥ 0) [9]–[12]. The

challenge with this approach is that high Al content typically leads to poor material

quality and device performance [13], [14]. Al content is sometimes completely avoided

2 despite resulting in a top cell with a lower than optimal bandgap [15]. III-V metamorphic

epitaxy enables alternative pathways to achieve high-performance top cells at optimal

bandgaps while simultaneously reducing or eliminating Al content.

The major challenge with III-V metamorphic epitaxy is that lattice-mismatched growth can lead to the incorporation of defects that reduce material quality and subsequently device performance. However, for over 20 years our research group has specialized in the development of nucleation layers, graded buffers, and high-quality

III-V metamorphic materials and devices to demonstrate that this challenge can be overcome [16]–[58]. Building upon this experience, this dissertation aims to leverage

III-V metamorphic epitaxy to develop various critical components of III-V MJSCs grown by both molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition

(MOCVD). This includes the development of metamorphic tunnel junctions to enable

III-V/Active-Si MJSC approaches for future terrestrial applications and the development of wide bandgap (AlzGa1-z)xIn1-xP top cells (lattice-matched vs. metamorphic) to push

the efficiency limits of III-V MJSC approaches for future space applications.

The following sections provide a more thorough analysis of the terrestrial and

space markets to indicate where the focuses of this dissertation fit into the bigger picture.

The specific III-V MJSC components that are developed within this dissertation are also

introduced in more detail. This is followed by the objectives of this dissertation and the

layout of the remaining chapters.

3 1.2. TERRESTRIAL SOLAR

For terrestrial applications, crystalline silicon held ~93% of the market share in

2017; mono-crystalline Si (mono-Si) held ~32% of that crystalline silicon share, whereas multi-crystalline silicon (multi-Si) held ~61% [59]. Due to the mono-Si industry upgrading to PERC (passivated emitter rear local contact) solar cells in recent years, some forecasts have suggested mono-Si will hold the majority share by 2019 [60]. Others believe that both mono-Si and multi-Si will continue to coexist for some time [61]. In either case, it appears mono-Si will play a significant role into the foreseeable future.

However, although the PERC cell has pushed the solar conversion efficiency of mono-Si to 25% [1], the theoretical limit of silicon is 29% [62], [63]. This means that there is relatively little room for further improvement in efficiency for the mono-Si solar cell.

A clear pathway to overcome the theoretical limit of Si is that of Si-based MJSCs.

Such approaches are capable of significantly higher conversion efficiencies than Si alone

due to reduced thermalization and transmission losses [64] For example, a tandem solar

cell (i.e. MJSC with two junctions) with a top cell bandgap of ~1.7 eV and the bottom

cell bandgap constrained to that of Si (1.1 eV) is theoretically capable of over 40%

efficiency under the AM1.5G standard global spectrum [48], [64]. This is demonstrated

by the isoefficiency contour plot in Figure 1.1(a). In this example the efficiency limit was

calculated via detailed balance (section 2.4) and predicts a maximum efficiency of 45.0%

when using a 1.12 eV Si bottom cell. Note that this is close to the global maximum of

45.7%, suggesting that the use of a Si bottom cell does not theoretically limit

performance significantly for the dual-junction. By adding a third junction, the

Figure 1.1. AM1.5G detailed balance isoefficiency contours of a monolithic, 2-terminal (a) dual-junction solar cell highlighting a maximum efficiency of 45.0% when using a 1.12 eV Si bottom cell and (b) triple- junction solar cell with a fixed 1.12 eV Si bottom cell indicating a global maximum of 49.1%. Calculated using a MATLAB script developed by our group.

isoefficiency contour in Figure 1.1(b) indicates that the ideal bandgap profile when using

a 1.12 eV Si bottom cell is 2.0/1.5/1.12 eV and enables a maximum theoretical efficiency

of 49.1%. By operating this triple-junction under concentration, this efficiency can

exceed 50% [52], [64]. To demonstrate these MJSC approaches, various terminal configurations and sub-cell materials have been explored in the literature. A number of these approaches are highlighted below, along with associated advantages and disadvantages.

Traditional MJSCs have terminal configurations that result in the sub-cells either being connected in series or parallel. Using a tandem solar cell as an example, a 2- terminal configuration results in the sub-cells connected in series, and a 4-terminal configuration results in the sub-cells connected in parallel. In the 4-terminal

Figure 1.2. (a) 2-terminal, (b) mechanically-stacked 4-terminal, and (c) optically split 4-terminal configurations for a tandem solar cell.

configuration, the sub-cells can either be mechanically stacked or spatially separated with the use of optical splitters to direct the appropriate portion of the spectrum to each sub- cell. An advantage of a 2-terminal approach is that it is easier to manufacture. However, due to being connected in series each sub-cell must produce equal photocurrents (i.e. current matching) and are sensitive to variation in the solar spectrum. In addition, the 2- terminal configuration requires a low-resistance, optically transparent interconnect between adjacent sub-cells to avoid parasitic losses due to the two adjacent sub-cells being in direct contact with one another. Fabrication of the 4-terminal configuration is more complex than the 2-terminal configuration, although it is much less sensitive to changes in the solar spectrum and doesn’t require the sub-cell interconnects. These configurations are shown in Figure 1.2 and reviewed in [64]. In addition to the 2- and 4- terminal configurations, the 3-terminal configuration has also been explored in an attempt to benefit from the advantages of both the 2- and 4- terminal configurations [65], [66].

6 Note that the detailed balance calculations in Figure 1.1 were performed assuming the 2-

terminal approach.

A variety of materials have been explored in the literature as potential candidates

to integrate with Si to demonstrate Si-based MJSCs. Perovskites are one such material that have been explored for perovskite-Si tandem solar cells. This approach has rapidly improved in efficiency in recent years, having exceeded 25% [67]. However, the stability of the perovskite material is a major concern for this approach since factors such as oxygen, moisture, UV light, solution process, and temperature degrade the material [67]–

[69]. Chalcogenides such as CdTe have also been explored, although a major issue with this group of materials is that their bandgaps are much lower than the ideal 1.7 eV target for a Si-based tandem [64]. III-V material, on the other hand, do not suffer from stability issues and their compositions can be adjusted to achieve the appropriate bandgaps. This makes the concept of III-V/Active-Si MJSCs a very attractive choice.

A major technological challenge with the III-V/Active-Si MJSC approach is that

the necessary III-V sub-cells have a significantly different lattice constant than silicon.

This is indicated in Figure 1.3, which plots bandgap vs. lattice constant for Si, Ge, and

relevant III-V arsenide and phosphide materials. To overcome this challenge, various

epitaxial approaches have been explored in the literature to demonstrate III-V/Si MJSCs.

These include epitaxial lift-off and wafer bonding [70]–[72], direct mismatched epitaxy

[73], [74], and graded mismatched epitaxy [32], [75]–[77]. Epitaxial lift-off and wafer

bonding add additional processing steps that increase the manufacturing cost, which may

in turn make such a technique prohibitively expensive for large scale terrestrial

applications. Direct mismatched epitaxy results in a monolithic, 2-terminal device that is

simpler to manufacture. However, such an approach yields poor material quality in the

mismatched, metamorphic sub-cell(s). This may limit device performance to levels that

are too low to be viable for large scale terrestrial applications. The graded mismatched

epitaxy approach can be used to achieve the simpler monolithic, 2-terminal configuration

without sacrificing material quality by controlling and limiting the formation of

performance-degrading defects via the use of graded buffer layers.

In addition to lattice mismatch, taking an epitaxial approach for achieving

III-V/Active-Si introduces additional technological challenges. For example, the thermal coefficient of expansion (TCE) of Si is 2.6×10-6 °C-1, whereas for III-V arsenide and

phosphide materials that are relevant for III-V on Si the TCE is significantly higher in the 8 range of 4.5 – 5.7 ×10-6 °C-1 [78]. Therefore, upon post-growth cooling residual stress can result in epilayer cracking and wafer bowing [79]. Furthermore, III-V materials are polar and Si is nonpolar. Polar-on-non-polar epitaxy presents various challenges for achieving high quality III-V epilayers due to defects that this interface can introduce [80].

The combination of challenges such as lattice mismatch, TCE mismatch, and a polar/nonpolar interface makes it apparent that the demonstration of a III-V/Active-Si

MJSC is an ambitious goal. Fortunately, our research group has a rich history of experience with developing solutions to these specific challenges for a variety of applications. This experience encompasses epitaxial growth via both molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD). Although solutions were originally developed primarily for space applications, by exploring the evolution of our group’s expertise over the last 20 years it will become evident how our capabilities have enabled us to tackle the multifaceted challenge of demonstrating a

III-V/Active-Si MJSC for terrestrial applications.

Some of the earliest work in our group focused on materials systems that contained a subset of the challenges discussed above. Lattice-mismatched epitaxy on Si was explored by our group in 1995 to demonstrate strain-relaxed Si0.3Ge0.7/Si

heterostructure diodes [16]. This materials system is purely group IV material, and thus

does not introduce a polar/nonpolar interface. It was two years later when polar-on-

nonpolar epitaxy was explored to demonstrate defect-free GaAs grown on Ge [17]. This

was accomplished by identifying critical growth steps that suppress the formation defects

such as anti-phase domains, threading dislocations, and interface diffusion. A year later

in 1998 colleagues at MIT extended the use of SixGe1-x to demonstrate relaxed Ge grown

9 on Si via the use of a SixGe1-x graded buffer [81]. If grown via direct epitaxy, the large

lattice mismatch between Ge and Si would result in the nucleation of many threading

dislocations. However, by using the SixGe1-x graded buffer the threading dislocations

were controlled to enable high quality Ge on Si. Between the development of defect-free

GaAs/Ge and high-quality Ge/SixGe1-x/Si, this set the stage for our group’s first phase in

integrating III-V materials with Si. By forming a strong collaboration with Professor

Fitzgerald’s research group at MIT, high quality GaAs on Si became possible via

GaAs/Ge/SixGe1-x/Si virtual substrates (i.e. substrates that provide a lattice constant that differs from the substrates for subsequent epitaxial growth).

Our group first demonstrated GaAs on Si solar cells in 2000 [50]. The development of the GaAs/Si solar cell advanced over the next several years [19], [20],

[22], [23], [54]–[57], culminating in the demonstration of GaAs on Si solar cells on the

International Space Station aboard Materials International Space Station Experiment number 5 (MISSE5) in 2006 [24], [26]. During this period around 2005, this technology was expanded to begin the development of III-V MJSCs on Ge/SixGe1-x/Si virtual

substrates [21], [25]. This resulted in the demonstration of a GaInP/GaAs dual-junction solar cell in 2006 [82]. Since then, dual-junction and triple-junction solar cells on

Ge/SixGe1-x/Si virtual substrates have been demonstrated by 4Power LLC, a startup

company that was co-founded by my advisor Steven Ringel and Professor Fitzgerald

[83], [84].

The achievements listed above provided the foundation to begin the development

of III-V/Active-Si MJSCs. However, one major technological hurdle remained; although

Ge/SixGe1-x/Si virtual substrates provided an excellent platform for integrating III-V

10 materials with Si for a variety of III-V solar cell approaches, it does not permit

III-V/Active-Si. For a III-V/Active-Si approach that utilizes the silicon substrate as the

bottom sub-cell of the approach, all materials above the Si substrate/sub-cell must be

optically transparent to the portion of the solar spectrum designated for absorption. For

example, in the 1.7/1.12 eV dual-junction configuration, the Si bottom cell is designed to absorb photons in the range of 1.12 – 1.7 eV. Unfortunately, the use of a SixGe1-x graded

buffer would lead to significant parasitic optical absorption since SixGe1-x has a lower

bandgap than Si. Thus, an alternative method for interfacing III-V with Si was necessary

to achieve III-V/Active-Si. This began our group’s second phase of III-V on Si

integration.

Before determining the appropriate buffer material to replace SixGe1-x, it is

necessary to first identify the requirements of a III-V/Active-Si MJSC. Since the earliest

work on III-V/Active-Si MJSCs in our research group focused on a triple-junction solar

cell, this will be used as an example. Recall from Figure 1.1 that the ideal bandgap profile

for such as device is 2.0/1.5/1.12 eV. To visualize a possible approach for this bandgap

profile, Figure 1.3 has been replotted in Figure 1.4 with various features highlighted. The

highlighted bands represent the ideal bandgap profile for this MJSC approach. As can be seen, GaxIn1-xP and GaAsyP1-y possess the correct target bandgaps if the appropriate compositions are chosen. Thus, this bandgap profile can be achieved via a

Ga0.57In0.43P/GaAs0.9P0.1/Si triple-junction solar cell. However, since these compositions

have ~3.5% misfit with Si, III-V metamorphic epitaxy is necessary to grow these III-V

sub-cells with high material quality.

Figure 1.4. Approach to achieve a III-V/Active-Si triple junction solar cell via III-V metamorphic epitaxy.

Now that it is clear why III-V metamorphic epitaxy is required and that a SixGe1-x buffer is not an option, an alternative approach is necessary. As seen in Figure 1.4, an alternative approach is to first nucleate GaP directly on a Si substrate/bottom cell. Such an approach works for III-V/Active-Si since GaP has bandgap of 2.27 eV, significantly higher than the Si absorption band for the triple-junction (1.12 – 1.5 eV). Similar to

GaAs/Ge, GaP/Si requires polar-on-nonpolar epitaxy. In addition, whereas there is relatively little misfit between GaAs and Ge (~0.08%), there is ~0.4% misfit between

GaP and Si. There is also significant TCE mismatch, where the TCE of GaP is

4.65×10-6 °C-1 and of Si is 2.6×10-6 °C-1. The combination of these factors makes the

GaP/Si interface difficult to perfect, although our group has specialized in developing this 12 interface for a decade [29], [37], [38]. Furthermore, the requirement for a Si

substrate/bottom cell introduces further challenges, as this interface can impact the

performance of the Si bottom cell. Therefore, we have formed a collaboration with The

University of New South Wales to complement our groups knowledge of III-V

metamorphic epitaxy with their expertise in Si solar cells to address this challenge [42],

[85]–[87].

Upon successful GaP/Si nucleation, a GaAsyP1-y step-graded buffer can then be

grown to the target lattice constant [32]. Note that even though the bandgap of the buffer

reduces as the target lattice constant is approached, the buffer terminates at the same

composition as the GaAs0.9P0.1 middle cell. Thus, this buffer also meets the transparency

requirements of the III-V/Active-Si triple junction solar cell. At this point, the

metamorphic III-V devices can be grown on the GaAs0.9P0.1/GaAsyP1-y/GaP/Si virtual

substrate. In the case of the III-V/Active-Si dual-junction solar cell, recall that the ideal

bandgap profile is 1.7/1.12 eV (Figure 1.1(a)). This can be achieved by a similar process,

with the major difference being that the GaAsyP1-y step-graded buffer should terminate at

GaAs0.75P0.25 to achieve a GaAs0.75P0.25/Si dual-junction solar cell with the target bandgap profile.

Early development of III-V/Active-Si MJSCs began in our group around 2009 with a focus on fundamental research on materials and devices grown via the molecular beam epitaxy (MBE) growth platform [29], [31], [32], [36], [48] with the intent to ultimately demonstrate a triple-junction III-V/Active-Si MJSC structure (MBE 3J) designed for operation under high solar concentration (up to 500× under the AM1.5D spectrum). Over time, we began to transition the triple-junction to the more economically

13 viable metal-organic chemical vapor deposition (MOCVD) growth platform

(MOCVD 3J) [37], [52]. In addition, the structure was later changed to the dual-junction

III-V/Active-Si MJSC structure for the demonstration of both an MBE 2J and an

MOCVD 2J [48]. An advantage of the dual-junction approach is that it is easier to

manufacture and can be operated under AM1.5G, avoiding the use of high-cost

concentrator systems. In addition, as shown in Figure 1.1, transitioning from the triple-

junction to the dual-junction only reduces the theoretical efficiency from 49.1% to 45%.

Thus, the cost benefits of switching to the dual-junction are fortunately not accompanied

by a large reduction in the projected efficiency. Although all permutations of growth

method (MBE, MOCVD) and structure (3J, 2J) have been explored by our research group

to some extent, ultimately the MBE 3J and MOCVD 2J (as referred to throughout this

dissertation) received the most attention and development time and will be the primary

III-V/Si MJSC approaches of interest in the remainder of this dissertation. Active Si will

be assumed when discussing these approaches in subsequent chapters.

As mentioned earlier, the 2-terminal configuration of MJSCs requires a low resistance, optically transparent interconnect between adjacent sub-cells. For III-V

MJSCs, and consequently the III-V/Active-Si MJSC approaches explored by our research group, this is accomplished via the use of tunnel junctions [40], [43], [47]. Such devices can be fabricated with the required optoelectronic properties, and importantly can be grown using the same types of semiconductor materials that the III-V sub-cells are grown with. This enables the growth of all III-V components of the III-V/Active-Si MJSC in a single process.

The basic features of a tunnel junction can be seen with the aid of Figure 1.5. The

basic structure of the tunnel junction is a p-n junction. This is the same fundamental

device used for solar cells. Unsurprisingly, at high forward bias the current-voltage curve has the same exponential behavior expected of a p-n junction. However, the tunnel junction has a characteristic peak in the current at low forward bias. This is due to the tunnel junction having highly doped (i.e. degenerate) p++ and n++ layers. As seen by the

band diagram inset in Figure 1.5, this creates extremely strong band bending at the

junction interface. As a result, there is overlap between the highest energy states in the

p++ layer valence band and the lowest energy states in the n++ layer conduction band.

Under small forward bias, as long as this overlap remains, carriers are able to pass

through this barrier via quantum tunneling without a loss in energy and a tunneling

current occurs. This behavior results in a low resistance-area product (RA) at low forward

15 bias. As the forward bias increases further, the overlap reaches a maximum and a peak in

the tunneling current density (JP) occurs. After even higher bias, the overlap decreases and the current drops to a lower value and ultimately typical diode behavior occurs at high bias.

The key figures of merit of a metamorphic tunnel junction within a

III-V/Active-Si MJSC include a low RA to minimize series resistance losses and a high

JP to ensure the tunnel junction does not fail within the MJSC. In addition, a wide

bandgap (EG) is necessary to avoid parasitic optical absorption of photons designated for

collection in the sub-cell beneath the tunnel junction. Finally, the lattice constant should

ideally match that of the metamorphic III-V sub-cells to ensure high material quality. Due

to the need for metamorphic III-V sub-cells in the MBE 3J and MOCVD 2J approaches,

this leads to one of the primary focuses of this dissertation; the development of III-V metamorphic tunnel junctions at relatively unexplored lattice constants and alloy compositions that meet specific design criteria for use within the MBE 3J and

MOCVD 2J.

1.3. SPACE SOLAR

III-V MJSCs possess a variety of qualities that make them very attractive for

space applications. This includes factors such as their high efficiency, high specific

power, radiation hardness, and thermal cycling durability [7]. Over the past couple

decades, the efficiency of these devices has increased due to development of more

advanced device structures that aim to more effectively partition the solar spectrum via

an improved bandgap profile and/or additional sub-cells. The importance of the bandgap

16 profile will be explored in more detail in chapter 2, but the key concept is that the proper

bandgaps must be selected for each sub-cell of the MJSC to maximize the photon

utilization efficiency throughout the solar spectrum. This section begins with the original

triple-junction approach, followed by examples of alterations that can be made to this

design to improve performance. This leads into approaches containing more than three

junctions and requires wide bandgap (AlzGa1-z)xIn1-xP top cells, one of the major focuses

within this dissertation.

The Ga0.50In0.50P/Ga0.99In0.01As/Ge upright lattice-matched triple-junction solar, schematically shown in Figure 1.6, is the conventional approach to a III-V MJSC and was the first triple-junction launched into space in 2000 [88]. These first-generation triple- junctions had an efficiency of 25.8% under the AM0 spectrum [89]. This approach is considered an upright III-V MJSC design, meaning that the entire structure is grown such that the same orientation is maintained during device operation.

The conventional lattice-matched triple-junction has a major limitation that prevents it from reaching even high efficiencies; it possesses a non-ideal bandgap profile

Figure 1.6. Structure of the Ga0.50In0.50P/Ga0.99In0.01As/Ge upright lattice-matched triple-junction solar. 17 that arises from the constraint of lattice-matching the III-V sub-cells to the Ge substrate.

Using the same approach to calculate the isoefficiency contours that were shown in

Figure 1.1, the ideal bandgap profile of a triple-junction with no bandgap constraints

under AM0 is 2.0/1.4/1.0 eV. However, for approaches that are limited to using a 0.67 eV

Ge bottom cell, the ideal fixed-Ge bandgap profile becomes ~1.75/1.3/0.67 eV [90].

Since the bandgap profile of the lattice-matched triple-junction is 1.9/1.4/0.67 eV, the top

and middle cells have ~0.1 eV higher bandgaps than the ideal fixed-Ge bandgap profile.

This results in the Ge bottom cell generating approximately twice the photocurrent as the

III-V sub-cells, translating into a loss in efficiency [91]. In recent years, various

approaches have been developed to overcome the limitations of this conventional lattice-

matched triple-junction design.

The ideal fixed-Ge bandgap profile can be achieved using a metamorphic

GaxIn1-xP/GaxIn1-xAs/Ge triple-junction approach [90], [92]. Using metamorphic III-V

sub-cells allows their compositions and thus bandgaps to be adjusted appropriately. The major concern with this approach is that the growth of metamorphic materials tends to

degrade material quality due to the generation of threading dislocations. By using a

metamorphic GaxIn1-xAs step-graded buffer to minimize the number of threading

dislocations, this approach has enabled an AM0 efficiency of 27.3% [48], slightly higher

than the first-generation triple-junction discussed above.

The III-V MJSC approaches discussed thus far have the upright configuration and

are limited to using a Ge bottom cell. Another approach for optimizing the bandgap

profile is to replace the Ge bottom cell of the upright triple-junction with a metamorphic

GaxIn1-xAs sub-cell. However, if such an approach was done in the upright configuration,

18 a GaxIn1-xAs step-graded buffer would first be necessary to grade from either a Ge or

GaAs substrate to the target metamorphic GaxIn1-xAs composition for the bottom cell,

then an additional buffer would need to be grown to grade back to grow the lattice-

matched sub-cells. Such a method would result in threading dislocations propagating

through all three sub-cells, which as discussed previously can degrade material quality.

To minimize degradation due to threading dislocations, the inverted metamorphic

multijunction solar cell (IMM) approach was developed. As the name implies, the

structure is grown in the reverse order. The lattice-matched top cell is grown first,

followed by the lattice-matched middle cell, metamorphic GaxIn1-xAs step-graded buffer, and finally the metamorphic GaxIn1-xAs bottom cell. The sub-cells are then removed

from the substrate via an epitaxial lift-off technique, flipped over, then bonded to a low-

cost substrate. This approach limits dislocations to only the metamorphic GaxIn1-xAs

bottom cell and has been used to demonstrate an IMM triple-junction with an AM0 efficiency of 32.0% [93].

All the approaches discussed above have focused on triple-junction designs and aimed to target a more ideal bandgap profile than what is capable with the conventional lattice-matched triple-junction. However, it is possible to achieve even higher efficiencies by incorporating more sub-cells and adjusting the bandgap profile accordingly to maintain ideal partitioning of the solar spectrum. For example, the ideal AM0 bandgap profile for a quadruple junction becomes 2.09/1.58/1.21/0.93 eV [15]. This indicates that the top cell of a quadruple junction requires a higher bandgap than lattice-matched

Ga0.5In0.50P (~1.8-1.9 eV depending on ordering [94]). As demonstrated in Figure 1.7,

the optimal bandgap for the top cell increases from ~2.1 eV to ~2.3 eV as the number of

19 48

46 6J 5J 44 AM0 42 4J

40 3J

Modeled Efficiency (%) Efficiency Modeled 38 Currently viable with GaInP 36 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 Highest Energy Bandgap (eV)

junctions increases from four to six [95]. Although lattice-matched (AlzGa1-z)0.51In0.49P enables the necessary range of bandgaps for these devices, it also tends to getter (i.e. scavenges) oxygen, leading to lower device performance [13], [14]. As a result, some demonstrations of quadruple junction IMMs avoided the use of Al altogether, yet have reached AM0 conversion efficiencies of 33.6% [15]. Although this is a considerable improvement over the 25.8% AM0 efficiency of the first-generation lattice-matched triple-junction discussed at the beginning of this section, further improvement is possible if high-performance top cells at the ideal bandgaps can be achieved. Thus, a major portion of this dissertation explores the use of III-V metamorphic epitaxy to compare the traditional lattice-matched (AlzGa1-z).51In0.49P approach to a metamorphic GaxIn1-xP approach grown via MOCVD to determine if this alternative pathway to fabricate the wide bandgap top cell of future space MJSCs is advantageous.

20 1.4. DISSERTATION OBJECTIVES

The primary objective of this dissertation research is to leverage the advantages of

III-V metamorphic epitaxy to explore new III-V MJSC approaches for terrestrial and space applications. Although the device structures of each of these approaches differs

(i.e. terrestrial vs. space, concentrator vs flat plate, etc.), the methodologies for the fabrication and integration of the metamorphic materials remain the same. This begins with the growth method, which has a significant impact on performance of these materials. As such, a major effort of this research is to explore the properties of molecular beam epitaxy (MBE)- and metalorganic chemical vapor deposition (MOCVD)-grown

materials and devices to assess each growth method. High quality materials can then be

fabricated into device structures and integrated into their respective application.

The metamorphic materials of interest rely on the use of metamorphic graded

buffers. The buffers provide a virtual substrate graded to the necessary lattice constant

and are designed to minimize defects in the device layers that would otherwise be

detrimental to material quality and thus device performance. This buffer is a critical

component for the success of metamorphic III-V MJSCs. However, research on the graded buffer design is a parallel project within our research group, and thus the optimization of the buffer design is not a primary focus of this dissertation. Instead, this dissertation builds upon the existing buffer and virtual substrate technologies that we have already developed, using these technologies as a platform for the integration of all necessary metamorphic materials. Due to their importance, key aspects of the design of these virtual substrates are covered in chapter 3.

21 Detailed objectives on how III-V metamorphic epitaxy will be utilized to enhance

III-V/Si MJSCs for terrestrial applications and III-V MJSCs for space applications are listed below:

1.4.1. METAMORPHIC TUNNEL JUNCTIONS FOR III-V/SI MJSCS

1. Investigate and develop high-performance metamorphic tunnel junctions to

function as interconnects between adjacent sub-cells. Such devices require low

electrical resistance and high optical transparency to minimize electrical and optical

losses, respectively. To achieve low resistance, optimize growth conditions and

device structures to maximize tunneling performance. Growth conditions are

critical for optimization of the high doping levels required for such devices, while

device structures can provide a favorable band structure that results in enhanced

tunneling characteristics. To ensure transparency, utilize wide bandgap

semiconductors (relative to the subsequent sub-cell(s) beneath the tunnel junction)

and/or ultra-thin layers to minimize absorption.

2. Develop metamorphic tunnel junctions grown via MBE and MOCVD for

integration with the MBE 3J and MOCVD 2J, respectively. The MBE 3J requires

both a lower tunnel junction between the middle and bottom cells and an upper

tunnel junction between the top and middle cells. The MOCVD 2J only requires a

single metamorphic tunnel junction between the top and bottom cells. Since the

MBE 3J is designed for operation under high concentration and the MOCVD 2J is

designed for operation under AM1.5G, this must be accounted for when

determining the targeted metrics of these metamorphic tunnel junctions.

22 3. Integrate the various metamorphic tunnel junctions with test solar cells as well as

full III-V/Si MJSC devices to demonstrate functionality when integrated with solar

cells. Identify the impact of the thermal load of subsequently grown sub-cells on

metamorphic tunnel junction performance.

1.4.2. WIDE BANDGAP (ALZGA1-Z)XIN1-XP TOP CELLS FOR III-V MJSCS

1. Demonstrate 2.05 eV lattice-matched and metamorphic (AlzGa1-z)xIn1-xP materials

and devices (necessary for 4J space solar cells) grown via MOCVD.

2. Characterize and model 2.05 eV (AlzGa1-z)xIn1-xP approaches to identify

advantages and disadvantages of each approach.

1.5. DISSERTATION LAYOUT

The next few chapters expand on background information necessary to understand

how the dissertation objectives where achieved. Chapter 2 provides a background on

device operation, including solar cells, MJSCs, and tunnel junctions. In addition, detailed information is given on the III-V/Si MJSC approach, metamorphic tunnel junction requirements, and the III-V MJSC approaches for space applications. Chapter 3 provides

a background on the MBE and MOCVD growth methods, the challenges associate with

III-V metamorphic epitaxy, and device processing methods for fabricating the solar cells

and tunnel junctions developed herein. Chapter 4 provides a background on the

techniques used to characterize and model the solar cells and tunnel junction herein.

Chapters 5 and 6 cover the development of MBE- and MOCVD-grown metamorphic

tunnel junctions, respectively, and chapter 7 covers the development of MOCVD-grown

23 wide bandgap (AlzGa1-z)xIn1-xP top cells. Chapter 8 contains conclusions, including a discussion comparing MBE- vs. MOCVD-grown metamorphic tunnel junctions, and future optimization pathways for both metamorphic tunnel junctions and wide bandgap

(AlzGa1-z)xIn1-xP top cells.

24 CHAPTER 2:

SOLAR CELL, MJSC, AND TUNNEL JUNCTION OPERATION

2.1. BACKGROUND

This chapter focuses on the operation of solar cells, multijunction solar cells

(MJSC), and tunnel junctions (TJ). Section 2.2 begins with a discussion on the solar spectrum. This influences many aspects of how solar cells and TJs are designed.

Section 2.3 covers the fundamentals of solar cells under the assumption that the reader has a basic understanding of semiconductor theory. This includes subjects such as band structure, band diagrams, carrier statistics, generation and recombination, carrier transport, and basic p-n junction theory. For more information, the reader can refer to various textbooks on these subjects [96]–[98]. The operation of the solar cell is developed beginning with the photovoltaic effect to explain how the asymmetry of a p-n junction solar cell enables the generation of a photocurrent. The dark current-voltage characteristics of a p-n junction are then reviewed before covering the illuminated current-voltage characteristics of a p-n junction solar cell. This section concludes with using these concepts to demonstrate the basic structure of a solar cell.

25 The chapter then transitions to the elegant approach of detailed balance to derive the upper efficiency limit of solar cells in section 2.4. The mechanisms that limit the ideal solar cell efficiency are discussed, followed by how MJSCs can overcome the limitations of a single junction solar cell. Section 2.5 takes a closer look at the operation of MJSCs and highlights the need for TJs within MJSCs. Finally, section 2.6 discusses the operation of TJs, as well as detailed requirements of TJs that are designed for integration into the

MBE 3J and MOCVD 2J III-V/Si MJSC approaches that are focused on in this dissertation (section 0).

2.2. THE SOLAR SPECTRUM

The solar cell is a device that converts sunlight directly into electricity. Thus, before exploring the inner workings of a solar cell, it is worthwhile to discuss the nature of sunlight to understand the solar cell design. To begin with, the outer space solar spectrum incident on the earth’s outer atmosphere can be approximated as a blackbody at approximately 5800 K. However, the actual outer space and terrestrial (incident on the earth’s surface) solar spectra differ from this blackbody approximation due to various mechanisms. The outer space spectrum differs due to the presence of spectral lines. As the sunlight passes through the atmosphere, the spectrum is altered due to absorption and

Rayleigh scattering caused by molecules and particles in the atmosphere as well as sunlight reflected from the earth’s surface that is subsequently backscattered by the atmosphere. This results in unique terrestrial solar spectra under a variety of conditions.

Therefore, various standard solar spectra have been specified that are representative of relevant conditions.

Figure 2.1. The AM0, AM1.5G, and AM1.5D standard solar spectra (ASTM G173-03 standard [99]).

Standard solar spectra are defined by the air mass (AM), which is the normalized

path length that sunlight takes through the atmosphere relative to the pathlength of sunlight directly overhead. AM is calculated using Eq. 2.1, where θ is the zenith angle

(i.e. angle between the sun and the vertical).

AM = Eq. 2.1 1 cos 𝜃𝜃 When the sun is directly overhead, θ = 0° and the associated solar spectrum is referred to as AM1.

Three commonly used standard solar spectra are presented in Figure 2.1

(ASTM G173-03 standard [99]). These spectra can be integrated to determine the total irradiance (i.e. power per unit area). The AM0 spectrum is the standard outer space spectrum and has an irradiance of 1366.1 W m-2. This spectrum is relevant for space solar

cells. The terrestrial solar spectrum is more arbitrary⋅ since it varies significantly with 27 AM. However, two standard terrestrial spectra are commonly used. The AM1.5G global

standard spectrum is representative of relatively sunny locations in the US (48° north

latitude) and has an irradiance of 1000 W m-2. This spectrum includes both direct and

diffusely scattered sunlight (e.g. the blue sky).⋅ This spectrum is appropriate for non-

concentrator terrestrial solar cells that collect both direct and diffuse sunlight. AM1.5D is

the standard direct spectrum with an irradiance of 900 W m-2. This spectrum only

consists of a small portion of sunlight surrounding the sun⋅ that primarily consists of the

direct portion of sunlight in the AM1.5G spectrum. Specifically, this includes a 5.8°

angular field of view compared to the 0.53° angular field of view of the sun. The

AM1.5D spectrum is appropriate for terrestrial concentrator solar cells due to their small

acceptance angle.

2.3. SOLAR CELL FUNDAMENTALS

The solar cell operates based on the photovoltaic effect, which can be thought of

as two primary steps. First, photons from the solar spectrum are absorbed in a material

(i.e. absorber) and promote electrons (i.e. negative charge carriers) from their ground state where they are bound in the solid to an excited state where they are free to move around. This is known as photoexcitation or photogeneration. The second step is the electronic transport of photoexcited electrons from the absorber to the external circuit.

This extracts the excess energy of the excited electrons (i.e. the energy difference between the excited and ground states) to generate electrical power. If the excited electrons relax to the ground state prior to collection in the external circuit, their excess energy is lost in the form of light or heat and does not produce electrical power.

28 Both steps of the photovoltaic effect can be accomplished via the use of a

semiconductor p-n junction. The semiconductor is the material in which photogeneration occurs. However, both electron and hole charge carriers must be accounted for in the semiconductor. The p-n junction is the device structure that facilitates electronic transport

of these charge carriers to the external circuit. To generate electrical power, both a

photocurrent (resulting from photogeneration) and voltage (resulting from the excess

energy) are required. The photocurrent is discussed below, followed by the impact of

voltage on dark and illuminated p-n junction performance.

2.3.1. PHOTOCURRENT

To determine the photocurrent (IL), of the solar cell, various aspects of photogeneration and carrier transport must be understood. The interaction of photons

from the solar spectrum with a semiconductor determine the photogeneration of carriers

(i.e. photocarriers) throughout the semiconductor. Carrier transport subsequently impacts

the probability that photocarriers are collected. By combining these aspects, ISC can be determined.

Photons incident on the semiconductor can be reflected, absorbed, or transmitted.

Photons with energy below the bandgap are transmitted, whereas photons with energy equal to or greater than the bandgap can be absorbed and generate electron-hole pairs (i.e. photocarriers). The strength of absorption is determined by the absorption coefficient (α).

This is a parameter that depends on band structure and incident photon wavelength (λ0).

Absorption only occurs above the bandgap in semiconductors, resulting in an absorption

edge at the bandgap. The absorption edge is sharper in direct bandgap semiconductors

29 compared to indirect. Higher energy photons are also absorbed more strongly, and thus

higher energy ‘blue’ photons are on average absorbed near the front surface of the

semiconductor and lower energy ‘red’ photons are on average absorbed deeper in the

semiconductor.

Using the absorption coefficient, the photon flux as a function of depth and

wavelength (Φ(x,λ)) within the semiconductor can be determined. This is calculated in

Eq. 2.2, where R is the reflectance, Φ0(λ) is the photon flux incident on the surface as a function of wavelength, and x is the depth in the semiconductor relative to the surface.

( , ) = (1 ) ( ) ( ) Eq. 2.2 −𝛼𝛼 𝜆𝜆 ⋅𝑥𝑥 0 Since absorption results in𝛷𝛷 the𝑥𝑥 photogeneration𝜆𝜆 − 𝑅𝑅 ⋅ 𝛷𝛷of electron𝜆𝜆 ⋅ 𝑒𝑒 -hole pairs, Eq. 2.2 can be used

to derive the photogeneration rate as a function of depth and wavelength (G(x,λ)). This is

the rate that the photon flux is attenuated within the semiconductor and is thus found by

differentiating Eq. 2.2, shown in Eq. 2.3 [100].

( , ) ( , ) = = ( ) ( , ) Eq. 2.3 𝑑𝑑𝑑𝑑 𝑥𝑥 𝜆𝜆 𝑑𝑑𝑑𝑑 By integrating G(x,λ) over 𝐺𝐺all𝑥𝑥 wavelengths𝜆𝜆 − as in Eq.𝛼𝛼 𝜆𝜆 2.4⋅,𝛷𝛷 the𝑥𝑥 total𝜆𝜆 generation rate

throughout the semiconductor (G(x)) can be determined.

( ) = ( , ) Eq. 2.4

Note that equations Eq. 2.2 - Eq. 2.𝐺𝐺4 indicate𝑥𝑥 ∫ 𝐺𝐺 that𝑥𝑥 𝜆𝜆inte𝑑𝑑nsity𝑑𝑑 and generation rate decrease

exponentially as a function of depth into the semiconductor. This will be used later in this

section when discussing various aspects of a solar cell design.

If only a uniform slab of semiconductor was utilized to absorb sunlight, the

photocarriers would diffuse randomly in all directions and eventually recombine (i.e.

relax to their ground state). This would produce no photocurrent and thus no electrical 30 power. Thus, an asymmetry must be introduced into the semiconductor to drive the

electrons and holes in opposite directions before recombining to produce a photocurrent.

The p-n junction provides the asymmetry necessary to separate photocarriers.

By conceptually bringing p-type (i.e. majority carrier holes) and n-type (i.e.

majority carrier electrons) layers of semiconductor materials together, a p-n junction is

created. In doing so, carriers diffuse across the junction due to the difference in carrier

concentrations on either side of the junction. This leaves immobile charged ions behind,

which produce an electric field that opposes and eventually balances carrier diffusion.

This results in a depleted space charge region (SCR) that possesses an internal built-in

electric field (i.e. built-in voltage, Vbi). This built-in field is the mechanism that provides the asymmetry to separate carriers. Figure 2.2 schematically demonstrates a p-n junction to show the junction, the quasi-neutral (flat-band) regions (QNR), the SCR, as well as photogenerated carriers to describe the asymmetry. When a photon is absorbed in the p-type layer a majority carrier hole and a minority carrier electron are generated. If the majority carrier hole diffuses towards the built-in electric field, the field acts as a barrier

Figure 2.2. Band diagram schematic of a p-n junction to define various features and to demonstrate asymmetry of built-in electric field. 31 to prevent the majority carrier hole from passing. However, if the minority carrier electron diffuses to the built-in electric field it is swept to the other side of the junction by the field (i.e. carrier drift). It is also possible that the minority carrier electron recombines in the p-type layer before being swept by the field. A similar situation occurs in the n-type layer (with the carrier types flipped). This asymmetry thus explains how a photocurrent is produced within the solar cell. Every minority carrier (electron or hole) that is both photogenerated and swept across the built-in electric field (i.e. collected) contributes to the photocurrent; the sum of all collected minority carriers multiplied by the electric charge (q) yields the photocurrent.

Ideally, all photogenerated minority carriers are collected. However, it is possible for these carriers to recombine before being collected; the probability that they are collected is lower if they are generated further from the SCR. Thus, a method for determining the probability that they are collected as a function of distance from the SCR is necessary to ultimately determine the photocurrent. This is known as the collection probability (fc(x)) and is proportional to excess minority carrier concentrations within the device [101].

Excess minority carrier concentrations depend on factors such as bulk and surface recombination, as well as diffusivity. Bulk recombination occurs due to mechanisms such as band-to-band, Shockley-Read-Hall, and Auger recombination. The bulk recombination rate depends on the minority carrier lifetime (τ), which is the average time a minority carrier exists before recombining. Diffusivity (D) describes the rate of carrier diffusion.

An important property of solar cells can be derived from the minority carrier lifetime and

Figure 2.3. Example of a collection probability curve of a p-n junction solar cell, demonstrating bulk and surface-limited cases in the QNRs and unity collection in the SCR due to the built-in electric field.

diffusivity; the minority carrier diffusion length (LD). This is defined as the average

distance a minority carrier can travel before recombining and is calculated using Eq. 2.5.

= Eq. 2.5

D Surface recombination is caused by the𝐿𝐿 presence√𝐷𝐷 ⋅of𝜏𝜏 broken ‘dangling’ bonds at the

semiconductor surface that facilitate recombination. The surface recombination rate

depends on a parameter known as the surface recombination velocity (SRV). With

knowledge of parameters such as τ, D, LD, SRV, and the structure of the device, the

collection probability can be calculated using the continuity and minority carrier

diffusion equations, either analytically [101] or numerically.

Figure 2.3 demonstrates a collection probability curve for a p-n junction solar cell.

This example was designed to highlight three features. First, in the p-type QNR, fc(x) reduces linearly with distance from the QNR. This is characteristic of surface-limited

33 recombination (i.e. bulk recombination is negligible). In the n-type QNR, fc(x) reduces exponentially with distance from the QNR. This is characteristic of bulk-limited recombination. Finally, fc(x) equals unity within the SCR. Whereas carriers generated in

the QNRs must rely on diffusion to reach the SCR, carriers generated in the SCR are

immediately collected due to the strong built-in electric field, and thus essentially all carriers generated in the SCR are collected.

Finally, the photocurrent can be determined by integrating the collection probability with the total generation rate (Eq. 2.4) over the width of the device (W), shown in Eq. 2.6.

= ( ) ( ) Eq. 2.6 𝑊𝑊 L 0 𝑐𝑐 The concept of the collection probability𝐽𝐽 𝑞𝑞 ∫ is𝑓𝑓 powerful𝑥𝑥 ⋅ 𝐺𝐺 𝑥𝑥 for𝑑𝑑 𝑑𝑑visualizing the inner workings of

a solar cell. By normalizing the integrand in Eq. 2.6 with respect to the incident photon

flux, the internal quantum efficiency (IQE, section 4.3.2) can be determined.

Furthermore, by integrating over only the thickness of a specific device layer (i.e. the p-type layer in the p-n junctions that have been discussed thus far) the IQE of that specific layer can be determined. This is a powerful device modeling technique and is used in section 7.2 to model IQE of (AlzGa1-z)xIn1-xP solar cells.

Experimentally, the collection probability is challenging to measure as it requires

an impulse of minority carriers to be produced at a specific depth within the device. This

can be achieved via cross-sectional electron beam induced current (EBIC) measurements.

In this technique, an electron beam irradiates the cross section of a device to generate an

approximate impulse of minority carriers [102]. However, this is a specialized technique

34 and was not used in this dissertation (although plane-view EBIC was used for another

purpose as discussed in section 4.2.5).

2.3.2. DARK I-V CHARACTERISTICS OF P-N JUNCTIONS

Thus far, the p-n junction has been analyzed under no forward bias (short-circuit

conditions) to explore how the asymmetry of the p-n junction enables a photocurrent

when under illumination. Although the next step to understanding the p-n junction under illumination is to observe its current-voltage (I-V) characteristics with an applied voltage, it is worthwhile to first review the I-V characteristics and band diagrams of a p-n junction in the dark; illumination will be applied in the next section.

A p-n junction is in equilibrium conditions when in the dark at zero bias (short- circuit conditions). The band diagram of this case is shown in Figure 2.4(a). The Fermi level (EF) is uniform throughout the p-n junction, indicating that the entire structure is at

the same potential and no current flows (i.e. equilibrium). When a forward bias is applied, the p-n junction barrier is reduced, as seen in Figure 2.4(b). As the forward bias is increased, this barrier further reduces and majority carriers begin to overcome this barrier. The number of majority carriers that overcome this barrier depends exponentially on the barrier height, leading to the dark I-V characteristics of an ideal p-n junction. This is described by Eq. 2.7, where I0 is the dark saturation current, q is the electric charge, V

is the applied voltage, k is Boltzmann’s constant, and T is the absolute temperature.

= 1 𝑞𝑞𝑞𝑞 Eq. 2.7 𝑘𝑘𝑘𝑘 dark 0 Under forward bias, the majority𝐼𝐼 carrier𝐼𝐼 �𝑒𝑒 electrons− � in the n-type layer are injected

into the p-type layer and thus become minority carrier electrons. This results in an excess

Figure 2.4. Band diagrams of a p-n junction in the dark at (a) zero bias and (b) forward bias.

minority carrier electron concentration in the p-type layer. Under these conditions, the

majority carrier hole and minority carrier electron concentrations in the p-type layer are no longer in equilibrium with one another, and thus a single Fermi level cannot be used to describe both carrier concentrations. In other words, the Fermi level is only valid in equilibrium; a biased p-n junction is not under equilibrium, and thus a single Fermi level is not valid. Instead, a quasi-Fermi level (QFL) for each carrier type can be defined to describe each carrier population independently in nonequilibrium. The electron (EFn) and

hole (EFp) QFLs for the p-n junction in the dark under forward bias can be seen in Figure

2.4(b). Consider electrons; the electron QFL in the n-type layer is essentially flat since

36 the electron is the majority carrier concentration, which is close to equilibrium. Upon

injection of the electrons into the p-type layer, they become minority carriers. The electron QFL begins to drop as it extends into the p-type layer due to recombination. The rate of recombination (and thus the slope of the QFL in the p-type layer) depends on the

minority carrier lifetime. In addition, note that the slopes of the QFLs are an indication of

the current direction; a positive QFL slope represents a current flowing in the positive

direction, as is the case here. Another important parameter that can be observed in Figure

2.4(b) is the QFL splitting (EFn - EFp). Although this parameter varies as a function of position throughout the p-n junction, it is related to the applied voltage using Eq. 2.8.

Here, and are the electron and hole QFLs at the n- and p-type contacts, n p Fn Fp respectively𝐸𝐸 [103]𝐸𝐸 .

= Eq. 2.8 n p 𝑞𝑞𝑞𝑞 𝐸𝐸Fn − 𝐸𝐸Fp 2.3.3. ILLUMINATED I-V CHARACTERISTICS OF P-N JUNCTIONS

With an understanding of QFLs, the characteristics of the p-n junction under

illumination can now be discussed. The band diagram when under illumination and at

zero bias is shown in Figure 2.5(a). Illumination results in the generation of excess minority carriers, indicated by the minority carrier QFLs deviating significantly from the majority carrier QFLs. The band diagram indicates that the excess minority carriers produce a photocurrent in the negative direction (i.e. the minority carrier QFLs have a negative slope). In addition, Eq. 2.8 indicates that the voltage is zero as expected.

The n-p junction under illumination and at forward bias, shown in Figure 2.5(b), can now be used to explain how electrical power is produced. At the specific forward bias

Figure 2.5. Band diagrams of a p-n junction under illumination at (a) zero bias and (b) forward bias.

in this example, the slopes of the minority carrier QFLs indicate that the p-n junction is still producing a negative current. The magnitude of the positive bias can also be observed due to the majority carrier QFL splitting at the contacts (Eq. 2.8). The combination of the positive bias and a negative current implies power generation.

The illuminated I-V (LIV) characteristics of the p-n junction can now be determined. Recall that in the example above (Figure 2.5), the photocurrent flows in the negative direction. Ideally, the photocurrent is independent of applied voltage. If this holds true, then the superposition principle can be used to determine the LIV characteristics [104] and is calculated using Eq. 2.9.

38 = 1 𝑞𝑞𝑞𝑞 Eq. 2.9 𝑘𝑘𝑘𝑘 light 0 L Examples of dark I-V (Eq. 2.7) and𝐼𝐼 LIV 𝐼𝐼(Eq.�𝑒𝑒 2.9−) curves� − 𝐼𝐼 are plotted in Figure 2.6.

The power of the solar cell is the product of the current and voltage, given by

Eq. 2.10.

= Eq. 2.10

The LIV and power of the solar cell in Figure𝑃𝑃 𝐼𝐼 2⋅.𝑉𝑉6 are both plotted in Figure 2.7. The LIV

curve has been flipped on the x-axis, a common convention in the photovoltaic community. Various solar cell figures of merit are also highlighted. The short-circuit current (ISC) is the current at zero bias. This can be approximated as IL except under

severely non-ideal conditions (such as a high series resistance). The open circuit voltage

(VOC) is the voltage at zero current, which occurs when the photocurrent is exactly

balanced by the dark current. VOC strongly depends on the bandgap of the solar cell; for

Figure 2.6. Example of dark I-V and LIV curves of a solar cell that obeys the superposition principle. 39

high performance solar cells, the VOC is approximately 0.4 V lower than the bandgap

[105]. This difference is termed the WOC, given by Eq. 2.11.

= Eq. 2.11 𝐸𝐸G 𝑊𝑊OC 𝑞𝑞 − 𝑉𝑉OC The maximum power (PMAX) is determined by the product of the voltage at the maximum

power point (VMAX) and current at the maximum power point (IMAX). Using these

parameters, the fill factor (FF) can be calculated using Eq. 2.12.

= Eq. 2.12 𝐼𝐼MAX⋅𝑉𝑉MAX 𝐹𝐹𝐹𝐹 𝐼𝐼SC⋅𝑉𝑉OC The fill factor is a measure of how square the LIV curve is. The efficiency (η) of the solar cell is the ratio of the power generated by the solar cell (Pcell) to the incident power from

the sun (Psun) (section 2.2).

= = Eq. 2.13 𝑃𝑃cell 𝑉𝑉OC⋅𝐼𝐼SC⋅𝐹𝐹𝐹𝐹 𝜂𝜂 𝑃𝑃Sun 𝑃𝑃Sun

40 Note that in Figure 2.7 the power increases essentially linearly up until PMAX. It is

at this point that the p-n junction barrier is reduced enough by the forward bias that

majority carriers begin to overcome this barrier. This leads to an appreciable dark

(positive) current as the bias is increased beyond this point. This counteracts the

photocurrent, resulting in reduced power output and eventually power consumption

beyond VOC.

Up to this point, only ideal diode characteristics have been considered. In reality,

other factors may impact the performance of the solar cell. For example, shunt resistance

(RSH) in parallel with the solar cell and/or series resistance (RS) serve to reduce the fill

factor and thus efficiency of the solar cell. A parameter known as the ideality factor (n) determines how closely the I-V curve follows that of the ideal diode. The value of the ideality factor depends on the recombination mechanism that dominates the p-n junction performance (only minority carriers were assumed to limit recombination above, in which case n = 1). Although the non-idealities of solar cells are important to understand for fully characterizing a solar cell, they will not be focused on in detail here. The next section explores the design of the solar cell structure based on the fundamental solar concepts described thus far.

2.3.4. SOLAR CELL DESIGN

This section explores several aspects that must be considered to design the

structure of a typical p-n junction solar cell. It is important to realize that the device

structure plays a significant role in terms of the collection of photocarriers. A poorly

designed structure can lead to a low photocurrent despite potentially high material

41 quality. For example, if the junction is poorly positioned such that the majority of

photocarriers are generated multiple diffusion lengths away, most photocarriers will

recombine before being collected and thus result in a poor photocurrent. Note that the

design decisions below have many trade-offs. The point of this design section is to not

explore all possible permutations, but rather introduce general design concepts.

To begin the design of the solar cell structure, first consider an arbitrary p-n junction. Ohmic contacts are required at both terminals to extract current from the solar cell and minimize resistive losses. This presents the first design challenge; light must be coupled into the p-n junction for subsequent photogeneration and collection. An opaque metal contact does not assist in accomplishing this. Thus, to couple light into the solar cell the top contact (where light is incident) can be patterned into a grid that results in very low metal coverage yet enables carriers to be efficiently extracted from the solar cell. Narrower grid fingers extract photocurrent from a small region of the solar cell and are connected to a thicker busbar where all extracted photocurrent from the solar cell is delivered to the external circuit.

The next challenge arises from the high index of refraction of semiconductors.

For example, the refractive index of GaAs is ~3.5 at λ0 = 1 μm. Using the Fresnel

equations, this indicates that the reflectance is ~30% for normal incidence light. This is a

significant portion of incident light and would result in a significantly lower generation

rate according to equations Eq. 2.2 - Eq. 2.4. To minimize the amount of reflection, an anti-reflection coating (ARC) can be applied to the top surface. This is accomplished using a material that has an intermediate index of refraction between that of air and the

42 semiconductor and is a form of impedance matching. A high-quality ARC can result in a reflectance that approaches zero; in this case the solar cell would appear black.

Now that light has efficiently been coupled into the solar cell, the generation profile should next be considered to determine how thick the solar cell should be to absorb most of the light. This is material-dependent since the absorption coefficient varies between materials. If the solar cell is too thin photons above the bandgap will be transmitted through the cell (with more transmission of lower energy photons that have a lower absorption coefficient). If the solar cell is too thick the generation rate will drop to essentially zero within the solar cell and the material beyond that point will serve no purpose.

After determining the total thickness of the solar cell, the thickness of the individual p-type and n-type layers must be determined. Referring back to Figure 2.3, note that the p-type layer is much thinner than the n-type layer. Since the majority of photocarriers are generated near the front surface of the solar cell (see equations

Eq. 2.2 - Eq. 2.4), the concept is to have the junction located closer to the front surface to ensure efficient collection of these photocarriers.

The thinner top layer is referred to as the emitter and the thicker bottom layer is referred to as the base. These names are derived from the names of the layers in the bipolar transistor. With respect to solar cells, the general design is for the emitter to be relatively highly doped and the base to be relatively lower doped. Although higher doping results in a larger built-in voltage and thus larger VOC, it also degrades material quality and reduces diffusion length. Higher doping can be utilized in the emitter to achieve a boost in VOC; although the diffusion length will be reduced, carriers generated

43 in the emitter are all relatively close to the junction since the emitter is thin and thus they can still efficiently be collected. Lower doping is necessary in the base since carriers must on average diffuse much longer distances to the junction.

The final consideration that will be made here is related to recombination at surfaces and contacts. Recall that dangling bonds on the surface lead to surface recombination. If the collection probability is surface-limited as discussed in section 2.3.1, regardless of how high the bulk material quality is the performance will be limited by the surface. In addition, minority carriers recombine at the interface between the semiconductor and the ohmic contacts. To avoid recombination at surfaces and ohmic contacts, a double heterostructure can be employed [106], [107]. The concept is to sandwich (i.e. clad) the emitter and base layers between two wider bandgap materials. If the cladding layers are properly designed, very little recombination will occur at the cladding/emitter and base/cladding interfaces; compared to a surface, the dangling bonds have been satisfied by the cladding layers. The cladding layers should have a small band offset for majority carriers to prevent resistive losses, but a large band offset for minority carriers. This creates a barrier for the minority carriers at the cladding/emitter and base/cladding interfaces, blocking the minority carriers from entering the cladding layers.

By highly doping the cladding layer with the same carrier type as the adjacent solar cell layer, the barrier can be increased further. Thus, minority carriers are confined in the emitter and base layers, improving their chance of collection. The cladding layer on the top of the solar cell is known as the window; in addition to confining minority carriers, it must also have a wide enough bandgap to avoid parasitic absorption of photons. The

44 cladding layer on the back surface is known as the back surface field (BSF), in reference to the built-in field at the base/cladding interface that confines minority carriers.

The schematic of a p+/n solar cell and its band diagram are shown in Figure 2.8 to highlight all aspects of the solar cell design that have been discussed in this section. Note the location of the junction; the highly-doped emitter results in an asymmetric p+/n junction, and thus the SCR extends much further into the lower-doped base. Although this chapter has remained consistent with using p/n (i.e. p-on-n) polarity to describe p-n junctions, it is worth noting that the solar cells and MJSC approaches focused on in this dissertation have n+/p polarity. However, all concepts still apply.

This chapter will now transition focus to an elegant derivation of the ideal efficiency of a solar cell via detailed balance. This approach defines clear limits to solar cell performance and reveals how the mechanisms that limit performance can be addressed via the use of MJSCs.

46 2.4. DETAILED BALANCE EFFICIENCY LIMIT

Detailed balance states that every microscopic process has an equal reverse process and that the rate of a given process and its reverse process are equal at equilibrium. Regarding solar cells, this includes all generation-recombination processes such as radiative, Shockley-Read-Hall (SRH), and Auger processes. Although seemingly obvious, this implies that under equilibrium a process such as optical generation cannot be balanced by SRH recombination.

By making a few assumptions, the concept of detailed balance can be applied to predict the theoretical efficiency limit of solar cells. The first assumption is that all photons with energy greater than the bandgap of the solar cell are absorbed and generate photocarriers (i.e. no reflected photons) and all photons below the bandgap are transmitted. The second assumption is that carriers have infinite mobility, and thus all photogenerated carriers are collected. This eliminates the electronic transport aspects of the solar cell, and thus the exact device structure does not need to be accounted for. The third assumption is that radiative recombination is the only recombination method, which must occur due to detailed balance.

2.4.1. SINGLE JUNCTION SOLAR CELLS

The following derivation of the detailed balance efficiency limit for a single

junction solar cell follows those in [103], [108], which follows after the original method

by Shockley and Queisser [109]. To determine this limit, first the efficiency (η) is defined

as the ratio of power generated by a solar cell (Pcell) to the power of the solar spectrum

(PSun), given by Eq. 2.14. 47 = Eq. 2.14 𝑃𝑃cell 𝜂𝜂 𝑃𝑃Sun The power of the solar cell depends on photon fluxes absorbed from the sun and

surrounding earth (optical generation) and emitted from the solar cell (radiative recombination). In the fundamental case, the sun and earth can be treated as blackbodies and the solar cell can be treated as a pseudo-blackbody with an emissivity/absorptivity of

1 above the bandgap and 0 below the bandgap. All three of these photon fluxes can be derived using the general form of Planck’s law. The photon flux (Φ) is given by Eq. 2.15, where E is the photon energy, Cx is the solar concentration, Cm is the maximum solar concentration (46,200), h is Planck’s constant, c is the speed of light, k is the Boltzmann

constant, T is absolute temperature, and μ is the quasi-Fermi level (QFL) splitting that results from the chemical potential of radiation [110], [111].

= Eq. 2.15 ℎ 2 𝐶𝐶x 2𝜋𝜋 𝐸𝐸 3 2 𝐸𝐸−𝜇𝜇 m 𝛷𝛷 𝐶𝐶 ⋅ 𝑐𝑐 ⋅ ∫ exp� 𝑘𝑘𝑘𝑘 �−1 𝑑𝑑𝑑𝑑 Since the solar cell only absorbs and emits above the bandgap, this integral only needs to

be performed at photon energies greater than the bandgap for subsequent calculations.

The power generated by a solar cell is the product of the operating current (I) and

external voltage (V) (Eq. 2.10).

To determine I, the net photon flux in the solar cell must be determined. The photon flux absorbed from the sun and the surrounding earth (Φabs) can be calculated

with the aid of Eq. 2.15, where μ = 0. The emitted photon flux from the solar cell (Φemit)

can also be calculated using Eq. 2.15, where μ can be approximated by the external

voltage. The emitted photon flux is thus a function of μ. The solar cell current is then the

net photon flux multiplied by the electronic charge (q). PSC is thus given by Eq. 2.16.

Figure 2.9. AM1.5G detailed balance efficiency limit as a function of bandgap.

= ( ) Eq. 2.16

SC abs emit Since the sun is treated as a blackbody𝑃𝑃 �𝛷𝛷 in this− calculation,𝛷𝛷 𝜇𝜇 � ⋅ the𝜇𝜇 Stefan-Boltzmann law can then be used to calculate PSun. The resulting equation for η is given by Eq. 2.17, where σ

is the Stefan-Boltzmann constant and Tsun is the blackbody temperature of the sun.

( ) = Eq. 2.17 �𝛷𝛷abs−𝛷𝛷emit 𝜇𝜇 �⋅𝜇𝜇 4 𝜂𝜂 𝜎𝜎𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠 By varying the external voltage, or μ, maximum power point and thus maximum

efficiency of the solar cell can be determined.

Eq. 2.17 can be used to calculate the maximum efficiency as a function of

bandgap to determine the ideal solar cell bandgap. By modifying Eq. 2.17 to account for

an arbitrary solar spectrum rather than a blackbody, this procedure can be performed for

one of the solar spectra discussed at the beginning of this chapter. An example of this

calculation using the AM1.5G spectrum is shown in Figure 2.9, performed using a

MATLAB script written by our research group. For this calculation, a maximum

49 efficiency of 33.8% occurs at a bandgap of 1.34 eV. Note that the ‘wiggles’ in this curve

are due to the shape of the AM1.5G spectrum.

The concept of photon utilization efficiency (ηγ) can be used to understand why

the efficiency reduces at the low and high end of the bandgap range in Figure 2.9. This is

defined by Eq. 2.18, where EG is the bandgap and Eγ is the photon energy [112].

if G ( ) = 𝐸𝐸 Eq. 2.18 𝐸𝐸γ 𝐸𝐸 ≥ 𝐸𝐸G 0 if < 𝜂𝜂γ 𝐸𝐸 � G Photons with energy equal to the bandgap energy 𝐸𝐸are absorbed𝐸𝐸 and all the photon energy

(Eγ) goes into the creation of an electron-hole pair and the photon utilization efficiency

equals one. Photons at energies higher than the bandgap also generate one electron-hole pair. However, the excess photon energy (Eγ -EG) results in the carriers initially being generated deeper within the conduction and/or valence bands. These carriers quickly

thermalize to the band edges and the excess photon energy is lost as heat. This results in

the photon utilization efficiency reducing with increasing photon energy. Photons at

energies lower than the bandgap are completely transmitted, and thus the photon

utilization efficiency is zero. Thus, if the bandgap of the solar cell is reduced, then less

transmission loss occurs but higher thermalization loss occurs, and vice versa if the

bandgap is increased; the bandgap that enables the highest efficiency minimizes the total

loss due to transmission and thermalization.

2.4.2. MULTIJUNCTION SOLAR CELLS

The detailed balance efficiency limit of the single-junction solar cell was derived

in the previous section. It was shown that the bandgap is the most significant factor in

Figure 2.10. Photon utilization efficiency of the Ga0.57In0.43P/GaAs0.9P0.1/Si triple junction solar cell.

determining the efficiency of the solar cell since it determines the magnitude of transmission and thermalization losses. To achieve efficiencies greater than what is possible with a single-junction solar cell alone, it is necessary to minimize these loss mechanisms.

The goal of the MJSC is to minimize transmission and thermalization losses, or in other words maximize the photon utilization efficiency (ηγ). This concept is illustrated in

Figure 2.10 for the Ga0.57In0.43P/GaAs0.9P0.1/Si triple junction solar cell. The three sub- cells all have different bandgaps and are selected such that each sub-cell absorbs a specific band of the solar spectrum. The order of the sub-cells is such that high-energy

Figure 2.11. AM1.5G isoefficiency contour plot of an ideal triple-junction solar cell with the ideal 0.7 eV bandgap bottom sub-cell.

photons are collected in the wider-bandgap top cell(s), and low-energy photons are transmitted through these sub-cells to be collected by the subsequent lower-bandgap bottom cell(s). Such a design partitions the solar spectrum to minimize both transmission and thermalization losses. High-energy photons are absorbed by the wider-bandgap top cell(s), minimizing thermalization loss, and low-energy photons are absorbed by the lower-bandgap bottom cell(s) to minimize transmission loss. Based on this concept, even higher photon utilization efficiency is possible using additional sub-cells.

To visualize how sensitive a MJSC is to variations from the ideal bandgap profile, an isoefficiency contour plot of an ideal, monolithic, series-connected triple-junction solar cell with a bottom sub-cell bandgap of 0.70 eV is shown in Figure 2.11. The calculation was done under the AM1.5G solar spectrum using a MATLAB script developed by our research group. Under these conditions, the ideal bandgap profile is

52 1.78/1.19/0.70 eV and can achieve a theoretical efficiency of 51.2%. However, an

~100 meV change in one of the sub-cell bandgaps can reduce the theoretical efficiency

by as much as 10% absolute. This makes it clear why achieving the correct bandgap

profile is critical for high efficiency MJSCs. However, such an ideal design is not

straightforward to achieve in reality and thus tradeoffs must be made to approach such a

design. For example, by performing this calculation using a 1.1 eV Si bottom cell (as was

done in Figure 1.1), the resultant bandgap profile motivates the metamorphic III-V/Si

MJSC approaches that were discussed in section 1.1.1 [46], [52]. This ultimately

motivates the development of metamorphic tunnel junctions in this dissertation.

Similarly, performing this calculation for 4+ junction MJSCs reveals the need for wide

bandgap top cells [15], motivating the development of 2+ eV (AlzGa1-z)xIn1-xP top cells

in this dissertation.

2.5. MONOLITHIC MULTIJUNCTION SOLAR CELL OPERATION

All the III-V MJSC approaches explored within this dissertation are limited to two-terminal MJSCs. This section takes a closer look at how these devices operate. The general operation can be explained with the aid of band diagrams for a

GaAs0.75P0.25/Si 2J, which is the structure of the MOCVD 2J. These are shown in Figure

2.12 and were calculated using Silvaco ATLAS. The device structure is also shown in the

inset in Figure 2.12(c). The metamorphic GaAsyP1-y buffer shown in this structure has

been omitted from the band diagrams for clarity. Note that the general concepts explained

using this specific device can be extended to the other III-V MJSCs explored within this

dissertation.

53 The basic design for this 2J consists of monolithically stacked GaAs0.75P0.25 and

Si sub-cells. However, these sub-cells are n/p diodes. If they were stacked back-to-back, a parasitic p/n diode (i.e. the opposite polarity) would be created at their interface. Any photocurrent or voltage produced by this parasitic diode would work against the sub-

cells, negatively impacting 2J performance.

To prevent the formation of a parasitic diode, a tunnel junction (TJ) is inserted

between each sub-cell. Although detailed operation and design requirements of TJs

within III-V/Si MJSCs are the topic of section 2.6, it is worthwhile to briefly introduce

their behavior here. The basic structure of a TJ is a p+/n+ diode. When a diode is

degenerately doped on each side, the device no longer behaves like a typical diode. The

strong band bending at the p+/n+ interface creates a narrow potential barrier. This allows

electrons in the conduction band of the n+ layer to tunnel through the barrier and

recombine with holes in the valance band of the p+ layer. This tunneling process allows

large currents to flow at low forward bias, which is the typical operating voltage of a

tunnel junction in a MJSC. The TJ therefore acts as a low-resistance interconnect

between the sub-cells. It is designed to be transparent to the filtered portion of the solar

spectrum that is transmitted to the subsequent sub-cell(s) beneath it. If the MJSC has

more than two sub-cells, a TJ is required between each pair of adjacent sub-cells. For the

simulations shown in Figure 2.12, the tunnel junction was replaced with a perfect,

transparent conductor to simplify the model. Although this prevents visualization of the

bands within the TJ layers, note that this does not impact the location of the sub-cell

bands adjacent to the TJ layers.

54 The band diagram of the 2J under equilibrium is shown in Figure 2.12(a). This represents the 2J under no illumination or bias conditions, and thus the Fermi level is uniform throughout the entire device. Note that the Fermi level is chosen as the reference in the band diagrams and is thus labeled as 0 eV.

By illuminating the 2J under the AM1.5G spectrum and keeping it in short-circuit conditions, the band diagram transitions to that shown in Figure 2.12(b). For the 2J structure used in this model, even though the entire structure is at short-circuit conditions, the GaAs0.75P0.25 top cell is under forward bias and the Si bottom cell is under reverse

bias. This is due to the current-matching conditions not being met exactly. In a two- terminal MJSC, each sub-cell must generate equal photocurrents to prevent one sub-cell

from limiting the current flowing throughout the entire device. However, in this example

the Si bottom cell is the current limiter; this is due to an unoptimized 2J design. It should be noted that the short-circuit condition is not entirely clear in Figure 2.12(b). The quasi-

Fermi levels return to 0 eV at each terminal, but due to the x-axis scale (for clarity) this cannot be seen in the Si bottom cell since it is 380 μm thick.

Ultimately, MJSCs are designed to operate at their maximum power point. This operating condition is shown in Figure 2.12(c), where both sub-cells can be seen to be under forward bias. The slopes of the quasi-Fermi levels through the diode junctions indicate that a reverse current is flowing, and thus the device is generating power.

Figure 2.12. Band diagrams of a GaAs0.75P0.25/Si 2J at a) at equilibrium, b) under illumination and at short- circuit conditions, and c) under illumination and at the maximum power point (structure in inset).

56 2.6. TUNNEL JUNCTION OPERATION

The interband tunneling diode, or tunnel junction (TJ) as it is referred to within this dissertation, was invented by Leo Esaki in 1957 [113]. Due to its unique J-V curve with a low-resistance state at low forward bias, this device can meet the electronic and optical requirements of the sub-cell interconnects within MJSCs. An example of a J-V

curve for a 1.55 eV GaAs0.9P0.1 TJ (suitable for the MBE 3J) is shown in Figure 2.13,

highlighting the four regions of interest in a TJ; (a) equilibrium, (b) peak current, (c)

excess current, and (d) thermal current. This specific TJ design was chosen to

quantitatively describe various aspects of the TJ performance. The sections below first

discuss the theory behind the operation of the TJ, followed by an analysis of the design requirements for TJs within the MBE 3J and MOCVD 2J devices.

Figure 2.13. Example J-V curve of a 1.55 eV GaAs0.9P0.1 TJ. Labeled regions of interest include (a) equilibrium, (b) peak current, (c) excess current, and (d) thermal current.

57 2.6.1. TUNNEL JUNCTION THEORY

The most basic form of the TJ that is of interest for MJSCs is a degenerately doped p+-n+ junction. It is therefore not surprising that at high forward bias, the J-V curve assumes typical diode behavior (region (d) in Figure 2.13). However, this device has the characteristic peak current at low forward bias that is not expected for typical diode behavior. This peak arises due to interband tunneling and can be explained by inspecting the band diagram of the TJ in these four regions of interest, presented in Figure 2.14. The equilibrium band diagram (Figure 2.14(a)) immediately highlights two key features. First,

Figure 2.14. Band diagrams of the four regions of interest in a 1.55 eV TJ. The blue and red lines are the electron and hole quasi-Fermi levels, respectively. 58 there is overlap between the highest energy states in the p+ layer valence band (VB) and the lowest energy states in the n+ layer conduction band (CB). Second, there is extremely strong band bending at the TJ interface. This results in a tunneling barrier at the TJ interface that enables direct tunneling of carriers between these bands (i.e. perpendicular momentum of the carriers is conserved) [114]. However, for electrons in the n+ layer CB to directly tunnel through to the p+ layer VB, empty states in the p+ layer VB must exist at the same energies as the filled states in the n+ layer CB. At equilibrium (Figure 2.14(a)), the Fermi level is flat and this condition is not met, resulting in no current flow.

As a forward bias is applied and the bands bend, an overlap between filled n+ layer CB states and empty p+ layer VB states occurs, enabling the direct tunneling current to flow. This direct tunneling current continues to increase with forward bias until this overlap is greatest, at which point the peak tunneling current occurs (Figure 2.14(b)). As the forward bias continues to increase and the bands bend further, this overlap begins to reduce and the direct tunneling current begins to go down, resulting in a region with an unusual negative differential resistance (NDR). Eventually, the overlap is eliminated, the direct tunneling current goes to zero, and the current reaches a minimum ‘valley current’.

As an aside, the NDR region results in bias instabilities that can prevent the DC behavior from being measured correctly [115]. This is why the J-V curve is not completely smooth within the NDR region in Figure 2.13. Although methods exist to stabilize the TJ in the NDR region for correct DC measurements [115], [116], the precise characteristics of this region are ultimately not critical to consider for TJs integrated into

MJSCs.

Figure 2.15. Semi-log plot of the 1.55 eV GaAs0.9P0.1 TJ J-V curve. Labeled regions of interest include (a) equilibrium, (b) peak current, (c) excess current, and (d) thermal current. Dotted and dashed exponential curves with ideality factors of 8 and 2, respectively, are plotted as a visual aid.

At forward biases just beyond the valley current (~0.5-1.2 V), the bands bend to

further separate the previously overlapping filled n+ layer CB states and empty p+ layer

VB states (Figure 2.14(c)) and current begins to increase exponentially. However, quantitative analysis reveals that the current in this region exceeds the expected thermal current of the diode and has an ideality factor (n) that greatly differs from typical diode behavior. To aid in seeing this, Figure 2.13 has been replotted on a semi-log plot in

Figure 2.15. On this plot, an exponential region with an unusually high n = 8 ideality factor is clearly seen. This is the excess current region, resulting from indirect tunneling where momentum is conserved by indirect phonon scattering [114], [117], [118].

As the bias increases further (1.2+ V), the bands bend enough to now permit thermionic emission over the barrier (Figure 2.14(d)), resulting in the typical thermal current of the diode. The onset of this region can be seen in Figure 2.15 and appears to be

60 approaching a region with an n ≈ 2 ideality factor, a typical ideality factor for the relatively wide bandgap 1.55 eV GaAs0.9P0.1 diode used for this example due to depletion

region limited recombination.

When integrated into MJSCs, the primary region of interest of the TJ is the direct

tunneling region between 0 V and the peak tunneling current (JP). This is the low-

resistance region that TJ operates in within a MJSC. In general, it is desirable for the TJ

to have a high JP, a low resistance-area product (RA) at low forward bias, and to be optically transparent to minimize losses in the MJSC due to the TJ. These are discussed in more detail in the next section.

2.6.2. III-V/SI MJSC TUNNEL JUNCTION DESIGN REQUIREMENTS

TJs must meet various design requirements to function correctly in III-V MJSCs.

This leads to the need for high-performance TJs that must each meet specific target

values for various TJ figures of merit. The TJ figures of merit relevant for MJSCs are

listed below, with their symbol and units, followed by a detailed analysis for determining

target values:

1. Low resistance-area product (RA [Ω cm2])

-2 2. High peak tunneling current (JP [A cm⋅ ])

3. Wide, optically transparent bandgap⋅ (EG [eV])

4. Internally lattice-matched to III-V sub-cell(s) (a [Å])

Target values for each of the TJ figures of merit can be defined to ensure each TJ

operates correctly within the MBE 3J and MOCVD 2J. This analysis will first be

performed for the MBE 3J, then applied to the MOCVD 2J.

61 2.6.2.1. MBE 3J TUNNEL JUNCTIONS

To define target values for RA and JP of the TJs within the MBE 3J, the short-

circuit current density (JSC) of the MBE 3J must be estimated. Assuming the MBE 3J has perfect photon collection above the bandgap of Si, ~39 mA/cm2 is available for collection

under the AM1.5D spectrum based on detailed balance calculations. Assuming ideal

2 partitioning of the solar spectrum, this results in JSC = 13 mA/cm . Therefore, under 500×

2 concentration, JSC = 6.5 A/cm . Although this JSC value is higher than what is

realistically achievable under 500× concentration due to the assumptions that were made,

developing the MBE TJs with respect to this target JSC will guarantee proper operation in the MBE 3J.

2 Assuming JSC = 6.5 A/cm , a targeted RA can be specified such that the total

series resistance loss due to both the lower and upper TJs results in ≤ 0.1% loss in the

absolute efficiency of the MBE 3J. Although this loss value is somewhat arbitrary, it is

regarded as negligible loss within the scope of this dissertation. If it is assumed that all

sub-cells in the MBE 3J have 100% fill factors (FF), a RA of 1.06×10-3 Ω cm2 results in

0.1% absolute efficiency loss. Considering that there are two TJs in the MBE⋅ 3J that will

contribute to the RA, then the maximum RA of the individual TJs is half of this (i.e.

RA = 5.3×10-4 Ω cm2). This is assuming each TJ has equal RA values, which may not be

the case due to the⋅ different optical requirements of each TJ that can impact electrical

performance, but it is an appropriate initial estimate. Note that the assumption of 100%

FF is done to ensure that the current density at the maximum power point (JMPP) equals

JSC to ignore details of actual sub-cell performance. In fact, this assumption places more

stringent requirements on RA since in reality JMPP is slightly lower than JSC. Thus, if this 62 targeted RA value is met it will guarantee that the ≤ 0.1% absolute efficiency loss target is

met in the MBE 3J.

The targeted minimum JP can be defined with respect to JSC. If JP > JSC, only RA

impacts the performance of the MBE 3J. However, if JP < JSC, the TJ will operate within its thermal current region near JSC and in the tunneling current region near VOC, leading

to heavy distortion in the current density-voltage curve (J-V) of the MJSC. Both of these scenarios are demonstrated in Figure 2.16 [119]. To ensure the issues associate with

JP < JSC are avoided the targeted JP can be specified as JP ≥ 5× JSC to guarantee proper

operation.

equal to or greater than the bandgap of the sub-cell above the TJ. If the sub-cell above the

TJ collects all photons above its bandgap, then none of the solar spectrum is available for absorption within the TJ, and no optical loss will occur. However, it is worth noting that in cases where a significant number of photons above the bandgap of the sub-cell above the TJ are designed to be collected in the sub-cell beneath the TJ, a wider bandgap TJ is necessary. This scenario arises when either thinning of the sub-cell above the TJ is necessary for current-matching [90], or when luminescent coupling (i.e. emission from the sub-cell above the TJ that can be re-collected by the sub-cell beneath the TJ) is non- negligible [120]. However, these scenarios are outside of the scope of this dissertation and were thus not considered when defining the minimum bandgap of the TJ.

Since the III-V sub-cells in the MBE 3J are at bandgaps that require metamorphic

growth on Si at a unique lattice constant of 5.633 Å, this results in an additional design

requirement; the TJs should be grown at the same lattice constant as the III-V sub-cells, also referred to as internal lattice-matching. Although in general this is not a strict design requirement (e.g. strained TJs can be utilized for such applications), this requirement aids in simplifying the overall MBE 3J structure. This leads to the requirement of metamorphic TJs for use in the MBE 3J at a unique lattice constant that is relatively

Table 2.1. Target values of TJ figures of merit for the TJs within the MBE 3J operated at 500× AM1.5D. MBE 3J (500× AM1.5D) Figure of Merit Lower TJ Upper TJ Max. RA (Ω cm2) 5.3×10-4 5.3×10-4 -2 Min. JP (A cm ) 32.5 32.5 Min. EG (eV)⋅ 1.55 1.95 Lattice Constant⋅ (Å) 5.633 5.633 64 unexplored. Table 2.1 summarizes the target metrics for the TJs developed for the

MBE 3J.

2.6.2.2. MOCVD 2J TUNNEL JUNCTION

The same analysis as was done in section 2.6.2.1 can be used to determine target

values for the tunnel junction figures of merit for the TJ in the MOCVD 2J. These values

are summarized in Table 2.2. Although the MOCVD 2J was designed to operate under

AM1.5G, operation under medium concentration (100× AM1.5D) and high concentration

(500× AM1.5D) were also considered as design points to broaden the applicability of the

MOCVD-grown TJ. The high concentration target was chosen to match the concentration

target of the MBE 3J. Note that due to a dual-junction configuration, this slightly alters the RA and JP requirements compared to a triple-junction configuration for a given

concentration. For the dual-junction, the solar spectrum is split between two junctions

rather than three, resulting in a higher JSC for a given concentration. This results in higher

JP and lower total RA requirements for the MOCVD 2J compared to the MBE 3J for a

given concentration. Chapters 5 and 6 discuss the development of the lower and upper

MBE-grown TJs and the MOCVD-grown TJ, respectively.

Table 2.2. Target values of TJ figures of merit for the TJ within the MOCVD 2J operated at various concentrations. One Sun Medium Conc. High Conc. Figure of Merit (AM1.5G) (100× AM1.5D) (500× AM1.5D) Max. RA (Ω cm2) 1.8×10-1 2.3×10-3 4.7×10-4 -2 Min. JP (A cm ) 0.11 9.75 48.8 Min. EG (eV)⋅ 1.72 1.72 1.72 Lattice Constant⋅ (Å) 5.603 5.603 5.603

65 CHAPTER 3:

EPITAXIAL GROWTH AND DEVICE FABRICATION

3.1. BACKGROUND

The realization of the solar cell and tunnel junction devices discussed in chapter 2 requires both epitaxial growth of the semiconductor materials and a method to process the growth structures into functional devices. Section 3.2 explains various fundamental aspects of epitaxy. This sets the stage to discuss various aspects of III-V metamorphic epitaxy in section 3.3. Section 3.4 next focuses on the operating principles and capabilities of the two epitaxial growth methods that were utilized to grow the materials and device structures explored in this dissertation; molecular beam epitaxy (MBE) and

Figure 3.1. Simplified schematic demonstrating sequence to grow and process solar cell and tunnel junction devices (dimensions not to scale). 66 metal-organic chemical vapor deposition (MOCVD). Section 3.5 ends the chapter with a discussion on the processing techniques required to fabricate devices from the epitaxially grown device structures. In general, this device processing involves mesa isolation of the necessary layers to define the active electronic area of the device, followed by metallization of the device to make electrical contact. A schematic of the growth and processing sequence is shown in Figure 3.1.

3.2. FUNDAMENTAL ASPECTS OF EPITAXY

The word ‘epitaxy’ is derived from the Greek words ‘epi’ and ‘taxis’, meaning

‘upon’ and ‘arrangement’, respectively [121]. This describes the method of growing a monocrystalline ‘epilayer’ upon a monocrystalline substrate, where the atomic arrangement, or lattice, of the epilayer matches that of the substrate. MBE and MOCVD are two growth platforms that enable the growth of epilayers with high quality and purity.

Both platforms enable the control of various aspects of the epilayers such as atomic-scale thickness, composition, and the optical and electronic materials properties. This control offers the flexibility to grow the necessary III-V metamorphic materials for the solar cell and tunnel junction devices studied in this dissertation.

Figure 3.2. Steps of the general epitaxial process.

67 At the highest level, the general approach of both MBE and MOCVD involves the mass transport of source materials to a heated substrate where epitaxial growth commences. Figure 3.2 summarizes these three steps. General aspects of the source materials, mass transport, and epitaxial process that are shared by MBE and MOCVD are discussed in the remainder of section 3.2. Aspects that are specific to MBE and MOCVD are covered in section 3.4.

3.2.1. SOURCE MATERIALS

Various qualities of the source materials are critical in determining the quality of the grown epilayers. For example, the source material must be of very high purity to avoid the incorporation of unwanted contaminants into the epilayer. Purity can be defined using the ‘nines’ notation; for example, 5N purity means 99.999% purity. Although theoretically it is best to have sources with the highest purity, the cost of the source increases significantly with increasing purity. A realistic purity can be defined based on a desired materials property such as the background doping. Consider GaAs, which has an

22 -3 15 -3 atomic density of 4.42×10 cm ; if a background doping of 4.42×10 cm is acceptable, then 7N source purity is sufficient as a first order approximation [122].

The source materials come in different forms. For example, they can be in a pure elemental form or in a molecular form that contains the desired atomic element. The form of the source material impacts the method in which it is stored within the growth system.

The specific methods to store source materials in MBE and MOCVD will be discussed in section 3.4. However, it is worth noting here that the method of storage can contaminate

68 the source and must also be considered when determining factors such as the background doping as discussed above.

3.2.2. MASS TRANSPORT

Although the mechanism for mass transport of the source material from the source to the substrate differs for MBE and MOCVD, one common factor between both growth methods is that mass transport occurs in the vapor phase. This has impacts on the free energy driving force (i.e. the difference in Gibb’s free energy between the vapor phase and the solid phase) for subsequent epitaxial growth at the surface [123]. For example, the source materials are transported at partial pressures that are intentionally greater than the vapor pressures of these materials within the material being grown. This results in the supersaturation of the source materials in the vapor phase, leading to a large driving force for epitaxially growth to commence. Although many thermodynamic aspects are involved with this vapor-solid phase transition, the details are beyond the scope of this dissertation and the reader is referred to [123] for further detail. Here, it is important to understand that this driving force is what delivers an atomic flux to the surface. The next section explores how the atoms ultimately incorporate into the crystal.

3.2.3. ATOMISTIC VIEW OF EPITAXY

The atomistic approach describes the epitaxial growth process by considering what happens to an atom that adsorbs onto the substrate surface and becomes an adatom.

To understand the behavior of the adatom on the surface and how it ultimately leads to epitaxial growth, it is important to understand factors such as the nature of the substrate

Figure 3.3. The Kossel crystal, highlighting flat, stepped, and kinked surfaces.

surface, the possible surface sites that the adatom can occupy, and the various atomic processes that the adatom can undergo.

The nature of the substrate surface can be conceptualized using the Kossel crystal model, shown in Figure 3.3 [121]. This model treats each atom as a cube, where each face of the cube represents a single atomic bonding site; this implies that each atom in this model has 6 bonds, all with 90° bond angles (i.e. octahedral bonding). Atoms are considered bonded to one another where adjacent cube faces meet. If the face of a cube is exposed to atmosphere, this results in an unsatisfied ‘dangling’ bond. Based on this model, three surfaces are possible; flat, stepped, and kinked. Atoms exposed to atmosphere have one dangling bond on a flat surface, two on a stepped surface, and three on a kinked surface.

The concept of the three surfaces described above can be used to define various atomic sites that an adatom can occupy, shown in Figure 3.4. Adatoms can occupy flat, stepped, and kinked sites, and can also become embedded within a step or flat surface.

These five sites have 1 to 5 bonded faces, respective. Note that an atom with 6 bonded 70

faces in this model would be fully surrounded by other atoms, and thus is considered incorporated into the crystal. As the number of bonds for a particular adatom increases, the overall bond strength between the adatom and substrate increases and the total energy of the system decreases. Thus, an adatom on a flat site is at higher energy then when in a kink site. This has important consequences for the epitaxial process, as discussed below.

Various atomistic processes can occur to an adatom on the surface, shown in

Figure 3.5. For example, an adatom can diffuse along a flat surface, nucleate into clusters with other adatoms on a flat surface, incorporate at a site such as a step edge or kink, or

Figure 3.5. Various atomistic processes that occur on the surface during epitaxial growth. 71 even desorb from the surface (i.e. return to the vapor phase). The growth temperature is

an important parameter that controls the rate that these processes occur at; it controls the

kinetic energy, or adatom mobility, of adatoms on the surface. This leads to the concept

of adatom diffusion length; the mean distance the adatom travels before incorporation or

desorption. Generally, it is desirable to have long adatom diffusion lengths to ensure that the adatoms can incorporate into the lowest energy lattice sites (e.g. kink sites) to ensure high-quality, single-crystalline growth. In the limit of very low growth temperatures, the

adatoms do not diffuse at all and thus stick to where they adsorb. This results in

deposition rather than epitaxy. As the growth temperature increases, the adatom mobility

and diffusion length increases, enabling epitaxy to occur. However, if the growth

temperature increases further, adatoms will have enough kinetic energy to desorb from

the surface, the reverse process of epitaxy. Thus, the growth temperature is typically

tuned to ensure that high-quality epitaxy occurs while simultaneously avoiding

significant desorption.

3.2.4. EPITAXIAL GROWTH MODES

The basic atomistic description of epitaxy described in the previous section does not account for differences in attractive forces between the epilayer and substrate materials. However, this is important to consider, particularly for heteroepitaxial growth

where the epilayer and substrate materials are different. A difference in attractive forces

leads to different growth modes. For example, if the epilayer material is more strongly

attracted to the substrate than itself, the atomically flat layer-by-layer (Frank-Van der

Merve) growth mode will occur. On the other hand, if the epilayer material is more

Figure 3.6. The four primary growth modes at different levels of monolayer coverages.

strongly attracted to itself rather than the substrate, the three-dimensional island (Volmer-

Weber) growth mode will occur. An intermediate layer-plus-island (Stranski-Krastanov) growth mode may also occur where the first atomic layer is smooth but subsequent island growth occurs. This can be due to strain in the initial atomic layer causing a change in the attractive forces. These growth modes are schematically shown in Figure 3.6.

Of these growth modes, the layer-by-layer growth mode is preferred for achieving smooth, uniform epilayers. However, vicinal (offcut) wafers were primarily used within this dissertation for reasons explained in section 3.3.2. The atomic structure of (100) on- axis and vicinal surfaces is shown in Figure 3.7. This results in an additional growth

Figure 3.7. Atomic arrangement of (a) a (100) and (b) a vicinal (100) surface. 73 mode due to the atomic structure of a vicinal surface, which has alternating flat surfaces

(terraces) and step edges.

When the adatom diffusion length is greater than the terrace width, adatoms predominantly incorporate at step edges (recall that step sites have more dangling bonds than flat sites and are thus the preferred bonding sites). An adatom on a terrace can either diffuse to a ‘step-up’ or ‘step-down’ edge, and these situations are not identical. Whereas an adatom approaching a ‘step-up’ edge sees a potential well at the step (due to more dangling bonds at step site), an adatom approaching a ‘step-down’ edge may see a potential barrier before it sees the potential well at the step site. This potential barrier is caused by the fact that for the adatom to step down, it effectively has to break all bonds with the substrate as it goes over the edge of the step. The presence of this potential barrier is known as the Ehrlich-Schwoebel effect [124].

If the Ehrlich-Schwoebel effect is present, adatoms on a terrace only incorporate at the ‘step-up’ edges. Thus, if one terrace happens to be wider than adjacent terraces, more adatoms will adsorb on this terrace due to the highly probability of landing on the larger terrace. As a result, the ‘step-up’ edge of this terrace grow faster until the terrace width equals that of its neighbors. This is a stabilizing process that results in all step edges advancing together during growth and is known as the step-flow growth mode, also shown in Figure 3.6. If the Ehrlich-Schwoebel effect is not present, adatoms can incorporate at either the ‘step-up’ or ‘step-down’ edges and the terrace widths are no longer stabilized. This instability can ultimately lead to step-bunched during growth, which is not desirable for achieving smooth epilayers. Thus, step-flow growth is the preferred growth mode for the vicinal wafers used throughout this dissertation.

74 3.3. III-V METAMORPHIC EPITAXY

The fundamental aspects of epitaxy discussed in section 3.2 set the stage for the

discussion on III-V metamorphic epitaxy, the primary focus of this dissertation. This

section covers all the relevant topics than enable III-V metamorphic epitaxy (as well as

III-V/Si metamorphic epitaxy). This begins with a discussion on various crystal properties of the relevant materials explored in this dissertation in section 3.3.1. These crystal properties introduce concepts necessary to understand topics such as polar-on- nonpolar epitaxy, metamorphic epitaxy, and metamorphic buffers, which are discussed in sections 3.3.2 through 3.3.4.

3.3.1. RELEVANT III-V AND IV CRYSTAL PROPERTIES

The various materials explored in this dissertation include the group III materials

AlxGa1-xAsyP1-y, (AlzGa1-z)xIn1-xP (and various ternary and binary subsets of these

quaternaries such as GaAsyP1-y and GaAs), and group IV material Si. Although Ge was

not directly explored, it is also relevant for III-V MJSCs for space applications so is also

considered here. The crystal structure of these materials introduces additional concepts

that must be considered for the successful epitaxial growth of these materials. This includes their crystal structure, polarity, surfaces, as well as various crystal defects that may occur.

3.3.1.1. CRYSTAL STRUCTURE

The crystal structure of the relevant group IV and III-V materials are different but related to one another. The group IV elements Si and Ge have the diamond cubic crystal

Figure 3.8. The diamond cubic and zincblende crystal structures.

structure, which can be thought of as a face-centered cubic lattice with a two-atom basis with atoms on the (0, 0, 0) and (¼, ¼, ¼) lattice sites. The III-V materials all have the zincblende structure, shown in Figure 3.8. This is nearly identical to the diamond cubic structure, where the difference is that the group III elements sit on the (0, 0, 0) lattice sites and the group V elements sit on the (¼, ¼, ¼) lattice sites. Both crystal structures result in tetrahedral bonding; this is critical, as it enables the epitaxial growth of any of the relevant III-V materials on any of the other relevant III-V materials, as well as the relevant group IV materials.

3.3.1.2. POLARITY

Since Si and Ge only consist of a single element, they do not exhibit polarity.

However, III-V materials consist of different types of atoms on the (0, 0, 0) and

(¼, ¼, ¼) sites in their zincblende structure, and thus exhibit polarity. This has a variety of consequences. For example, whereas opposite {111} faces are identical in the diamond 76

Figure 3.9. Demonstration of the polarity of the zincblende structure.

cubic structure, they are different in the zincblende structure. This can be seen with the

aid of Figure 3.9. The {111} planes can be defined as either type I or type II planes. If the

crystal was cleaved to create either type I or II surfaces, a type I surface would result in

one dangling bonds per atom and a type II surface would result in three dangling bonds

per atom. Therefore, it is energetically favorable for type I surfaces to exist. If the III-V

material is defined such that the (0, 0, 0) lattice sites are occupied by A atoms and the

(¼, ¼, ¼) lattice sites are occupied by B atoms, then this results in the (111) surface being terminated by A atoms and the (111) surface being terminated by B atoms and are

thus referred to as the (111)A and (111�)B�� faces. These two faces exhibit different

properties such as oxidation rates, etch�� rates, and growth rates [125]. Here, the primary

concerns are the challenges of growing a III-V polar material on nonpolar IV materials,

the topic of section 3.3.2.

Figure 3.10. Schematic of surface reconstruction at a crystal surface.

3.3.1.3. CRYSTAL SURFACES

Real crystals do not have lattices that extend infinitely, but instead terminate at

surfaces. These crystal surfaces have a variety of properties that are important regarding

epitaxy. One of these properties is surface reconstruction. Up until now, it has been

assumed that the dangling bonds of atoms at a surface maintain the same tetrahedral

structure that they exhibit in the bulk crystal structure. However, this is not an

energetically favorable state. Instead, the atoms on the surface of the crystal tend to relax

or reconstruct to form a new atomic arrangement at the surface. Surface reconstruction is schematically shown in Figure 3.10 where pairs of surface atoms, known as dimer pairs, bond to one another to minimize the surface energy.

Although actual surface reconstructions have more complex geometries, this basic description can be used to describe various factors that influence III-V metamorphic epitaxy. For example, although CuPt-B ordering in GaxIn1-xP (i.e. where the group III

element arrange on alternating {111} planes) is not an energetically favorable bulk

structure, the strain associated with the distorted bonds of dimer pairs can induce ordering

78 at the surface [126]. The surface reconstruction can also introduce an asymmetry in atom

mobilities on (100) surfaces depending on the orientation of the dangling bonds and

dimer pairs. This has relevance for polar-on-nonpolar epitaxy and is discussed further in section 3.3.2.

3.3.1.4. CRYSTAL DEFECTS

Real crystals do not have perfect crystal structure and possess a wide variety of

bulk defects, including point defects such as vacancies, anti-sites, and interstitials, as well

as extended defects such as dislocations, stacking faults, grain boundaries, and

precipitates. Although all these defects impact materials and device performance, anti-

phase domains and dislocations are particularly important defects with respect to III-V

metamorphic epitaxy.

3.3.1.5. ANTI-PHASE DOMAINS

In the zincblende crystal structure, A elements sit on the (0, 0, 0) lattice sites and

B elements sit on the (¼, ¼, ¼) lattice sites. However, it is also possible to have the reverse polarity where B elements sit on the (0, 0, 0) lattice sites and A elements sit on the (¼, ¼, ¼) lattice sites. If two regions, or domains, of a crystal lattice have these different polarities, they are referred to as anti-phase domains (APD); the atomic order of

the two-atom basis is swapped in each domain. The boundary where these domains meet

is known as the anti-phase boundary (APB). Due to the difference in polarity between the

domains, incorrect bonding occurs at the APB; rather than A-B bonds, there are either

incorrect A-A or B-B bonds. The type(s) of incorrect bonds at the APB depends on the

atomic plane that the APB resides on. An example of an APD and the associated APBs is schematically show in Figure 3.11 [127]. The concept of APDs and APBs is important in

understand the challenges associated with polar-on-nonpolar epitaxy, which is discussed in section 3.3.2.

3.3.1.6. DISLOCATIONS

Dislocations are line defects that occur in crystals due to areas where atoms are

out of position from their theoretical lattice sites. Two basic types of dislocations exist;

the edge and screw dislocation. The atomic arrangement of edge and screw dislocations

are depicted in Figure 3.12 [128]. The edge dislocation can be thought of as the addition

or removal of an extra atomic half-plane within the crystal that terminates at the

dislocation line DC. A screw dislocation can be thought of as a sheared a portion of a

plane within the crystal, resulting in a helical pattern of atomic planes along the

Figure 3.12. Atomic arrangement of (a) edge and (b) screw dislocations. © 2011 Fong Kwong Yam, Li Li Low, Sue Ann Oh, and Zainuriah Hassan. Adapted from Gallium Nitride: An Overview of Structural Defects, Optoelectronics Padmanabhan Predeep, IntechOpen; originally published under CC BY-NC-SA 3.0. Available from: 10.5772/19878

dislocation line DC. It is also possible for a dislocation to have a mixed geometry with both edge and screw components.

Dislocation can move within the crystal structure to facilitate plastic (permanent) deformation. This can be accomplished by either the glide or climb mechanisms. Using an edge dislocation as an example, glide can be visualized by the reconfiguration of bonds at the dislocation line such that the extra half plane of atoms propagates through the crystal. This proceeds along a specific crystallographic direction known as the glide plane and can propagate at a velocity that depends on aspects such as applied stress, crystal purity, and temperature. For dislocation motion in a direction besides the glide plane, dislocation climb is necessary. This involves the diffusion of atoms to or away from the dislocation line to move the dislocation line into another plane. Except at very high temperatures where diffusion is significant, dislocation motion is primarily due to glide [129]. The strong covalent bonding of semiconductors has various consequences on

81 dislocation formation and motion. For example, the directional nature of covalent

bonding results in dislocations that are aligned in specific crystallographic directions

[125]. Another consequence of the strong covalent bonding is that high temperatures (i.e.

high growth temperatures) are required for significant glide motion to occur.

The presence of a dislocation within the crystal structure results in dangling bonds

along the dislocation line as well as a strain field in the vicinity of the dislocation. This

gives rise to various electronic and optical defects within the material. The specific types

of dislocations and their associated defects that result from lattice-mismatched

heteroepitaxy are discussed in section 3.3.3. The importance of controlling the nucleation

and motion of these dislocations for metamorphic buffers is discussed in section 3.3.4.

3.3.2. POLAR-ON-NONPOLAR HETEROEPITAXY

The III-V materials explored in this dissertation are designed to ultimately be

grown on either Si substrates in the case of III-V/Si MJSCs for terrestrial application or

on Ge in the case of the wide bandgap (AlzGa1-z)xIn1-xP top cells for space application.

This requires the heteroepitaxial growth of polar III-V materials on nonpolar IV

substrates. The challenges and solutions to polar-on-nonpolar heteroepitaxy are discussed below.

Without proper control of epitaxy at this polar/nonpolar interface, antiphase domains (APD) will be present within the epitaxial layer (see section 3.3.1.5). This arises due to single atomic-height steps on the nonpolar substrate surface, as was shown in

Figure 3.11. These steps will still be present to some degree even on an on-axis wafer due to either slight deviation from on-axis, or more fundamentally, due to entropy preventing

82 a perfectly smooth surface at finite temperatures [121]. Consequently, anti-phase boundaries (APB) form between adjacent APDs. APBs are known to act as nonradiative recombination centers [130] that can be detrimental to device performance if present within the active layers.

Various solutions for eliminating APDs and APBs exist. One solution involves

growth on a (211) surface, as it possesses two unique surface sites with different numbers

of dangling bonds. This creates preferential bonding sites for the A and B atoms in the

III-V polar material, and thus naturally eliminates APDs even with the presence of single

atomic-height steps [80]. However, this dissertation focused on epitaxy on vicinal (100) surfaces due to its technological relevance. Thus, an alternative solution is necessary. The solution for vicinal (100) surfaces involves preparing the nonpolar substrate in such a way that only double atomic-height steps are present on the surface. This double step will prevent like-atoms from bonding and forming APBs since the epitaxy of the polar material will occur with the same crystal registry on adjacent terraces [80].

A double atomic-height step can be accomplished by performing an appropriate anneal on a vicinal (100) vicinal surface with an offcut on the order of a few degrees [29].

This is possible due to the asymmetric properties of the two surface domains present on a

(100) diamond cubic surface. Surface reconstruction leads to dimer pairs that are aligned

perpendicular to one another on adjacent terraces when separated by a single atomic-

height step, resulting in a surface similar to the scanning tunneling microscopy (STM)

image shown in Figure 3.13 [131]. This asymmetry leads to asymmetry in the adatom

mobilities on each surface domain and sticking coefficient to the two different step edges

(Sa and Sb in Figure 3.13). During the anneal, adatoms preferentially incorporate at the

Sb-type steps. Thus, the Sb-type steps advance faster than the Sa-type steps until they reach the adjacent Sa-type step to form the double step. The substrate can then be

quenched to the desired growth temperature to freeze in this double step, enabling

subsequent APD-free polar-on-nonpolar heteroepitaxial growth.

3.3.3. LATTICE-MISMATCHED HETEROEPITAXY

Lattice-mismatched heteroepitaxy is the growth of one material upon a different

material with a different lattice constant. When lattice-mismatched heteroepitaxial growth

first commences, the epilayer initially conforms to the lattice constant of the substrate and

is known as pseudomorphic growth. For the relevant III-V materials in this dissertation, this distorts their cubic zincblende crystal structure into a tetragonal structure, schematically shown in Figure 3.14(a). This results in a build-up of strain energy in the epilayer that increases linearly with epilayer thickness. The strain energy stored in the epitaxial layer is balanced via wafer bowing such that there is no net moment on the

epilayer/substrate system, and can be modeled to first order using Stoney’s equation

[132]. As long as the growth remains pseudomorphic, internal stresses exist in both the epilayer and substrate. Eventually, the stresses will be high enough to facilitate dislocation formation and motion (see section 3.3.1.6). Although the formation of dislocations has an energy cost due to breaking bonds and the formation of a local strain field around the dislocation core, the associated reduction in bulk epilayer strain energy leads to a total reduction in energy, relaxing the epilayer. The thickness at which this relaxation begins to occur is known as the critical thickness [133]. Upon relaxation, the layer becomes metamorphic; a metamorphic heteroepitaxial layer with a misfit dislocation is schematically shown in Figure 3.14(b). Upon 100% relaxation, the epilayer possesses its natural ‘relaxed’ lattice constant and once again has a cubic crystal structure.

The relaxed lattice constant, strain, misfit, and relaxation have been qualitatively described above. To quantitatively define these parameters the lattice constant of the substrate (as) and the in-plane ( ) and out-of-plane ( ) lattice constants of the epilayer

ǁ ┴ must be known; these can be determined𝑎𝑎 via high resolution𝑎𝑎 X-ray diffraction reciprocal 85 space mapping (see section 4.2.1). Eq. 3.1 can then be used to calculate the relaxed lattice

constant (ar) of the epilayer, where ν is Poisson’s ratio and can be calculated from

materials elastic constants [78], [134], [135].

= + Eq. 3.1 1−𝜈𝜈 2𝜈𝜈 𝑎𝑎r 1+𝜈𝜈 𝑎𝑎ǁ 1+𝜈𝜈 𝑎𝑎┴ Using ar, the in-plane strain ( ) in the epilayer can be defined by Eq. 3.2.

ǁ 𝜖𝜖 = Eq. 3.2 𝑎𝑎ǁ−𝑎𝑎r 𝜖𝜖ǁ 𝑎𝑎r The misfit (f) is defined by Eq. 3.3.

= Eq. 3.3 𝑎𝑎s−𝑎𝑎r 𝑓𝑓 𝑎𝑎r A positive (negative) value for and f indicates the epilayer is under tension

ǁ (compression). The relaxation (𝜖𝜖R) percentage can be defined by Eq. 3.4 using and f.

| | ǁ = 1 × 100 𝜖𝜖 | | Eq. 3.4 𝜖𝜖ǁ 𝑅𝑅 � − 𝑓𝑓 � The relaxation process consists of the formation of misfit dislocations along the

lattice-mismatched interface. The misfit dislocation can either nucleate at an existing

threading dislocation in the substrate (one that propagates through the crystal in the

growth direction) or can nucleate a dislocation half loop. A dislocation half loop is shown

schematically in Figure 3.15. In either case, the dislocation line must terminate at a

surface due to their atomic arrangement.

Threading dislocations can severely degrade device performance if present at

sufficiently high threading dislocation densities (TDD). Figure 3.16 demonstrates that

above a critical TDD, the minority carrier lifetime in the semiconductor (in this example

GaAs) begins to exponentially decrease [22]. This results in a lower minority carrier

Figure 3.15. Depiction of a dislocation half loop consisting of a misfit dislocation and two threading dislocations on a (111) plane.

diffusion length, reducing collection in a photovoltaic device. It is therefore ideal to remain below this critical TDD value to achieve high-performance devices.

Figure 3.16. Dependence of GaAs minority carrier lifetime (τ) as a function of threading dislocation density. Reprinted from [22], with the permission of AIP Publishing.

87 3.3.4. METAMORPHIC BUFFER DESIGN

The relaxation process described above can be highly controlled for low values of misfit. However, if metamorphic epitaxy is required that has significant misfit with the substrate, it becomes very difficult to promote misfit dislocation glide significantly and thus minimize the TDD. The large amount of misfit at the interface will result in the nucleation of many misfit and thus threading dislocations. Although it is possible to perform an anneal to promote dislocation glide and annihilation [136], this is typically not capable of reducing the TDD below the critical value necessary to prevent a reduction in minority carrier lifetime. At larger misfit values (>1.5% strain), growth may even proceed in a 3D island fashion [137], which is not acceptable for the devices developed in this dissertation.

To achieve a high-quality metamorphic epilayer that possesses significant misfit with the substrate, a metamorphic graded buffer can be utilized. In this approach, a series of epilayers are grown where each layer has only slight misfit with the previous layer.

This allows relaxation to occur in incremental steps rather than one step with large misfit.

Two approaches include linearly or step-graded metamorphic buffer, although step grades have found the most success [137]. For the step-graded approach, each subsequent buffer layer is able to recycle the threading dislocation present in the previous layer to generate new misfits. If this relaxation mechanism only occurs in the buffer layers (i.e. no new dislocation half loops are generated), the threading dislocation density will not increase further as subsequent buffer layers are grown.

88 In this dissertation, both compressive GaAsyP1-y/Si and tensile GaAsyP1-y/GaAs

step-graded buffers are utilized to demonstrate the metamorphic III-V devices herein.

Compressive GaAsyP1-y/Si buffers initially requires the nucleation of GaP on Si,

involving both polar-on-nonpolar and lattice-mismatched heteroepitaxy with ~0.4%

misfit. Other challenges with GaP/Si nucleation include a significant difference in

thermal expansion coefficients for GaP (4.65×10-6 °C-1) and Si (2.6×10-6 °C-1) [78], as

well as the high reactivity of phosphorous with a Si surface [29]. However, details on

how to overcome these challenges and produce high-quality GaP/Si grown via both MBE

[29] and MOCVD [37] have been previously published by our research group. After

GaP/Si nucleation, the compressive GaAsyP1-y step-graded buffer can then be grown.

7 -2 Currently, this enables TDDs on the order of 5×10 cm . Tensile GaAsyP1-y/GaAs

buffers with less misfit can achieve lower TDDs. For example,

GaAs0.9P0.1/GaAsyP1-y/GaAs buffers have been demonstrated with TDDs as low as

105 cm-2 in our research group.

3.4. EPITAXIAL GROWTH METHODS

Up until this point, this chapter has focused on general aspects of epitaxy.

However, the specific epitaxial growth method introduces additional aspects that must be

considered. This section explores various factors of MBE and MOCVD, including their

operating principles and capabilities.

3.4.1. MOLECULAR BEAM EPITAXY

The MBE growth method can be described with the aid of Figure 3.17, which shows a schematic of a typical MBE reactor. A defining property of MBE is that the 89

Figure 3.17. Schematic of a typical MBE reactor. “Molecular Beam Epitaxy” by Nikhil P. is licensed under CC BY-SA 3.0

reactor operates at ultra-high vacuum (UHV). Typically, elemental source materials

contained in effusion cells are either evaporated or sublimated and transported to the

substrate surface in molecular beams. The substrate manipulator heats the substrate to

growth temperature, enabling subsequent epitaxial growth on the substrate surface as

described by sections 3.2 and 3.3. The UHV environment also enables various in situ diagnostic tools. Reflection high-energy electron diffraction (RHEED) is one such technique that is invaluable in the MBE. The remainder of this section describes each of these aspects in more detail, followed by a description of the MBE used for the research in this dissertation.

3.4.1.1. ULTRA-HIGH VACUUM

A defining feature of MBE is operation within a UHV environment. Typical

operating pressures are in the range of 10-8 – 10-12 Torr. These pressures are achieved

90 through the use of various vacuum pumps, including turbomolecular, cryogenic, ion, and

gettering pumps [138]. In addition to these standard pumps, a cooling shroud

(cryoshroud) filled with liquid nitrogen surrounds the substrate manipulator to pump

residual gases that condense at liquid nitrogen temperatures.

The UHV environment is extremely clean, which enables the growth of high- quality epitaxial layers. A general rule of thumb is that the time to deposit one monolayer of background particles (assuming a unity sticking coefficient) should be 105 times longer

than for a monolayer of the desired material to limit impurity concentrations to

mid - 1017 cm-3 levels. However, in reality the sticking coefficients of typical background

gases are much lower than unity, resulting in even lower impurity concentrations. As an

example, for a growth rate of approximately one monolayer per second, the time to

deposit a monolayer of background particles should be ~28 hours. Since the beam flux

necessary to deposit one monolayer is on the order of 1015 cm-2 s-1, the pressure (P) to

achieve the condition above can be calculated using Eq. 3.5, where⋅ F is the flux, kB is

Boltzmann’s constant, m is the mass of the particles, and T is the temperature [121].

= 2 Eq. 3.5

B A pressure of ~1×10-11 Torr is adequate𝑃𝑃 to𝐹𝐹 �meet𝜋𝜋𝑘𝑘 the𝑚𝑚𝑚𝑚 conditions above, which is within the

range of typical MBE operating pressures.

The UHV environment enables the use of molecular beams (one of the core

features of MBE) due to the very long mean free path (λ) of particles at low pressures.

This is the average distance particles travel before colliding and can be calculated using

Eq. 3.6, where d is the particle diameter and n is the particle concentration.

= Eq. 3.6 1 91 2 𝜆𝜆 √2𝜋𝜋𝑑𝑑 𝑛𝑛 This equation indicates that the mean free path at 10-11 Torr and room temperature is

~5000 km, immensely greater than the dimensions of the reactor [121], [138]. Thus, particles within the UHV environment essentially do not interact with one another. This creates an environment suitable for molecular beams, discussed below.

3.4.1.2. MOLECULAR BEAM SOURCES

Molecular beams are necessary within MBE to avoid gas phase reactions among

the various source elements that may negatively impact material quality by, for example,

nucleating clusters of particles in the gas phase that subsequently deposit on the substrate.

In addition, molecular beams ensure efficient delivery of the source materials to the

substrate; if the source material is not directed in a beam, more source material is lost to

deposition on the reactor walls. An effusion cell is typically used to store solid source

material and to produce the molecular beam, although sublimation, valved cracker, and

gas sources are also used. Within the effusion cell, elemental sources are stored in a

crucible that is commonly made of pyrolytic boron nitride due to its thermally insulating

properties and ability to be manufactured with low impurity levels to minimize source

contamination [139]. The cell can be heated up to temperatures as high as ~1300 °C to

evaporate the source material. The evaporated material exits an orifice in the effusion cell

and is directed towards the substrate surface.

To ensure the evaporated material is transported to the substrate surface in a molecular beam, the pressure of the vapor phase of the source material between the orifice and substrate must be low enough to ensure a mean free path greater than this distance (~10-1 m). Eq. 3.6 indicates that this limits the source pressure to ~5×10-4 Torr.

92 This is larger than the typical source pressures used within the MBE for achieving growth

rates on the order of 1 monolayer per second, thus ensuring the source material is

delivered to the substrate in the form of a molecular beam.

As mentioned above, other sources besides effusion cells exist. For arsenide and

phosphide materials, large arsenic and phosphorous fluxes are typically used during growth. Thus, a source capable of holding a large quantity of these materials is necessary to avoid frequently resupplying source material. However, it is not practical to control the flux via the source temperature due to the associated large thermal mass of the source material. A valved source can instead be used to mechanically control the flux while keeping the source material at operating temperature. In the case of arsenic and phosphorous, dimer and tetramer (e.g. As2 and As4) molecules are present in the vapor

phase. However, dimers are ideal for epitaxy, and thus a cracker stage can be used to

dissociate the tetramer molecules into dimers at temperatures around 800-1000 °C [121].

If source contamination is a concern, a sublimation source can be used. Whereas effusion

cells can contaminate source materials due to the heated metal and ceramic parts

surrounding the source material, a sublimation source can be used to avoid this by

directly heating a filament of pure source material. This contamination is particularly

problematic for source materials that require high temperatures for adequate deposition

rates, such as silicon. Finally, gas sources can be used to avoid the limited lifetime of

solid sources since they can be externally stored. If metal-organic precursors are used,

such as trimethylgallium (TMGa), the reactor begins to resemble an MOCVD operated in

UHV.

93 A gauge can be inserted into the path of the molecular beam to measure the beam

equivalent pressure (BEP). This allows the flux of each source to be calibrated to achieve

the desired growth. To control beam fluxes delivered to the surface, shutters can be

inserted into the path of the molecular beam to block the beam from impinging on the

substrate.

3.4.1.3. SUBSTRATE TEMPERATURE

Once the source material is delivered to the substrate surface, epitaxy can

commence. To do so, the substrate manipulator must heat the substrate to the necessary

growth temperature. The substrate is mounted in a substrate holder, and a sapphire wafer

can be placed between the holder to uniformly transmit infrared radiation to heat the

wafer. The temperature is controlled using a thermocouple that is in contact with the

backside of the substrate holder (i.e. sapphire). However, this is not an accurate

representation of the temperature of the substrate surface, which is the more critical

temperature with respect to epitaxy. To monitor the surface temperature, pyrometry can

be utilized. The concept is to monitor the amount of infrared radiation emitted from the

substrate surface to determine its temperature. This is achieved by externally mounting a

pyrometer detector that has direct line-of-sight with the substrate surface through an optical view port. A challenge with this technique is that it requires proper calibration to account for factors such as the emissivity of the substrate and any coating on the pyrometer viewport. Methods to calibrate the temperature include using the eutectic temperature of a combination of materials such as Al and Si or the oxide desorption

94 temperature. These methods thus require a technique to monitor changes to the substrate

surface.

3.4.1.4. RHEED

Reflection high-energy electron diffraction (RHEED) is a surface-sensitive

diffraction technique that relies on the use of an electron beam. For such techniques, a

vacuum environment is necessary to avoid scattering the electron beam. Thus, this

technique is possible within the MBE due to the UHV environment. By directing an

electron beam at a glancing incident angle on the substrate, a portion of the beam is

diffracted due to two mechanisms; kinematic and dynamic scattering.

Kinematic (single) scattering occurs at the surface. The electrons that contribute

to this diffraction only penetrate the first few monolayers due to the glancing incidence of

the electron beam. This means the electrons are effectively only sampling a two-

dimensional crystal. The reciprocal lattice of a 2D crystal consists of infinite rods

extending perpendicular to the surface rather than points as is for a 3D crystal. By using

the Ewald construction (see section 4.2.1), diffraction conditions are met when the Ewald

sphere intersects with the rods. Due to the use of a high-energy electron beam the k vector is large, resulting in an Ewald sphere with a very large radius compared to the reciprocal lattice. Also, due to the electron beam having a finite energy resolution the

Ewald sphere has a finite ‘fuzzy’ thickness. These two factors result in the Ewald sphere overlapping with the reciprocal lattice rods over a large distance, resulting in diffraction streaks in the RHEED pattern. Since RHEED is a surface sensitive technique and crystal surfaces undergo surface reconstruction (see section 3.3.1.3), the RHEED pattern has a

symmetry that reflects that of the surface reconstruction. Thus, the RHEED pattern can

reveal information about what surface reconstruction is present under the corresponding

growth conditions. Examples of RHEED patterns of GaAs(100) are shown in Figure

3.18. For typical growth conditions of GaAs(100) (610 °C, V:III =18), a 2×4 (two-by-

four) pattern occurs where the 2× pattern is along the [011] direction and the 4× pattern

occurs along the [011] direction. The 2× and 4× values indicate that the surface

reconstruction unit ‘mesh’� (analogous to the unit cell of a bulk crystal) has dimension that

are two times and four times the dimensions of the unit cell, respectively.

Dynamic (multiple) scattering arises due to electrons that make it into the bulk of

the crystal and scatter diffusely in all direction. A portion of these diffusely scattered

electrons meet the diffraction conditions for a given set of atomic planes and diffract in

the form of a cone shape (Kossel cone). When the Kossel cones intersect with the

detector, the projection of the Kossel cone forms Kikuchi lines that appear in pairs

(bands) [140]. In the case of RHEED, only a small angular range is visible due to the

96 measurement configuration. This limits the number of Kikuchi bands that can be seen at a given time, as shown in Figure 3.18. The Kikuchi bands can be used to determine the substrate orientation.

RHEED can be used to monitor oxide desorption to calibrate growth temperature.

For example, when an oxide is still present on the substrate, the oxide obscures the

RHEED pattern of the crystal. By increasing the growth temperature, eventually the oxide will reach its desorption temperature. Once the oxide has desorbed, the crystal surface is exposed and the RHEED pattern is visible. By desorbing an oxide with a known desorption temperature, that temperature can be identified by the temperature at which the RHEED transition occurs. Observing the oxide desorption is also useful on a routine basis to ensure the surface is of high quality and oxide-free before commencing growth.

RHEED can also provide information on the growth rate. If growth proceeds in the layer-by-layer (Frank-Van der Merve) growth mode, the substrate surface oscillates between monolayers with partial and full coverage. When partial coverage occurs, the electron beam is partially scattered. This reduces diffraction intensity compared to the case of full coverage. As a result, the diffraction intensity oscillates one cycle per monolayer. The frequency of oscillation can be monitored to determine growth rate.

3.4.1.5. THE OHIO STATE ASP/SI MBE

The reactor used in this dissertation was a Varian Gen II solid-source MBE system capable of III-V As/P growth and Si. Effusion cells were used for group III sources (Ga, In, and Al) and dopant sources (Si and Be for n- and p-type doping,

97 respectively). A sublimation source was available to grow Si, although it was not used for

the specific research in this dissertation. Valved As2 and P2 cracker sources were used for

group V sources. The typical base pressure in the growth chamber was < 2×10-10 Torr,

maintained using a cryopump, cryoshroud, and titanium sublimation ‘getter’ pump. At the time, the source flange was also cooled with liquid nitrogen. Growth temperature was monitored via pyrometry, measured through an optical viewport that is in direct line-of- sight with the substrate. In situ monitoring was possible with RHEED, as well as a residual gas analyzer (RGA) to monitor the composition of gases present in the reactor.

The growth temperature was calibrated via desorbing the oxide from a GaAs wafer, which occurs at ~582 °C. Rather than the commonly used method of desorbing the

thermal oxide, an ozone oxide was desorbed for temperature calibration. A thin layer of

GaAs was first grown at an uncalibrated temperature slightly above the oxide desorption temperature until a well-defined 2×4 RHEED pattern was observed; this indicates an atomically smooth surface. The sample was then unloaded, a thin ozone oxide was grown, and the oxide desorption temperature calibration was performed with this ozone oxide rather than the thermal oxide. The combination of the smooth GaAs surface and the

thin oxide enabled a very sharp RHEED transition to occur over a window of a couple of

degrees. This method proved to be a more reliable for temperature calibration.

3.4.2. METAL-ORGANIC CHEMICAL VAPOR DEPOSITION

Metal-organic chemical vapor deposition (MOCVD) is a growth method that can

be performed over a wide range of pressures including atmospheric, low pressure

(10 - 760 Torr), very low pressure (0.1 – 10 Torr), and UHV. This section will focus on

Figure 3.19. Schematic of a typical low pressure MOCVD reactor.

low pressure MOCVD since this was the method used for the research in this dissertation.

However, note that the topics discussed herein can also apply to other pressure ranges as well. General features of low pressure MOCVD can be described with the aid of Figure

3.19. Chemical precursors such as metal-organics and inorganic hydrides contain the constituent elements for epitaxy. These precursors are delivered to the reactor via a carrier gas such as H2 or N2. Within the reactor a heated substrate provides thermal energy to both pyrolyze (i.e. decompose) the precursors and enable subsequent epitaxy. A detailed analysis of the entire MOCVD growth process can be found in [123]. This section highlights key aspects of MOCVD that are discussed therein, including the chemical precursors, pyrolysis reactions, and mass transport to aid in understanding the various growth regimes that occur within the MOCVD. A description of the MOCVD reactor used for the research in this dissertation is provided at the end of the section.

99 3.4.2.1. PRECURSORS

MOCVD relies on the use of various metal-organic and inorganic precursors to supply the constituent elements for epitaxy. A wide variety of precursors are used for

MOCVD and require many considerations for proper selection. This section discusses the chemical nature of precursor molecules to aid in understand subsequent steps that occur in the MOCVD growth process. This includes the molecular structure, ligands, and the metal-ligand bond strength. These aspects are then used to explain various gas properties of the precursors.

Many common MOCVD precursors have the MRn molecular structure, where M represents the constituent element required for epitaxy and R represents the organic ligand (i.e. molecules that bind to the central element M). The number of ligands bonded

to the central element and the resultant molecular geometry can be explained by orbital

hybridization. For example, the outer shell of group III elements such as aluminum

contains two s electrons and one p electron. To ensure all three electrons can be paired

after bonding, these three orbitals are mixed to form three sp2 hybridized orbitals.

Valence shell electron pair repulsion theory (VSEPR) states that these orbitals repel, resulting in trigonal planar geometry in the case of sp2 hybridization. Thus, three ligands can bond to a group III element and have 120° bond angles. The hybridization and molecular structure of group II, III, and V molecules, as well as examples of precursors and visualizations of their molecular structure, are listed in Figure 3.20.

The metal-ligand bond strength is an important parameter of these molecules since it impacts factors such as precursor stability and vapor pressure. This bond strength

100

Figure 3.20. Molecular structure of group II, III, and V precursors.

is influenced by factors such as the electronegativity of the central element M and the type of radicals that occupy the ligands. Two organic radicals are shown in Figure 3.20; the methyl (CH3) radical in trimethylgallium (TMGa) and the ethyl (C2H5) radical in diethylzinc (DEZn). Hydrogen radicals are also shown in the case of arsine (AsH3). As the number of carbon-bonds to the central carbon atom of the radical increases, the bond strength between the radical and metal atom decrease. Methyl radicals only have one central carbon atom and thus no carbon-bonds to this carbon atom, whereas ethyl radicals have a central carbon atom bonded to one other carbon atom. As a result, for a given metal, the bond strength will be lower with ethyl compared to methyl radicals. For example, the metal-ligand bond strength of trimethylaluminum (TMAl) is ~66 kcal/mole, whereas for triethylaluminum (TEAl) it is only 58 kcal/mole [123]. The metal-ligand bond strength of hydrogen radicals in also generally stronger than organic radicals.

101 The stability of the precursor is an important factor to consider. From a logistics

perspective, stable precursors are desirable since they are easier to manufacture and can

be stored for years without decomposing. From a growth perspective, precursors must be

unstable enough to pyrolyze at typical growth temperatures. Lower stability enables

efficient pyrolysis at lower growth temperatures, providing access to a wider range of

growth parameters. For example, the nucleation of GaP on Si performed in our group

relies on low-temperature (~450 °C) atomic layer epitaxy of GaP [37]. Therefore,

triethylgallium (TEGa) is used over TMGa due to its lower pyrolysis temperature.

Similarly, tertiarybutylphosphine (TPB) is used over phosphine (PH3) to supply phosphorous; the strong metal-ligand bond between phosphorous and hydrogen radicals in PH3 requires high temperatures for pyrolysis.

The vapor pressure of the precursor is also an important consideration. One

general trend is that lighter molecules tend to have higher vapor pressures. However,

molecules with complex geometries result in less intermolecular interactions and can also

have high vapor pressures. Logistically, it is ideal to have precursors with suitable vapor

pressures at room temperature to avoid complex gas handling systems to deliver the

precursor. For example, if the precursor must be heated significantly to achieve an appropriate vapor pressure, the gas deliver lines must also be heated to avoid condensation that would otherwise deplete the precursor.

The metal-organic precursors are stored primarily in liquid form in gas bubblers.

These devices are held at a fixed temperature and pressure to achieve the desired

equilibrium vapor pressure of the precursor within the bubbler. As seen in Figure 3.19,

the carrier gas is bubbled through the liquid precursor. This process saturates the gas

102 bubbles with precursor vapor and stores the saturated gas in a volume above the

precursor. Since equilibrium vapor pressure is known, the molar flow in the saturated

carrier gas can be determined [141]. Inorganic sources such as AsH3, PH3, and silane

(SiH4) are stored in gas cylinders.

3.4.2.2. PYROLYSIS REACTIONS

Pyrolysis of the precursors is in important step in the MOCVD process. After the precursors have been transported to the vicinity of the substrate, the growth temperature of the substrate provides thermal energy to decompose the precursor molecules and release the constituent elements. This results in a minimum achievable growth temperature for a given precursor since below this temperature the precursor does not pyrolyze. The complexity of the pyrolysis process can also result in unwanted reactions that can, for example, result in the incorporation of contaminants. Pyrolysis reactions can

either be homogeneous or heterogeneous. Examples of each are discussed below.

Homogeneous reactions are those that occur in the gas phase. An example of such

a reaction for trimethylindium (TMIn ≡ In(CH3)3) is given in Eq. 3.7.

In(CH ) In(CH ) + CH Eq. 3.7

3 3 3 2 3 This reaction is known as homolytic fission,→ where a metal-ligand bond between In and

one of the methyl radicals has been broken. This can occur sequentially until all methyl

ligands have been removed, resulting in an indium atom that can then be incorporated

into the crystal. Hydrogenolysis is another homogeneous reaction given in Eq. 3.8, where

hydrogen breaks down the metal-ligand bond.

In(CH ) + H HIn(CH ) + CH Eq. 3.8

3 3 2 → 3 2 4 103 Heterogenous reactions are those that occur at the surface. These types of reactions tend

to occur at faster rates than homogeneous reactions since the surface serves to weaken the

metal-ligand bonds. As a result, heterogeneous reactions can lower the pyrolysis temperature of a precursor.

The types of pyrolysis reactions that occur can result in methyl radicals (Eq. 3.7).

These methyl radicals can subsequently decompose on the surface and result in carbon contamination in the epilayer. It is possible for hydrogen to recombine with a methyl radical to form methane (CH4), which can then be removed through the exhaust.

Alternatively, specific radicals can be introduced into the reactor with the intent of

efficiently scavenging unwanted radicals.

When studying homogeneous versus heterogeneous reactions, the products that

result from pyrolysis can be studied via mass spectroscopy. Homogeneous versus

heterogeneous reactions can be distinguished by, for example, loading chips of

semiconductor material into the reactor to provide varying degrees of surface area. If

pyrolysis is dominated by heterogeneous reactions, an increase in the concentration of the

products will be observed when higher surface area is available. These types of

experiments were not possible with the MOCVD used for the research in this dissertation.

However, these types of studies provide a deeper understanding of the MOCVD growth

process.

3.4.2.3. MASS TRANSPORT

The viscous flow of gas during low (and atmospheric) pressure MOCVD,

opposed to molecular flow in UHV MOCVD or MBE, plays an important role in mass

104

Figure 3.21. Velocity profile of a boundary layer formed by a gas flowing at an initial velocity v0 over a surface.

transport of the precursors from the vapor phase to the substrate surface. When a viscous

gas flows over a surface, the velocity (u) of the gas goes to zero at the surface. Beyond a

critical distance δ above the surface, the velocity profile is uniform. This results in a

velocity profile u(y) that varies between the surface and δ and is known as the boundary

layer. This phenomenon is schematically shown in Figure 3.21. The mass transport of

precursor through this boundary layer controls the flux of precursor delivered to the

substrate surface. The flux (J) can be determined via Eq. 3.9, where D is the diffusion

coefficient, p* is the input partial pressure of the precursor, pi is the partial pressure of

the constituent element of the precursor, R is the universal gas constant, and T is the

temperature [123].

( ) = ∗ Eq. 3.9 𝐷𝐷⋅ 𝑝𝑝 −𝑝𝑝i 𝑅𝑅⋅𝑇𝑇⋅𝛿𝛿 This relationship can be used to𝐽𝐽 explain various phenomena observed during

MOCVD growth. For example, note that during typical III-V growth the partial pressure of the group III element is close to zero (pi ≈ 0). According to Eq. 3.9, this results in a

linear relationship between the flux and the input partial pressure (which corresponds to

105 the input molar flow). When within the mass transport limited growth regime, this leads to a linear relationship between the flux and growth rate, as discussed below.

3.4.2.4. MOCVD GROWTH REGIMES

MOCVD growth can be classified into different growth regimes due to different rate-limiting mechanisms. These mechanisms include the pyrolysis reactions and mass transport discussed above, as well as other parasitic reactions. Since the rate of the pyrolysis reactions and mass transport through a boundary layer depend on growth temperature, these regimes exist within different temperature ranges. They are shown schematically in Figure 3.22 and discussed in detail below.

At low growth temperatures, pyrolysis reactions lack the thermal energy required to rapidly release the constituent element. This results in the growth rate reducing exponentially with decreasing growth temperature in the kinetically-limited growth

Figure 3.22. Primary MOCVD growth regimes. 106 regime. The growth rate in this regime is also independent of the precursor flow rate.

Various aspects of the substrate surface can impact growth rate such as substrate orientation and surface reconstruction.

At moderate growth temperatures, pyrolysis reactions happen rapidly enough that precursor molecules delivered to the substrate effectively pyrolyze immediately and all constituent elements incorporate. At this point, the growth rate becomes limited by the amount of precursor that is delivered to the substrate. This is known as mass transport limited growth and controlled by the flux calculated in Eq. 3.9. It is often desirable to be within this growth regime since the growth rate varies linearly with flow rate, making calibrations straight-forward.

At high growth temperatures, a variety of parasitic reactions can occur that result in reduced growth rates. For example, heterogeneous pyrolysis on hot reactor walls can deplete precursors prior to reaching the substrate surface (i.e. sidewall deposition). It is also possible that the epilayer begins to decompose or evaporate, counteracting the growth process and reducing growth rate.

By inspection of Figure 3.22, varying the flow rate will shift the position of the mass transport limited regime up and down on the plot. Naturally, at a low flow rate the mass transport limited regime can be extended to a wider range of growth temperatures.

By understanding the various types of pyrolysis reactions and mass transport considerations, the grower can navigate these growth regimes to obtain desired results.

107

Figure 3.23. Schematic of a close-coupled showerhead MOCVD.

3.4.2.5. THE OHIO STATE ASP/SI MOCVD

The reactor used for the research in this dissertation was an AIXTRON 3×2” close-coupled showerhead (CCS) reactor designed for III-V and Si materials. The schematic of such a system is shown in Figure 3.23. Both metal-organic and hydride precursors were used; both types of precursors remain unmixed in separate gas lines before entering the reactor to avoid parasitic reactions. Within the showerhead, separate plenums deliver the precursors to numerous small tubes that enter the top of the reactor.

These tubes have a density of 100 per square inch and a diameter of 0.6 mm. The purpose of these tubes is to mix the process gases evenly within the reactor. The susceptor, which supports, rotates, and heats the substrate(s), is located approximately 16 mm beneath the showerhead. With this reactor geometry, the process gases exit the showerhead vertically but then begin to move radially across the susceptor surface before exiting at the gas outlet at the perimeter. A number of publications describe how to model the hydrodynamics and growth rate when using this type of reactor [142]–[144].

108 Group III metal-organic precursors include trimethylgallium (TMGa), triethylgallium (TEGa), trimethylaluminum (TMAl), and trimethylindium (TMIn). Metal- organic dopant sources include diethylzinc (DEZn), diethyltelluride (DETe), and bromotrichloromethane (CBrCl3). Tertiarybutylphosphine (TBP) is the only metal- organic group V precursor. The other group V precursors are hydrides, including arsine

(AsH3) and phosphine (PH3). Other hydride sources include silane (SiH4) and disilane

(Si2H6).

This reactor was equipped with a LayTec EpiTT system for in situ reflectance-based monitoring of growth rate and substrate temperature. All growths were performed at a reactor pressure of 150 mbar, a total flow rate of 6000 sccm using H2 as the carrier gas, and a susceptor rotation speed of 50 rpm.

Figure 3.24. Fully processed solar cells, diodes, and test structures.

109 3.5. DEVICE PROCESSING TECHNIQUES

A variety of processing techniques were utilized to fabricate the solar cells and

tunnel junctions developed in this dissertation from epitaxial growth structures. These

techniques are discussed below; more information on these techniques can be found in

[145], [146]. Figure 3.24 is an image of a fully processed wafer with solar cells, diodes,

and test structures. The sequence in which these techniques were used to fabricate the

various devices explored are discussed within the chapters that cover their development.

3.5.1. ELECTRON BEAM EVAPORATION

Electron beam evaporation is a technique for depositing a wide range of target materials. Each target material is contained in its own crucible to avoid contamination.

The technique consists of directing an electron beam into a crucible that contains the target material to be deposited. The electron beam heats the target material, causing it to evaporate; the crucible is water-cooled to minimize contamination. The electron beam evaporation chamber is held under high vacuum, resulting in a mean free path length of particles (i.e. atoms/molecules) in the gas phase (i.e. the vacuum) that is much greater than the size of the chamber (see section 3.4.1). As a result, the evaporated metal travels in direct line-of-sight path to the sample where it is deposited. The thickness of the deposited layer is controlled with angstrom resolution using a quartz crystal monitor.

In this dissertation, this technique was used to deposit metals for making ohmic contact to the materials and devices explored within. Typically, these materials and devices were grown with a highly doped ‘contact epilayer’, or ‘cap’, designed to ensure low-resistance ohmic contact could reproducibly be made. Depending on the material

110 (e.g. GaAsyP1-y or Si) and carrier type of the contact epilayer, different metal stacks were used that consisted of a combination of metals including Ni, Ge, Au, Cr, Al, and Ti.

Specific contacts are discussed within this dissertation where appropriate.

3.5.2. RAPID THERMAL ANNEALING

Rapid thermal annealing (RTA) is a technique to anneal a sample with high temperature ramp rates (up to 100 °C per second). The sample is heated using a lamp source and is mounted on a stage designed to minimize thermal conduction pathways to ensure fast ramp rates.

In this dissertation, RTA was used for various applications. An RTA process was necessary in some cases to reduce the contact resistance of specific ohmic contacts that were deposited via electron beam evaporation. Another RTA process was used to anneal highly carbon-doped AlxGa1-xAsyP1-y epilayers to activate the carbon (see chapter 6).

3.5.3. SPIN COATER

The spin coater is a tool used to produce uniform layers of photoresist on a wafer.

The photoresist is initially a solution consisting of a polymer dispersed in a solvent. This solution is applied to the wafer surface and the wafer is spun in the spin coater at rotational speeds up to 10,000 rpm to evenly distribute the solution. The wafer can then be baked on a hot plate to evaporate the solvent, leaving behind a solid, uniform photoresist film.

In this dissertation, spin coating photoresist was performed for subsequent photolithography (section 3.5.4). It was also performed at times to apply a protective photoresist film to the frontside of a wafer to protect this surface during subsequent 111 processing to the backside of the wafer. For example, this was done when depositing the

backside contact via electron beam evaporation to prevent the frontside of the wafer from

being in direct contact with the sample mount within the tool.

3.5.4. PHOTOLITHOGRAPHY

Photolithography is a technique to print micro-and nanoscale features on a

substrate surface. This is accomplished by first selectively exposing photoresist (see

section 3.5.3) to UV light using a patterned mask. The exposed regions are chemically changed. For a positive (negative) photoresist, the exposed (unexposed) areas can be selectively etched away using a developer solution, leaving the unexposed (exposed) photoresist behind. The substrate with the patterned photoresist can then be used for further processing.

In this dissertation, photolithography was used to patter metal contacts on the top surface. After depositing a contact on a photoresist-patterned wafer, the wafer could then be submerged in a solvent such as acetone to dissolve the remaining photoresist. This also removed the metal that was deposited on top of the photoresist, leaving behind metal only in the regions where the patterned substrate surface was exposed. Photolithography was also used to pattern the substrate surface for subsequent mesa isolation. Photoresist was patterned to define and protect the surface area of a device. The mesa isolation could then be performed by etching the exposed surface material via either ICP-RIE

(section 3.5.5) or wet etching.

112 3.5.5. INDUCTIVELY COUPLED PLASMA REACTIVE-ION ETCHING

Reactive-ion etching (RIE) is a dry etching technique used to produce anisotropic etch profiles. One approach to this technique is through the use of a parallel-plate reactor where the sample substrate sits on a powered electrode and the ground electrode is attached to the opposite chamber wall. By flowing a process gas through the system and powering the substrate electrode with a radio frequency power supply (e.g. 13.56 MHz), a plasma is formed in the reactor by ionizing the process gas. This produces free electrons that accelerate in the reactor in response to the radio frequency. Whereas these electrons can conduct through the ground electrode, they collect on the wafer. This results in a negative charge on the wafer, which in turn attracts positive ions in the plasma. These ions bombard the surface, resulting in etching via chemical reactions with the substrate material and/or physical sputtering. The exact process configuration, such as the process gas chemistry, chamber pressure, reactor geometry, and radio frequency power, significantly impacts the details of the etching process but are beyond the scope of this dissertation.

In standard RIE, the radio frequency power can be increased to increase the etch rate. However, this also generates higher energy ions that can cause damage to the crystal lattice during etching. Inductively coupled plasma reactive-ion etching (ICP-RIE) is a modified version of RIE to overcome this issue. This is done by applying a separate radio frequency (i.e. 2 MHz) to a coil to induce a magnetic field within the plasma. The magnetic field increases the path length of the free electrons, which in turn increases the

113 plasma density. The higher density plasma is thus able to bombard the surface with more ions, opposed to higher energy ions, to increase the etch rate.

In this dissertation, ICP-RIE was used for mesa isolation of devices. For both solar cells and tunnel junctions, the material was etched deeper than the junction depth to define the electronic device area. The etch was performed on wafers that were patterned via photolithography (section 3.5.4). Although the regions of the sample with photoresist were protected from etching, the photoresist was slowly sputtered during the etching process. This placed an upper limit on the etch depth which depended on the photoresist type and thickness. For deeper etches on the order of 10 μm that were required for full

MJSC structures, a thicker photoresist was necessary.

3.5.6. SUPPLEMENTAL TECHNIQUES

A variety of other minor techniques were also utilized for device processing.

Optical microscopy was used throughout device processing to monitor various aspects such as the quality of a photolithographically patterned wafer. Plasma ashing was used to remove residual photoresist after developing photoresist. Wet etching using various chemistries was performed as either an alternative to ICP-RIE for mesa isolation or to selectively etch away the contact layer in between the metal grid fingers of solar cells.

Profilometry was used to measure the height of surface features with nanometer resolution in the vertical direction via a line scan. Thin film reflectometry was used to measure the thickness of photoresist films. The combination of profilometry and thin film reflectance could be used to determine the etch rate after an ICP-RIE process step.

114 CHAPTER 4:

MATERIALS AND DEVICE CHARACTERIZATION TECHNIQUES

4.1. BACKGROUND

A variety of techniques are necessary to characterize the materials and devices

explored in this dissertation, including metamorphic tunnel junctions in III-V/Si MJSCs for terrestrial applications and wide bandgap (AlzGa1-z)xIn1-xP top cells in III-V MJSCs

for space applications. This chapter summarizes the primary techniques used to

characterize these materials and devices.

4.2. MATERIALS CHARACTERIZATION TECHNIQUES

4.2.1. HIGH RESOLUTION X-RAY DIFFRACTION RECIPROCAL SPACE MAPPING

High resolution X-ray diffraction (HRXRD) reciprocal space mapping (RSM) is a technique capable of determining the in-plane and out-of-plane lattice constants of an epilayer, which can then be used to calculate parameters such as the relaxed lattice constant, strain, misfit and relaxation of the epilayer, all which were defined in chapter 3.

In addition, the composition of ternary compounds can be determined from the relaxed

115 lattice constant using Vegard’s law. This technique is therefore invaluable for

characterizing the III-V metamorphic materials and devices explored in this dissertation.

This section first explains the basic principle of X-ray diffraction via Bragg’s law, then via the Ewald sphere construction. The concept of RSMs is then explained using this construction as a visual aid.

X-rays incident upon a crystal are scattered by the atoms within the crystal and

undergo constructive interference when a specific geometric condition is met, known as

the Bragg condition. This is given by Bragg’s law in Eq. 4.1, where n is an integer (the

reflection order), λ is the X-ray wavelength, dhkl is the distance between adjacent (hkl)

planes, and θ is the angle of incidence [121].

= 2 sin Eq. 4.1

hkl Bragg diffraction is schematically shown𝑛𝑛𝑛𝑛 in 𝑑𝑑Figure 4𝜃𝜃.1, which visually shows that the

diffraction conditions of Eq. 4.1 are met when the path length difference between X-rays

scattered by adjacent (hkl) atomic planes is equal to an integer multiple of the X-ray

wavelength.

Figure 4.1. Bragg diffraction condition for X-rays incident upon a crystal.

116

Figure 4.2. Ewald sphere construction to determine diffraction conditions in reciprocal space.

An alternative approach to deriving the diffraction conditions can be done in

reciprocal space. This results in Eq. 4.2, where G is a reciprocal lattice vector, k0 is the wavevector of the incident X-ray, and k is the wavevector of the scattered X-ray [121].

= ( ) Eq. 4.2

𝟎𝟎 Since the incident and scattered X-rays𝐆𝐆 have𝐤𝐤 the− 𝐤𝐤same wavelength (due to elastic

scattering), k0 and k have the same magnitude. Similar to how Eq. 4.1 can be

schematically represented in real space using Figure 4.1, Eq. 4.2 can be schematically

represented in reciprocal space using Figure 4.2. The Ewald sphere construction can then

be used to easily visualize various diffraction conditions. The position of the Ewald

sphere is defined by k0; the origin of the Ewald sphere is the origin of k0, and k0 is the

radius of the Ewald sphere. The tip of k0 is located at the origin of reciprocal space.

Every wavevector along the radius of the Ewald sphere has the same magnitude as k0,

117 and thus represents all possible scattered wavevectors k for a given k0. However,

constructive interference will only occur when Eq. 4.2 is satisfied. This condition is

graphically met in Figure 4.2 when the circumference of the Ewald sphere intersects with

a reciprocal lattice point. To satisfy different diffraction conditions, the incident angle of

k0 can be swept across the sample. This in turn sweeps the Ewald sphere through an arc

of reciprocal space, indicated by the largest arc in Figure 4.2. Whenever the circumference of the Ewald sphere intersects with a reciprocal lattice point, the diffraction conditions are met and constructive interference will occur. Thus, the visible reciprocal lattice points within the arc represent all possible diffraction conditions that can be met for 0° ≤ θ ≤ 180° (i.e. for an X-ray beam incident from above the sample).

Note that although the diffraction conditions may be met, there is an additional factor known as the structure factor that determines the intensity of the diffracted beam.

Structure factor rules exist to determine the intensity of diffraction from a particular plane in a particular crystal system, and in some cases diffraction is forbidden or weak [121].

Experimentally, it is typical for the X-ray source to be stationary. Thus, for the diffraction condition to be met, the sample is rotated some angle ω with respect to the sample surface and the detector is rotated 2θ to meet these conditions. The angle ω equals

θ only when the (hkl) atomic plane being measured is parallel to the sample surface. It is important to keep track of these angles for subsequent analysis.

For HRXRD, high resolution implies that precautions are taken to further monochromize the X-ray beam by, for example, using channel cut crystals in the path of the incident and scattered beams. This provides the necessary resolution to enable the

118

measurement of adequet RSMs. Reciprocal space mapping is the process of scanning ω,

2θ, or ω-2θ to map out a portion of reciprocal space. The paths mapped out by these three scans are shown by the three black arrows in Figure 4.3.

Consider the example of an epilayer grown on top of a substrate where the epilayer has a slightly larger lattice constant and is thin enough that the incident X-ray beam can sample both layers (i.e. the epilayer is partially transparent). The larger (red) and smaller (black) reciprocal lattice points in Figure 4.3 then represent the substrate and epilayer, respectively. By scanning, for example, ω and ω-2θ in a raster pattern in the vicinity of the 224 reciprocal lattice points, a 224 RSM can be constructed (outlined in

Figure 4.3 around the points labeled 224).

The in-plane and out-of-plane lattice constants can be extracted through the use of a symmetric scan such as an 004 RSM and an assymetric scan such as a 224 RSM. The symetric scan extracts the tilt of the epilayer. Once tilt is accounted for, the assymetric 119 scan can be used to extract the in-plane and out-of-plane lattice constants of the epilayer from its (tilt-corrected) in-plane and out-of-plane reciprocal lattice vector components.

These lattice constants can then be used to calculate strain, misfit, and relaxation of the epilayer (see chapter 3). Further information on this method of using symetric and assymetric RSMs is provided in [147].

4.2.2. PHOTOLUMINESCENCE

The photoluminescence characterization technique spectroscopically measures the

emission of light from a semiconductor sample where carriers have been optically excited

(by, for example, a high-energy laser) and subsequently undergo radiative recombination.

This is a powerful technique for characterizing the bandgap or other near-bandgap emission, shallow impurity emission, and deep level emission, although characterizing some of these properties requires low temperature measurements as low as 2 K [148].

In this dissertation, room temperature photoluminescence has primarily been used to characterize the bandgap of direct bandgap III-V semiconductors. Determination of the bandgap of relaxed quaternary alloys such as (AlzGa1-z)xIn1-xP was a primary use of this

technique. Due to having four elements, the composition of quaternaries is not uniquely

defined by the lattice constant alone. Consider a bandgap vs. lattice constant chart;

whereas ternaries are defined by a tie-line, quaternaries are defined by an area

(composition space). Thus, a vertical line through this composition space of the

quaternary defines the possible compositions at a given lattice constant. By determining

the bandgap via photoluminescence and the lattice constant via XRD, the exact

composition of the quaternary can be determined. It is worth noting that if the quaternary

120 is not fully relaxed, residual strain shifts the bandgap and thus strain also needs to be

accounted for if determining the composition of a strained quaternary [149].

4.2.3. HALL EFFECT

The Hall effect is a technique that measures various electronic properties of a slab

of semiconductor (such as an epilayer), including carrier type, majority carrier

concentration, and Hall mobility. These properties are important for calibrating the

materials use in the solar cells and tunnel junctions developed in this dissertation.

The Hall effect can be explained with the aid of Figure 4.4. If a magnetic field is

applied to a slab of semiconductor material that has current flowing through it, carriers

are deflected due to the Lorentz force. This is defined in Eq. 4.3, where F is the force on charge q that is moving at a velocity v due to a magnetic field B.

= × Eq. 4.3

𝐅𝐅 𝑞𝑞 𝐯𝐯 𝐁𝐁

Figure 4.4. Schematic of the Hall effect where the magnetic field is applied in the z direction (orthogonal to plane of image). 121 If the magnetic field is applied in the z direction (Bz) and the current density is flowing in

the x direction (Jx) as shown in Figure 4.4, carriers with a velocity (vx) will be deflected

in the y direction and generate a Hall voltage (VH), or electric field (EH), in the y

direction. The carriers continue to deflect until the force due to EH balances the force due to Bz. Based on this phenomenon, an equation can be derived for the Hall coefficient

(RH), a measurable quantity, defined in Eq. 4.4 [150].

= Eq. 4.4 𝐸𝐸H 𝑅𝑅H 𝐽𝐽x𝐵𝐵z The Hall coefficient can also be related to carrier concentrations with the use of Eq. 4.5

[151], where r is the scattering factor between 1 and 2, b = μn/μp (the ratio of the electron

mobility to the hole mobility), n is the electron concentration, and p is the hole concentration:

= Eq. 4.5 ( 2 ) 𝑟𝑟�𝑝𝑝−𝑏𝑏 𝑛𝑛� 2 𝑅𝑅H 𝑞𝑞 𝑝𝑝+𝑏𝑏𝑏𝑏 For n- and p-type material, Eq. 4.5 reduces to = and = , respectfully. 𝑟𝑟 𝑟𝑟 𝑅𝑅H − 𝑞𝑞𝑞𝑞 𝑅𝑅H 𝑞𝑞𝑞𝑞 Therefore, the carrier type and concentration can be determined by the sign and

magnitude of RH, respectfully. If the resistivity (ρ) of the material is known, then the Hall

mobility can be determined with the use of Eq. 4.6 [150]:

= Eq. 4.6 𝑅𝑅H 𝜇𝜇 𝜌𝜌 To fabricate an epilayer for characterization via the Hall effect, the layer can be

grown on a semi-insulating substrate to electrically isolate the epilayer for measurement.

It is also possible to grow the epilayer on a substrate with the opposite carrier type. This

creates a p-n junction to electrically isolate the epilayer from the substrate. This technique

was used frequently within this dissertation, particularly for metamorphic epilayers 122 grown on graded buffers since it is easier to dope the graded buffer with the opposite carrier type rather than semi-insulating. However, care must be taken when using this technique to ensure leakage current through the junction is not so high that it removes the electrical isolation between the epilayer and substrate [152].

The Hall effect was used extensively in this dissertation, particularly for all the doping studies performed for metamorphic tunnel junction development. Although the capacitance-voltage techniques discussed in section 4.2.4 below also measure carrier concentration, they are not as accurate as Hall for the high doping concentrations explored for the tunnel junctions since the highly doped samples have a high conductance.

4.2.4. CAPACITANCE-VOLTAGE

The capacitance-voltage (C-V) measurement is a versatile technique capable of extracting a wealth of information about semiconductor materials and devices [151]. For this dissertation, the primary use was to extract doping concentration and doping profiles for materials calibration. This section begins with the theory behind this measurement, and then describes the specific C-V techniques that were uses, including standard C-V on solar cell diodes, electrochemical capacitance-voltage, and mercury probe.

The principle of C-V is based on how the width of the space charge region (W) of a reverse biased Schottky diode or p-n junction can be modulated with voltage. For a

Schottky diode, the depletion region is essentially completely in the semiconductor, whereas for a p-n junction it can extend into both sides. However, for a one-sided diode such as the n+/p solar cells studied in this dissertation, the depletion region is primarily

123 within the lightly doped side (i.e. the base of a solar cell). Thus, the analysis below holds

true for Schottky diodes and p-n junctions characterized within this dissertation. This

analysis is based on those in [96], [151].

To perform the C-V measurement, a fixed DC voltage is first applied to reverse

bias the junction to define W. This is given by Eq. 4.7, where KS is the dielectric

constant, ϵ0 is the permittivity of free space, q is the electric charge, NB is the doping

concentration in the semiconductor layer of a Schottky diode or the lightly doped side of

a one-sided p-n junction, Vbi is the built-in voltage, and VA is the applied bias.

= ( ) Eq. 4.7 2𝐾𝐾S𝜖𝜖0 𝑊𝑊 � 𝑞𝑞𝑁𝑁B 𝑉𝑉bi − 𝑉𝑉A A small amplitude AC voltage (~10 kHz to 1 MHz frequency, ~10 to 20 mV amplitude

[151]) is then applied to modulate a small amount of charge at the edge of the depletion

region. Although this also slightly modulates W, the small amplitude of the AC signal

results in a correspondingly small change in W and the situation can be treated like a

parallel plate capacitor. The diode capacitance (CJ) is thus given by Eq. 4.8, where A is the area.

= Eq. 4.8 𝐾𝐾Sϵ0𝐴𝐴 J 𝑊𝑊 By measuring capacitance as a function 𝐶𝐶of applied DC voltage and manipulating Eq. 4.7 and Eq. 4.8, NB can be determined as a function of W using Eq. 4.9 to give the doping

profile, where W is determined by rearranging Eq. 4.8.

( ) = 3 Eq. 4.9 𝐶𝐶 2 𝑁𝑁B 𝑊𝑊 𝑞𝑞𝐾𝐾S𝜖𝜖0𝐴𝐴 𝑑𝑑𝑑𝑑⁄𝑑𝑑𝑑𝑑 Experimentally, this measurement can be performed in a variety of ways

depending on the required doping information. For fully processed solar cells, it is 124 possible to perform C-V on the device to extract the doping concentration and profile of

the base layer. However, it is often necessary to determine the doping concentration in a

calibration layer where full device processing is not practical. In these cases, the mercury

probe technique is very useful. This technique can be used to form a temporary Schottky

barrier with an epilayer using liquid mercury [151]. A well-defined small-area mercury contact acts as the Schottky contact, and the back contact is made via either an adjacent large-area mercury contact that acts as an Ohmic-like contact or the sample stage. The

C-V measurement can then be performed by applying the bias between the small-area

contact and back contact.

Although the standard C-V technique (on diodes or via mercury probe) measured

doping as a function of depth (W), the range of depths is limited by breakdown at high

reverse bias. To measure the doping profile at greater depths, one method is to manually

etch the sample in between C-V measurements. For such a technique, the etch depth must

be kept track of. Although this approach is unrealistic to measure the doping profile as a

continuous function of depth, it was found to be useful for characterizing multilayer

structures where the epilayers of interest were separated by spacer layers that could act as

selective etch stops. For example, consider a structure with four uniformly doped n-GaAs

epilayers of different doping, separated by p-Ga0.51In0.49P spacer layers. After measuring

C-V on the top n-GaAs epilayer, wet etching could be used to selectively etch the top

n-GaAs epilayer, then a different chemistry could be used to selectively etch the

p-Ga0.51In0.49P spacer layer. This exposes the second GaAs epilayer, which can then be

measured, and so on. Mercury probe C-V can optionally be measured on the

125 p-Ga0.51In0.49P spacer layer as a confirmation that the etch reached the spacer layer by

measuring the polarity change.

If a continuous doping profile as a function of depth is desired, the

electrochemical capacitance-voltage (ECV) technique can be used. This technique

involves forming a Schottky contact using an electrolyte [153]. The typical C-V measurement can be performed when this electrolyte-semiconductor Schottky junction is reverse biased. The sample can then be etched by dissolving the semiconductor, which requires the presence of holes. This is achieved in p-type material with forward bias and in n-type material with illumination and reverse bias. Since both the C-V measurement and etching process are performed using the same electrolyte- semiconductor Schottky junction, these processes can be alternated to profile the doping concentration to theoretically unlimited depth. However, a variety of issues such as increasing roughness of the etch crater with increasing etch depth place practical limits on the technique. In this dissertation, this technique was used to characterize the doping profile of multilayer structures up to 5 μm thick.

4.2.5. SCANNING ELECTRON MICROSCOPY TECHNIQUES

Electron beam induced current (EBIC) is a scanning electron microscopy (SEM)

based technique that provides a means to measure various properties of the epilayers

within a junction device such as a solar cell. These properties include the minority carrier

diffusion length [102], [154], [155] and threading dislocation density (TDD) [156]–[158].

126

Figure 4.5. EBIC image of a metamorphic Ga0.63In0.37P solar cell. The dark circular spots occur due to recombination in the vicinity of threading dislocations.

Within this dissertation, EBIC was used to characterize TDD in metamorphic III-V

devices to correlate device performance with TDD.

To measure TDD via EBIC, a plane-view SEM image of a junction device is

captured using the signal generated by the device rather than one of the standard SEM

detectors. The incident electron beam generates electron-hole pairs within the device and minority carriers that diffuse to the junction are then collected and contribute to the signal. However, if the minority carriers are within the vicinity of a threading dislocation

(i.e. within approximately a diffusion length), they will likely recombine and the signal in that region of the image will be weaker. This results in a dark spot where the threading dislocation is located. By imaging a large enough area, the TDD can be calculated. An example of an EBIC image of a metamorphic Ga0.63In0.37P solar cell is shown in Figure

4.5. Note that the lines of contrast in the background are due to misfit dislocations, which can also produce contrast in EBIC images when in the vicinity of the depletion region

[159], [160].

127 Electron channeling contrast imaging (ECCI) was another SEM technique that aided in metamorphic materials development [161]–[163]. This technique enables the characterization of various crystal defects such as threading dislocations, misfit dislocations, stacking faults, and anti-phase domains. Although transmission electron microscopy (TEM) is often used for characterizing these defects, long sample preparation time results in low sample throughput. ECCI, on the other hand, is a high-throughput technique that is possible in most SEMs equipped with a backscattered electron detector.

Performing ECCI in the SEM enables the characterization of a large area over a single sample, making it attractive for large-area solar cell devices.

4.2.6. ATOMIC FORCE MICROSCOPY

Atomic force microscopy (AFM) is a technique that can produce topographic images of a sample surface at the atomic scale. The basic principle is that a probe with a sharp tip is scanned over the sample and measures the height of surface features [164].

The tip is controlled by piezoelectric transducers, enabling angstrom resolution in the vertical direction. By scanning the tip in a raster pattern, the topographic image can be formed. This is fundamentally different than light or electron microscopes since nothing is focused on the sample. AFM was used within this dissertation to extract information such as the surface morphology and surface roughness, both of which are useful for characterizing epilayers and ensuring high-quality epitaxial growth.

4.2.7. NOMARSKI MICROSCOPY

Nomarski imaging, or differential interference contrast imaging, is an optical microscopy technique to enhance the contrast of surface features and give a three- 128 dimensional appearance to the surface [165]. This is accomplished by splitting incident light into two orthogonally polarized beams, passing the beams through the sample at slightly separated lateral positions, merging the beams, then using an analyzer (polarizer) to enable both beams to interfere with one another. Since the beams pass through the sample at slightly different lateral positions, differences in optical thickness (e.g. a difference in surface roughness) of the two positions will alter the degree of interference between the two beams and thus create contrast. Nomarski imaging was used within this dissertation to analyze the quality of epilayers and observe surface features such as cross- hatch that results from the misfit network of metamorphic epilayers.

4.3. DEVICE CHARACTERIZATION TECHNIQUES

4.3.1. CURRENT-VOLTAGE

Current-voltage (I-V), or current density-voltage (J-V), characterization is an

essential technique to understand the fundamental operation of solar cells, MJSCs, and

tunnel junctions. Several of the key equations used to describe the performance of these

devices were covered in chapter 2. Here, details on various experimental current-voltage

techniques for characterizing these devices are discussed.

4.3.1.1. DARK CURRENT-VOLTAGE

The J-V behavior of a solar cell can be modeled to determine its various diode

properties. To experimentally measure this behavior, J-V measurements must be performed in the dark to achieve the high level of sensitivity required to observe these

129 properties. In addition to its diode properties, dark J-V also provides information on shunt

and series resistance.

Although the information provided by dark J-V is useful, care must be taken when using it to predict the performance of a solar cell under illumination (see section 4.3.1.2).

Often times, the principle of superposition is assumed, which states that the illuminated

J-V curve of the solar cell is the sum of the dark J-V curve and the short-circuit photocurrent [166]. When this holds true, the performance under illumination can accurately be predicted from dark J-V measurements. However, various mechanism may prevent superposition from holding true [167].

Besides solar cell characterization, dark J-V is also the primary technique used in this dissertation for characterizing tunnel junctions. From the dark J-V curve of a tunnel junction, the electronic figures of merit (peak current density and resistance-area product) can be extracted. All tunnel junction dark J-V measurements were performed using a forward voltage sweep. Series resistance can cause an instability in the J-V curve in the negative differential resistance region of the tunnel junction, and thus the forward sweep ensured that the peak tunneling current could be extracted [119].

4.3.1.2. ILLUMINATED CURRENT-VOLTAGE

Illuminated current-voltage (LIV) measurements provide the basic parameters of

a solar cell, including the short-circuit current density (JSC), the open-circuit voltage

(VOC), the fill factor (FF), and the efficiency (η). The measurement is performed by running a current-voltage measurement while the solar cell is illuminated by a light source.

130 The light source is typically calibrated to match one of the standard solar spectra,

such as AM0 or AM1.5G. For single junction solar cells, a single-zone solar simulator can be used, which only contains one light source. Although the spectrum of the light source may not exactly match the solar spectrum on interest, the light source intensity can be calibrated in various ways to ensure the correct JSC is measured. However, more care

must be taken when measuring MJSCs. Consider a dual-junction solar cell where the top and bottom sub-cell absorb blue and red light, respectively. If the spectrum of the light source is blue-shifted compared to the solar spectrum of interest, then the top cell will always produce a higher photocurrent than expected and vice versa with the bottom cell.

Adjustments to the light source intensity alone can never provide the correct amount of photocurrent to each sub-cell simultaneously. An alternative approach is to use a multizone solar simulator that has multiple light sources [168]. Such a simulator may contain one light source per sub-cell. The spectral band of a given light source is selected such that it is absorbed in its corresponding sub-cell. Using this approach, the intensity of each light source can be adjusted independently, allowing for fine tuning to better match the shape of the solar spectrum of interest.

To calibrate the intensity of the zone(s) of the solar simulator, various methods exist. One method is to use a commercially available calibration solar cell. Parameters such as JSC are known for this cell, and the intensity of the zone(s) can be adjusted

accordingly. Regardless of the number of zones, it is ideal to have a calibration cell with

the same bandgap as the test solar cell to ensure both devices absorb the same portion of

the spectrum. For a multi-zone simulator, it is thus ideal to have calibration cells for each

zone and at the bandgaps of the sub-cells within the MJSC under testing. An alternative

131 method for calibrating the light sources is with the use of QE, which can be integrated

with the solar spectrum of interest to calculate JSC (see section 4.3.1.2) [169].

4.3.1.3. JSC-VOC

The JSC-VOC measurement was originally developed as a method to estimate the

dark J-V performance of a solar cell in the absence of series resistance [170]. The

technique is performed by recording the JSC and VOC values of a solar cell at various light intensities and constructing a J-V curve from this data. Since VOC is not impacted by

series resistance, the series resistance is eliminated from the curve. However, JSC-VOC is

also capable of altering other aspects of the J-V curve. For example, in solar cells where

Shockley-Read-Hall recombination is a function of light intensity, the JSC-VOC will be

displaced from both the dark J-V and LIV curves [167]. In this dissertation, JSC-VOC

curves were used to estimate the performance of (AlzGa1-z)xIn1-xP solar cells in the

absence of voltage-dependent carrier collection.

4.3.2. QUANTUM EFFICIENCY

Quantum efficiency (QE) is a solar cell characterization technique that quantifies

the efficiency that photons of wavelength λ0 generate electron-hole pairs that are subsequently collected by the solar cell. Two forms of quantum efficiency can be defined; the external and internal quantum efficiency (EQE, IQE). EQE accounts for external losses due to transmission T(λ0) and reflection R(λ0), whereas IQE only accounts

for photons absorbed by the solar cell. EQE(λ0) is defined by Eq. 4.10 [171], where

JL(λ0) is the photocurrent density and Φ(λ0) is the photon flux at wavelength λ0.

132 ( ) EQE( ) = ( ) Eq. 4.10 𝐽𝐽L 𝜆𝜆0 𝜆𝜆0 𝑞𝑞⋅𝛷𝛷 𝜆𝜆0 IQE is then defined by Eq. 4.11.

( ) QE( ) = I ( ) ( ) Eq. 4.11 EQE 𝜆𝜆0 𝜆𝜆0 1−𝑇𝑇 𝜆𝜆0 −𝑅𝑅 𝜆𝜆0 The IQE is useful for understanding the upper limit of collection if transmission and

reflection are minimized. Transmission can be minimized by ensuring the absorber layer

is thick enough for complete absorption, and reflectance can be minimized with the use

of an anti-reflection coating. It is worth pointing out that the IQE measurement described

above is a function of wavelength, and thus photogeneration occurs throughout the full

thickness of the device. This prevents the IQE of each individual layer from being

extracted independently. To determine the IQE of individual layers, IQE must be

calculated using another method based on collection probability and generation rate. This

was used as a powerful modeling technique in section 7.2. However, as discussed in

section 2.3.1, to determine this experimentally a specialized technique such as cross- sectional EBIC is necessary, which was not explored in this dissertation.

Quantum efficiency is valuable for diagnosing how efficient carrier collection is in various regions of the solar cell. This is possible since photons of different wavelengths have different absorption coefficients (see chapter 2). Short wavelength photons have higher absorption coefficients and thus on average get absorbed at the frontside of the solar cell, whereas long wavelength photons have lower absorption coefficients and thus on average get absorbed at the backside of the solar cell. Figure 4.6 plots the EQE and IQE of a GaAs0.9P0.1 solar cell as an example. At short wavelengths,

133 1 0.9 0.8 0.7 0.6 0.5 0.4

Quantum EfficiencyQuantum 0.3 0.2 EQE IQE 0.1 0 350 450 550 650 750 850 Wavelength (nm)

Figure 4.6. EQE and IQE of a GaAs0.9P0.1 solar cell.

the QE drops to zero due to absorption near the top surface where surface recombination

is likely. At long wavelengths, the cut-off is determined by the bandgap of the solar cell.

Another useful aspect of QE is that it enables the calculation of the short-circuit

current density (JSC) of the solar cell under an arbitrary solar spectrum. For example,

Eq. 4.12 can be used to calculate JSC under the Φspec spectrum by integrating the EQE

with Φspec over the range of relevant wavelengths.

= EQE( ) ( ) Eq. 4.12

SC spec As mentioned in section 4.3.1.2𝐽𝐽 , this−𝑞𝑞 is∫ one of𝜆𝜆 several⋅ 𝛷𝛷 ways𝜆𝜆 𝑑𝑑 to𝑑𝑑 calibrate the LIV

measurement.

The entire shape of the QE can be modeled by accounting for the optical and

electronic properties of the various layers. This in turn provides information such as the

minority carrier diffusion lengths in the emitter and base layers, as well as surface and

interface recombination velocities. Such an approach was used to model the 134 (AlzGa1-z)xIn1-xP solar cells discussed in chapter 8, where more specific details on that

model can be found. Voltage-dependent QE can also be measured to provide additional

information about the solar cell [172], [173], although all QE measurements in this

dissertation were performed at short-circuit conditions.

To characterize the quantum efficiency of a 2-terminal MJSC, additional factors must be accounted for to extract the quantum efficiency of the individual sub-cells. This is done by applying appropriate light and voltage biasing [174], [175]. If light biasing is applied such that the sub-cell under measurement becomes the current limiter, then chopped monochromatic light can be used to measure the quantum efficiency of this sub- cell. This is because the chopped monochromatic light produces an AC signal when at wavelengths that the sub-cell under measurement responds to. The AC signal is superimposed on the DC signal that is caused by the light biasing. In this dissertation, light biasing was performed via a combination of high-power LEDs to selectively bias all sub-cells besides the sub-cell under measurement (i.e. the sub-cell under measurement was effectively in the dark).

When only light biasing is performed and the MJSC is kept in short-circuit conditions, the light biased sub-cells will be operating at their open-circuit voltage. Since the entire device is at short-circuit conditions, this results in the sub-cell under measurement to be reverse biased. Since QE can vary with voltage, it is desirable to ensure that each sub-cell is measured when it is at short-circuit conditions (opposed to the entire MJSC at short-circuit conditions). To achieve this state, the open-circuit voltage of the MJSC can be measured when only the light biasing is applied. When the MJSC is in short-circuit conditions under light bias, the sub-cell under measurement will be reverse

135 biased by the same magnitude as the open-circuit voltage of the MJSC when under light

bias. Therefore, starting with the MJSC in short-circuit conditions, applying a positive bias equal to the previously-measured open-circuit voltage of the MJSC will bring the sub-cell under measurement into short-circuit conditions. This happens because the sub- cell under measurement is in a high-resistance reverse biased state, whereas the light biased sub-cells are in a low-resistance forward biased state. Thus, the voltage bias essentially completely drops across the sub-cell under measurement.

136 CHAPTER 5:

MBE-GROWN METAMORPHIC TUNNEL JUNCTIONS

5.1. BACKGROUND

This chapter focuses on the development of tunnel junctions (TJ) grown via

molecular beam epitaxy (MBE) for use in the MBE-grown Ga0.57In0.43P/GaAs0.9P0.1/Si

triple-junction solar cell (MBE 3J) approach that was discussed in chapter 2. The structure of the MBE 3J is shown in Figure 5.1, highlighting the need for both a lower TJ

Figure 5.1. Structure of the MBE 3J, highlighting the need for lower and upper TJs. 137 between the GaAs0.9P0.1 and Si sub-cells and an upper TJ between the Ga0.57In0.43P and

GaAs0.9P0.1 sub-cells. Since the design specifications of the MBE 3J target operation

under high concentration (i.e. 500× AM1.5D), this led to the need for high-performance

lower and upper TJs that must each meet specific target values for various TJ figures of

merit. The full analysis on determining target values for these figures of merit was

performed in chapter 2. However, recall that the TJ figures of merit are:

1. Low resistance-area product (RA [Ω cm2])

-2 2. High peak tunneling current (JP [A cm⋅ ])

3. Wide, optically transparent bandgap⋅ (EG [eV])

4. Internally lattice-matched to III-V sub-cell(s) (a [Å])

Targeted values for these figures of merit are summarized in Table 5.1. To ensure that the

absolute efficiency loss of the MBE 3J due to RA is ≤ 0.1%, the maximum allowed total

RA of both TJs is 1.06×10-3 Ω cm2. The values in Table 5.1 assume the RA values of each

TJ are equal and thus half of this⋅ total RA. The minimum JP target is defined as 5× the

short-circuit current density (JSC) to avoid failure of the TJ when operated within the

MBE 3J. The minimum bandgap target ensures the TJ is optically transparent, and the

Table 5.1. Target values of TJ figures of merit for the TJs within the MBE 3J operated at 500× AM1.5D. MBE 3J (500× AM1.5D) Figure of Merit Lower TJ Upper TJ Max. RA (Ω cm2) 5.3×10-4 5.3×10-4 -2 Min. JP (A cm ) 32.5 32.5 Min. EG (eV)⋅ 1.55 1.95 Lattice Constant⋅ (Å) 5.633 5.633

138 constraint of internal lattice-matching to the GaAs0.75P0.25 top cell defines the target lattice constant of the metamorphic TJ.

As indicated in Table 5.1, the only difference in requirements between the lower

/ and upper TJs is the minimum bandgap. Since the tunneling probability has an ( ) 3 2 − 𝐸𝐸G dependence on bandgap (see chapter 2) [176], it was hypothesized that it should𝑒𝑒 be easier

to demonstrate a high-performance TJ with a minimum bandgap of 1.55 eV compared to

1.95 eV to achieve the targeted RA and JP values. Thus, design began on the lower TJ,

which was then modified to meet the requirements of the upper TJ. The development of

both the lower and upper TJs are discussed in the sections below.

5.2. MBE 3J LOWER TUNNEL JUNCTION

To meet both the 1.55 eV minimum bandgap and 5.633 Å lattice constant

requirements for the lower TJ, initial work focused on the development of a metamorphic

GaAs0.9P0.1 homojunction TJ. This is the same composition and bandgap as the middle

sub-cell, making it the most obvious choice for the fabrication of the lower TJ.

5.2.1. APPROACH

All GaAs0.9P0.1 (EG = 1.55 eV) materials and device structures were grown via

solid-source MBE in a Varian Gen II system with valved As2 and P2 cracker sources.

Doping sources were Si and Be for n- and p-type doping, respectively. The typical base pressure in the growth chamber was < 2×10-10 Torr. All substrate growth temperatures

(TG) reported were measured via infrared pyrometry, calibrated to the GaAs native oxide

desorption temperature. Constituent molecular beam fluxes were measured using a beam

equivalent pressure ion gauge mounted on the backside of the sample manipulator/heater 139 assembly, and all beam flux values and/or V:III ratios reported are with respect to those

measurements. Growths were monitored in-situ via reflection high-energy electron

diffraction (RHEED).

To maximize the TJ performance, growth conditions were optimized with respect

to carrier concentrations via impurity doping with Si and Be. Due to the relative

proximity in both bandgap and composition/lattice constant of the target metamorphic

GaAs0.9P0.1 material, this optimization was initially performed via the growth of

homoepitaxial GaAs. Additionally, the same growth and fabrication conditions were used

for both GaAs and GaAs0.9P0.1 test devices to ensure fair comparison.

All growths (metamorphic and lattice-matched) utilized n-type (100)-oriented

GaAs wafers, intentionally offcut 6° toward the nearest (111)A. This offcut was selected to remain consistent with the requirements for III-V epitaxy on Si, as this is necessary to prevent the formation of anti-phase domains in such structures [80]. All GaAs0.9P0.1 TJs

and test structures were grown via MBE on step-graded (~0.18% misfit/µm) metamorphic GaAs0.9P0.1/GaAsyP1-y/GaAs virtual substrates that were grown by

metalorganic chemical vapor deposition (MOCVD) in a close-coupled showerhead style reactor. Although the goal is the integration of such device structures with Si, this work focused on TJs that possess the appropriate GaAs0.9P0.1 composition and lattice constant

and made use of the more convenient GaAs-based virtual substrates compared to Si- based. The use of the high-throughput MOCVD system, rather than the research-level

MBE, made such substrate production even more convenient. The GaAs0.9P0.1 virtual

substrates possessed a residual threading dislocation density (TDD) of approximately

5×105 cm-2 as measured by electron beam induced current (EBIC) imaging. Triple-axis

140 X-ray diffraction (XRD) reciprocal space map (RSM) analysis of the as-grown virtual

substrates indicated that the terminal GaAs0.9P0.1 layer was typically relaxed to 80-90%,

with a small level of residual tensile strain.

Doping level test structures were characterized via secondary ion mass

spectroscopy (SIMS) to verify impurity levels, as well as electrochemical capacitance-voltage (ECV) measurements to characterize realized carrier concentrations

as a function depth for various growth parameters. MBE-grown TJ test devices with a total thickness of 50 nm (25 nm p-type and n-type each) were fabricated using a standard

GaAs-based process involving a wet etch for the mesa isolation and standard III-V metal contact stacks (see chapter 3) [32]. Current density versus voltage (J-V) measurements on the test devices were performed at 300 K using a Keithley 2400 source-measurement unit. For tunnel junctions integrated with solar cells, external and internal quantum efficiency (EQE, IQE) and reflectance measurements of the solar cells were performed on a custom-built, small spot spectral response system. Illuminated J-V (LIV) measurements were performed on the solar cells with a single-zone, Xe lamp-based solar simulator (OAI TriSOL) filtered for AM1.5G.

5.2.2. RESULTS

5.2.2.1. DOPING STUDIES

Initial doping studies, with the goal of achieving maximized carrier

concentrations, were performed via homoepitaxial growth of GaAs as a starting

condition, with the anticipation that similar behavior would be observed in the low-P content GaAs0.9P0.1 composition of interest. Achievement of a sufficiently high n-type

141

carrier concentration via Si doping at typical MBE growth conditions was anticipated to

be difficult due to its well-known amphoteric behavior. This can limit the highest

achievable electron concentration to 6×1018 cm-3 [177], a value wholly insufficient for

high-performance TJs.

To overcome this intrinsic limitation, somewhat nontraditional MBE growth

conditions were employed. Consistent with literature reports, reduced growth temperature

and increased V:III ratio resulted in measured electron concentrations as high as

2×1019 cm-3 [178]. Figure 5.2 presents comparisons between SIMS and ECV

measurements of multilayered test structures, with nominal Si doping of 2×1019 cm-3, exploring growth temperature and V:III ratio. These results demonstrate the impact these growth parameters have on realized n-type carrier concentrations. Through these measurements it was determined that the optimum practically-achievable growth

142 conditions to achieve maximum n-type carrier concentration (via Si doping) were

TG = 500 °C and V:III = 30. Slight further improvement of Si activation may indeed be achievable at even lower growth temperatures, higher V:III ratios, or different growth

rates. However, issues such as low-temperature pyrometer accuracy, generally usable group-V source flux ranges, temperature-dependent As:P incorporation kinetics, and low- temperature material quality concerns provide practical limitations for this study. These growth conditions are significantly different from traditional growth conditions for

18 -3 nominally high (ND 5×10 cm ) doped GaAs (TG = 585 °C and V:III = 18). Similar studies were performed≳ for p-type doping with Be at a nominal doping level of

3×1019 cm-3, but ECV results indicated that Be is effectively completely activated

regardless of growth conditions (at least within the scope of those considered here). This

is consistent with the literature [179].

To confirm the validity of these optimized growth conditions for the metamorphic

material of interest, 1.0 µm layers of GaAs0.9P0.1, with nominal n-type (Si) doping of

19 -3 2×10 cm , were grown on GaAs0.9P0.1/GaAsyP1-y/GaAs virtual substrates at both the

“traditional” and optimized conditions for high doping; carrier concentration was

characterized via van der Pauw geometry Hall measurements. The electron concentration

resulting from the “traditional” growth conditions was found to be 5.2×1018 cm-3, while

the optimized growth conditions resulted in a concentration of 1.2×1019 cm-3. However, it

must be noted that these values were extracted using an assumed Hall scattering factor of

one, which in reality can lie between 1 and 2 [180]. Since the carrier concentration scales

proportionally with the scattering factor, the true carrier concentration can be up to 2×

greater. Therefore, while the Hall results certainly show an improvement due to the

143 optimized growth conditions, the actual carrier concentration values are likely to be higher, and thus closer to the previously-measured GaAs ECV results. As will be discussed later, device modeling is in stronger agreement with ECV values, consistent with a scattering factor greater than one in this case. Nonetheless, these Hall results still indicate a significant improvement in carrier concentration with the optimal growth conditions. Although they are not quantitatively comparable to previous ECV results on

GaAs samples, they are still in agreement with the intended goal of improving growth conditions.

5.2.2.2. TUNNEL JUNCTION CHARACTERIZATION

For verification of the applicability of the doping study results, prototype homoepitaxial GaAs TJ structures were grown at the new quasi-optimal growth

Contact 100 p+-GaAs(P) Cap p++-GaAs(P) TJ - 25 nm ) 2 80 n++-GaAs(P) TJ - 25 nm n+-GaAsP SGB n+-GaAs Substrate 60 Contact

GaAs Current Density (A/cm 20 GaAsP-A GaAsP-B GaAsP-C 0 0.0 0.5 1.0 1.5 Voltage (V)

fabricated into 60×60 μm2 diodes. The inset in Figure 5.3 presents a schematic of the

device structure. J-V results for a typical GaAs TJ are also presented in Figure 5.3. Note that the instability of the J-V in the negative differential resistance (NDR) region is a result of regularly-observed bias oscillations, which do not impact the extraction of the

-2 critical figures of merit [115]. The GaAs TJ test devices yielded JP = 50.0 A·cm at

0.09 V and RA = 8.7×10-4 Ω·cm2 at 0 V, sufficient for operation of the MBE 3J under

reasonably high optical concentrations. Although these results do not meet the targeted

RA value of the lower TJ, it was determined that this performance was sufficient to justify

transitioning the TJ to the target lattice constant. Subsequently, the studies on GaAs were

applied to a series of GaAs0.9P0.1 TJs lattice-matched to GaAs0.9P0.1/GaAsyP1-y/GaAs

virtual substrates. An initial GaAs0.9P0.1 TJ was grown using identical nominal doping

and growth conditions as the GaAs TJ for direct comparison, with an interpolated 30:1

equivalent total group-V (As2 + P2) flux, which also accounts for the relative As2 versus

P2 ionization sensitivity. The associated J-V measurements, presented in Figure 5.3

-2 (GaAsP-A), reveal a significant reduction in performance, with JP = 9.0 A·cm at 0.08 V

and RA = 3.3×10-3 Ω·cm2 at 0 V.

Further GaAs0.9P0.1 TJ test structure growths, as displayed in Figure 5.3

(GaAsP-B and -C), consisted of modifications to the original (GaAs, GaAsP-A) doping

levels with the intention of improving the metamorphic TJ performance. GaAsP-B used

n- and p-type doping levels of 2×1019 and 6×1019 cm-3, respectively, to test the capability

of achieving higher p-type doping levels, as seen in literature [181]. Another structure

145 Table 5.2. GaAs and GaAs0.9P0.1 homojunction tunnel junction results. -3 -3 -2 2 Structure n (cm ) p (cm ) JP (A cm ) RA (Ω cm ) GaAs 2×1019 3×1019 50.0 8.7×10-4 GaAsP-A 2×1019 3×1019 9.0⋅ 3.3×10⋅ -3 GaAsP-B 2×1019 6×1019 103.9 4.5×10-4 GaAsP-C 1×1019 6×1019 2.6 1.3×10-2

(GaAsP-C) used n- and p-type doping levels of 1×1019 and 6×1019 cm-3, respectively, to

ascertain whether the n-type material was acting as the overall limiting agent.

Results from the subsequent TJs showed that an increase in the p-type doping

level, as in GaAsP-B, resulted in significantly improved performance, yielding a JP of

103.9 A·cm-2 at 0.08 V and minimum RA of 4.5×10-4 Ω·cm2 at 0 V. These results

correspond to the highest quality homojunction TJ that was fabricated. Reducing the

n-type doping (GaAsP-C) resulted in substantially degraded performance, with a JP of

2.6 A·cm-2 at 0.08 V and minimum RA of 1.3×10-2 Ω·cm2 at 0 V. This trend suggests that

the original n-type doping level is most likely not detrimentally amphoteric but is nonetheless likely the limiting agent in this structure. These results are summarized in

Table 5.2.

Judging by the results presented in Figure 5.3, the doping profile of GaAsP-B yields the highest performance homojunction TJ of the structures explored and resulted in an excellent metamorphic TJ capable of integration into the MBE 3J. This device also meets the targeted values of all the figures of merit of the lower TJ, a very promising

+ result. As a test, a non-optimized GaAs0.9P0.1 n /p solar cell structure was grown and

fabricated, on an n-type GaAsyP1-y/GaAs metamorphic substrate, with and without (on a

146 15 ) 2

5 Current Density (mA/cm

With TJ Without TJ 0 0.0 0.5 1.0 Voltage (V)

+ Figure 5.4. LIV data obtained for nominally-identical, non-optimized n /p GaAs0.9P0.1 solar cell structures

on p-type (no TJ) and n-type (with TJ) metamorphic GaAsyP1-y/GaAs substrates. Measurements were made using a Class AAA AM1.5G simulator.

p-type GaAsyP1-y/GaAs metamorphic substrate) the optimized GaAs0.9P0.1 TJ (GaAsP-B) integrated beneath the solar cell to obtain the correct polarity for current flow. The purpose of this experiment was to test the efficacy of the TJ integrated within a full solar cell structure by a comparison of the same cell with and without the TJ. Figure 5.4 presents a comparison of the lighted current-voltage (LIV) response for both device types, under AM1.5G illumination. Since the GaAs0.9P0.1 sub-cell growth constitutes the major component of the thermal load seen by the TJ in an MBE-grown III-V/Si device structure – Ga0.57In0.43P is typically grown about 100 °C colder – the negligible difference in measured sub-cell performance indicates the successful integration of the TJ

into a multijunction solar cell analogue.

147 5.2.2.3. DEVICE SIMULATIONS

Device simulations were performed with the Silvaco ATLAS TCAD suite using a non-local band-to-band model, which offers a more accurate model of TJs for multijunction solar cells compared to local tunneling models [182]. Representative modeling results, along with comparison to the counterpart experimental measurements, are shown in Figure 5.5. The simulated structure was based on the GaAsP-B device, using nominal n- and p-type carrier concentrations of 2×1019 and 6×1019 cm-3, respectively. In addition, the exact composition of GaAsP-B, GaAs0.89P0.11, was used, as determined via high-resolution XRD. This is due to the strong dependence of JP on bandgap, which is dictated by composition. For example, a change of only ±1% absolute

As content in GaAsyP1-y near y = 0.9 was found to yield a change of ±15% in the

100 ) 2 80

Current Density (A/cm T=300K 20 Device Simulation 0 0.0 0.4 0.8 1.2 Voltage (V)

-2 components of the device, with JP = 98.3 A·cm at 0.08 V, coming out just slightly below the measured value.

The excess current component [118] is known to not be easily simulated in TCAD programs such as Silvaco ATLAS and Synopsys Sentaurus [182], [183]. As a result, the excess current component observed in the actual devices was not accounted for in the

ATLAS simulation. To account for all current components, the empirically derived excess current was added to the ATLAS-derived tunneling and thermal components.

Although this approach to including the excess current does not provide any physical insight such as trap assisted tunneling [182], it does provide for a better overall visual fit to the experimental data in the mid-voltage range, making direct comparison easier. This approach yielded an excellent overall fit, as shown in Figure 5.5.

Nonetheless, the key result of this modeling effort is the agreement with the peak tunneling current. Any reduction in the concentration of either carrier type, such as due to amphoteric behavior of Si in the n-type case or incomplete activation of either dopant, would result in a significantly reduced peak current density relative to the simulation, which assumes complete activation. Indeed, variance of the ATLAS simulation input parameters yielded a strong JP sensitivity to the n- and p-type carrier concentrations, consistent with what was observed experimentally (Figure 5.3). As such, the agreement in peak currents, combined with previous ECV results, suggests that the achieved doping levels are indeed very close to the nominal values, indicating little to no amphoteric behavior of Si in the GaAs0.9P0.1, at least within any reasonable experimental uncertainty.

149 Such a result confirms the applicability of the improved growth conditions to the metamorphic GaAs0.9P0.1.

5.2.3. DISCUSSION

Given the identical device structure, doping profile, and growth conditions of the

GaAsP-A and GaAs TJs, enabling a direct comparison, it is interesting to consider the nature of the significant difference in realized performance between these compositions.

One possible cause for such a decrease in performance is a slight reduction in carrier activation. The donor ionization energy of Si within GaAs and GaP is 0.006 eV and

0.085 eV, respectively, a difference of a factor of over 14 [184], [185]. Similarly, the ionization energy of Be in GaAs and GaP is 0.028 eV and 0.057 eV, respectively, a difference of a factor of only two [179], [185]. As such, assuming systematic dependence on alloy composition, the ionization energies of both impurity species should be slightly higher in GaAs0.9P0.1 than in GaAs, especially for n-type doping, yielding a slight reduction in active carrier concentrations in the GaAs0.9P0.1 device layers. The lower carrier concentrations will in turn lead to an increased tunneling barrier height and width.

It is possible that this effect is contributing to the reduced carrier concentration observed

19 -3 in the GaAs0.9P0.1 Hall measurements relative to GaAs ECV results (1.2×10 cm versus

2×1019 cm-3). However, the actual realized TJ performance in the GaAsP-B structure is more consistent with complete activation according to simulations.

Another factor that is likely to play a role in the decreased performance is the increased bandgap of GaAs0.9P0.1, which is approximately 0.14 eV greater than GaAs at

300 K, further increasing the tunneling barrier. Any alteration to the band structure can

150 have a significant impact on the behavior of the device due to the exponential dependence

of the tunneling on the magnitude of the potential barrier. In this case, the combination of

reduced carrier concentration and increased barrier would likely produce a significant reduction in tunneling performance, consistent with the GaAsP-A test device results. That said, it should be noted that the situation is also complicated by the fact that degenerate doping levels tend to lead to additional effects, such as bandgap narrowing, potentially altering ionization energies from those reported in the literature. Other phenomena exist that may impact device performance as well, including residual strain, threading dislocation density, and interfacial roughness (i.e. due to cross-hatch). However, the degree to which these characteristics impact the device performance here is outside the scope of this study.

5.2.4. CONCLUSIONS

To summarize the work done to demonstrate the lower TJ of the MBE 3J,

optimization of MBE growth conditions was performed to maximize carrier

-2 concentrations via Si and Be doping. A GaAs0.9P0.1 TJ test device with JP = 103.9 A·cm

and RA = 4.5×10-4 Ω·cm2 was demonstrated, exceeding the requirements of the lower TJ.

Numerical simulations indicated that effectively complete dopant activation was achieved using these optimized growth conditions, enabling the production of a high-performance

homojunction TJ at the relatively unexplored lattice constant of 5.633 Å. These results

provide a pathway for the development of the MBE 3J for which idealized bandgap

profiles are achievable when grown at a lattice constant that is equivalent to the

GaAs0.9P0.1 TJs explored here, such that internal lattice-matching is maintained.

151 5.3. MBE 3J UPPER TUNNEL JUNCTION

5.3.1. MOTIVATION

The GaAs0.9P0.1 homojunction TJ discussed above does not meet the optical

requirements for the upper TJ in the MBE 3J. It consists of 50 nm of GaAs0.9P0.1, and

thus if it was used as the upper TJ it would result in significant parasitic absorption of

light that is designed to be absorbed by the middle GaAs0.9P0.1 sub-cell. Thus, an

alternative TJ design is required to avoid parasitic absorption.

5.3.2. RESULTS

5.3.2.1. DOUBLE HETEROSTRUCTURE TJ DESIGN

The impact that the 50 nm GaAs0.9P0.1 homojunction TJ would have on the EQE

if integrated above the GaAs0.9P0.1 middle cell is presented in Figure 5.6, calculated via a

numerical device simulation. Also shown is the projected EQE in the case that the TJ is

thinned to 10 nm. When only taking the GaAs0.9P0.1 middle cell absorption band into

account (i.e. 635-800 nm; shorter wavelengths are absorbed by the Ga0.57In0.43P top cell),

the parasitic optical absorption can be greatly reduced if the TJ is thinned to 10 nm.

However, thinning alone is not practical from an electrical perspective. Simulations of a

5 nm GaAs0.9P0.1:Be/5 nm GaAs0.9P0.1:Si TJ (10 nm total) indicate that the entire device would effectively be depleted with the doping levels achieved for the GaAs0.9P0.1

homojunction TJ (n = 2×1019 cm-3, p = 6×1019 cm-3). If adjacent layers were not

sufficiently doped, resonance between the valence band of the p-type side and the conduction band of the n-type side may not be achieved, resulting in poor performance. 152

+ + + Figure 5.6. EQE simulations of a n /p GaAs0.9P0.1 solar cell with a p /n -GaAs0.9P0.1 tunnel junction located above the solar cell. The GaAs0.9P0.1 middle cell spectral region of interest within the MBE 3J is indicated by the shaded region (λGaAsP).

To achieve proper band alignment, highly-doped, wide bandgap Ga0.57In0.43P

cladding layers, lattice-matched to the GaAs0.9P0.1 tunneling layers, were investigated.

Figure 5.7 shows the band structure of this double heterostructure TJ. which yields proper alignment of the p-GaAs0.9P0.1 valence band with the n-Ga0.57In0.43P conduction band.

5.3.2.2. DOUBLE HETEROSTRUCTURE TJ CHARACTERIZATION

With the modeling as a guide, double heterostructure TJs at the GaAs0.9P0.1 lattice

constant were co-grown via MBE on both tensile (GaAs-based) and compressive (Si-

based) virtual substrates and fabricated into test devices. This direct comparison served to

demonstrate the impact of using a Si substrate versus GaAs, as well as the influence of

different threading dislocation density (TDD) values and cross-hatch induced surface roughening, on the performance of the double heterostructure tunnel junction.

153

Figure 5.7. Band diagram simulation of the Ga0.57In0.43P/GaAs0.9P0.1 double heterostructure TJ at zero bias condition.

To demonstrate these devices, tensile (step-graded GaAsyP1-y on GaAs) and

compressive (step-graded GaAsyP1-y on Si) virtual substrates with the desired lattice

constant were first grown via MOCVD, thereby providing an ample supply of

comparable templates to support the subsequent MBE growth experiments. The MBE- grown double heterostructure TJs were doped with Si and Be for n- and p-type doping,

respectively, using the same growth conditions used in the MBE 3J Lower Tunnel

Junction section. Real-time growth quality and rates were monitored in-situ via reflection

high-energy electron diffraction (RHEED) and growth temperature was monitored via

infrared pyrometry. Doping (carrier concentration) was characterized via Hall effect

measurements. Devices were processed and characterized in the same manner as done in

the MBE 3J Lower Tunnel Junction section.

154

Figure 5.8. Performance of various double heterostructure TJs with respect to the optimized GaAs0.9P0.1 homojunction TJ (GaAsP-B in the MBE 3J Lower Tunnel Junction section).

The double heterostructure TJs performed exceptionally well with respect to the

homojunction TJ (GaAsP-B in Table 5.2), showing significant improvement in electrical

performance. Typical J-V results for the tensile and compressive double heterostructure

TJs are presented in Figure 5.8. Note that the instability of the J-V in the negative

differential resistance (NDR) region is a result of regularly-observed bias oscillations that

occur for very high tunnel currents and NDR values, which do not impact the extraction

of the critical figures of merit [115]. The double heterostructure tunnel junction on the

-2 GaAs-based tensile buffer (DH-TJ A) yielded a JP of 149 A·cm at 0.10 V and a RA of

4.5×10-4 Ω·cm2 at 0 V; the same tunnel junction on the Si-based compressive buffer

-2 (DH-TJ B) showed very similar performance, yielding a JP of 123 A·cm at 0.15 V and a

RA of 1.0×10-3 Ω·cm2 at 0 V. This is an impressive result and shows that very high-

performance tunnel junctions can be created on Si-based virtual substrates for solar cell

155 applications. Indeed, these tunnel junctions on GaAs0.9P0.1/Si outperform the optimized

homojunction tunnel junctions grown on GaAs0.9P0.1/GaAs (discussed in the MBE 3J

Lower Tunnel Junction section), even though the test buffers in this study possessed a

TDD in the low 107 cm-2 range, accompanied by an increase in surface roughness due to crosshatch. However, note the increase in series resistance when grown on Si versus

GaAs. This has been found to be an artifact due to back contact resistance and can be eliminated via an all-front contact measurement. The choice of substrate did not have a

7 significant effect on JP, despite the higher TDD present in the device on Si (low 10 vs. mid 105 cm-2). This performance on such a test buffer indicates these tunnel junctions are very adequate for use in the MBE 3J operating under reasonably high optical

concentrations.

The increased performance relative to the homojunction tunnel junction is

potentially due to hole accumulation at the p-Ga0.56In0.44P/p-GaAs0.9P0.1 heterojunction.

Simulations using BandEng indicate the hole concentration peaks at 4.7×1020 cm-3 in

GaAs0.9P0.1 at this interface, which is within range of the junction for sufficient tunneling

to occur. Further refinement of the p-GaAs0.9P0.1 layer thickness is expected to enable the

ability to tune the tunnel barrier width between the hole accumulation region and the

resonant conduction states, enhancing the tunneling performance even further. Due to the

negligible conduction band offset of the heterostructure on the n-type side, an analogous

electron accumulation region is not present.

It should be noted that while the doping in the double heterostructure TJs

discussed above was targeted to match the optimized homojunction TJ (GaAsP-B)

doping, a calibration error resulted in an approximately 35% higher growth rate. This

156 Table 5.3. Double heterostructure TJ figures of merit. GaAsP-B is the optimized homojunction TJ in the MBE 3J Lower Tunnel Junction section. -3 -3 -2 2 Structure n (cm ) p (cm ) JP (A cm ) RA (Ω cm ) GaAsP-B 2×1019 6×1019 104 4.5×10-4 DH-TJ A 1.5×1019 4.4×1019 149⋅ 5.0×10⋅ -4 DH-TJ B 1.5×1019 4.4×1019 123 1.0×10-3 DH-TJ C 2×1019 6×1019 510 2.0×10-4

resulted in thicker layers with lower nominal doping. Nonetheless, as seen in Figure 5.8,

JP of both DH-TJ A and DH-TJ B exceeded the value of the homojunction TJ. Regrowth

of the double heterostructure TJ on GaAs with the target growth rate, layer thicknesses,

-2 -4 2 and doping resulted in a JP of 510 A·cm and RA of 2.0×10 Ω·cm (DH-TJ C). This is a

significant improvement in electrical performance over the homojunction TJ, in addition

to the significant reduction in optical thickness. Note that this is therefore the most

appropriate device to compare to the homojunction TJ (GaAsP-B). Figures of merit of the various double heterostructure TJs are summarized in Table 5.3.

5.3.2.3. TOWARDS INTEGRATION INTO THE MBE 3J

To demonstrate the performance of an integrated double heterostructure TJ, a

Ga0.57In0.43P/GaAs0.9P0.1 dual-junction on a GaAs0.9P0.1/GaAsyP1-y/GaAs virtual

substrate was fabricated. Such a structure is a subset of the full MBE 3J, consisting of the

top cell, upper TJ, and middle cell. EQE, IQE, and LIV of the device are presented in

Figure 5.9. As can be seen by the LIV, the dual-junction is operating correctly, with

proper voltage addition of the sub-cells. This is a direct indication that the double

heterostructure TJ can withstand the additional thermal load present during the growth of

the Ga0.57In0.43P top cell and still maintain a JP > JSC. Furthermore, this device was

157 1.0 InGaP EQE GaAsP EQE Reflectance 7

InGaP IQE GaAsP IQE ) 2 6 0.8 5 0.6 4 0.4 3 GaAs0.9P0.1 Voc: 1.04V Ga0.57In0.43P Voc: 1.28V

QE / Reflectance 2 0.2 2 Voc (V) Jsc (mA/cm ) FF (%) η (%) 1 2.28 6.53 74.7 11.1 0.0 (mA/cm Density Current 350 450 550 650 750 850 0 Wavelength (nm) 0 0.4 0.8 1.2 1.6 2 2.4 Voltage (V)

Figure 5.9. QE and LIV of a Ga0.57In0.43P/GaAs0.9P0.1 dual-junction.

operated under ~164 suns concentration with no sign of failure of the TJ. Due to experimental limitations the dual-junction could not be taken to high enough concentrations to determine when the TJ failed, but this is still a very promising result for future integration into the MBE 3J.

5.3.3. CONCLUSIONS

The original hypothesis was that the upper TJ would be more challenging to develop compared to the lower TJ due to the wider minimum bandgap requirement. This in turn was expected to result in a higher RA compared to the lower TJ in similarly optimized upper and lower TJ designs. Although the double heterostructure TJ demonstrated herein does not fully meet the wider bandgap requirement due to the use of

10 nm GaAs0.9P0.1, the demonstration of the Ga0.57In0.43P/GaAs0.9P0.1 dual-junction using this TJ design suggests that negligible absorption occurs in the GaAs0.9P0.1 TJ layers, effectively indicating that the bandgap target was met. To ensure that negligible

158 absorption occurs, further optimization of the GaAs0.9P0.1 thickness (i.e. reduced to

below 10 nm) can be done if necessary. Finally, although the double heterostructure TJ

structure was originally intended to thin the GaAs0.9P0.1 layers to reduce absorption, the

fortunate consequence of higher JP and lower RA resulted in this device performing better

than the homojunction TJ in all aspects. Therefore, it was determined that the double

heterostructure TJ was suitable for use as both the upper and lower TJ of the MBE 3J,

accomplishing the goals described for this entire chapter. However, due to the evolving

design of the III-V/Si multijunction solar cell approach, it was around the time that the

double heterostructure TJ was developed that interest transitioned to the MOCVD-grown

GaAs0.75P0.25/Si dual-junction solar cell. Therefore, subsequent TJ development transitioned to MOCVD-grown devices at a new target lattice constant and bandgap.

Development of MOCVD-grown TJs is the topic of the next chapter.

159 CHAPTER 6:

MOCVD-GROWN METAMORPHIC TUNNEL JUNCTIONS

6.1. BACKGROUND

This chapter focuses on the development of a tunnel junction (TJ) grown via

metal-organic chemical vapor deposition (MOCVD) for use in the MOCVD-grown

GaAs0.75P0.25/Si dual-junction solar cell (MOCVD 2J) approach that was discussed in chapter 2. The structure of the MOCVD 2J is shown in Figure 6.1, highlighting the need for a TJ between the GaAs0.75P0.25 and Si sub-cells. Although the design specifications of

the MOCVD 2J targeted operation under AM1.5G, operation under concentration was

Figure 6.1. Structure of the MOCVD 2J, highlighting the need for a metamorphic TJ. 160 considered as an option when determining the specifications of this TJ to broaden the

applicability of this TJ. Thus, the goal was to demonstrate this TJ with the highest

performance possible.

Similar to the MBE-grown TJs discussed in chapter 5, target values for various TJ

figures of merit can be defined to ensure the MOCVD-grown TJ operates properly within

the MOCVD 2J. The full analysis on determining target values for these figures of merit

was performed in chapter 2. However, recall that the TJ figures of merit are:

1. Low resistance-area product (RA [Ω cm2])

-2 2. High peak tunneling current (JP [A cm⋅ ])

3. Wide, optically transparent bandgap⋅ (EG [eV])

4. Internally lattice-matched to III-V sub-cell(s) (a [Å])

Targeted values for these figures of merit are summarized in Table 6.1. The maximum

RA target ensures that the absolute efficiency loss of the MOCVD 2J due to the series

resistance of the TJ is ≤ 0.1%, and the minimum JP target is defined as 5× the short- circuit current density (JSC) to avoid failure of the TJ when operated within the

MOCVD 2J. The minimum bandgap target ensures the TJ is optically transparent, and the

Table 6.1. Target values of TJ figures of merit for the TJ within the MOCVD 2J operated at one sun, medium concentration, and high concentration. One Sun Medium Conc. High Conc. Figure of Merit (AM1.5G) (100× AM1.5D) (500× AM1.5D) Max. RA (Ω cm2) 1.8×10-1 2.3×10-3 4.7×10-4 -2 Min. JP (A cm ) 0.11 9.75 48.8 Min. EG (eV)⋅ 1.72 1.72 1.72 Lattice Constant⋅ (Å) 5.603 5.603 5.603 161 constraint of internal lattice-matching to the GaAs0.75P0.25 top cell defines the target lattice constant of the metamorphic TJ.

The remainder of this chapter focuses on the development of an MOCVD-grown metamorphic TJ to meet these requirements, which resulted in a high-performance

Al0.2Ga0.8As0.75P0.25:C/GaAs0.75P0.25:Te heterojunction tunnel junction. Note that this structure differs from the MBE-grown double heterostructure tunnel junction developed in chapter 5. A comparison of theses designs and discussion on why the double heterostructure design was not used for the MOCVD-grown TJ is made in the MBE vs.

MOCVD TJ Approaches section in chapter 8 (conclusions).

This study successfully optimized several parameters to demonstrate a high- performance metamorphic tunnel junction at the target lattice constant capable of performing at various optical concentrations. Initial calibration was performed at the

GaAs lattice constant to simplify the process and provide a convenient comparison versus literature. This included doping studies, exploration of the well-known Te memory effect in MOCVD [186]–[188], and device demonstration. The optimized device design was then transitioned to the GaAs0.75P0.25 lattice constant and composition base, which is

complicated by the impact of the CBrCl3 dopant precursor on the composition of

AlxGa1-xAsyP1-y grown at low temperatures. A metamorphic heterojunction tunnel

junction was fabricated and exposed to various permutations of a top cell thermal load

anneal (to estimate performance within the MOCVD 2J) and post-growth performance-

enhancing carbon activation anneal (to explore potential flexibility in device fabrication

processes). Finally, negligible series resistance occurred upon integration into the current

world-record GaAsP/Si 2J operated under AM1.5G [1]. In addition, depending on the

162 inclusion of the carbon activation anneal, the excellent device performance enables

extension to operation under medium to high concentration.

6.2. APPROACH

Although the goal of this work was to demonstrate a metamorphic

AlxGa1-xAs0.75P0.25/GaAs0.75P0.25 heterojunction tunnel junction, an initial

lattice-matched study was used to optimize doping and tunnel junction devices at the

GaAs lattice constant (i.e. an AlxGa1-xAs/GaAs tunnel junction). This approach offered

several advantages. First, this decoupled the optimization of doping conditions from the

strong dependence of As/P incorporation on growth conditions. Second, this approach did

not require the growth of virtual substrates for each optimization study, greatly

accelerating the study. Third, due to sufficient literature on tunnel junctions

lattice-matched to GaAs, the results were directly comparable to literature to benchmark

performance.

In the lattice-matched study, AlxGa1-xAs:C (section 6.3) and GaAs:Te (section

6.4) growth conditions were optimized for use as the p- and n-type layers of the tunnel junction, respectively, and devices were demonstrated (sections 6.4.2 and 6.4.3). The optimal materials and device structure from the lattice-matched study were then transitioned to the target lattice constant (5.603 Å) using a tensile GaAsyP1-y/GaAs buffer

in the metamorphic study (section 6.5). Note that the optimal metamorphic tunnel

junction design is ultimately integrated into the MOCVD 2J using a compressive

GaAsyP1-y/Si buffer. However, the use of a tensile GaAsyP1-y/GaAs buffer works well for

tunnel junction development and ultimate implementation at the same lattice constant.

163 This was demonstrated for MBE-grown double heterostructure tunnel junctions in

chapter 5. Here, the primary benefit of the tensile buffers was the convenience.

All doping calibrations and tunnel junction devices were fabricated via MOCVD

using an AIXTRON 3×2” close-coupled showerhead reactor designed for III-V and Si

materials. This reactor was equipped with a LayTec EpiTT system for in situ

reflectance-based monitoring of growth rate and substrate temperature. All growths were performed at a reactor pressure of 150 mbar, a total flow rate of 6000 sccm using H2 as

the carrier gas, and a susceptor rotation speed of 50 rpm. MOCVD precursors included

trimethylaluminum (TMAl) and trimethylgallium (TMGa) for the group III elements and

arsine (AsH3) and phosphine (PH3) for the group V elements. Bromotrichloromethane

(CBrCl3) and diethyltelluride (DETe) were used for p-type and n-type doping,

respectively, of the active layers of tunnel junction devices. Silane (SiH4) was used for

n-type doping of the initial smoothing layer and, when applicable, the metamorphic

buffer layers. All doping calibrations and devices were grown on (001)-oriented n-GaAs

substrates with a 6° offcut toward the nearest (111)A. The native oxide was thermally desorbed under AsH3 flow (+ PH3 flow in the case of regrowth on metamorphic buffers) at 650 °C prior to growth initiation.

The Hall effect was used to characterize average carrier concentration of samples

in the doping studies. All Hall effect samples were nominally uniformly doped and

fabricated using pressed indium contacts arranged in the van der Pauw geometry. For

carbon doping calibrations, a post-growth carbon activation anneal was performed in a

rapid thermal anneal (RTA) system for 10 minutes at 480 °C under 1500 sccm N2. The

composition and relaxation of epilayers in all devices were determined via

164 high-resolution X-ray diffraction (HRXRD) reciprocal space map (RSM) analysis using a

Bede D1 system.

Tunnel junctions were fabricated using standard III-V processing techniques,

discussed in detail in chapter 3 and summarized below. Devices received the carbon

activation anneal unless stated otherwise. The front p-type ohmic contact was produced

via an un-annealed Cr/Au metal stack with 100% coverage. Device mesa isolation was

performed with an NH4OH:H2O2:DI (2:1:40) wet etch to create 60 μm × 60 μm and

1 mm × 1 mm devices. Due to the high current densities that tunnel junctions exhibit in

reverse bias, n-type back contact metallization was not necessary. Instead, back contact to

60 μm × 60 μm tunnel junctions was made using the Cr/Au front contact of an adjacent

1 mm × 1 mm tunnel junction. This method was found to be more reliable to ensure that

the back contact did not limit the measured RA. Current density versus voltage (J-V) measurements on the 60 μm × 60 μm devices were performed at 300 K using a

Keithley 2400 source-measurement unit in the 4-wire mode. It was found that the 4-wire mode was necessary to accurately measure the low RA values of the devices.

6.3. LATTICE-MATCHED P-TYPE TJ LAYER: ALXGA1-XAS DOPING STUDY

Carbon is an attractive dopant for use in p-type AlxGa1-xAs layers of tunnel

junctions due to the ability to achieve high doping levels with sharp doping profiles, as

well as its low diffusion coefficient [189], [190]. However, hydrogen incorporation has

been shown to result in the deactivation of carbon acceptors, although a post-growth

carbon activation anneal can be performed to decrease hydrogen content to ensure high

hole concentrations [191]–[193]. Furthermore, it has also been shown that a higher Al

165 fraction generally leads to increased hole concentrations [194], [195]. Since maximizing

the hole concentration in the p-type layer will enable higher tunnel junction performance,

it is important to optimize factors such as the growth conditions, carbon activation

anneal, and Al fraction.

In the present study, CBrCl3 was explored as the precursor to achieve p-type

GaAs:C and the initial doping study focused on maximizing the hole concentration.

Preliminary calibrations indicated that a growth temperature (TG) of 525 °C and input

V/III molar flow ratio of 197 was near-optimal within the explored parameter space in our reactor. Therefore, further optimization of the CBrCl3 flow was carried out at these

growth conditions. Figure 6.2 plots hole concentrations in as-grown and carbon activation annealed (described in section 6.2) GaAs:C, as well as the growth rate, as a function of

CBrCl3 flow. These results highlight two trends at these growth conditions. First, the

Figure 6.2. As-grown and post-growth carbon activation annealed hole concentrations (h) in GaAs:C, as well as growth rate, as a function of CBrCl3 flow at a growth temperature of 525 °C and V/III ratio of 197. The dotted lines aid in visualizing the trends and measurements were done at 300 K. 166 carbon activation anneal significantly increases the hole concentration and is more impactful at higher CBrCl3 flows. For example, the carbon activation anneal increased the hole concentration by ~37% at 25 sccm CBrCl3 and by ~185% at 100 sccm. Second, the growth rate reduces significantly with increasing CBrCl3 flow, potentially due to in situ etching.

Using the trends observed in the GaAs:C study (Figure 6.2) as a guideline, the effect of Al fraction and CBrCl3 flow on hole concentration in AlxGa1-xAs was looked at next. In this study, the CBrCl3 flow was limited to 35 sccm CBrCl3 to avoid a severe reduction in growth rate, which only serves to complicate calibrations and reproducibility. Data from this study are plotted in Figure 6.3; all hole concentrations are measured after the carbon activation anneal. The 35 sccm CBrCl3 data in Figure 6.3 clearly show that increasing the Al fraction linearly increases the hole concentration at

20 -3 concentration of 2.7×10 cm in Al0.64Ga0.36As was achieved using a CBrCl3 flow of

35 sccm, high non-uniformity across the wafer was observed at this Al content and

deemed unacceptable for use in a tunnel junction since uniformity is critical for the

MOCVD 2J. As a result, it was determined that Al0.2Ga0.8As with a hole concentration of

1.23×1020 cm-3 was suitable as the p-type layer of subsequent tunnel junction devices.

This hole concentration is significantly (~1.8×) higher than the highest hole concentration achieved in the GaAs:C study.

6.4. LATTICE-MATCHED N-TYPE TJ LAYER: GAAS:TE DOPING STUDY

Tellurium is an attractive dopant for use in n-type GaAs layers of tunnel junctions

due to the ability to achieve high doping levels [187], [196]. However, it possesses a well-known memory effect [186]–[188] that has been attributed to adsorption on reactor walls and gas lines, which can result in a non-abrupt doping profile [186], [187].

Consequently, this can lead to lower-than-expected carrier concentrations in ultra-thin tunnel junction layers. It is therefore important to optimize growth conditions to both maximize the electron concentration (section 6.4.1) and mitigate the Te memory effect to enable an abrupt doping profile (sections 6.4.2 and 6.4.3).

6.4.1. BULK DOPING STUDY

In the present study, DETe was explored as the precursor to achieve n-type

GaAs:Te. Optimization of growth conditions began with an initial bulk doping study to identify the optimal growth temperature and DETe flow. Bulk GaAs:Te doping data are presented in Figure 6.4, which plots the average electron concentration as a function of 168

DETe flow and growth temperature. Electron concentrations were measured by Hall on

~1 μm thick GaAs:Te epilayers. An input V/III molar flow ratio of 110 was used for all samples. Within the growth window explored, a maximum average electron concentration of 1.87×1019 cm-3 at a growth temperature of 600 °C was achieved. As can be seen in Figure 6.4, GaAs:Te becomes heavily compensated at high DETe flows. For example, a 2× increase in the DETe flow that yields the maximum electron concentration reduced the electron concentration by ~100×. In the literature, compensation in GaAs:Te has been attributed to the formation of Ga vacancy-donor complexes [197], a plausible mechanism for the compensation observed here. Alternatively, the literature has shown that Te-rich precipitates also limit electron concentration [187]. However, that mechanism was shown to result in a saturation in electron concentration and is not consistent with the results in the present study.

169 Due to the non-uniform doping profile that is expected to result from the Te

memory effect, the bulk doping study was not fully adequate to optimize doping in the

GaAs:Te tunnel junction layer. The Hall results from the bulk doping study only provides

the average electron concentration in a thick epilayer. In a tunnel junction, the local

electron centration at the tunnel junction interface (nint.) has the strongest impact on

device performance. It is therefore necessary to characterize the non-uniform doping

profile using an alternative technique to more accurately estimate nint. Although it is

possible to characterize the local carrier concentration using electrochemical

capacitance-voltage (ECV) profiling or the local doping profile using secondary ion mass

spectroscopy (SIMS), an alternative approach was taken; a series of tunnel junctions was fabricated and characterized to leverage the high sensitivity of JP on carrier

concentration. Two Te memory effect studies were performed; the first (section 6.4.2)

explored the impact of the GaAs:Te tunnel junction layer thickness on device

performance and the second (section 6.4.3) explored DETe pre-dosing strategies prior to growing the GaAs:Te device layer to mitigate the memory effect in a practical manner.

Table 6.2. Parameters of lattice-matched (LM) TJs grown for the GaAs:Te thickness study (devices A-D) and DETe pre-dosing study (devices C, E, F), as well as the metamorphic (MM) TJs.

THICK LATTICE PRE- GAAS:TE DETE TOTAL . DETe Pre-dose JP Modeled nint. ID CONSTA DOSING THICK. DOSE STUD (cm3 at STP) (A cm-2) (cm-3) NT STUDY (NM) (cm3 at STP) Y A LM 25 0 2.4 750⋅ 1.65×1019 ✓ B LM 100 0 9.5 1050 1.74×1019 ✓ C LM 500 0 47.4 1750 1.88×1019 ✓ ✓ D LM 2000 0 189.6 2800 2.03×1019 ✓ E LM 100 37.9 47.4 1650 1.86×1019 ✓ F LM 100 37.9 47.4 3120 2.06×1019 ✓ G1 MM 100 37.9 47.4 279.1 N/A G2 MM 100 37.9 47.4 49.5 N/A G3 MM 100 37.9 47.4 13.1 N/A 170 All results of the two memory effect studies are summarized in Table 6.2, Figure 6.5, and

Figure 6.6.

Figure 6.5. Structures of tunnel junctions fabricated for the (a) GaAs:Te Thickness Study and (b) the DETe Pre-dosing Study to understand how the Te memory effect impacts device performance.

Figure 6.6. JP of tunnel junctions from the GaAs:Te Thickness Study (devices A-D) and the DETe Pre- dosing Study (devices C, E, and F).

171 6.4.2. TE MEMORY EFFECT: GAAS:TE THICKNESS STUDY

To determine the extent of the Te memory effect, four tunnel junction devices

were fabricated with the structure shown in Figure 6.5(a). The optimal Al0.2G a0.8As:C

(section 6.3) and GaAs:Te (section 6.4) growth conditions were used to grow the 25 nm p-type and variable thickness n-type tunnel junction layers, respectively. The four devices had GaAs:Te thicknesses of 25, 100, 500, and 2000 nm, labeled as devices A-D,

respectively, in Table 6.2 and Figure 6.6. Device performance results, shown in Figure

6.6, demonstrate that increasing the GaAs:Te layer thickness from 25 nm to 2 μm led to a

-2 significant increase in JP from 750 to 2800 A cm . This suggests that the Te memory effect is indeed present, resulting in a non-uniform⋅ doping profile which significantly impacts device performance.

To estimate the magnitude of the non-uniformity in the electron concentration in the GaAs:Te epilayers in these lattice-matched devices, TCAD device modeling was performed using Silvaco ATLAS to model JP. Material parameters from the NSM

Archive were used [78]. The only fitting parameter was the electron concentration of the

GaAs:Te layer. Furthermore, tunnel junctions were simulated assuming a uniform

GaAs:Te doping profile. While this may appear counterintuitive, this was believed to be a

good approximation assuming that the doping profile varies slowly on a thickness scale

that is relevant for tunneling to occur (i.e. variation across 10 nm is small compared to

across 100+ nm). The doping of the GaAs:Te layer in the model can then be regarded as

nint. of the experimental devices. The modeling results highlight the sensitivity of JP on

-2 electron concentration, indicating that an increase in JP from 750 to 2800 A cm for

19 19 -3 devices A to D only requires a change in nint. from 1.65×10 to 2.03×10 cm⋅ , 172 respectively, listed in Table 6.2. To determine the validity of these modeled nint. values,

they were used to estimate the non-uniform doping profile in a 1 μm thick GaAs:Te layer.

The calculated average doping of such a layer strongly agreed with Hall results of corresponding experimental material (section 6.4.1), suggesting the modeled nint. values

are accurate.

While such a small change in the electron carrier (doping) concentration may

appear within the noise in ECV (SIMS), this device study clearly demonstrated that such

a change has a significant impact on device performance. However, it is impractical for

the tunnel junction to be grown with a GaAs:Te epilayer that is 2+ μm thick, motivating

the need for an alternative solution to mitigate the Te memory effect.

6.4.3. TE MEMORY EFFECT: DETE PRE-DOSING STUDY

García et al. demonstrated via SIMS that the Te memory effect is significant in

GaInP, with the doping concentration increasing by approximately an order of magnitude

over the first several hundred nanometers of growth prior to saturating [188]. On the

other hand, they reported that the Te doping profile of a GaAs:Te layer was abrupt,

suggesting no memory effect in GaAs:Te. However, the GaAs:Te Thickness Study in the

current study clearly suggests that the Te memory effect is present in GaAs:Te, although

to a much less extent; doping only varied by 1.23× across a 2 μm GaAs:Te layer

according to device modeling. Therefore, it appeared worthwhile to develop a technique

to mitigate the memory effect in GaAs:Te. Ebert et al. demonstrated that pre-dosing

DETe prior to the growth of GaInP led to a sharp doping profile [198]. It was

hypothesized that such a technique may be applicable to achieve an abrupt doping profile

173 in GaAs:Te and would be more practical for mitigating the Te memory effect compared to growing a thick tunnel junction layer as was done in the GaAs:Te Thickness Study.

To determine if pre-dosing is beneficial for GaAs:Te, two strategies were tested to achieve a more uniform doping profile, shown in Figure 6.7. The goal was to provide an identical total dose of DETe (pre-dose + dose during growth = 47 cm3 STP) prior to the

GaAs:Te growth stop (i.e. tunnel junction interface). Device C served as a reference; no pre-dosing was used and it had a 500 nm thick GaAs:Te layer doped using 3.5 sccm

DETe. The goal of device E was to thin the layer thickness to 100 nm and to uniformly pre-flow DETe such that the total DETe flow time and rate were the same as that used for device C. The goal of device F was to shorten the pre-flow time by pulsing DETe with a

10× DETe flow (35 sccm) but keeping the same total DETe dose of 47 cm3 STP relative to the tunnel junction interface to meaningfully compare strategies. AsH3 flowed

Figure 6.7. TMGa and DETe flow sequences for a reference (device C), the uniform DETe pre-dosing strategy (device E), and the pulsed DETe pre-dosing strategy (device F) designed to mitigate the Te memory effect in the GaAs:Te tunnel junction layer. 174 throughout the displayed portion of each sequence. Details of these devices are summarized in Table 6.2, including the total dose and pre-dose of DETe.

JP of devices C, E, and F is summarized in Figure 6.8. Nearly identical JP values of 1750 and 1650 A cm-2 for devices C and E, respectively, were observed. Since the

GaAs:Te Thickness ⋅Study indicated that device C possesses a non-uniform doping profile

(i.e. the electron concentration was not saturated after 500 nm of growth), these results suggest that the non-uniform doping profile in both devices C and E are similar near the

TJ interface, ultimately suggesting identical nint. values. It is also worth comparing device E to device B from the GaAs:Te Thickness Study, which had the same thickness but no pre-dosing; device E demonstrated a 57% improvement in JP with the inclusion of pre-dosing. In the case of device F, despite having the same total DETe dose as devices C

-2 and E, substantially higher performance was observed with JP = 3120 A cm . This is also surprising close to the peak current of device D in the GaAs:Te Thickness⋅ Study, which

Figure 6.8. JP values for devices C, E, and F, highlighting the significant improvement in performance that the pulsed DETe pre-dosing used in device F has over the uniform pre-dosing used in device E. 175 -2 had the 2 μm GaAs:Te epilayer and JP = 2800 A cm . These results suggest that perhaps

the non-uniformity in the electron concentration ⋅has been eliminated or minimized due to

the high DETe flow quickly saturating the walls and/or lines in the reactor.

The performance of device F is comparable to devices in the literature. For

example, JP is only ~3× lower than an AlGaAs:C/GaAs:Te tunnel junction developed by

García et al. for concentrator solar cells [196]. However, since the goal of this work was

to demonstrate a metamorphic tunnel junction, the lattice-matched device F was chosen as the structure (and pre-dosing strategy) to use for subsequent metamorphic devices.

6.5. METAMORPHIC DOPING CALIBRATIONS AND TJ DEVICES

The lattice-matched doping studies enabled a 25 nm Al0.2Ga0.8As:C/

-2 -5 2 100 nm GaAs:Te tunnel junction with JP = 3120 A cm and RA = 3.0×10 Ω cm . These

metrics provide important headroom to accommodate⋅ the reduction of JP and ⋅increase of

RA associated with the addition of phosphorous and associated increase in bandgap of the target metamorphic alloys, as well as the expected reduction in performance after exposure to the thermal load of the GaAs0.75P0.25 top cell. This section focuses on

transitioning the alloy compositions to the target lattice constant and the associated

impact on the doping calibrations (section 6.5.1), followed by the performance of a

metamorphic Al0.2Ga0.8As0.75P0.25:C/GaAs0.75P0.25:Te tunnel junction exposed to various

anneal conditions (section 6.5.2).

176

Figure 6.9. UID and C-doped GaAsyP1-y composition calibrations at a growth temperature of 525 °C. Compositions were determined via HRXRD RSM analysis.

6.5.1. TRANSITION TO METAMORPHIC ALLOYS

The first step in transitioning each tunnel junction layer to the target lattice

constant was to understand the impact of the CBrCl3 and DETe flows used for high doping (determined in sections 6.3 and 6.4, respectively) on As/P incorporation. Tensile

GaAsyP1-y multilayer structures were grown to construct a composition calibration using

the chosen dopant precursor flows. Throughout the multilayer structure growth, the total

group V flow (AsH3 + PH3) was held constant at 75 sccm. To calibrate the composition

of the p-type layer, unintentionally doped (UID) and C-doped GaAsyP1-y multilayer

structures were grown at 525 °C. HRXRD RSM analysis indicated that 25 sccm CBrCl3

flow had a significant impact on As/P incorporation. As shown in Figure 6.9, C-doped

GaAsyP1-y exhibited significantly enhanced P-incorporation compared to UID GaAsyP1-y

177 for given group V flows. It is plausible that the presence of CBrCl3 enhances P

incorporation due to the Cl and Br radicals selectively etching GaAs over GaP.

To achieve the target Al0.2Ga0.8As0.75P0.25 composition, the group V flows

necessary to grow GaAs0.75P0.25 doped with 25 sccm CBrCl3 (from Figure 6.9) were used

and the TMAl and TMGa flows were adjusted accordingly. The lattice constant was

confirmed via HRXRD RSM. Hall results for Al0.2Ga0.8As0.75P0.25:C doped with 25 sccm

20 -3 CBrCl3 indicated a hole concentration of 1.6×10 cm after the carbon activation anneal,

72% higher than the 25 sccm data in Figure 6.3 projects for Al0.2Ga0.8As

(~9.3×1019 cm-3) using the same growth conditions besides the group V flows. This

higher hole concentration in the metamorphic alloy can be explained by the significantly

lower AsH3 flows used for the metamorphic alloys (~10 sccm) compared to the lattice- matched alloys (75 sccm). As demonstrated by Dimroth et al., AsH3 suppresses carbon

incorporation [199]. Thus, the use of lower AsH3 flow for the metamorphic alloy leads to a higher hole concentration in the metamorphic alloy. It is also plausible that reducing the

V/III ratio in general, and not just the reduction of AsH3, improves C incorporation due

to group V site competition between As, P, and C. Although a total group V flow of

75 sccm is used for both the lattice-matched and metamorphic materials, the V/III ratio of

pyrolized (i.e. active) precursor at the surface is lower in the metamorphic case. This is

because PH3 is significantly less pyrolized compared to AsH3 at the low growth

temperature of 525 °C, evidenced by the highly nonlinear As/P incorporation shown in

Figure 6.9.

The n-type GaAs0.75P0.25:Te layer of the tunnel junction was calibrated next. Both

UID and Te-doped GaAsyP1-y buffers were grown at 600 °C. HRXRD RSM analysis

178 indicated that the optimized DETe flow (3.5 sccm as determined in section 6.4.1) did not

significantly impact As/P incorporation. Hall results for GaAs0.75P0.25:Te doped using

3.5 sccm DETe indicated an electron concentration of 1.2×1019 cm-3, lower than for

GaAs:Te using the same doping conditions (1.9×1019 cm-3). Additional analysis indicated

that this discrepancy doesn’t appear to be due to a difference in the optimal DETe flow

for high doping in GaAs0.75P0.25 vs. GaAs. Therefore, it is plausible that the difference

may be due to a larger ionization energy of Te in GaAs0.75P0.25 due to its wider bandgap.

6.5.2. METAMORPHIC TUNNEL JUNCTION DEMONSTRATION

Using the growth conditions of the metamorphic alloys described above, a

25 nm Al0.2Ga0.8As0.75P0.25:C/ 100 nm GaAs0.75P0.25:Te metamorphic heterojunction

tunnel junction was demonstrated (device G). The bandgap of the p- and n-type layers of

this device were ~1.7 and ~2.0 eV, respectively, ensuring that the entire tunnel junction

was optically transparent to the absorption band of the Si bottom cell in the MOCVD 2J.

J-V curves of this metamorphic heterojunction tunnel junction under various

permutations of the post-growth carbon activation anneal and an MOCVD anneal are

shown in Figure 6.10. The C activation anneal consisted of the same RTA process used in

the AlxGa1-xAs:C doping study (section 6.3). The MOCVD anneal was performed at

625 °C for 1 hr under AsH3 and PH3 overpressure to emulate the thermal load the tunnel

junction would experience due to the growth of the GaAs0.75P0.25 top cell.

Device G1 only received the C activation anneal to indicate the best possible

-2 performance that is achievable with this device, demonstrating JP = 279.1 A cm and

-4 2 RA = 3.0×10 Ω cm . Device G2 received both the C activation anneal and MOCVD⋅

⋅ 179

anneal to estimate the tunnel junction performance in the MOCVD 2J with the C

-2 activation anneal. Metrics for this device reduced to JP = 49.5 A·cm and

-4 2 RA = 3.5×10 Ω·cm . This ~5.6× reduction in JP is greater than the ~2.9× reduction that

García et al. observed after annealing a lattice-matched AlGaAs:C/GaAs:Te tunnel junction at 650 °C for 30 min [196], which is not surprising due to the larger thermal load in the present study. Device G3 only received the MOCVD anneal to determine the performance in the MOCVD 2J if the C activation anneal is omitted. With respect to the

MOCVD 2J, this is the best-case scenario to avoid unintended challenges that the C activation anneal may present for other components of the MOCVD 2J. Metrics for this

-2 -3 2 device further reduced to JP = 13.1 A·cm and RA = 1.5×10 Ω·cm . These devices are summarized in Table 6.2. Note that due to uncertainties in materials parameters of the

180 Table 6.3. Carrier concentrations determined via Hall in thick epilayers representative of the metamorphic tunnel junction layers under various anneal combinations.

CARRIER CONC. LAYER C ACT. ANNEAL MOCVD ANNEAL (CM-3) 5.7×1019 1.6×1020 ↑ Al0.2Ga0.8As0.75P0.25:C ✓ Thickness: 0.44 μm 6.5×1019 ↑ ✓ ✓ 2.7×1019 ↓ ✓ 1.2×1019 N/A GaAs0.75P0.25:Te ✓ Thickness: 1.07 μm 8.4×1018 ↓ ✓ ✓ N/A ✓

metamorphic alloys, TCAD modeling of these devices was not performed and thus the

modeled nint. values for these devices are not included in Table 6.2.

To give insight into the variation in performance between devices G1, G2, and G3, further analysis was performed. Thick Al0.2Ga0.8As0.75P0.25:C and GaAs0.75P0.25:Te layers were grown with the same growth conditions used in the metamorphic heterojunction tunnel junction layers. Samples under various permutations of the C activation anneal and the MOCVD anneal were characterized via Hall and the results are summarized in Table

6.3. Although only partial GaAs0.75P0.25:Te data are available, it can be seen that

including both anneals led to an ~30% reduction in the electron concentration compared

to as-grown material. In the case of Al0.2Ga0.8As0.75P0.25:C, going from only the C

activation anneal (representative of device G1) to only the MOCVD anneal

(representative of device G3) led to an ~5.9× reduction in the hole concentration due to higher hydrogen passivation. These results suggest that variations in the hole concentration in the Al0.2Ga0.8As0.75P0.25:C layer may be the primary reason for the

variation in performance of devices G1, G2, and G3. Note that diffusion of C and Te

likely plays no role, as García et al. demonstrated that dopant diffusion is negligible

181 under similar anneal conditions for an AlGaAs:C/GaAs:Te tunnel junction [196]. It is

reasonable to expect similar behavior for the metamorphic device in the present study.

Despite the degradation upon including the MOCVD anneal and omitting the C

activation anneal, the metrics observed for device G3 are very promising. It is estimated

that an absolute efficiency loss of less than 0.001% due to RA would occur in the

MOCVD 2J operating under AM1.5G. Furthermore, only an ~0.1% loss in efficiency

would occur if device G3 is operated under 155 suns concentration (AM1.5D,

-2 JSC = 3.02 A·cm ). This enables the use of this tunnel junction up to medium

concentration applications. Inclusion of the C activation anneal (device G2) further

improves device metrics and enables use up to 670 suns concentration (AM1.5D,

-2 JSC = 13.1 A cm ). As a result, all target metrics in Table 6.1 have been achieved with

either the use⋅ of device G3 for operation under AM1.5G up to medium concentration, or device G2 for operation up to high concentration. It should also be noted that for practical

GaAsP/Si 2Js, perfect collection and 100% fill factor will not occur (which were assumed

in the calculation of JSC at various concentrations in chapter 2), and the losses due to RA

will be slightly lower than the estimates here.

Finally, this metamorphic tunnel junction was recently integrated into the current

world-record monolithic GaAsP/Si 2J [1]. When operated under AM1.5G, negligible

series resistance occurred up to voltages beyond the open-circuit voltage (VOC),

indicating the successful integration of this metamorphic heterojunction tunnel junction

in the GaAsP/Si 2J structure.

182 6.6. CONCLUSIONS

An Al0.2Ga0.8As0.75P0.25:C/GaAs0.75P0.25:Te metamorphic tunnel junction has

been developed for use in the MOCVD 2J. Development began by optimizing growth

conditions of AlxGa1-xAs:C and GaAs:Te lattice-matched to GaAs to decouple the

optimization of doping conditions from the strong dependence of As/P incorporation on

growth conditions. Lattice-matched tunnel junction devices were fabricated to

demonstrate the impact of the Te memory effect on device performance and to develop

an optimized pre-dosing strategy to mitigate this effect. The optimized lattice-matched

device was then transitioned to the target lattice constant to demonstrate a metamorphic

heterojunction tunnel junction. High-doping calibrations of metamorphic GaAsyP1-y

demonstrated the significant impact CBrCl3 has on As/P incorporation at low growth

temperatures. Using the optimized metamorphic growth conditions, the metamorphic

-2 heterojunction tunnel junction was demonstrated with JP = 279.1 A cm and

-4 2 RA = 3.0×10 Ω cm . Upon exposure to the thermal load of the GaAs⋅ 0.75P0.25 top cell and

omission of a hole⋅ concentration-enhancing carbon activation anneal, these metrics

reduced to 13.1 A·cm-2 and 1.50×10-3 Ω·cm2, respectively. This excellent performance

has been shown to lead to negligible series resistance in the current world-record

monolithic GaAsP/Si 2J and is projected to enable operation of the MOCVD 2J up to medium or even high concentration with the inclusion of the carbon activation anneal.

183 CHAPTER 7:

WIDE BANDGAP ALGAINP SOLAR CELLS

7.1. BACKGROUND

Multijunction solar cells (MJSC) are capable of high conversion efficiency,

making them attractive for space applications. For instance, France et al. demonstrated a

quadruple-junction (4J) solar cell designed for AM0 insolation with 35.3% efficiency

using a bandgap (EG) profile of 1.8/1.4/1.04/0.74 eV [200]. However, theoretical

efficiency modeling by Aiken et al. predicts that practical efficiencies over 42% are

possible for 4J devices using a more ideal EG profile [95]. Specifically, they indicated

that a top cell with a bandgap in the range of 2.05-2.10 eV is necessary. Although

lattice-matched (AlzGa1-z)xIn1-xP is capable of achieving a direct bandgaps in this range,

the addition of Al content has historically led to reduced device performance [201].

Therefore, it is worthwhile to explore this alloy further to either improve the performance of lattice-matched (AlzGa1-z)xIn1-xP top cells or determine an alternative pathway within

the (AlzGa1-z)xIn1-xP alloy family.

184 Various approaches for achieving (AlzGa1-z)xIn1-xP with a bandgap close to this

range have been explored in the literature, as discussed below. It is therefore important to

have a meaningful way to compare these approaches. The bandgap-voltage offset at

open-circuit (WOC = EG/q – open-circuit voltage (VOC)) is a useful figure of merit for

comparing cells of various bandgaps or, as is the case in this dissertation, comparing

different approaches for achieving the same bandgap. As a reference, WOC 0.4 V is

typically considered an indication of both excellent material quality and ideal≲ transport

properties [105].

Both molecular beam epitaxy (MBE) [10], [45], [202] and metal-organic chemical

vapor deposition (MOCVD) [9], [203], [204] have previously been used to grow

(AlzGa1-z)xIn1-xP cell structures. For example, via MBE, a lattice-matched 2.0 eV

(AlzGa1-z)xIn1-xP cell has been demonstrated with a WOC of ~0.59 V in the as-grown

state, which was improved to 0.52 V following a post-growth anneal [10]. Another

MOCVD study explored the use of lattice-matched (AlzGa1-z)xIn1-xP and optimized

growth conditions to achieve a WOC of 0.44 V in 2.03 eV material [9]. Recent work exploring the use of direct bandgap (In-rich) AlxIn1-xP, grown by MOCVD, achieved a

WOC of 0.57 V in 2.07 eV material [204]. Taken as a whole, these results indicate that this materials system is promising for the target applications, but that further work is necessary to understand the key performance limiters and to improve materials and device quality.

This work focuses on two approaches that target MOCVD-grown 2.05 eV direct bandgap top cells. The devices possess nominally identical device structures for appropriate comparison. Figure 7.1 outlines these two approaches. The first is to maintain

185

lattice-matching (LM) to GaAs via alloying with Al to produce a target quaternary

composition of (Al0.32Ga0.68)0.52In0.48P. The second is the use of metamorphic (MM)

grading to adjust the lattice constant (via the Ga:In ratio) to achieve a target ternary

composition of Ga0.66In0.34P. For clarity, these two approaches will be referred to as

“LM-AlGaInP” and “MM-GaInP,” respectively. Although (AlzGa1-z)xIn1-xP with a lattice constant larger than GaAs is an alternative pathway for achieving a 2.05 eV top cell, this approach was not explored here due to the corresponding reduction in the direct bandgap of the associated internally lattice-matched AlxIn1-xP window material. As

demonstrated herein, window composition plays an important role in short wavelength

photon collection.

Both the increase of Al content associated with LM-AlGaInP and the introduction

of lattice mismatch associated with MM-GaInP are expected to increase concentrations of 186 point defects and/or threading dislocations. This can degrade material quality and device performance by decreasing minority carrier lifetime and diffusion length (LD) and/or by increasing recombination currents in the depletion region. For instance, increasing the Al content of (AlzGa1-z)xIn1-xP alloys during MOCVD growth has been linked to increased oxygen incorporation into the material [205]. This in turn has been correlated with high concentrations of deep levels that can act as recombination centers and can reduce LD

[13], [14]. In the case of threading dislocations, a strong correlation between minority carrier lifetime (as well as LD) and threading dislocation density (TDD) for n- and p-type

GaAs has been demonstrated when the TDD exceeds a doping concentration-dependent critical value [22], [28], [54], [206]–[208]; this is expected to be a generally applicable trend. Thus, with the different defect issues introduced by the two approaches, it is of interest to compare and contrast these methods to ultimately determine an optimal pathway toward achieving high performance 2.05 eV bandgap top cells. Understanding the advantages and challenges of each could also identify alternative design optimization pathways for each, and this aspect further motivates this work. Here, analytical modeling and detailed device characterization is carried out to provide insight into the connections between material quality, relative limitations and advantages, and device design approaches.

7.2. APPROACH

LM-AlGaInP and MM-GaInP n+/p prototype solar cells and diodes, with a common target (nominal) bandgap of ~2.05 eV, were grown via MOCVD for a detailed comparative study of material quality and device performance. The MOCVD system used

187 was an AIXTRON 3×2” close-coupled showerhead designed for III-V materials and

equipped with a LayTec EpiTT system for in situ reflectance-based measurement of

growth rate and emissivity-corrected pyrometric measurement of substrate temperature.

MOCVD precursors used were trimethylaluminum (TMAl), trimethylgallium (TMGa),

and trimethylindium (TMIn) for the group-III elements, whereas phosphine (PH3) and

arsine (AsH3) supplied the group-V elements. Silane (SiH4) and diethylzinc (DEZn) were used for n-type (Si) and p-type (Zn) doping, respectively. All devices (LM and MM) were grown on (001)-oriented p-GaAs substrates with a 6° offcut toward the nearest

(111)A. The native oxide was thermally desorbed under AsH3 flow at 650 °C prior to

growth initiation. A growth temperature of 625 °C was used throughout for all

LM-AlGaInP and MM-GaInP device structures. This growth temperature was

semi-optimized previously within our research group for the growth of MM-Ga0.57In0.43P

[209]. The LM-AlGaInP and MM-GaInP compositions explored in the present study can

be viewed as deviations from the MM-Ga0.57In0.43P composition, and thus the 625 °C growth temperature was determined to be a suitable starting point for comparison.

However, it is worth noting that higher growth temperatures have been demonstrated to improve (AlzGa1-z)xIn1-xP material quality [9], indicating a clear pathway for future

optimization of unique growth conditions for LM-AlGaInP and MM-GaInP.

Figure 7.2 provides schematics of the device structures discussed herein. The structure of the devices (solar cells and test diodes) consisted of a 1.5 μm thick p-type

17 -3 + base (nominal doping concentration: NA = 1×10 cm ) with a 50 nm n -type emitter

18 -3 + (ND = 2×10 cm ) and 70 nm p -type doping back surface field (BSF,

18 -3 + NA = 3×10 cm ), all the same composition. A 20 nm n -AlxIn1-xP window layer

188

Figure 7.2. Device structures of the ~2.05 eV (a) LM-AlGaInP and (b) MM-GaInP cells.

18 -3 (ND = 5×10 cm ) was grown internally lattice-matched to the respective devices, along

++ with a highly doped, internally lattice-matched n -GaAsyP1-y contact layer. The BSF,

base, and emitter layers of both devices were grown at a growth rate of ~1.3 μm/hr and at

an input molar V/III ratio of ~350, whereas the window layers were grown at a growth

rate of ~1 μm/hr and an input molar V/III ratio of ~500. The composition and relaxation

of epilayers in all devices were determined via high-resolution X-ray diffraction

(HRXRD) reciprocal space map (RSM) analysis using a Bede D1 system.

The MM-GaInP devices were grown on tensile, p-GaAsyP1-y step-graded buffers

on p-GaAs substrates to reduce the residual TDD within the device layers to

1-2×106 cm-2, as measured via electron-beam induced current (EBIC) imaging. The

p-GaAs0.70P0.30 terminal buffer layer was 89% relaxed with an in-plane lattice constant

(a ) of 5.593 Å. This is the correct lattice constant to internally lattice-match the target

∥ 189 metamorphic Ga0.66In0.34P composition. This buffer design mitigates further dislocation

nucleation or significant glide during growth of the device layers.

The primary purpose of the GaAsyP1-y buffer here is to provide a platform to evaluate MM-GaInP at a realistically achievable TDD. However, it is worthwhile to consider how one might integrate the MM-GaInP cell within a monolithic MJSC structure. For an upright architecture, integration would be relatively straightforward, requiring only a tensile graded buffer to adjust the lattice constant prior to the top junction growth. Application to an inverted metamorphic multijunction (IMM) architecture would most likely be achieved via initial growth of a tensile buffer to the target lattice constant, prior to any sacrificial lift-off layer, followed by the MM-GaInP top cell growth. There would then be two choices for the second junction: immediately grading back toward GaAs with a compressive strain buffer and continued growth via a relatively standard set of materials or use of a lattice-matched AlxGa1-xAsyP1-y

composition as the second junction, followed by a compressive buffer to the target lattice

constant for the third junction. In all cases, where metamorphic buffer transparency is

needed (i.e. within the device structure), the (AlzGa1-z)xIn1-xP alloy system would be the

most likely choice [210], [211].

Solar cells and diodes were fabricated using standard III-V processing techniques.

The front n-type Ohmic contact was produced using an annealed Ni/GeAu-based metal stack, with 8.6% coverage for the solar cells and 100% coverage for the test diodes. The rear p-type contact was made via blanket, un-annealed Cr/Au metallization. Device mesa

isolation was performed with a BCl3/Ar-based dry/plasma etch. The fabricated solar cells

190 were 2 mm × 2 mm total area, whereas the diodes ranged from 60 μm × 60 μm to

1 mm × 1 mm. No antireflection coating (ARC) was applied.

Internal and external quantum efficiency (IQE and EQE) and reflectance

measurements were performed on a custom-built, small spot spectral response system.

Illuminated J-V (LIV) measurements were performed with a single-zone, Xe lamp-based

solar simulator (OAI TriSOL) filtered for AM0 and calibrated for photocurrent using a

lattice-matched Ga0.51In0.49P reference cell. JSC-VOC measurements, offset by the

experimentally determined JSC of the corresponding device, were used to demonstrate the

LIV characteristics of cells without the impact of voltage-dependent carrier collection

(VDCC) or series resistance. Dark J-V (DIV) measurements performed on the test diodes were used to identify the dominant VOC-limiting mechanism. Capacitance-voltage (C-V)

measurements were used to characterize p-type base layer doping.

Analytical device modeling was employed for predictive purposes, as well as to

aid in understanding the characterization results. Specifically, a 1-D model, which uses

separately calculated photogeneration and collection probability functions, was used to

model IQE and extract relevant device parameters, such as LD [101], and is described by

Eq. 7.1.

( ) ( , ) ( ) = Eq. 7.1 ( ) 𝑊𝑊 𝑓𝑓c 𝑥𝑥 ∗𝐺𝐺 𝑥𝑥 𝜆𝜆 Here, fc(x) is the collection probability𝐼𝐼𝐼𝐼𝐼𝐼 𝜆𝜆 as ∫a0 function𝛷𝛷 𝜆𝜆 of depth,𝑑𝑑𝑑𝑑 G(x,λ) is the photogeneration as a function of depth and wavelength, and Φ(λ) is the incident photon

flux as a function of wavelength. The function is integrated over the entire device

thickness (W). The collection probability is calculated based on standard drift-diffusion

relations, with a few assumptions for simplification and computational efficiency: unity

191 collection probability within the space charge region (SCR) and negligible collection

from the window and BSF layers, which were treated solely as parasitic absorbers.

Various datasets were used as the basis for the optical properties of the

(AlzGa1-z)xIn1-xP alloys [212]–[222]. The complex refractive index was interpolated

according to the methodology described by Lumb et al. [223]. This method uses

empirically-determined compositional dependencies of the dielectric function critical

point positions to guide interpolation of the optical constants. Reports of the critical point

peaks for (AlzGa1-z)0.5In0.5P lattice-matched to GaAs [213], GaxIn1-xP [216], and

AlxIn1-xP [217] were used for the various alloys in the LM-AlGaInP and MM-GaInP approaches.

It is worth noting here that important materials parameters extracted via the analytical modeling, such as LD, can be very sensitive to the optical constants used.

However, available optical data within the literature possess a non-negligible spread, with

no obvious best choice. Therefore, to determine a range of plausible material parameters,

and to provide clarity with respect to the resultant uncertainties in the extracted materials

parameters, the IQE of each cell was modeled using several different interpolated optical

datasets. The resultant output ranges, and where appropriate the median values, of any

computed terms are reported herein. The selected datasets shown herein thus provide

comprehensive coverage of the available optical data in the literature.

7.3. RESULTS AND DISCUSSION

Whereas the LM-AlGaInP and MM-GaInP cells possess nominally identical cell

structures, one innate difference arises due to the use of the internally lattice-matched

192

Figure 7.3. Modeled spectrally-resolved transmission through the 20 nm internally lattice-matched Al0.54In0.46P and Al0.69In0.31P windows on the LM-AlGaInP and MM-GaInP cells, respectively.

Al0.54In0.46P and Al0.69In0.31P windows, respectively. These compositions have similar

indirect minimum bandgaps of 2.30 eV and 2.34 eV, respectively. However, the direct

bandgaps are 2.49 eV and 2.76 eV, respectively, which is a significant difference. Very

little indirect absorption is expected in the 20 nm window at energies below the direct bandgap, but significant parasitic optical absorption is expected to occur at energies above the direct bandgap due to high resultant absorption coefficients (α). Consequently, assuming similar transport properties for each cell, the MM-GaInP cell, with its wider direct bandgap window, is then expected to provide superior short wavelength collection compared to the LM-AlGaInP cell.

Optical modeling of the nominal devices (see Figure 7.2) was performed to predict the magnitude of this effect. Figure 7.3 shows the calculated spectrally-resolved transmission through the associated 20 nm window layer for the two device designs using interpolated optical data based on [212], [220]. Significantly higher relative window 193 transparency in the 350-500 nm range is clearly seen for the MM-GaInP cell, regardless

of the optical dataset considered. The window transmission can be used to calculate the

short wavelength photon flux reaching the regions of active collection (i.e. the emitter,

SCR, and base) in each device. The difference in these photon fluxes can then be used to

predict how much more photocurrent MM-GaInP should produce compared to

LM-AlGaInP due to the higher transmission of its corresponding window. To determine

the full potential of this effect, perfect photon coupling (i.e. a perfect ARC) was assumed

to determine the difference for subsequent comparison to experimental IQE.

If transmission out to 280 nm (the standard AM0 short-wavelength cutoff) is accounted for, and the additional photon flux reaching the MM-GaInP active layers is assumed to be fully absorbed and all photogenerated carriers collected, the additional photon flux is predicted to provide an additional 0.64-0.80 mA/cm2 (~0.72 mA/cm2) of

photocurrent under short-circuit conditions. The same calculation over the range of

350-500 nm predicts an additional, though slightly reduced, 0.54-0.69 mA/cm2

(~0.62 mA/cm2) of photocurrent. Note that because of high quantum efficiency

instrumental uncertainties for wavelengths shorter than 350 nm, subsequent experimental

analysis is restricted to a short-wavelength cutoff of 350 nm (instead of 280 nm) and

quantitative comparisons are made against the ~0.62 mA/cm2 additional photocurrent

prediction.

The experimentally obtained IQE data from the cells are shown in Figure 7.4,

revealing bandgaps of 2.06 eV and 2.02 eV for LM-AlGaInP and MM-GaInP, respectively. These are both close to the 2.05 eV nominal target. Note that the discrepancy in IQE at long wavelength (~600 nm) is due to this slight difference

194

Figure 7.4. IQE of LM-AlGaInP and MM-GaInP cells reveals the superior short wavelength response, as well as the slightly higher overall response, of MM-GaInP.

Table 7.1. Modeled emitter and base LD of each device using interpolated optical data.

Cell Emitter LD (nm) Base LD (nm) LM-AlGaInP 34-46 255-623 MM-GaInP 88-92 341-440

(0.04 eV) in bandgap between the two cells. The IQE results clearly demonstrate the

superior short wavelength response in the MM-GaInP cell, as predicted by the optical

modeling. However, an unexpected slightly higher response across all wavelengths is

also observed in the MM-GaInP cell. By taking the difference in the integrated

photocurrents from the IQE in of the range of 350-500 nm, the actual experimental difference was found to be ~1.1 mA/cm2. This is significantly higher than that predicted

due to window transmission alone (~0.62 mA/cm2), suggesting that better front-side (i.e.

emitter) collection is also playing a role. Full IQE modeling is thus necessary to

understand the optical and electronic effects.

195 Analytical IQE modeling based on fitting against the experimental data revealed

that two factors play a role in the superior carrier collection in MM-GaInP: higher window transmission and a longer emitter LD. The modeling revealed ≥90% collection

probability throughout the MM-GaInP emitter, compared to ≥70% in LM-AlGaInP. This

corresponds to an ~2.3× higher emitter LD in MM-GaInP compared to LM-AlGaInP

(~90 nm vs. ~40 nm), as indicated in Table 7.1. Because the characteristic absorption depth (1/α) of MM-GaInP for 350-500 nm photons varies from 14-165 nm (based on median optical data), most of these photons generate carriers that are thus collected from the combined emitter and SCR regions, which extend to ~175 nm depth within the cell.

Thus, the near-unity collection probability in the emitter and unity collection in the SCR in the MM-GaInP cell results in the collection of the majority of the additional photocarriers generated due to the wider direct bandgap of the window. Furthermore, the higher emitter LD in MM-GaInP versus LM-AlGaInP provides generally higher IQE

across all wavelengths with any level of non-negligible absorption within the combined

emitter-SCR region. It is worth noting that the best fit in the modeling was achieved

when setting the window/emitter interface recombination velocity (IRV) values as equal

for both cells. Nonetheless, it is possible that a difference in IRV could still be

responsible for the observed differences in performance, similar to that reported for

MBE-grown AlGaInP devices [202]. However, no growth pause was required for the

emitter-to-window transition within the MOCVD growths, which are typically required

in MBE to change effusion cell temperatures. This likely leads to MOCVD-grown

interfaces that are both higher quality and more uniform regardless of composition.

196 Although the difference in photocurrent due to the difference in emitter LD may

be minimized by further optimization of each device structure, it is worth emphasizing

here that, assuming unity collection of 280-500 nm photons, the superior short

wavelength collection of the MM-GaInP cell over the LM-AlGaInP cell, based entirely

on relative optical properties, should still approach ~0.72 mA/cm2. The additional

transmission, and thus accessible photocurrent, accounts for ~3.9% of the total available

photocurrent for a 2.05 eV cell. As such, this stands as an innate advantage of the

MM-GaInP approach over the LM-AlGaInP, irrespective of material quality. Combined with the higher emitter LD in MM-GaInP that was observed, the resultant additional

~1.1 mA/cm2 of photocurrent corresponds to ~6.0% of the total available photocurrent

for a 2.05 eV cell.

Going further, IQE modeling also revealed details of the relative base material

quality between the two approaches; base LD values are listed in Table 7.1. Interestingly,

whereas the variance in the optical datasets used resulted in only small variances in the

emitter LD values, the higher uncertainty in the long wavelength optical constants observed in the literature lead to higher uncertainties in the base LD values. The

LM-AlGaInP base LD was found to vary widely, 255-623 nm, whereas the MM-GaInP

base LD yielded a tighter distribution of 340-440 nm. Although this uncertainty makes it

difficult to accurately compare the base LD terms for the two devices, note that the median values (440 nm and 390 nm, respectively) are relatively similar, thereby suggesting that overall material qualities within the base layers are not substantially different. It is worth noting that there is a slight difference in the experimental base doping determined via C-V in the LM-AlGaInP and MM-GaInP cells; 1.0×1017 cm-3 and

197 16 -3 9.0×10 cm , respectively. This difference could either impact the SCR width and/or LD.

However, modeling indicates that this changes the SCR width by ~8 nm, which results in

only a 0.06 mA/cm2 change in the total integrated IQE and is negligible. Although this difference could also impact LD, the hypothesis of nearly-identical base LD values for

each cell is supported by the experimental LIV and DIV data, presented in Figure 7.5.

The above front-side performance differences (i.e. window transmission and

emitter LD) also manifest in the LIV results shown in Figure 7.5(a), with

2 2 JSC = 8.3 mA/cm for the LM-AlGaInP cell and JSC = 9.8 mA/cm for the MM-GaInP

cell. The 0.04 eV smaller bandgap of the MM-GaInP cell is responsible for only

~0.4 mA/cm2, meaning there is still an ~1.1 mA/cm2 difference due entirely to front-side

performance. Note that this value is not directly comparable to values in the previous

discussion since those were based on IQE, but this value is in good agreement with

integrated EQE results. The JSC-VOC measurements, offset by JSC of the corresponding

device and plotted on the same graph in Figure 7.5(a), also suggest that the slope of the

LIV data below the maximum power point is likely due to the presence of voltage-

dependent carrier collection (VDCC) in both devices (rather than a shunt). Although the

origin of this effect is not definitively known, it is plausible that it is caused by the

reduction in the thickness of the depletion region (primarily in the low-doped base) under

forward bias. The reduced SCR then exacerbates the effect of the relatively poor (short)

base LD values by shifting the quickly decaying collection probability profile toward the front of the cell. As such, the nearly identical slope below the maximum power point voltage, shown in the inset in Figure 7.5(a), suggests that both materials possess a similar base LD, in general agreement with the IQE modeling results (see Table 7.1).

198

199 Unlike the JSC, the VOC and WOC (= EG/q – VOC) values are very similar, with

VOC = 1.52 V for LM-AlGaInP and VOC = 1.48 V for MM-GaInP, corresponding to

WOC = 0.54 V for each cell. This is within the range of values cited in the literature,

which suggests comparable material quality. Note that after accounting for the

logarithmic influence of JSC on VOC, the slightly larger VOC for the LM-AlGaInP cell

does indeed correspond to its ~0.04 eV larger bandgap, as seen in the experimental IQE

data in Figure 7.4.

To understand why both cells possess the same WOC, a more thorough analysis

was done via DIV characterization, shown in Figure 7.5(b). By fitting the DIV curves of

both devices using a standard double-diode model, an n ≈ 2 ideality factor was revealed for voltages up to VOC. This signifies a depletion region dominated recombination

mechanism within typical operating conditions, as expected for such relatively wide

bandgaps; n = 1 transport dominates at higher voltages. This is similar behavior to high

quality (AlzGa1-z)xIn1-xP cells demonstrated in the literature [9]. J02 values extracted

from the double-diode fits are provided in Figure 7.5(b). The MM-GaInP was found to

possess an ~20× larger J02. Qualitatively, this is consistent with the 0.04 eV smaller bandgap of MM-GaInP due to the exponential impact of bandgap on the intrinsic carrier concentration (ni), which in turn is proportional to J02. Quantitatively, it is difficult to

demonstrate that this is the expected difference due to the uncertainty in the effective

density of states at these (AlzGa1-z)xIn1-xP compositions, which is necessary to

compute ni.

Ultimately, the combination of the equal WOC values and the similar DIV

performance at operating conditions suggests that the distribution of defect states in

200 LM-AlGaInP (e.g. Al-related point defects) and MM-GaInP (e.g. threading dislocations)

has a similar overall net effect on depletion region recombination. Since this behavior is

expected for devices of similar material qualities, which both analytical modeling and

VDCC trends indicate, it is reasonable to conclude that the overall electronic transport

quality of the base layers is indeed effectively similar. Knowledge of the energy

position(s) and concentrations of any deep levels within the bandgap for both approaches

would be required to provide further explanation of the relative impact of Al versus

dislocation content. As such, characterization via deep level transient spectroscopy is

planned to explore this in the future.

7.4. CONCLUSIONS

Two approaches, LM-AlGaInP and MM-GaInP, for achieving 2.05 eV top cells

have been explored. The MM-GaInP approach has the innate benefit of enabling a wider

direct bandgap, more transmissive internally lattice-matched window, leading to

substantially higher short wavelength collection. This effect alone enables a

~0.72 mA/cm2 higher photocurrent in MM-GaInP compared to LM-AlGaInP (assuming a perfect ARC), which corresponds to ~3.9% of the total available photocurrent for a

2.05 eV bandgap solar cell. However, modeling demonstrated that the difference in collection in the experimental devices was due to both the higher window transmission

2 and emitter LD in MM-GaInP. As a result, this enables a ~1.1 mA/cm higher

photocurrent in MM-GaInP (assuming a perfect ARC), corresponding to ~6.0% of the

total available photocurrent for a 2.05 eV solar cell. Modeling also indicated that both

approaches possess a similar base LD, and the VDCC trend supported this. Further

201 analysis revealed that both cells possess a nominally identical WOC of 0.54 V, implying a similar net depletion recombination current in each device. Overall, merits to both approaches have been demonstrated and warrant further exploration of the impact of Al and/or dislocation content on the performance of (AlzGa1-z)xIn1-xP top cells.

202 CHAPTER 8:

CONCLUSIONS AND FUTURE WORK

III-V metamorphic epitaxy is a versatile technique that provides an additional degree of freedom to the design of a wide variety of III-V multijunction solar cell

(MJSC) approaches. This dissertation successfully leveraged this technique to develop critical components of various III-V MJSC approaches of the future, bringing these technologies one step closer to reality. These components included metamorphic tunnel junctions for use in III-V/Si MJSCs for terrestrial applications and wide bandgap

(AlzGa1-z)xIn1-xP top cells for III-V MJSCs for space applications.

III-V metamorphic epitaxy is a form of lattice-mismatched heteroepitaxial growth of III-V compounds to achieve bandgaps that are otherwise unobtainable via lattice- matched epitaxy on existing substrates. Lattice-mismatched epitaxy can either be strained or metamorphic. When a lattice-mismatched epilayer is grown thinner than its critical thickness it can remain strained and defect-free. However, for applications that require an epilayer thickness greater than this critical thickness, the epilayer begins to relax to its natural lattice constant and becomes metamorphic. This relaxation process is accompanied by the formation of dislocations to relieve the strain energy within the 203 epilayer. These dislocations can either be contained within the mismatched interface in the form of misfit dislocations or propagate vertically through device layers in the form

of threading dislocations. Ideally, the formation of threading dislocations should be

avoided since they can detrimentally impact device performance. It is very difficult to

avoid threading dislocations, though, in the case of direct lattice-mismatched epitaxy with

a significant amount of misfit. For such applications, metamorphic III-V graded buffers can be engineered to controllably relieve strain via the formation of misfit dislocations, thus minimizing threading dislocations and enabling high-performance metamorphic devices. The metamorphic components that were demonstrated in this dissertation built upon our research group’s expertise in the design of III-V graded buffer.

8.1. METAMORPHIC TUNNEL JUNCTIONS

8.1.1. SUMMARY

Crystalline silicon solar cells currently dominate the terrestrial market, although they are approaching their theoretical efficiency limit. III-V/Si MJSCs can overcome this limit by simultaneously enabling efficiencies well beyond the limit of Si alone and remaining economically viable due to the use of Si substrates to leverage lower manufacturing costs. However, this approach requires III-V metamorphic epitaxy to integrate the necessary III-V materials with Si. Building upon our research group’s

GaP/Si nucleation layer and metamorphic graded buffer expertise, this dissertation demonstrated various metamorphic tunnel junction designs suitable for use within

III-V/Si MJSCs.

204 Tunnel junctions serve as low-resistance, optically transparent interconnects between adjacent sub-cells within MJSCs. For III-V/Si MJSCs, these tunnel junctions are

ideally grown at the same lattice constant as the metamorphic III-V sub-cells. Therefore, metamorphic tunnel junctions with relatively unexplored lattice constants are necessary.

Development of these metamorphic tunnel junctions initially began with materials and devices grown via molecular beam epitaxy (MBE). At this earlier stage of research, the

III-V/Si MJSC approach primarily focused on an MBE-grown triple-junction solar cell

(MBE 3J) designed for operation under high concentration. This in turn specified a variety of requirements for the necessary lower and upper tunnel junctions of the

MBE 3J, including the necessary peak tunneling current (JP), resistance-area product

(RA), and bandgap to minimize parasitic losses within the tunnel junction.

MBE growth conditions were first explored to maximize carrier concentration in

lattice-matched Si- and Be-doped GaAs. Si doping was found to be particularly

challenging due to its amphoteric behavior. However, it was found that by using a relatively low growth temperature and high V:III beam flux ratio, this amphoteric behavior could be suppressed to enable high electron concentrations. After demonstrating preliminary p-GaAs:Be/n-GaAs:Si homojunction tunnel junctions, metamorphic p-GaAs0.9P0.1:Be/n-GaAs0.9P0.1:Si homojunction tunnel junctions were demonstrated at

the necessary lattice constant for the MBE 3J. The highest performance metamorphic

-2 -4 2 homojunction tunnel demonstrated JP = 103.9 A·cm and RA = 4.5×10 Ω·cm , meeting

the requirements of the lower TJ necessary for operation of the MBE 3J under high

concentration.

205 The GaAs0.9P0.1 homojunction tunnel junction design was next modified to meet

the optical transparency requirements of the upper TJ. This was accomplished by

significantly thinning the GaAs0.9P0.1 tunnel junction layers to reduce its optical thickness

as well as adding wide bandgap Ga0.57In0.43P cladding layers to demonstrate a metamorphic p-Ga0.57In0.43P:Be/p-GaAs0.9P0.1:Be/n-GaAs0.9P0.1:Si/n-Ga0.57In0.43P:Si

double heterostructure tunnel junction. This device performed significantly better than

-2 the metamorphic homojunction tunnel junction, demonstrating JP of 510 A·cm and RA

of 2.0×10-4 Ω·cm2. Thus, this double heterostructure metamorphic tunnel junction

became the preferred tunnel junction design for both the lower and upper tunnel junction

of subsequently grown MBE 3Js since it outperformed the homojunction tunnel junction

in all aspects. Finally, this double heterostructure tunnel junction was incorporated into a

Ga0.57In0.43P/GaAs0.9P0.1 dual-junction solar cell (a subset of the MBE 3J containing only

the III-V sub-cells and upper tunnel junction) to test its thermal stability. The dual-

junction performed with no indication of tunnel junction failure up to at least 164 suns

concentration, the highest achievable concentration with the experimental setup that was

available. This indicated that such a tunnel junction design was thus very promising for

future III-V/Si triple-junction solar cells.

As our research group continued to develop the III-V/Si MJSC approach, a

transition to the metal-organic chemical vapor deposition (MOCVD) growth platform

occurred due to interest in a more economically viable growth method. Along the same

lines, the MJSC structure was modified to a GaAs0.75P0.25/Si dual-junction (MOCVD 2J) to reduce manufacturing costs while maintaining a high practically-attainable efficiency.

This approach was also determined to be economically viable for AM1.5G applications,

206 eliminating the need for expensive concentrator systems. As a result of this transition,

development of a new MOCVD-grown III-V metamorphic tunnel junction at a different

target lattice constant was necessary.

Design of an MOCVD-grown tunnel junction proceeded in a similar fashion to

the MBE-grown tunnel junctions. Optimization of lattice-matched AlxGa1-xAs:C and

GaAs:Te growth conditions were first performed to maximize carrier concentrations. C

and Te were chosen as the dopants due to their superior properties with respect to tunnel

junctions; both dopants possess low diffusion coefficients and enable high carrier

concentrations. AlxGa1-xAs:C optimization revealed that an optional post-growth anneal

could be performed to further improve the hole concentration. GaAs:Te optimization

indicated that a method for mitigating the well-known Te memory effect needed to be developed to enable sharper doping profiles in the n-type tunnel junction layer. An initial

study to demonstrate the significance of the memory effect consisted of growing a series

of AlxGa1-xAs:C/GaAs:Te tunnel junctions with varying GaAs:Te thickness. Although

the performance improved significantly with increasing thickness due to increasing Te

incorporation throughout the nominally uniformly doped GaAs:Te layers, such an

approach was not realistic. Thus, a DETe pre-dosing routine was developed to achieve a more uniformly doped profile while still enabling a thin GaAs:Te layer. Extremely high- performance lattice-matched AlxGa1-xAs:C/GaAs:Te tunnel junctions were demonstrated

-2 using this technique, demonstrating JP = 3120 A cm .

The lattice-matched device design was transitioned⋅ to the necessary metamorphic

lattice constant. Metamorphic materials calibrations demonstrated that the carbon

precursor CBrCl3 significantly impacted As/P incorporation in AlxGa1-xAsyP1-y.

207 Accounting for this, an as-grown metamorphic Al0.2Ga0.8As0.75P0.25:C/GaAs0.75P0.25:Te

-2 -4 2 tunnel junction was demonstrated with JP = 279.1 A cm and RA = 3.0×10 Ω cm .

Anneal studies were performed to test this device under⋅ various conditions, including⋅ a

performance-reducing thermal load anneal to simulate the growth of the GaAs0.75P0.25 top

cell and a post-growth performance-enhancing carbon activation anneal to increase the

hole concentration in the Al0.2Ga0.8As0.75P0.25:C layer. Upon exposure to the thermal load

anneal, this tunnel junction maintained sufficient performance to enable operation of the

MOCVD 2J up to medium concentration with a minimal loss in efficiency. By including

the carbon activation anneal, operation up to high concentration is possible. Finally, this

tunnel junction design was incorporated into the current world-record monolithic

GaAs0.75P0.25/Si dual-junction solar cell [1].Series resistance from the tunnel junction did

not limit performance of the dual-junction.

8.1.2. ONGOING AND FUTURE WORK

Although our research team transitioned from the MBE 3J to the MOCVD 2J,

there is still opportunity for future development of the MBE 3J and thus the MBE-grown

tunnel junctions. In addition, although the metamorphic tunnel junctions were designed

specifically for the MBE 3J, it is possible that alternative III-V MJSC structures may

benefit from such devices. It is thus worthwhile exploring potential pathways for

overcoming various challenges our research group has identified to further improve the

performance of MBE-grown metamorphic tunnel junctions.

One concern with all the MBE-grown tunnel junctions was related to the use of

Be as the p-type dopant. The literature has shown that Be has a high diffusion coefficient

208 [224]. This can be problematic for a tunnel junction when exposed to the thermal load of

the subsequently grown sub-cell(s). If Be diffuses significantly during growth of the

subsequent sub-cells, the doping profile at the junction can be significantly altered and

result in lower device performance. Further characterization is necessary to determine the extent of this degradation in the MBE-grown double heterostructure tunnel junction.

Although a Ga0.57In0.43P/GaAs0.9P0.1 dual-junction solar cell operated up to over 164 suns without failure of the tunnel junction, it was not possible to identify how significantly the tunnel junction degraded due to experimental limitations. Furthermore,

the lower tunnel junction is expected to degrade even more since it experiences a

significantly greater thermal load. Whereas the upper tunnel junction only experiences

the thermal load of the Ga0.57In0.43P top cell, the lower tunnel junction experiences the

thermal load of both III-V sub-cells. In addition, the thermal load of the GaAs0.9P0.1

middle cell is significantly greater than that of the Ga0.57In0.43P top cell due to a ~100 °C higher growth temperature.

A possible solution to the high diffusivity issue of Be is to replace the dopant with another element such as C. As was discussed for the MOCVD-grown tunnel junctions in

chapter 7, C has a low diffusion coefficient; negligible diffusion has been observed in

AlxGa1-xAs:C tunnel junction layers in the literature [196]. In addition, C is similarly

capable of high p-type doping; hole concentrations over 2.5×1020 cm-3 were achieved with C doping in MOCVD, compared to 6×1019 cm-3 with Be doping in MBE within this

dissertation. Therefore, C appears to be an overall better p-type dopant for tunnel junction

applications. The next planned stage of MBE tunnel junction development was to explore

209 CBr4 as the source for p-type doping. This was postponed due to the transition to the

MOCVD growth platform but is an area to consider for future development.

Another area of improvement for the MBE-grown double heterostructure tunnel

junction is the optimization of the device structure. In this dissertation, this structure was

demonstrated as a proof of concept and the device structure was never optimized.

According to band structure modeling, the enhanced performance comes from the

enhanced hole concentration in the p-GaAs0.9P0.1 layer near the

p-Ga0.57In0.43P/p-GaAs0.9P0.1 interface due to the band alignment at this interface. It is

reasonable to assume that the thickness of the p-GaAs0.9P0.1 could be optimized to ensure

this enhanced hole concentration efficiently tunnels at the tunnel junction interface. If this

can be achieved by thinning the p-GaAs0.9P0.1 layer, this also simultaneously reduces the

optical thickness of this tunnel junction.

The transition to the MOCVD-grown devices resulted in the development of an

MOCVD-grown metamorphic tunnel junction with performance that significantly exceeded all required metrics for the MOCVD-grown dual-junction under AM1.5G.

Operation could be extended up to high concentration via the use of a performance- enhancing carbon activation anneal. However, the carbon activation anneal can potentially negatively impact other components of the dual-junction and adds an extra processing step that increases manufacturing cost. Therefore, additional optimization may allow for the omission of this anneal. Potential areas of improvement include further optimization of carrier concentrations and the device structure.

In this dissertation, the maximum average bulk GaAs:Te electron concentration achieved was 1.87×1019 cm-3, which modeling suggested reached a local maximum of

210 2.03×1019 cm-3 in the nonuniformly doped profile (see Table 6.2). However, the literature

has shown electron concentrations in GaAs:Te as high as 3×1019 cm-3 [196]. In terms of tunnel junction performance, such an increase in electron concentration would substantially improve device performance. Thus, a clear pathway for optimization is further optimization of the n-type layer growth conditions to achieve this higher electron

concentration.

The device structure is another potential area for future optimization. Note that

the MOCVD-grown tunnel junction uses a heterojunction compared to the MBE-grown

double heterostructure. Preliminary development of the MOCVD-grown tunnel junction

explored reproducing the MBE-grown double heterostructure design. However, all

devices resulted in poor performance, with as-grown peak tunnel current densities on the

order of 1 A cm-2. As a result, initial MOCVD-grown tunnel junction development

transitioned ⋅back to a homojunction until growth conditions were developed to achieve

significantly higher hole concentration in AlxGa1-xAsyP1-y compared to GaAsyP1-y. This

ultimately lead to the demonstrated heterojunction tunnel junction design.

The Te memory effect was not explored until well into the development of the

MOCVD-grown heterojunction tunnel junction. At this point, it was hypothesized that the Te memory effect could have been the reason for the poor performance of the attempted MOCVD-grown double heterostructure tunnel junctions; the thin 5 nm

GaAsyP1-y:Te layer at the tunnel junction interface was likely doped significantly lower

than expected due to no DETe pre-dosing routine. During the final stages of developing

the MOCVD-grown heterojunction, the concept of the MBE-grown double

heterostructure was re-explored. However, rather than testing the full double

211 heterostructure, a 25 nm p-AlxGa1-xAs:C/5 nm p-GaAs:C/500 nm n-GaAs:Te structure

(without DETe pre-dosing) was tested to introduce a valence band offset at the p-AlxGa1-xAs/p-GaAs interface to potentially enhance performance comparable to the

MBE-grown double heterostructure. Preliminary results indeed indicated that the peak

tunneling current of lattice-matched devices improved by ~50% using this structure

(without DETe pre-dosing). However, once this structure was integrated into the final

heterojunction design with 100 nm GaAs:Te (with DETe pre-dosing), the improvement

was no longer observed. Despite the unsuccessful integration of this structure into the

optimized heterostructure tunnel junction, it appears to be a promising approach that

warrants future exploration.

8.2. ALGAINP TOP CELLS

8.2.1. SUMMARY

Current research trends are pushing to increase the efficiency of III-V MJSCs via

the use of additional sub-cells. As the number of sub-cell increase from 4 to 6, the ideal

bandgap profile of the MJSC shifts the bandgap of the top cell from ~2.05 eV to ~2.3 eV,

respectively. Although the ideal bandgap required for the top cell can be achieved via

lattice-matched (AlzGa1-z)0.52In0.48P, the necessary Al content tends to reduce device performance due to increased oxygen content. In this dissertation, an alternative solution was explored for achieving a 2.05 eV top cell via the use of III-V metamorphic epitaxy.

Al content versus misfit was compared in lattice-matched (Al0.32Ga0.68)0.52In0.48P and metamorphic Ga0.66In0.34P solar cells. Results demonstrated that the metamorphic

Ga0.66In0.34P solar cell possessed substantially higher short wavelength current collection.

212 This was due to the wider-bandgap, internally lattice-matched window layer of the

metamorphic Ga0.66In0.34P cell, as well as a longer emitter diffusion length. Device

modeling and characterization results suggested similar base diffusion lengths in each

cell. Merits to both approaches were demonstrated and warrant further exploration of the

impact of Al and/or dislocation content on the performance of (AlzGa1-z)xIn1-xP top cells.

8.2.2. ONGOING AND FUTURE WORK

The (AlzGa1-z)xIn1-xP top cells explored in this dissertation where limited to

2.05 eV for use in 4 junction MJSCs for space applications. However, if future III-V

MJSCs are to increase to 6 junctions, the ideal bandgap increases to 2.3 eV (see Figure

1.7). The additional Al content required of lattice-matched (AlzGa1-z)0.52In0.48P makes

this approach even more challenging. Thus, opportunities for future development include

exploring metamorphic GaxIn1-xP and metamorphic (AlzGa1-z)xIn1-xP to achieve

bandgaps approaching 2.3 eV.

Metamorphic GaxIn1-xP eliminates Al content, but introduces a significant

amount of misfit to achieve these wider bandgaps. However, preliminary work has

already been done to demonstrate a 2.16 eV metamorphic Ga0.75In0.25P top cell. Although

this device achieved high short wavelength collection efficiency similar to the 2.05 eV

metamorphic Ga0.66In0.34P top cell due to the use of a wide bandgap internally lattice-

matched window, the larger misfit (~1.8% versus ~1.1%) led to a higher threading dislocation density and WOC (= EG – VOC) compared to the 2.05 eV device. This suggests

that improvement in the metamorphic graded buffer design would improve device performance, which is scheduled to be optimized in the near future. One optimization

213 pathway includes potentially grading with less misfit per step. This would result in lower

levels of strain at each buffer interface to promote glide of misfit dislocations over the

nucleation of addition dislocations [210].

Another challenge associated with metamorphic GaxIn1-xP is that a direct

bandgap up to 2.3 eV is likely not possible since tie-lines suggest the material becomes

indirect around 2.25 eV [94], [134]. The preliminary 2.16 eV metamorphic Ga0.75In0.25P

appeared to already begin to deviate from the GaxIn1-xP direct bandgap tie-line. This is

potentially due to a transition to indirect, or due to increased ordering. This can reduce the bandgap by up to ~100 meV in Ga0.75In0.25P [94]. Therefore, a future area of research is to identify the degree of ordering in this metamorphic GaxIn1-xP to determine if it

increases as a function of misfit or some other growth parameter. If ordering is higher in

metamorphic GaxIn1-xP with greater misfit, it may be possible to optimize the growth

conditions at these compositions to reduce ordering to achieve a higher bandgap.

If metamorphic GaxIn1-xP does not appear the be the most promising approach,

metamorphic (AlzGa1-z)xIn1-xP is an alternative. Such an approach can achieve the target

bandgaps using various combinations of misfit and Al content. This opens up the

opportunity to determine if an optimal balance of misfit and Al content exists. To date, a preliminary 2.22 eV metamorphic (Al21Ga0.79)0.68In0.32P cell has been demonstrated.

Although this device exhibited poor long wavelength response, it is entirely possible that further optimization of growth conditions specific to this composition is necessary.

Another potential area of future research includes the development of a transparent (AlzGa1-z)xIn1-xP compressive buffer. As discussed in section 7.2, such a buffer would be necessary to integrate a metamorphic GaxIn1-xP top cell into an inverted

214 metamorphic multijunction solar cell structure that utilizes any sub-cells lattice-matched

to Ge.

8.3. FINAL COMMENTS

This dissertation has demonstrated the versatility of III-V metamorphic epitaxy by

using this technique to develop components of two different MJSC approaches designed

for different applications. This included metamorphic tunnel junctions for use in III-V/Si

MJSCs for terrestrial applications and wide bandgap (AlzGa1-z)xIn1-xP top cells for III-V

MJSCs for space applications. Our research group will likely continue to leverage this

technique well into the future to push the capabilities of III-V MJSCs. However, this

technique is not only limited to developing future solar cells and MJSCs; III-V

metamorphic epitaxy should be viewed as an additional knob that any bandgap engineer can turn to optimize a wide variety of future semiconductor devices.

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