Design, modeling, and optimization of indium arsenide diodes for microscale thermophotovoltaics

Design, Modeling, and Optimization of Indium Arsenide

Diodes for Microscale Thermophotovoltaics

by

Michael Masakichi Masaki

B.S., Electrical Engineering

University of Hawai'i at Manda (1998)

BARKER

OF TECHNOLOGY

APR

_{2 4 2001}

LIBRARIES

Submitted to the Department of Electrical Engineering and Computer Science

in partial fulfillment of the requirements for the degree of

Master of Science

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

September 2000

@ MIT, MM. All Rights Reserved

The author hereby grants to MIT permission to reproduce and

to distribute copies of this thesis document in whole or in

.

Signature of Author.... . . .

...

...

.

. .

... . ...

Department ofElectrical Engineing and Computer Science

29 September 2000

Certified by...

.

Accepted by...

.

_.

_.

_..

.... ...

. .. . . ..

Professor of Electrical Engineering

Thesis Supervisor

...

Arthur C. Smith

Design, Modeling, and Optimization of Indium Arsenide Diodes for

Microscale Thermophotovoltaics

by

Michael Masakichi Masaki

Submitted to the Department of Electrical Engineering and Computer Science on 29 September 2000, in partial fulfillment of the

requirements for the degree of Master of Science

Abstract

The band gap of Indium Arsenide is 0.354 eV (3.48 pm) at room temperature, ideal for photovoltaic applications in the near infrared wavelength range. In order to facilitate the design of InAs photovoltaics, SimWindows@, a one dimensional Poisson equation solver, was used as a design and modeling tool for InAs photodiodes and to provide insight into their design. The validity of the modeling was confirmed by comparing its predictions with experimental data in the published literature.

Two InAs photovoltaics were also fabricated by Molecular Beam Epitaxy, followed by char-acterization. The I-V characteristics of the two devices differed greatly from theoretical pre-dictions. Since the discrepancy could not be explained by modifying the models created in SimWindows@, it was concluded that the results must be due to a more fundamental as-pect outside the scope of SimWindows@. Several tests were done to identify this asas-pect. It was found that the diode characteristics of the device resulted primarily from a metal-semiconductor junction on the back side of the wafer, not from the InAs p-n structure grown on the wafer as originally expected. Finally, a low temperature measurement revealed that the remaining non-linear I-V characteristic was due to the tunneling nature of the p-n junction.

Thesis Supervisor: Clifton G. Fonstad,Jr. Title: Professor of Electrical Engineering

Acknowledgments

At this time I would like to thank everyone who helped and supported me in this endeavor. Without their help and support, I would not be writing these words at this moment.

Firstly, I would like to thank God for too many reasons to list here.

I also thank my parents, Melvin Y. and Clara Y. Masaki, for their undying support and motivation, and their belief that an education is the most important gift of all. I would like to extend my warmest thanks to my brother Gavin for keeping me in line.

I owe a great debt of gratitude to Professor Clifton G. Fonstad. His unending patience, support,

and guidance were invaluable to me, and I would not be able to conduct the research without the use of Professor Fonstad's laboratories, experience, and research funding. I would also like to thank Professor Fonstad for giving me the opportunity to be the teacher's assistant for 6.012 (a rewarding and invaluable experience), and for reading over this document.

Henry Choy's friendship, honesty, advice, and knowledge was essential to finishing this work. The many nights spent on debating points and testing if I really understood things drove me to push harder that I have done before. Also, thank you Henry for teaching me how to use the many pieces of equipment in the laboratory, growing the samples 9722 and 9725 that were used in this thesis, and tolerating (barely) my Star Trek fanaticism. Many thanks go to Professor Sheila Prasad for tips (especially on how to write my thesis) and many cups of coffee. I also thank Karen Young-Waithe for processing the wafers and providing me with the necessary information in analyzing the photodiodes. I am grateful for the assistance of Gale Petrich, Joyce Wu, and Hans Callebaut for their assistance in the cryogenic measurements.

In addition, thank you Dr. P. Aitor Postigo Resa and Dr. M. H. Madhusudhana Reddy for your knowledge of the art of MBE growth, and Wojciech Giziewicz for your advice and humor. I would also like to thank my roommate Harry Lee for his advice, comments, and informing me of the existence of SimWindows@, and also for being a great roommate.

Thank you Junji Himeno and the MIT Kendo club for your words of encouragement and keeping me in shape, both physically and mentally, and Steve Wang for filling in for me at all the practices I could not attend.

Finally, I would like to thank Professor Kazutoshi Najita of the University of Hawai'i for encouraging me to attend graduate school instead of working in industry, Mrs. Suzuki and Mr. Mersereau for believing that I had a future, and Brandon Rai Mitsuda, Esq., for his friendship and support over the last 13 years.

Contents

1 Introduction 11

1.1 Why InAs Photovoltaics? . . . 11

1.2 SimWindows@ . . . 13

1.3 Overview of the Thesis . . . 13

2 Formulating a Model for Optimizing a Device Design 17 2.1 SimWindows . . . 17

2.1.1 D escription . . . . 17

2.1.2 Advantages . . . 18

2.1.3 InAs Model . . . 20

2.1.4 Shortcomings of SimWindows Simulations . . . . 27

2.2 Theoretical Results from InAs Model . . . . 29

2.2.1 Testing the SimWindows Model . . . . 29

2.2.2 Design Parameters from Model: . . . . 34

2.3 Summary of Chapter 2: . . . . 39

3 Application of SimWindows to MIT Diodes 40 3.1 InAs Photovoltaic Structure: . . . . 40

3.2 Comparison with the SimWindows Simulations . . . . 40

3.2.1 9725: . . . 40

3.2.2 9722: . . . 48

3.3 Explaining the Discrepancies . . . 52

3.3.2 Surface Inversion . . . 53

3.3.3 Bad Metal-Semiconductor Contact on the Bottom: . . . . 55

3.3.4 What Happened to the P-N Junction? . . . . 57

4 Conclusion 62 4.1 Summary of Accomplishments. . . . . 62

4.2 Future Avenues . . . . 63

A Optical Properties of Indium Arsenide 64 B Ideal Model of a Homojunction Photovoltaic Device 70 B .1 Basic Principles: . . . . 70

B.2 Circuit Model and Current-Voltage characteristics: . . . . 71

B .2.1 Circuit M odel . . . 71

B.2.2 The open circuit voltage V, and short circuit voltage I .. . . . . 72

B.2.3 Maximum Power Generation . . . . 73

B.3 Monochromatic Response . . . . 76

List of Figures

1-1 5000 C Black Body Spectrum, the energy spectrum of interest for InAs. . . . . . 14 1-2 InAs Band Structure. EO is the bandgap. Eo = 0.354 eV, Ao = 0.46 eV,

Al = 0.28 eV, and El = 2.50 eV . . . 14

1-3 Index of Refraction (Solid) and Extinction Coefficent (Grey) of InAs[5] . . . 15 1-4 Absorption Coefficient of InAs [5] . . . . 15

2-1 The model index of refraction data (gray) and the calculated index of refraction (solid) with respect to enegy. . . . . 22 2-2 The model absorption coefficient data (gray) and the calculated index of

refrac-tion (solid) with respect to enegy. . . . 22

2-3 Thermal Conductivity versus Temperature. The solid line represents the mea-sured data[11], and the thin line represents the model results. . . . 23 2-4 Electron Mobility versus Doping Concentration. Model (black line) and

mea-sured (grey line)[13] data. . . . 24

2-5 Hole Mobility versus doping. Model (solid line) and measured (diamond) [14] data. 25

2-6 The dominant Auger recombination processes in InAs. A: eeh recombination. B: ehh, recombination[18]. . . . . 26 2-7 IV characteristic from SimWindows@. Note that the IV characteristic changes

from exponential (ideal) to linear (R). . . . . 28

2-8 Lack of high level injection in SimWindows@. SimWindow data (black) and the ideal diode equation (grey). Note that the plot changes from exponential relationship (n=1) to resistive. . . . . 28 2-9 Structures used to verify model. Device A: pin diode. Device B: p-n diode. . . . 29

2-10 I-V characteristics of measured and simulated Results. Figure A is the I-V char-acteristic of the PIN structure and Figure B is I-V charchar-acteristic of the P-N structure. Note that the measured current does not saturate in Figure B. This

is caused by tunneling. . . . 31

2-11 I-V characteristics of measured and simulated Results. The simulation data uses a mobility 1.7 times smaller than the previous figure. Figure A is the

I-V

2-12 Photocurrent versus the location of the light impulse, calculated (black) and simulated by SimWindows@ (grey). . . . 33

2-13 Minority Carrier Lifetime versus Doping Concentration for P-type InAs. The data for Auger recombination is approximate. . . . 36

2-14 Minority Carrier Lifetime versus Doping Concentration for N-type InAs. . . . 36

2-15 Electron Diffusion Length versus Doping. Note the diffusion length is within the same order of magnitude of the substrate thickness for low p-type doping . . . . 37

2-16 Hole Diffusion Length versus Doping . . . . . 38

3-1 Device Structures used in this analysis . . . 41

3-2 A diagram of the device structure and surface of device 9725. . . . 41

3-3 Terminal Characteristics of a device fabricated on growth 9725 plotted on a linear scale.. . . ... .... .... . ... ... .... . .. . ... 42

3-4 Log plot of device 9725 and fit. . . . 43

3-5 Log Scale Plot of the 9725 Data, with the Results of the SimWindows@ Simulations. 43 3-6 Doping variations of the 0.56 pm 2x10181 p-type buffer layer. . . . . 45

3-7 Doping variations of the 1.0 pam 5x1017-1 p-type layer. . . . . 45

3-8 Doping varitation of the 1.0 pm 5x 10171 n-type layer. Doping this layer more n-type made no noticeable changes in the I-V curve. . . . . 46

3-9 Changes in the IV characteristics with changes in the SHR lifetime. . . . 47

3-10 The simulated effects of increasing series resistance in device 9725. . . . 48

3-12 The metalization pattern of device 9722. The top metal (shown in black) served

as etch mask to define the mesas. Areas A,B,C,F, and H are 4x10-4cm2 in area;

D and E are 4.9 x10-cm2

in area; and G is 2.24x10-2cm 2 . . . . . . 49

3-13 A comparison of the simulated I-V characteristics between the 9722 and 9725

d evices. . . . 50

3-14 The measured IV characteristics of the 9722 and 9725 devices. The data from device 9722 was multiplied by 9.78. . . . 50

3-15 Measurements taken from device 9722 from pad E to the back of the substrate

(gray) and from pad D to the back of the substrate (dotted black) . . . . 51 3-16 Measurements taken from 9722. These measurements were taken from A, B, C,

F,or H to the back of the substrate . . . . 51 3-17 I-V characteristics of several devices after thermal annealing. These plots

demon-strate the I-V plots that were symmetrical. . . . . 52 3-18 9722 Measurements. These figures display the more diode-like I-V characteristics. 53 3-19 Surface inversion in InAs. Note that the Fermi Energy at the surface penetrates

the conduction band. . . . . 53 3-20 Effects of Passivation on the InAs photodiodes. Note that the diode-like

charac-teristics dissapear after every treatment. . . . . 54

3-21 Through-substrate measurement of 9722 (grey) compared with 9725 I-V

charac-teristics (black) . . . . 55 3-22 Compensated 9722 Data (grey) with 9725 Data (Black). . . . 56 3-23 Through Substrate measurement of 9722, before back metal (Grey) and after

(Black). Note that all the diode-like characteristics dissapear. . . . 56 3-24 Room Temperature Measurements of device 9722. Note that the I-V

character-istics are sym m etrical. . . . 57

3-25 The differential resistances of the devices. Note that resistance is not symmetrical

about the origin . . . 58

3-26 Linear Plot of the I-V Characteristics of Device 9722 at room temperature (grey)

3-27 Log Plot of the I-V Characteristics of Device 9722 at room temperature (grey)

and 132 K (black). . . . 59

3-28 Tunneling Current in a P-N junction. Figure A demonstrates tunneling directly

from the condunction band to the valence band. Figure B indicates tunneling

by interband states. ... ... 60 3-29 Effect of Tunneling on the Size of Power Rectangle. Figure A represents an ideal

diode, Figure B represents a diode with tunneling. . . . 61

A-i Transitions of interest in InAs. . . . 65 A-2 Real Permittivity, 61, versus photon energy. eia is equation A.5, and deals with

the EO and EO + AO transitions. Eib is equation A.11, and deals with the El and E₁

+

ei1

El = + Eib b - 61c . . . . . 68

A-3 Imaginary Permittivity, E2, versus photon energy. 62a is equation A.6, and deals

with the EO and EO + AO transitions. 6

2b is equation A. 12, and deals with the E1 and E1 + A1 transitions. 62c is equation A.16, and deals with the E2 transitions. e2diand E2d2 is equation A.18, and deals with the EL indirect transitions. 2 = 6_{2a +} 6_{2b -}6

2c + 6

2d1 + 6

2d2. . . . . 69 B-1 An example side schematic of a p-n junction photovoltaic. . . . . 71

B-2 a) A photovoltaic under no illumination. No carriers are generated. b) A photo-voltaic irradiated by light. Excess holes and electrons are generated. . . . . 72

B-3 a) The cicuit diagram of a photovoltaic in operation. b) The idealized equivalent circuit of the photovoltiac operation. . . . . 73

B-4 a) I-V curves of a photovoltaic with and without illumination. b) The power rectangle of a photovoltaic. . . . . 74 B-5 A photovolatic with impulse illumination of area G at x.. . . . . 76

List of Tables

1.1 Bandgap energy of several semiconductors at room temperature, and the black body temperature necessary for the black body peak to be absorbed by the m aterial. [4] . . . . 12 2.1 SimWindows@ InAs Material Parameters . . . . 19

2.2 Values used for the photodiode . . . . 33 2.3 Electron and hole mobility of several semiconductors at 300 K[4]. 'NA' indicates

that the material does not have mobility data at room temperature. . . . . 35 A.1 InAs optical porperties calculation parameters. . . . . 66

Chapter 1

Introduction

The main source of power for most satellites and deep space probes are solar cells. For example, both the Stardust[1] and Deep Space 1 [2] probes use solar cells as their primary source of energy. However solar cells harvest increasingly smaller amounts of energy as the probe travels farther away from the sun. Eventually the solar cells become useless and reduced to excess weight as the probe leaves the confines of the solar system. A solution to this problem is to bring the luminous source with the satellite. An example of a luminous source is the black body spectrum from a hot object, which can be created readily from a sustained nuclear fission reaction. A photovoltaic is able to use the black body spectra produced from this reaction to produce electricity. The goal of this project is to analyze and diagnose a photovoltaic created for such an application. This effort is part of a larger project directed at using InAs photovoltaics in a new enhanced performance application called microscale themophotovoltaic (MTPV) energy conversion[3].

1.1

Why InAs Photovoltaics?

The power density of a black body is given by Equation 1.1:

27rhc2 _{h [ Watt}

PdA =- 5 e kBTX ) dA 1M

where c is the speed of light, and kB is the Boltzman constant. Also, from Wien displacement law, the black body peak is given by:

Material Bandgap Energy [eV] _{Blackbody Temperature [K]} Si 1.12 2483 Ge 0.664 1472 C (Diamond) 5.50 12194 BN 6.4 14189 BP 1.98 4390 BAs 1.46 3237 AiN 6.2 13745 AlP 2.41 5343 AlAs 2.153 4773 AlSb 1.615 3580 GaN 3.44 7929 GaP 2.722 6035 GaAs 1.424 3157 GaSb 0.75 1663 InN 1.89 4190 InP 1.344 2980 InAs 0.354 785 InSb 0.169 375

Table 1.1: Bandgap energy of several semiconductors at room temperature, and the black body temperature necessary for the black body peak to be absorbed by the material.[4]

T- _{2 2 1 7}

[-+1

(1.2)

E eV

where E is the black body photon energy in electron volts.

The bandgap of the material must be smaller or equal to than the black body peak in order for the material to absorb a significant amount of the incident black body radiation. The band gaps all group IV and III-V semiconductors are shown in Table 1.1. For TPV and MTPV applications one typically uses a blackbody temperature less than 1000 K so among the group IV and III-V semiconductors, the two best candidates are InAs and InSb.

An important figure of merit for a photovoltaic is the open circuit voltage, Vc, which determines the maximum efficiency of the photovoltaic and must be maximized (this is discussed in detail in Appendices B.2.2 and B.2.3). Since the maximum value for V, is the band gap of the material, InAs would be a better choice than InSb since InAs has a direct band gap of 0.354 eV (A - 3.48 fum) at room temperature, more than twice the bandgap of InSb (0.169 eV at room temperature). Also the band gap of InSb is too small to build diodes that operate properly at

room temperature and the MBE in the laboratory where the research was conducted does not have Antimony cells. Consequently, InAs was chosen for the initial work. In later work, closely related ternary alloys might also be of interest, but their use complicates the design too much at this stage.

The goal is to use a 500'C (773 K) black body (the spectrum is shown in Figure 1-1) as the radiation source, which is close to 784 K.

The band structure of InAs is shown in Figure 1-2. Other properties of InAs that will be important are the refractive index, shown in Figure 1-3, and the absorption coefficient, shown in Figure 1-4. [5]. The Figures 1-3 and 1-4 are derived in Appendix A by a method used

by Sadao Adachi[5][6] which uses a algebraic method of ascertaining the optical properties of

several semiconductors from the band structure.

1.2

SimWindows@

In order to develop an efficient photovoltaic design, a model must be developed for the device that takes in consideration the device dimensions, specifications, and the material prop-erties. One such program is SimWindows@. SimWindows@ is a one dimensional Poisson equation solver program that is able to simulate semiconductor devices. SimWindows@ has the capability to simulate the electrical, optical, and thermal properties of a device. For example, it can simulate optical generation of carriers in a semiconductor, or calculate the total amount of heat radiated from the device.

The models developed by SimWindows@ can ideally be adjusted to explain any discrepancies that may occur between the theoretical and measured result, and can also be used to reveal the limiting mechanisms of the device such as Auger recombination. SimWindows@ is discussed further in Section 2.

1.3

Overview of the Thesis

The purpose of this thesis was to create a simulation file using SimWindows@ to diagnose and design InAs photovoltaics. The model developed for SimWindows@ will be discussed, as well as the advantages of using SimWindows@ and its shortcomings. The model was tested and

500 C Black Body Spectrum 8.OOE-04 7.00E-04 P 5.00E-04 "E t! 4.00E-04 3.00E-04 2.00E-04 0 5 10 15 20 25 8.00E-05 7.00E-05 5.00E-05 4.OOE-05 3.00E-05 2.00E-05 1.00E-05 0.00E+00 Waveiungth (m"cmn)

Figure 1-1: 5000 C Black Body Spectrum, the energy spectrum of interest for InAs.

El

A

L

_F

_X

Figure 1-2: InAs Band Structure. EO is the bandgap. Eo = 0.354 eV, AO = 0.46 eV, A1 = 0.28

eV, and El = 2.50 eV

EgL

4. 3.5-al -2.5 2-1.5. 1. 0.5 0 2 3 4 5 6

Phown Energy (Electrmn Volts)

Figure 1-3: Index of Refraction (Solid) and Extinction Coefficent (Grey) of InAs[5]

1.00E+07

1.OO4(6

1.00E+05

1.OtE+04

0 2 3

Photon Energy Eectron Voas)

4 5 6

Figure 1-4: Absorption Coefficient of InAs [5]

l I I i i i

compared to InAs diodes in the literature. SimWindows@ was able to fit most of the data in the literature within the limitations of the program. Also, some design issues of InAs photodiodes will be discussed.

The model created by SimWindows@ was then applied to two InAs diodes grown by MBE in an effort to analyze them. The measurement revealed a diode characteristic, but the saturation current predicted by SimWindows@ was several orders of magnitude larger than what was actually measured. In addition, the current though the device did not scale properly with area. However, the model developed in SimWindows@ was unable to explain the discrepancy between the theoretical results and the measured results. Therefore, the discrepancy was due to a more fundamental aspect of the diode that was not included in the SimWindows@ model.

Several tests were done to isolate the problem. The top metal was annealed to provide a better top contact, which made no change in the I-V characteristics. Next, HF was used to passivate the surface, but this yielded a more ohmic behavior. Next, CP-4 was used to passivate the surface, and this also brought about no change. Metal was applied to the back of the substrate, which removed all diode-like behavior from the device. It was concluded, as will be discussed in Section 3.3.3, that the diode-like behavior was primarily due to the poor metal-semiconductor junction on the back of the device (substrate to probe station chuck), not from the p-n junction. In addition, a low temperature measurement revealed that the remaining non-linear I-V characteristic was due to the tunneling nature of the p-n junction.

Chapter 2

Formulating a Model for Optimizing

a Device Design

2.1

SimWindows

2.1.1

Description

SimWindows@ is a one dimensional Poisson equation solving program developed by David Wells Winston in 1996 as his Ph.D. thesis from the University of Colorado[7]. SimWindows@ was created to simulate VCSELs and as a tool for VCSEL design. However, SimWindows@ can be also used to simulate two terminal devices, such as resistors and diodes, and it can be used with devices which either emit or absorb light, making it ideal for photovoltaic simulation. Since it was designed to simulate VCSELs, the program can also simulate heterostructures.

SimWindows@ is able to simulate a user defined device under numerous conditions, such as different biasing conditions, AMO illumination conditions, and non-uniform temperature. In addition, the program uses material property files that are defined by the user that allow the development of more realistic material models. For example, the lattice and carrier tempera-ture and doping concentration can be taken into account when specifying the electron or hole mobility. Also, SimWindows@ can take into account many other phenomenon, such as finite surface recombination velocity. Thus SimWindows@ is ideal for designing and simulating a device, provided that the materials under construction have bee adequately characterized.

2.1.2

Advantages

There are several advantages of using SimWindows@ rather than other Poisson Equation solvers. Firstly, SimWindows@ is free', and Winston's thesis is readily accessible[7]. The inner workings of the program and the assumptions the program is based on can be found in this thesis. The thesis indirectly also provides the user knowledge of the limitations of his program since most aspects of the program are discussed in the thesis. By knowing the models that were used, one can judge when the results are valid or incorrect.

SimWindows@ is fairly easy to use. It is designed to run under Windows 95, 98, and NT , and most of the simulation aspects of program are menu driven. The most difficult

aspect of SimWindows@ is creating a good material data file. The material data file developed for InAs is detailed in Table 2.1. Creating a device then consists simply of specifying the thickness and doping of each layer. In addition, the material parameters can be changed when defining the device itself, allowing to user to change parameters in different layers, such as the mobility.

The program is able to simulate and diagnose most of the aspects needed in a device analysis through its ability to simulate the electrical, optical, and thermal environment and models of the device. The ability to control the use of Maxwell-Boltzman or Fermi-Dirac Statistics and to enable and disable different generation and recombination processes are the most useful of the electrical properties that can be controlled. Since the bandgap of InAs is small (0.354 eV at room temperature) compared to Silicon or Gallium Arsenide, it is essential that Fermi-Dirac Statistics is used for InAs. However, for low doped samples of InAs or samples at lower temperatures, Maxwell-Boltzman statistics can be used. This is useful since the computation time for Maxwell-Boltzman simulations is much shorter than for simulations that use Fermi-Dirac statistics.

The ability to enable or disable generation and recombination processes is an extremely useful feature of SimWindows@. The main recombination mechanisms in the program are Shockley-Hall-Read, radiative, and Auger recombination, and the main generation mechanism (besides thermal generation) is optical generation. The user is able to find out the dominant

Material=InAs Alloy=Default

BAND-GAP Model=Band-gap terms=0.35,0,0,-2.76e-4,83

ELECTRON-AFFINITY Model=Band-gap terms=4.9,0,0,1.38e-4,83 STATICPERMITIVITY Value=15.15

REFRACTIVEINDEX segments=4 start-e=0.00 end-e=0.20 value=3.5

start-e=0.20 end-e=0.35 value=0.867*e+3.33 start-e=0.35 end-e=0.63 value=-0.473*e+3.8 starte=0.63 end.e=10.00 value=3.5

ABSORPTION Segments=4 start-e=0.00 end-e=0.35 value=0

start-e=0.35 end-e=1.15 value=10 ^(0.306*e+3.69) start-e=1.25 end.e=1.80 value=10 ^(1.6*e-2.2) start-e=1.50 end.e=10.00 value=1.3e5

THERMALCONDUCTIVITY Value=1/(2/T ^2+.0001*T 2)

DERIVTHERMALCONDUCT Value=-2*T*(.0001*T^4-2)/(.0001*T^4+2)

ELECTRON-MOBILITY model=mobility terms= 10000,0,0,300,-1.66,3e8,0,0,-1.66,2.5e16,0 HOLEMOBILITY model=mobility terms=100,0,0,300,-2.3,3.5e6,0,0,-3.3,5e16,0

ELECTRONDOSMASS Value=0.027 HOLE-DOSMASS Value=0.43

ELECTRON.CONDMASS Value=0.027

ELECTRONSHRLIFETIME Value=1.e-7

ELECTRON-AUGERCOEFFICIENT Value=1.le-26

HOLEAUGER.COEFFICIENT Value=2.54e-26

ELECTRON.ENERGYLIFETIME Value=0.8e-12

ELECTRONCOLLISION-FACTOR Value=0.5

HOLE-COLLISIONFACTOR Value=0.5

recombination in the device by enabling or disabling any of the above processes. In addition, the program also plots the generation and recombination rate of each process throughout the length of the device. Finite surface recombination velocity and Schottky barriers at the surfaces can also be simulated, as well as intraband tunneling.

The most useful of the optical aspects (besides simulating optical generation of carriers, and light generation of the device) is that the user is able to define an incident radiation spectra, and to be able to incorporate the wavelength dependence of the index of refraction and absorption coefficient. Modeling either of these by hand or creating a program to do so would be tedious. In addition, the direction of light, area of illumination, and reflection between boundaries can also be simulated.

Finally, the program is able to simulate thermal effects in the device. The band gap, mobility, electron affinity, refractive index, absorption coefficient, and thermal conductivity can be evaluated at any temperature as long as the model created by the user incorporates the thermal effects. In addition, the device can be isothermal, have different temperature reservoirs at each terminal of the device, or the user is able specify the electron and hole temperature in the lattice.

2.1.3 InAs Model

The properties used for the InAs model is tabulated in Table .2.1, and are explained further in this section.

Band Gap, Electron Affinity, and Static Permittivity:

The band gap model[8] that was used is:

2.76 x 10--4T 2

Eg = 0.415 - x [eV] (2.1)

T+83

The electron affinity model[9] is:

X = 4.9 - 10 4T2 _{[eV] (2.2)}

T+83

The static permittivity[10] is E = 15.15.

Refractive Index and Absorption Coefficient:

The refractive index and absorption coefficient were taken from two articles from Sadao Adachi[5][6]. The relations are detailed in Appendix A. Since 500' C black body radiation is insignificant 1 eV, the model needs to be accurate only to 1 eV. Also, SimWindows@ tended to crash if the model was too complicated, and, for example, contained too many segments. The refractive index was specified as:

3.50, E < 0.20 eV

n(E) 0.867E + 3.33, 0.20 < E < 0.35 eV (2.3)

-0.473E + 3.80, 0.35 < E < 0.63 eV

3.50, E > 0.63 eV

The absorption coefficient was modeled as:

0, E < 0.35 eV a(E) = _{1 0}0.306E+3.69, 0.35 < E < 1.15 eV (2.4) io(E) = (2.4) 1 01.6E-2.2 1.15 < E < 1.80 eV .cm 1.3 x 105, E > 1.80 eV

The index of refraction model is plotted and compared to the data from Figure 1-3 in Figure 2-1, and the absorption coefficient model is plotted and compared to the data from Figure 1-4 in Figure 2-2.

Thermal Conductivity and the Derivative of the Thermal Conductivity:

Thermal conductivity was not essential for the photovoltaic simulations, so a rough model

was made that followed the correct trends in temperature. According to Shalyt [11], the thermal conductivity increases from 2 to 6 Kelvin as T2.2, and decreases from about 30 K as T-2 (see Figure 2-3). T2 provided a better fit while using the expression:

2 1 TWatt (

T

.rn ~. - ~ - - - ~-,--~.-

--2 3 4 5 6

Photon Energy (Electron Volts)

Figure 2-1: The model index of refraction data (gray) and the calculated index of refraction (solid) with respect to enegy.

. E 07 I _ I I . . . . . . . . .

2 3

Phown Energy (lecben Valtm)

4 5 6

Figure 2-2: The model absorption coefficient data (gray) and the calculated index of refraction (solid) with respect to enegy.

5 4.5 3 r 2.5 2 1.5 0.5 0 0 1.OTE+06 E1.00m+05 1 .0+04 0 f 1I I

The derivative of the thermal conductivity is given by:

&-

dT T4 +2 K2 - cmJ

A plot of the model versus measured results[11] is shown in Figure 2-3.

100

10

E

(2.6)

Thermal Conductivity Versus Temperature

____--Thermll Conductivity Model -Measured I/ I / 4 10 Temperature (Kelvin) 100

Figure 2-3: Thermal Conductivity versus Temperature. The solid line represents the measured data[11], and the thin line represents the model results.

Electron and Hole Mobility:

The mobility model in the program is of the form:

Peh (T, NA, ND) = A

(-)

+

_1±

NA+ND G

(2.7)

where, A, B, C, D, E, F, and G are constants. This function does not provide InAs with a good fit, but it is better to use the built in models whenever possible, since SimWindows@ is able to evaluate the built in models faster compared to user defined models. Also, the mobility is not a well defined parameter since it depends greatly on the growth conditions. Thus, only the

general shape of the curve is of prime importance. The electron mobility was defined to be:

Pe (T, NA, ND) = 10000 ( -300 3 x 108T-1.66 + N+ V 2.5 x 101U cm2 V . S (2.8)

The model versus measured data is shown in Figure 2-4. The poor fit is due to forcing the model to saturate at 3.3 x 104 C,2 a value given for a pure piece of material[12].

Voltsr bC

Electron Mobility Versus Doping Concentration

1.00E+03 1 1.00E

-4-..- I I I 11111

1.OOE+16 1.OOE+17 1.00E+18 1.00E+19 1.OOE+20

Doping Cancentration (1/cma

Figure 2-4: Electron Mobility versus Doping Concentration. Model (black line) and measured (grey line)[13] data.

The hole mobility was defined to be:

ph (TNA, ND) =

100 (3T0y23

3.5

10'T-2.3

[

.2 1

(2-9)

The model versus measured data is shown in Figure 2-5. There is a lack of mobility data for holes for lightly doped InAs. The small band gap makes lightly doped p-type InAs intrinsic at high temperatures[15].

zI

Hole Mobility Versus Doping Concentration 1000

I

1.00E+15 1.OOE+16 1.OOE+17 1.OOE+18

Doping Concentration (1/cm3]

1.00E+19 1.00E+20

Figure 2-5: Hole Mobility versus doping. Model (solid line) and measured (diamond) [14] data. Effective Mass:

The electron density of states mass is given by Equation 2.10:

d 2 2 1

me= Nim₁"m?" _(2.10)

where N = _{1 at the F minimum, and the mt, m, are the transverse and longitudinal masses}

of the minima (mt = _{ml of the r minimum). For InAs, md = 0.027. The electron conduction} effective mass is given by Equation 2.11:

1

Tnc 3 mt mi (2.11)

For InAs, mC = 0.027[16].

The hole density of states mass is given by Equation 2.12:

mn = )2 _(2.12)an

U.

1UU

where mih, mhh _{are the light and heavy hole effective mass. For InAs, mlh = 0.43, mhh = 0.026,} and md = 0.43.

The hole conduction effective mass is given by Equation 2.13:

5 5 d mIAmhh mh - 3 3 m1h + hh (2.13) For InAs, md = 0.42[17]. Lifetime:

The Shockley-Hall-Read (SHR) lifetime is another parameter that is not well defined since the density of deep level states depends on the growth conditions, and impurity content. The SHR lifetime was taken to be 1 x 10-7 seconds based on the work done by N. P. Esina and N. V. Zotova[18].

The electron Auger coefficient has been reported to be

A

A)

F

C

B)

C

F

Figure 2-6: The dominant Auger recombination processes in InAs. A: eeh recombination. B: ehh, recombination[18]. ['V r7V '6C E₈V r ₇V

and is expected to be roughly twice the electron Auger coefficient[18] [19]. Thus, the average was chosen, A = 2.54 x 1 0-26cm S . The hole Auger recombination process is dominated by the

ehh, (electron, hole, hole, spin-orbit) process, shown in Figure 2-6B. The ehhs process does not require an activation energy (this is due to the fact that AO (split orbit band energy, AO = 0.46 eV) and EO (Band gap, Eo = 0.36 eV) are close in energy (see Figure 1-2), and since the

lifetime depends exponentially on this energy, the lifetime is very short [18]). At high doping levels (ND > 2 x 1017 ,the recombination shifts from SHR to Auger[20]. The radiative recombination lifetime was reported to be Rd = 1.1 x 1010m[21], and the electron and hole

energy lifetimes were reported to be 0.8 x 10-12s[22].

Scattering Coefficients:

Due to the polar nature of III-V materials, InAs has optical mode phonons. In III-V materials, the relative movement of the two different atoms in the basis causes a polarization in the of the crystal, and a strong interaction may result. The scattering coefficient for polar scattering is 0. However InAs, GaAs, and InP experience impurity scattering as well, and the scattering coefficient of ionized impurity scattering is [23]. In light of this, the scattering parameter was set to 1, the same value that the program used for the GaAs model.

2.1.4 Shortcomings of SimWindows Simulations

Unfortunately, SimWindows@ is not a perfect simulator. There are several shortcomings of SimWindows@ simulations. Firstly, SimWindows@ is unable to simulate high level injection in a device. This can be seen in Figures 2-7 and 2-8. Note that the characteristics change from exponential to resistive without entering a region where 1 < n < 2. This severely limits the accuracy of the I-V characteristics in the forward bias regime.

Also, SimWindows@ is unable to simulate interband tunneling. This prevents accurate simulation of devices such as Esaki and Zener diodes. Unfortunately, Zener tunneling currents dominate the I-V characteristics of InAs diode at low temperatures. However, at 300 K, diffusion currents dominate. [25]. In addition, SimWindows@ is a semiconductor simulator: it is not designed to simulate metals. This prevents SimWindows@ from simulating Schottky barrier diodes.

Current Density Versus Applied Potential

-Sin Wu~dsA deal

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Applied Potential (Volts]

Figure 2-7: IV characteristic from SimWindows@. Note that the IV characteristic changes from exponential (ideal) to linear (R).

Current Density Versus Applied Potential

-0.25 0.00 Applied Potantial (Voltal

Figure 2-8: Lack of high level injection in SimWindows@. SimWindow data (black) and the ideal diode equation (grey). Note that the plot changes from exponential relationship (n=1) to resistive. 4.50E+06 4.00E+06 3.50E+06 3.00E+06 E 2.50E+06 2.00E+06 0 1.50E+06 0 1.OOE+06 5.00E+05 0.00E+00 0.70 0.80 0.90 1.00 1.00E+06 1.00E+04 1.00E+02 1.006+00 . -1.0 -0.75 -0.50 0.25 0.50 0.75 1.00 1111 I I

'

0

Finally, SimWindows@ is unable to simulate space charge generation and recombination and avalanche breakdown. In Figure 2-8, the reverse bias characteristic has a slightly higher current magnitude than what would be expected. However, this additional current is only due to base width modulation. The inability of SimWindows@ to simulate avalanche breakdown severely limits the accuracy of simulations of InAs in the reverse bias regime. Like other small band gap materials, the critical field strength for avalanche breakdown in InAs low (8 x 104 -1.2 x 105V

roughly a third of that of Silicon).[9].

In the present application, the parameters of interest are mobility, refractive index, ab-sorption coefficient, and recombination. For the most part, SimWindows@ can be expected to perform well in these areas.

2.2

Theoretical Results from InAs Model

2.2.1 Testing the SimWindows Model

Dark Analysis:

1x1019

cm4, p+ InAs, 0.1 prm

1x1018 cm-4, p InAs, 0.1 gm

IxO1 9 cm-3, p+ InAs, 0.1 jim Undoped InAs, 0.7 gm _1x1018

cmr3, p InAs, 0.1 jim

lxlOt8cm-3, n InAs, 0.2 jim 1x118cm-3, n InAs, 0.2 pm

A) B)

Figure 2-9: Structures used to verify model. Device A: pin diode. Device B: p-n diode.

The Indium Arsenide model was constructed with the model discussed in Section 2.1.3. To ensure that the model was valid, it was tested by simulating devices in the literature, and comparing the real and simulated I-V characteristics. The devices used were reported by C. H. Kwan, R.-M. Lin, and S.-F. Tang[25][26]. The two diode structures are shown in Figure 2-9.

ND>1x1018 cm4, n InAs, Substrate

ND>lxlO1 8 cm4, n InAs, Substrate

The device area is 3.14x 10- 4cm2 for both devices. The substrate thickness was assumed to be

300 um for both cases.

The data from the simulation and measurements are shown in Figure 2-10. The difference in reverse saturation current can be explained by the mobility. The simulated saturation current is 1.7 times larger than the measured current. The mobility in the model can be 1.7 times larger than the acutal mobility in the device. The compensated data (the simulated data was divided

by 1.7), is shown in Figure 2-11. The excess reverse current of the measured p-n junction is

due to a shunt leakage current[26], most likely due to tunneling, which SimWindows@ cannot model. The nonideality factor of the measured data is 1.3, and this is most likely due to high level injection, another feature which SimWindows@ cannot simulate. A reasonably good fit can be achieved by SimWindows@ within the capabilities of the program.

Illuminated Analysis:

The SimWindows@ program was tested at irradiated conditions by using localized genera-tion in a photodiode, as discussed in Appendix B.3. Impulse illuminagenera-tion was chosen since the program can convolve the results of the impulse generation function along the length of device to find the effects of a generalized generation function. This also tested the optical parameters of the model. For impulse illumination conditions, the user only specifies the energy of each photon and the incident power. The generation rate is given by:

P ~

G = ce(E)~ (2.14)

where a(E) is the absorption coefficient of InAs for a photon with energy E, P is the incident power density, in units of W , and E is the photon energy in Joules. For this analysis, E = 0.45 eV, P = 100 ", and the associated a(E) is 6.73 x 103 1. G was found to be 6.34 x 1024

cm-.s. M is defined as:

M = G -6x

where 6x is the width of the pulse in centimeters. In this case, 8x = 2 x 10- 7 cm, and M was calculated to be 1.86806 x 1018 '

Current Density Versus Applied Potential 1.0XE-02 -- SimWindows Si diode, Uncompe --- Measurement, 1.lOE-03 -1.00E-04

A

A)

.~~ .

I

Applied Potential (Volts]

Current Density Versus Applied Potential

... . .. . .. . .... -0-- SimWindows Simulation, PN Diode

Uncompensated Data.

-0- Measurement PN Diode

1.XE-04

1.OOE-0

-0.50 -0.40 -0.30 -0.20 .0.10

Applied Potential (Volts)

0.00 0.10 020

Figure 2-10: I-V characteristics of measured and simulated Results. Figure A is the I-V char-acteristic of the PIN structure and Figure B is I-V charchar-acteristic of the P-N structure. Note that the measured current does not saturate in Figure B. This is caused by tunneling.

E 0) N CL E 4 0 a) 0

K

..

...

B)

...

...

1.11-

1-

1..

...

...

....

. - 1.

I I

Current Density Versus Applied Potential

-0- SimWindows Simlutation, PIN

diode. Compensated Data j

-A- Measurement, PIN diode

-

T

T

VI

:i-

'1

4

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

Applied Potential (Volts)

A)

Current Density Versus Applied Potential

1.00E-02 .

-0- SimWindows Simulation, PN Diode, Compensated Data. E _{-0- Measurement, PN Diode} U 1.01E-03 CL ... ... - --0.5 -0.4 -0.3 -0.2 -0.1

Applied Potential (Volts]

B)

On.

Figure 2-11: I-V characteristics of measured and simulated Results. The simulation data uses a mobility 1.7 times smaller than the previous figure. Figure A is the I-V characteristic of the PIN structure and Figure B is I-V characteristic of the P-N structure. Note that the measured current does not saturate in Figure B. This is caused by tunneling.

1.00E-02 E S1 .00rE-03 -C aL E 0 1.00)E-04 C _I 0 1.00OE-05 -0. '-C

I ~

ii

"

Values used for the photodiode

shown in Figure 2-12. There is good collaboration between the calculated and simulated data,

-Calculated - Simulated

-1 1 1

-F-I I r

Photocurrent Versus Location

.4 2.50E-01 5.OOE-01 I I

f

~1:!bJ-!

Photocurrent versus the location of the light impulse, calculated (black) and SimWindows@ (grey).

which means that SimWindows@ should give accurate results for the generated photocurrent in the device. The simulated data is slightly larger for regions closer to the junction due to base width modulation: the calculated data assumed that the depletion region did not change in size for different biasing conditions.

Variable Value NA I x 101-ND 1 X 1017 In 1[Pm

4,

t t

Ii

2.2.2 Design Parameters from Model:

Repercussions on Photovoltaic Design:

The ideal diode equation is:

p

Ye Ph [Amp]

J(V) = J ekBT 1

nkBT

e

(2.16)

weNA W*ND _)cm2

where ni is the intrinsic concentration (ni = 1015 for InAs at room temperature) , and w* and w* are the effective region lengths for the p-type and n-type regions. In order to have the maximum conversion efficiency for a photovoltaic, the reverse saturation current, J', must be minimized, as discussed in Appendix B.2.3. As a result, the hole and electron components must be minimized jointly. The first step would to maximize the dopings NA and ND across the junction to minimize J. The effects of mobility and electron and hole effect lengths will be discussed currently. The discussion will be limited to homojunctions.

Mobility:

The ratio between electron and hole mobility in InAs is much larger than the ratios of the other III-V or group I-V compounds, other than InSb and possibly a-Sn (grey Tin). Table

2.3 lists the electron and hole mobility of all group III-V and group I-V (except for a-Sb), and

ratios, if defined.

Since the electron mobility is two orders of magnitude larger than the hole mobility and the doping level and other parameters are comparable, the hole contribution can usually be ignored. Equation 2.16 can be rewritten as:

J (V) = nTkBTBe - [ (2.17)

w*NA cm2

As a general rule then, the p-type regions in a diode structure will dominate the diode char-acteristics, and the I-V characteristics depend little on the doping and thickness of the n-type regions.

Minority Carrier Lifetime and its Dependence on Doping:

Table 2.3: Electron and hole mobility of several semiconductors at that the material does not have mobility data at room temperature.

300 K[4]. 'NA' indicates

needs to be examined. Plots of the simulated minority lifetimes are shown in Figures 13 and 2-14. In the model, the dominant recombination mechanism is assumed to be SHR recombination

for NAD < 2 x 10161, and for NA,D > 10171, the recombination is limited by Auger

recombination. Radiative recombination does not affect the recombination time. Note that the recombination times are roughly the same in both n and p-type materials. Since both sides of the junction are doped heavily to minimize J, the dominant recombination process will be Auger recombination.

Electron and Hole Effective Diffusion Lengths:

In photovoltaic design, the electron and hole effective diffusion lengths, w* and w*, need to be maximized to minimize J. The upper limit of the effective diffusion length is the minority carrier diffusion lengths, which is defined by:

Le,h - _V q _kTTh: e [cm] (2.18) Material

e

Electron Recombination Time Versus Doping Level 1 flE-fl6 1.OE-1 0 I.DE- II 1.OE- 12 - 0 -All -oG -SHR -, -- Auger -0--Radiative 1.OE-13 I-1.OE+16 1.OE+17 Doping Level (1/cm3) 1.OE+ 18

Figure 2-13: Minority Carrier Lifetime versus Doping Concentration for P-type InAs. The data for Auger recombination is approximate.

Hole Recombination Time Versus Doping Level 1.OE-06 1.DE-07 - All -U-SHR *Auger - -Radiative 16 1.DE+ 17 Doping Level (1/cm3) 1.OE+1S

Figure 2-14: Minority Carrier Lifetime versus Doping Concentration for N-type InAs.

0 E I.OE+19 1.OE-08 E 1-.2 1.OE-O9 E S1.OE-1 1 1.DE-11 -1.OE-12 -1.oE+ 1.0E+19 1.&0 1.0E-08-- -1.OE 09 -g

Doping versus Minority Carrier Diffusion Length, Electrons 1000 100 0) E 1 0 0.1 -_ --- _ _ __ _ _ _ __ __ _ 0.01

1. 0E+16 1.00E+17 1.OE+18 1.00E+19 1.00E+20 Doping Concentration (cm-)

Figure 2-15: Electron Diffusion Length versus Doping. Note the diffusion length is within the same order of magnitude of the substrate thickness for low p-type doping

where A,,h is the carrier mobility and Te,h is the carrier lifetime. The carrier lifetimes are within the same order of magnitude for electrons and holes, but the difference between electron and hole mobilities is quite large. Table 2.3 lists the electron and hole mobilities of several semiconductors. The electron mobility of Indium Arsenide is about two orders of magnitude larger than the hole mobility. Thus the minority diffusion length is about an order of magnitude larger for electrons than holes at a given doping, as seen in Figures 2-15 and 2-16.

Also note that the electron diffusion length is extremely long. For low dopings (NA =

1016 ) the electrons can travel over 100 pm before recombining.

Ramifications on Photovoltaic Design:

To minimize the saturation current, the effective length, w*, should be the electron

diffusion length and the p-type region should be longer than the electron diffusion length. Since the type region must be much larger, the photovoltaic structure should be a n-on-p, p-substrate structure, opposed to p-on-n, n-p-substrate structure. Growing upon a p-type p-substrate would 'give' the electrons the necessary length to diffuse, allowing the electron diffusion length

Doping versus Minority Carrier Diffusion Length, Holes 100.00 10.00 - _-_- _-_-o 1.00-0 . -J C o 0.10 __ 0.01

1.OOE+16 1.OoE+ 17 1.00E+18 1.OOE+ 19 1.00E+20

Doping Concentration (cm-)

Figure 2-16: Hole Diffusion Length versus Doping.

to be used for w*.

The n-region is much more difficult to design: the n-type region needs to be thin enough such that a large fraction of the generated carriers are created near to the junction, but yet thick enough to minimize the saturation current. As seen in Figure 2-12 (and discussed in Appendix B.3), the photocurrent peaks when the carriers are generated close (or inside) the junction. Therefore, the n-type region cannot be thicker than the optical absorption coefficient.

The best structure to use would be a n+vp+ pin structure. The v serves as a large region where the generation is maximized (see Appendix B.3. This is caused by the relative lack or carriers to recombine with in the v region). In addition a v region prevents leakage tunneling current, as seen in Figures 2-11 and 2-10[25]. The reverse current for the p-n junction does not saturate in Figure 2-10B due to a shunt leakage current which was postulated to be a tunneling current by the authors. The v region decreases the probability of a carrier from tunneling from the n to p regions as seen in Figure 2-10A by increasing the width of the barrier formed by the band gap. The v region cannot be longer than the minority carrier diffusion length (in this case, the hole diffusion length at that doping), since carriers would recombine in a longer v

region.

2.3

Summary of Chapter 2:

The simulation software SimWindows@ was proposed in this chapter for use of simulating devices. Advantages and shortcomings of SimWindows@ were also discussed and a material model was developed for simulating InAs devices. The model was then tested under dark and illuminated conditions, and was compared to results found in literature or calculated results. Finally, InAs photovoltaic device design issues were discussed, and how the doping, mobility, carrier lifetime, and minority carrier diffusion length influence device design.

The SimWindows@ model developed in this chapter was applied to InAs devices fabricated in our laboratory. The results are discussed in the next chapter.

Chapter 3

Application of SimWindows to MIT

Diodes

3.1

InAs Photovoltaic Structure:

The two devices analyzed for this thesis were grown in a three chambered RIBER 2300 system used for the molecular beam expitaxial (MBE) growth of III-V devices. The devices were grown by Henry Choy, and cross-sections of the structures are shown in Figure 3-1.

Both of these devices were not grown for photovoltaic operation: these were test structures. Structure 9725 was designed to be a symmetrical pin diode, and the unintentionally doped region generates a larger depletion region in the device. The concentration of carriers in the depletion is very low, which would decrease the carrier recombination rate. Therefore, most of carriers that are optically generated in this region will contribute to the photo current. Structure 9722 was designed to be a simple p-n diode structure.

3.2

Comparison with the SimWindows Simulations

3.2.1

9725:

Analysis was first done on a device made from Structure 9725. A diagram representing the different areas of the device is shown in Figure 3-2. The contact ring and grid are made of gold. The Cathode region consists of a 0.05 [im thick n+ cap layer doped at 1 x 10191, followed by

1x10'9 cm-3, n+ InAs, 0.05 pm 5x1017 cm-3, n InAs, 1.0 um

Unintentionally Doped InAs, 0.013 pm

5x10' 7 cm-3

, p InAs, 1.0 tm 2x10'8 cm-3_{, p}

InAs, 0.56 pm NA>2-4xlO8 cm-3, p InAs, Substrate

A) 9725

0.3

B) 9722

Figure 3-1: Device Structures used in this analysis.

Contact Ring _Grid

Mesa Top

Anode

Substrate