DESIGN AND SIMULATION OF SINGLE-CRYSTAL DIAMOND DIODES  FOR HIGH VOLTAGE, HIGH POWER AND HIGH TEMPERATURE APPLICATIONS  By Nutthamon Suwanmonkha            A DISSERTATION  Submitted to Michigan State University  in partial fulfillment of the requirements  for the degree of  Electrical Engineering  - Doctor of Philosophy  2016   ABSTRACT  DESIGN AND SIMULATION OF SINGLE-CRYSTAL DIAMOND DIODES  FOR HIGH VOLTAGE, HIGH POWER AND HIGH TEMPERATURE APPLICATIONS  By  Nutthamon Suwanmonkha  Diamond has exceptional properties and great potentials for making high-power semiconducting electronic devices that surpass the capabilities of other common semiconductors including silicon. The superior properties of diamond include wide bandgap, high thermal conductivity, large electric breakdown field and fast carrier mobilities. All of these properties are crucial for a semiconductor that is used to make electronic devices that can operate at high power levels, high voltage and high temperature. Two-dimensional semiconductor device simulation software such as Medici assists engineers to design device structures that allow the performance requirements of device applications to be met. Most physical material parameters of the well-known semiconductors are already compiled and embedded in Medici. However, diamond is not one of them. Material parameters of diamond, which include the models for incomplete ionization, temperature-and-impurity-dependent mobility, and impact ionization, are not readily available in software such as Medici. Models and data for diamond semiconductor material have been developed for Medici in the work based on results measured in the research literature and in the experimental work at Michigan State University.  After equipping Medici with diamond material parameters, simulations of various diamond diodes including Schottky, PN-junction and merged Schottky/PN-junction diode structures are reported. Diodes are simulated versus changes in doping concentration, drift layer thickness and operating temperature. In particular, the diode performance metrics   studied include the breakdown voltage, turn-on voltage, and specific on-resistance. The goal is to find the designs which yield low power loss and provide high voltage blocking capability. Simulation results are presented that provide insight for the design of diamond diodes using the various diode structures. Results are also reported on the use of field plate structures in the simulations to control the electric field and increase the breakdown voltage.  iv ACKNOWLEDGEMENTS   First and foremost, I would like to express my sincere appreciation to my advisor, Professor Dr. Timothy Grotjohn for his guidance, encouragement and support throughout the development of this research and the writing of this dissertation. His attention to details and patience allowed me learn the way to apply theoretical knowledge to the actual practice of semiconductor device designing.  I would also like to thank the other members of my dissertation committee: Professor Dr. Donnie Reinhard, Professor Dr. Tim Hogan and Professor Dr. Greg Swain for their knowledgeable insights and constructive comments during my study. I have gained good understandings in physical electronics from the course ECE-874 taught by Dr. Reinhard. He also spent some time going through my experimental data at the beginning of my research study and helped me make sense of it from which my knowledge expands. I received several helps from Dr. Hogan when I was working in the cleanroom and on the cryogenic probing station. Through observations, I learned from Dr. Swain the techniques to give effective and comprehensible academic presentations. All of this support has been much appreciated.  I would also like to mention the following members of the research group, MSU staff members and colleagues, including Professor Dr. Jes Asmussen, Michael Becker, Karl Dersch, Brian Wright, Dzung Tri Tran, Robert Rechenberg, Jing Lu, Yajun Gu, Ayan Bhattacharya and Shreya Nad who have contributed their knowledge and expertise to my research study and personal growth as an engineer.    v  Importantly, I would like to thank my family members, relatives and good friends whose support has been my cornerstone. My grandparents, aunts, uncles, cousins and Rob, my brother have been very supportive. Grandma Sukanya, the pillar of our family, has always given me wise words and sent good wishes. Likewise, I would like to give special thanks to my Spartan parents, Professor Dr. Christopher Wheeler and his wife, Penny Wheeler for their advice, encouragement and many wonderful home-cooked meals. Their kind actions have touched my family and I since before I came to MSU to my commencement day and beyond. Furthermore, I am thankful for and very much appreciate the longtime friendship with a few of my elementary school classmates especially Da and Dr. Ling. Also, I am sincerely grateful to have Ton, Dr. Natee Limsuwan, in my life.  Thank you for keeping me smiling.  Finally, I would like to express my deepest gratitude to my dearest parents,  Dr. Rungsit and Dr. Siripaarn Suwanmonkha who have been everything to me, and everything that I am. Thank you for being my super backbone, always sending me love and cheering me on from the other side of the Pacific Ocean for the past 18 years.  Your tremendous support, encouragement and understanding have enabled me to overcome many obstacles in my academic and life journey. This PhD thesis is dedicated to you, Mom and Dad.          vi TABLE OF CONTENTS  viii  ix  KEY TO . xii  CHAPTER1 1 1.1 Motivation1 1.2 Research Objectives3 4  CHAPTER 2 CURRENT STATE OF THE ART 5 5 2.2 Challenges of Diamond Diodes8 2.3 Literature Review..10  CHAPTER 3 SINGLE-CRYSTAL DIAMOND MATERIAL MODELS AND PARAMETERS FOR SEMI23  23  26   3.2.1 Bulk Properties 26   3.2.2 Incomplete 27   3.2.3 Temperature-and-impurity-dependent Mobility Model29   31   3.32 3.3 Summary of Diamond Parameters for the Simulations in this Study 32  CHAPTER 4 SCHOTTKY DIAMO34  434   4.1.1 Desig37   4.1.2 Space Ch42  4.2 Simulation Setup 44   4.2.1 Schottky Diamond Diode Simulations in Forward Bias.45   4.2.2 Schottky Diamond Diode Simulations in Reverse Bias52  4.3 Schottky Diamond Diode with Field Plate Structures61  4.4 Summary of Chapter62    vii CHAPTER 5 COMPARISON OF DIAMOND DIODE DESI64  5.1 PN-.............. 64   5.1.1 Basic Operation of PN-junction Diode.......... 65   5.1.2. Structure Setup and Simulation of PN-junction Diamond Diode............ 67   5.1.3 Performance Comparison of Schottky and PN-junction               Diamond Diode............................................................................................................... 72  5.2 Merged Diamond Diode................................................................................................................ 77   5.2.1 Basic Operation of Merged Diode Structures.................................................... 77   5.2.2 Structure Setup and Simulation of M78   5.2.3 Comparison of Schottky, PN-junction and                  80  5.3 Summary of Chapter 83  CHAPTER 6 CONCLUSION AND FUTURE RESEARCH84  6.1 Conclusion of Findings84  6.2 Future Research87  APPENDICES APPENDIX A: Input File of Schottky Diamond Diode     (p- = 1x1017 cm-3; 450 K)90  APPENDIX B: Input File of Schottky Diamond Diode with Field Plate     (p- = 1x1017 cm-392  APPENDIX C: Input File of PN-junction Diamond Diode     (p- = 1x1017 cm-3; 450 K)95  APPENDIX D: Input File of Merged Diamond Diode     (p- = 1x1017 cm-3; 450 K; spacing = 1 m97  99                  viii LIST OF TABLES  Table 1.1: Basic Bulk Properties of Diamond Compared to Si, GaAs, 4H-SiC            Table 3.1: Bulk Properties of Diamond Compared to Si, GaAs, 4H-SiC                Table 3.2: Hall Mobility Data Obtained from Hall Measurement of          the Actual Diamond Samples Grown in MSU Lab   Table 3.3: Diamond Material Parameters Used in All the Simulations of this Work  Table 4.1: Breakdown Voltages, Specific On-resistance and Maximum Electric Field of                     Schottky Diamond Diode Simulations at 300 K when Drift Layer was 5  54  Table 4.2: Electric Field at the Edge of Schottky Contact and Breakdown Voltage          at 700 V Reverse Bias when Varying Thickness of Field Plate was Used  Table 5.1: Results of PN-junction Diamond Diode Simulations (structure displayed          in figure 5.1) with Varying Temperature and Doping Concentration  Table 5.2: Peak Electric Field at Breakdown of PN-junction and          Schottky Diode at 450 K  Table 5.3: Breakdown Voltage, Turn-on Voltage and Specific On-resistance         for PN-junction, Schottky and Merged Diamond Diodes Simulated         at 450 K and Drift Layer Doping of 1x1017 cm-3             ix LIST OF FIGURES  Figure 2.1: (a) Sign convention of a diode; (b) Ideal diode I-V characteristic;            (c) Non-ideal diode I-V characteristic;            6  Figure 2.2: Schematics of (a) a Schottky diode and (b) a PN-junction diode7  Figure 2.3: Comparison of I-V characteristic of Schottky and PN-junction diodes8  Figure 2.4: Unipolar vertical Schottky diode structure11  12  Figure 2.6: IV Characteristic of PN-junction diode and merged diode            (from 100-µm diameter diode13  Figure 2.7: Structur15  Fig16  Figure 2.9: Measurement of boron concentration versus device distance            17  18  Figure 2.11: Mobility measurement of delta doping di19  Figure 2.22: Structure of H-terminated diamond MISFET20  Figure 2.23: Proposed MISFE21  Figure 2.23: MISFET ID-VDS 21  Figure 3.1: Summary of Medici solution process  Figure 3.2: N-type and P-type dopant levels in single-crystal diamond  Figure 3.3: Ionized impurity carriers versus temperature in single-crystal diamond  Figure 3.5: H  Figure 4.1: Structure of Schottky diamond diode35    x Figure 4.2: Band diagram of Schottky diode36  Figure 4.3: Block of semiconductor (left); Electric field distribution in the drift region           in reverse bias (right)37  Figure 4.4: Four basic transport processes in forward bias: (1) thermionic emission            (2) tunneling (3) recombinatio40  Figure 4.5: Band diagram of Schottky diamond diode in SCLC regime42  Figure 4.6: I-V Characteristic of Schottky diamond diode at 300K and p- was 1x1016 cm-3            for different thicknesses of the p- layer46  Figure 4.7: Semi-log plot of current density versus forward bias voltage of            Schottky diamond diode simulations at 300K and p- was 1x1016 cm-3            for different thicknesses of p- layer47  Figure 4.8: Log plot of current densities versus voltage of            Schottky diamond diode simulations at 300K and p- was 1x1016 cm-348  Figure 4.9: Log plot of current densities versus voltage of            Schottky diamond diode simulations for varying thickness and            temperature based on p- = 1x1016 cm-349  50  Figure 4.11: Log plot of current density versus voltage at 300K and p- = 2 m thick51  Figure 4.12: Schottky diode structure and dimension for easy electric field compariso52  Figure 4.13: Electric field versus drift layer when biased at VBR53  Figure 4.14: Semi-log plot of current versus voltage in the reverse bias at 300 K54  Figure 4.15: Electric field versus drift layer dimension at 300 K at 1000 V reverse bias55  Figure 4.16: Breakdown voltage versus doping concentration of Schottky diamond diode              with drift layer (p-) of 5 m thick57  Figure 4.17: Breakdown voltage versus p- layer thickness when p- doping was fixed              at 1x1016 cm-38  Figure 4.18: Breakdown voltage versus temperature for varying p- layer thickness               when p- doping was fixed at 1x1016 cm-359    xi Figure 4.19: Specific on-resistance versus breakdown voltage when p- layer thickness              was fixed at 5 m and p- doping was fixed at 1x1016 cm-30  Figure 4.20: Simulation setup and results of electric field vectors in the device              at 400 V reverse bias, 300 K61  Figure 4.21: Electric field at the edge and middle of Schottky contact              without field plate (left); with 1.0 m thick field plate (middle);              with 0.5 m thick field plate (right)62  Figure 5.1: Basic operations of a PN-66  Figure 5.2: Setup structure of PN-junction diode68  Figure 5.3: J-V plot of a PN-junction diamond diode when NA            in p- layer was 1x1017 cm-3 and 5 m thick69  Figure 5.4: J-V plot of a PN-junction diamond diode when p- layer was          5 m thick and operating temperature was 450K70  Figure 5.5: Specific on-resistance versus doping concentration in            the drift layer of PN-junction diode70  Figure 5.6: Breakdown voltage versus drift layer doping concentration of            a PN-junction diamond diode based on 5-m thick drift layer 71  Figure 5.7: Specific on-resistance versus breakdown voltage of            PN-junction diamond diode at 300 K72  Figure 5.8: Comparison of the turn-on voltages (Von) of Schottky and PN-junction diodes           at 450 K based on NA of 1 x 1017 cm-3 and p- was 5 m thick73  Figure 5.9: Comparison of Ron,sp of PN junction and Schottky diamond diodes 74  Figure 5:10 Semi-log plot of current versus voltage in reverse bias of Schottky and             PN-junction diamond diodes at 450 K and drift layer doping of 4x1017 cm-375  Figure 5.11: Breakdown voltage versus p- layer doping concentration of Schottky and              PN-junction diamond diodes based on p- layer of 5 m thick and              operating temperatures at 300 K and 450 K76  Figure 5.12: Structure of merged diode design77  Figure 5.13: The intersection of depletion regions in merged diamond diode               under reverse bias78    xii Figure 5.14: Merged diode setup for simulations78  Figure 5.15: Dimension configurations of merged diode dimensions79  Figure 5.16: Electric field vector of the merged diode with 2-             drift layer doping of 1x1017 cm-3 and simulated at 450 K81  Figure 5.17: Forward conduction of Schottky, PN junction and merged diamond diode             simulated at 450 K and drift layer doping of 1x1017 cm-3 (the inset is              zoomed in on the x and y axes)82                      xiii KEY TO SYMBOLS  Ron On-state resistance VBR Breakdown voltage Emax Peak electric field at breakdown  Electron concentration  Hole concentration  Ionized donor concentration  Ionized acceptor concentration   Dielectric permittivity    Intrinsic Fermi potential  Surface charge density EA Activation energy Fn Electron quasi-Fermi energy Fp Hole quasi-Fermi energy    Electron current density vector  Hole current density vector  Electron recombination rate  Hole recombination rate  Electron mobility  Hole mobility  Electron diffusivity  Hole diffusivity   xiv   Measured electric field  Hole impact ionization rates  Electron impact ionization rates   Surface potential   Built-in potential Eg  Bandgap energy   Electron affinity of the semiconductor Nc  Electron density of state Nv  Hole density of state q  Electric charge which equals to 1.6 x 10-19 C  k  Boltzmann constant, equals to 8.62 x 10-5 eV/K NA  Doping concentration of boron in the lowly doped (p-) layer ND Doping concentration of phosphorus T  Operating temperature m  Metal work function p  Barrier potential EC  Conduction band energy EV  Valence band energy EF,m  Femi energy level of metal Evac  Vacuum energy level EF,p  Femi energy level of p-type semiconductor J  Current density A*  R   xv m*  Effective mass of carrier h  P-34 Js   1 CHAPTER 1  INTRODUCTION  1.1 Motivation Energy consumption has become the essential part of human everyday life. Our modern societies are driven by telecommunication systems, transportation systems and electrical systems, all of which require some forms of energy to run. In fact electricity is a kind of energy that is very versatile. Several natural resources such as oil, natural gas and nuclear reactions are used to create electrical energy. But these resources are limited and the production of electricity yields CO2 emission, which contributes to global warming and climate change. The International Energy Agency (IEA) estimates the global electricity demand to rise over 70% from 16,400 terawatt-hours per year (TWh/year) in 2007 to 29,000 TWh/year in 2030. [1,2] Moreover, IEA estimates CO2 emission due to electricity production to increase by 40% from 28 gigatonnes per year (Gt/year) in 2007 to 40 Gt/year in 2030. [1,2] As a result, efficient energy management and reduction of environmental impact are major concerns for the sustainable development of all countries across the globe.  To handle the issues of rising demands of energy while keeping the environmental impact minimal, engineers and scientists have begun to find ways to improve the efficiency of electronic devices. Silicon has been the well-known material and it is the material used in most appliances for control of electrical systems. However, it dissipates energy, so it does not handle high power levels efficiently.  Plus, its physical properties have limits beyond   2 breakdown. Therefore, the field of power electronics for many applications is now shifting to wide bandgap semiconductors such as gallium nitride (GaN), silicon carbide (SiC) and diamond, which possess better electrical properties than silicon. The comparison of material properties between diamond and other semiconductors are shown in table 1.1. Among several wide bandgap materials, diamond has the most exceptional properties. This is due to its superior physical and electrical properties such as wide bandgap (5.5 eV) and high thermal conductivity (20W/cm K), which is useful for electronic devices operating at high power levels [3]. Moreover, diamond possesses a high electric breakdown field of up to 10 MV/cm and high carrier mobilities (4500 cm2/V·s for electrons and 3800 cm2/V·s for holes at room temperature) allowing diamond to be a potential choice for high frequency and high voltage electronic devices.  Property Si GaAs 4H-SiC GaN Diamond Bandgap Energy, Eg (eV) 1.1 1.4 3.2 3.4 5.45 Electric Breakdown Field, Ec (MV/cm) 0.3 0.4 3 5 20 Electron Mobility, µn (cm2/V·s) 1450 8500 900 2000 4500 Hole Mobility, µp (cm2/V·s) 480 400 120 200 3800 cm·K) 1.5 0.55 3.7 1.3 24 Table 1.1: Basic Bulk Properties of Diamond Compared to  Si, GaAs, 4H-SiC and GaN at 300K [4, 5, 6]  Being a new material, unlike silicon, diamond-based devices are mostly still at the research and development stage in Japan, Europe and the US. The recent progresses in diamond growth, doping, surface treatment, and etching has allowed scientists and engineers to fabricate diamond electronic devices. [7,8] Both fabrication processes and device designs are the keys for achieving efficient high-power diamond electronics. A computer-based semiconductor device simulator is an efficient tool for exploring the   3 possible and best designs of single-crystal diamond devices that are suitable for high power and high temperature applications. The design process can be less expensive and more efficient by using the simulator to come up with the best design that meets the requirements. Then the structure of the device can be fabricated according to the design the simulator yields. Medici is the commercialized semiconductor device simulation software that is available at Michigan State University and is the simulator used throughout this study [9].   1.2 Research Objectives Since single-crystal diamond is not a traditional semiconductor, many of its physical material parameters are not readily available in Medici as is the case for other well-known semiconductors such as silicon. So the objective of this study is to gather diamond parameters and use them to simulate various diode structures. They are listed as follows:   1. To develop a complete set of material parameters for single-crystal diamond, which include the effects of incomplete ionization, carrier mobility temperature and impurity scattering dependence, and impact ionization, for the simulator.  2. To simulate various structures of diamond diodes including Schottky diodes, PN-junction diodes and merged diodes. 3. To investigate the simulation results in details for both the forward-bias and reverse-bias mechanisms through the analysis of the IV characteristic, on-resistance and breakdown field versus device dimension and temperature. 4. To compare simulation results with existing experimental data that has been obtained in our research group.   4 1.3 Outline of Dissertation The layout of this research is described as follows. Following the brief introduction of the need for diamond-based electronic devices, the theory of diodes and the state of the art of diamond diodes as found in the literature are discussed in chapter 2. In chapter 3, physical parameters of diamond for Medici simulations have been compiled. These include the bulk properties, incomplete ionization, impact ionization, mobility models and values from Hall measurements. The design and simulation of Schottky diamond diodes are presented in chapter 4. The effect of ohmic current and space-charge-limited current is studied in the forward bias. Avalanche breakdown is studied in the reverse bias. Chapter 5 presents the simulations of three different diode structures, which are Schottky, PN-junction and merged. Performance is compared between different diode structures and with existing experimental data. The summary of the work done in this research is presented in chapter 6.             5 CHAPTER 2  CURRENT STATE OF THE ART OF HIGH POWER DIAMOND DEVICES  A brief overview of diodes in general is presented below followed by the challenges in making diamond diodes and a literature review of diamond-based power electronic devices.  2.1 Theory of Diodes A diode is a two-terminal electronic device, which allows current to pass through one direction while blocking current from flowing in the opposite direction. The sign convention and symbol of a diode is shown in figure 2.1a. The I-V characteristic of an ideal diode is displayed in figure 2.1b, while figure 2.1c exemplifies the non-ideal case.    6  Figure 2.1: (a) Sign convention of a diode; (b) Ideal diode I-V characteristic;  (c) Non-ideal diode I-  The specific on-state resistance (Ron,sp) is the combination of the resistance along the current flow path including all the interfaces when the diode is conducting current in the forward bias multiplied by the surface area of the current flow. So the unit is -cm2. As shown in the figure 1a, VAK is the voltage drop across a diode and IF is the current through a diode in forward bias. Hence,   Von is VAK when the diode is on. The breakdown voltage or VBR is where the magnitude of the current starts to increase indefinitely in the reverse bias. The leakage current, Ileak, is the current in the reverse bias direction before breakdown occurs and typically very small (~nA range). It is the result of an increase in generation current as the                -                7 reverse bias is increased. Figure 2.that the current is being injected at a certain VAK between 1 and 2. It tends towards 1 when diffusion current dominates. When          Figure 2.2: Schematics of (a) a Schottky diode and (b) a PN-junction diode  Two common types of semiconductor diodes are the Schottky diodes and PN-junction diodes. The Schottky diode, shown in figure 2.2(a), is formed when a metal-to-semiconductor interface is created. It is considered a majority carrier device where the depletion region is only formed on the semiconductor side. This results in smaller turn-on voltage (Von) and hence performs generally well in the forward-bias direction. The PN-junction diode, shown in figure 2.2(b), has a semiconductor-to-semiconductor interface. It is when two types (n and p) of semiconductors are brought together. It is a minority carrier device and the depletion width extends on both sides of semiconductor junction. It has higher Von and also larger VBR. Therefore, the PN-junction diode generally performs better in the reverse bias. These comparisons are exemplified in the I-V plot in figure 2.3.    -    - -    8  Figure 2.3: Comparison of I-V characteristic of Schottky and PN-junction diodes  2.2 Challenges of Diamond Diodes Diamond is an allotropic form of carbon. Strong covalent sp3 bonds hold the tetrahedral arrangement of carbon atoms that crystallizes into the diamond lattice, which is a variation of the face centered cubic structure. Diamond diodes are expected to out perform diodes fabricated from Si, SiC or GaN because of the more superior bulk properties of diamond. Among all the other existing semiconductors, diamond has the widest bandgap, which affords diamond devices to have greater VBR allowing for greater blocking voltage capability and subsequently the ability to function in high power circuits. It also has better thermal conductivity, which provides diamond devices with greater heat sink capability. Thus, it will be able to operate at very high temperatures. Previously reported challenges in fabricating diamond diodes involve the difficulty to synthesize large, high-quality, single-crystal diamond, as well as, to make the n-type and p-type doping layers that are good quality with low resistance. Nowadays, two types of diamond substrates are available in the market. The first is created from graphite phase by the high pressure and high temperature process (HPHT). The second is created from the   9 gaseous phase under low pressure in a chemical vapor deposition process (CVD). A substrate size of 3x3 mm2 with (100) top surface orientation is commonly available in the market. The most important donors (phosphorus) and acceptors (boron) in diamond have large activation energies. Nevertheless, p-type doping by boron as an acceptor with activation energy of 0.37 eV has been quite well controlled. [10] N-type doping still needs more research to make it efficient. Thus this has restrained the design fabrication of the diamond-based devices to be mostly unipolar p-type devices. The deep donors and acceptors of diamond along with the wide bandgap lead to incomplete ionization of the donors and acceptors at room temperature. At very high temperature, ionization of carriers becomes more complete. Higher impurity concentration, which will improve conductivity, may be necessary for diamond devices that operate at room temperature. At high doping levels, the carriers flow by a hopping conduction between dopant sites as the current flow mechanism. In terms of device design, some physical parameters of diamond are not well known. Updated values of diamond parameters are also not readily embedded in Medici, the device simulator. Although most of the bulk properties of diamond have been well studied, some parameters for charged carrier mobility and impact ionization rate model have been interpolated from the values of other semiconductors including silicon and silicon carbide. [11] This causes the simulation to yield inaccurate results. Thus, the design in question will not represent the expected performance of the fabricated device precisely.      10 2.3 Literature Review Several types of diamond devices such as Schottky diodes and field effect transistors (FETs) have been fabricated in the past decades. This section highlights some technological breakthroughs that several research groups have made on the fabrication of diamond-based power devices and their performances. In 2001, diamond PN junctions were successfully fabricated for the first time. [12] This achievement is a result of successfully creating n-type diamond by phosphorus doping. Nevertheless, the n-type diamond presented quite high resistivity of about 105 - 106 -cm at phosphorous concentrations of 1018 cm-3. This causes the Ron for PN-junction diode to be too high, which is not good for fast switching and high power diodes. In the literature, the state-of-the-art of p-type diamond is more advanced than the n-type. [3] Specific contact c, is an area-independent parameter and includes a part of metal immediately above the contact and semiconductor below it. Experimentally, it can be defined from an I-V measurement by taking the reciprocal of the slope when the voltage tends to zero (since the voltage required to drive current through a good ohmic contact is small) and the unit is -cm2.  The specific contact resistance is as low as 10-5 -cm2 for p-type diamond with boron concentration of 1020 cm-3. For n-type diamond with phosphorus concentration of 1020 cm-3, the specific contact resistance is reported to be around 14 -cm2. [13] Therefore, using just p-type diamond to create Schottky diodes have advantages such as lower built-in voltage and faster turn-on/turn-off properties than those of PN diodes.  In 2004, a group of researchers led by D. J. Twitchen and A. J. Whitehead reported successful results of their high-voltage single-crystal Schottky diamond diode. [14] This diode was implemented with a vertical structure and designed to be a unipolar device and   11 is favorable to achieve large operating input currents.  The intrinsic layer serves as the drift region in the forward conduction and depletion region in the reverse bias. Due to its thin thickness, space charge limited current was observed. The result shows that VBR was -2.5kV. The electric field was 4 MV/cm. The hole mobility was measured to be 4100 ±400 cm2/Vs.   Figure 2.4: Unipolar vertical Schottky diode structure  Next, in 2007 M.Kubovic, H. El-Hajj, J.E. Butler and E. Kohn reported a merged  Schottky junction and PN junction diode structure. [15] Merged diodes between PN junction and Schottky junction are composed of small size Schottky contacts embedded into the PN junction.  Schottky contact contributes to a low forward threshold voltage since the metal-semiconductor junction results in a lower barrier in the forward bias. However, the Schottky barrier on the reverse bias gives high current leakage and low breakdown voltage. Therefore, a PN junction, which has a low reverse leakage current and a high breakdown voltage on reverse bias was implemented.  The merging the two kinds of junctions together yielded a better performance in both forward and reverse biases. Thus, a PN junction is placed next to a Schottky barrier on that same contact in order to create a merged structure as shown in figure 2.5.    12  Figure 2.5: Structure of the merged diode [15]   The IV characteristics of the PN junction diode (taken before the Schottky contacts were patterned) and the merged diode (taken after the Schottky contact areas were patterned) are shown in figure 2.6. This was measured from a diode with a diameter of 100 µm (diameter of the p- layer). The results show improvements of the merged diodes over those with just PN junction diodes.     13  Figure 2.6: IV Characteristic of PN-junction diode and merged diode  (from 100-µm diameter diode) [15]   In the range of ±8V, both diodes exemplified a high current rectification ratio of about 109. The ideality factor in the forward for the merged diode is 2.1 and for the PN junction is 7. In the ideal case, the ideality factory is 1 resulting from zero defects and that the total diode current is diffusion current. More defects give more space-charge recombination, which increases the ideality factor. The ideality factor of 7 for the PN junction diodes indicated that there was current injection in the forward direction by defect states at the interface. The merged diode yielded an improved ideality factor of 2, indicating fewer defects at the interface. Additionally, figure 7 also confirms that the forward turn-on voltage for the PN junction diode is higher than that of the merged. Thus the merged diode outperformed the PN junction diode in both ideality factory as well as turn-on voltage. Additionally, the breakdown voltage is reported to be approximately -25 V,   14 which corresponds to a breakdown field of 2.5 MV/cm. This measured value of breakdown voltage is lower because of the thinner drift layer (p- doped region) than the design by another research group that achieve the blocking voltages in the kV range. [15] Thus far, the fabricated merged diode utilizes the better characteristics of a Schottky diode in forward bias, and the PN junction behavior in reverse bias. However, this diode still has a trade-off relationship between Ron and VBR shown in equation 2.2. In order to decrease the Ron, it is needed to decrease the resistance of the p-type layer. This can be done by increasing the acceptor concentration or decreasing the p-type layer thickness. [7,8] However, this induces narrowing of the space-charge layer width of the p-type layer causing VBR to decrease [12]   where Emax = peak electric field at breakdown, p = hole mobility, p = hole concentration in the drift layer. In order to overcome the trade-off relationship between Ron and VBR of the merged diode, Makino and his team of scientists in Tsukuba and Kanazawa Japan have published a paper on a merged diode without any trade-off relationship between Ron and VBR. [12] They referred to their new design as the Schottky-PN diode (SPND), which is composed of a lightly phosphorus-doped n-type layer placed in between highly boron-doped p-type layer and Schottky metal layer. [12] This structure is similar to the merged diode in [15], but the difference is the PN junctions were formed tandem to the Schottky junctions instead of the PN junctions being embedded in the Schottky. The n-type layer, which is the key structure of the SPND, was designed to be fully depleted in both forward and reverse operations.   15 Thus, only the width of the n-type layer determines VBR of the diode. In addition, the forward current and Ron are controlled only by the resistivity in the p-type layer. Essentially, this means having a highly boron-doped p-layer, which will give low resistivity or low Ron and thus high forward current. It also means having a wide n-type layer to have high VBR as long as the layer is fully depleted. Therefore Ron and VBR can be designed independently as they are determined by different device parameters. [12]  Figure 2.7: Structure of the SPND diamond diode [12]  The thickness and doping concentration of each layer are as follows: NA = 4x1020 cm-3 and 1.3 microns for p+ layer; NA = 6x1018 cm-3 and 700nm for p layer; and ND =7x1016 cm-3 and 70nm for n-layer. SPND showed an improved result and reached over 60,000 A/cm2 with specific on resistance of 0.03 mcm2 at the forward bias of 6V. This is comparable to the estimation from the bulk resistivity of the p+ layer (about 5 mcm2). The author noted the important part that the high resistance of the n-type layer (in the order of 102 cm2) does not affect the total value of the series resistance of the SPND, which is consistent to the analysis of the operation mechanisms. [12] VBR was measured to be 55 V at which the   16 electric field reached 3.4 MV/cm. The authors elucidated that the higher VBR was a result of the larger width in the n layer as described by the operational mechanism. Although, it is worth mentioning that n-type doping is still a great challenge nowadays. Thus creating thicker layer of n-type doping puts the limit on the value of VBR this design tries to achieve.  In 2014, Umezawa and his coworkers at National Institute of Advanced Industrial Science and Technology and Osaka University, demonstrated a vertical-structured high current diamond Schottky diode using a thick Al2O3 field plate as the edge termination technique to reduce large field crowding at Schottky contacts. [16] The structure is shown in figure 2.8.   Figure 2.8: Structure of Schottky diode with field plates [16]  The thickness of the Al2O3 field plate is 1.8 um. The estimated effective Schottky barrier height was 1.85 eV. The maximum forward currents reached 1 A at 2.4 V and 5 A at 7.3 V. The specific on-resistance was 29.2 m-cm2 at RT. The maximal blocking voltage of 300 V with the breakdown field of 0.3 MV/cm reported.   Apart from many diamond diode structures previously discussed, many designs and tilize the higher carrier   17 mobilities of the bulk material. A few groups have studied the delta doping technique for the p-type layer. This is when boron concentration is heavily doped near the surface to allow for a full activation at room temperature. [17,18]   Figure 2.9: Measurement of boron concentration versus device distance  from delta doping technique [17, 18]  Kuech et al presented a metal-semiconductor FET (MESFET) structure which incorporated delta doping technique for the p-layer is shown in figure 2.10. [19]   18  Figure 2.10: Diamond MESFET structure [19]  The point worth mentioning is that the ohmic contacts for this MESFET by treating the surface with oxygen (O-termination) followed by the deposition of Au. In most practice, Ohmic contacts on diamond are formed by Ti/Au. Ohmic contacts are done by treating the surface with hydrogen (H-termination) immediately followed by Au sputtering or evaporation are the less popular method. The H-termination induces a hole conductive channel near the surface and in cooperation with Au, the work function difference is low at the interface resulting a tunneling path. However, the adhesion of Au to the H-terminated diamond surface relies on the van der Waals bonding and is considered weak. The covalent bonding yields stronger adhesion. Nevertheless, this delta-doping technique of boron yielded low hole mobility at room temperature. The hole mobility less than 100 cm2/V-s was measured, so it was not a good device for high frequency operation. [18]   19  Figure 2.11: Mobility measurement of delta doping diamond MESFET [19]   With the goal of improving hole mobility, H-termination was used instead of delta doping technique. In 2014, Kawarada et al demonstrated H-terminated diamond FET with an oxide layer of Al2O3 that was capable to operate at 500 V, 400 C and 40 GHz. [20] Normally, the C-H bonds created by H-termination are lost when the temperature goes beyond 200 C, but the technique to use atomic layer deposition (ALD) of Al2O3 in this case prevents the bonds from being destroyed at very high temperature.    20  Figure 2.22: Structure of H-terminated diamond MISFET   Also in 2014, a researcher group from collaboration across Japan has fabricated a diamond MISFET. [21] The group intended to utilize the gate insulator to suppress the leakage current and increase the breakdown voltage. H-terminated diamond surface was the chosen technique over delta doping in this study due to the difficulty to control the abruptness of the doping profile [22]. Ta2O5 was the insulator chosen because it has high k value, larger than 20, on diamond. An insulator with high k value can provide the same charge response at a smaller electric field [23]. A thin layer of Al2O3 is used to prevent damage to the diamond surface when Ta2O5 is sputtered onto hydrogenated diamond surface. The electrode contacts for gate, drain and source are identical and are composed of 200 nm Au, 20 nm Ti and 10 nm Pd. The structure is shown in figure 2.23.    21  Figure 2.23: Proposed MISFET structure [21]   For the channel length (LG) of 4 um, the maximal IDS is 97.7 mA/mm shown in figure 2.23. This research group is satisfied with Ta2O5 as the choice of insulator since they acquired the largest IDS value for diamond MISFET to date.   Figure 2.23: MISFET ID-VDS performance [25]   Through the discussion of several diamond-based devices in this section, the keys to achieve successful performance include advancement in diamond synthesis and doping, having good fabrication schemes and techniques, and having the right structural design.   22 The focus of this research is in the design. The next chapter will present the tool, which will allow device structures to be simulated and designed.                         23 CHAPTER 3  SINGLE-CRYSTAL DIAMOND MATERIAL MODELS AND PARAMETERS FOR SEMICONDUCTOR DEVICE SIMULATION   This chapter introduces the semiconductor simulator software that was used in this study. Then it presents physical models for material parameters of single-crystal diamond.  3.1 Medici Device Simulator MediciTM is an industry-standard semiconductor device simulation tool that predicts electrical, thermal and optical characteristics of arbitrary 2-D structures under user-specified operating conditions. A wide variety of devices can be modeled in 1-D and 2-D such as pn-diodes, BJTs and MOSFETs. Medici allows device designs to be optimized for best performance without having to go through the entire process of fabrication, which eliminates the need for costly experiments. Furthermore, it assists the fabrication methods in helping to verify experimental results.  Figure 3.1: Summary of Medici solution process   24  To analyze a device, five basic equations are solved numerically in Medici. These equations are as follows:    This governs the electrical behavior of semiconductor devices.  Continuity equations for electrons and holes:     These also govern the electrical behavior of semiconductor devices.  Electron and hole transport equations:   This governs the drift and diffusion aspect of the carriers. The definitions of the parameters in the above five equations are:  is the electron concentration  is the hole concentration  is the ionized donor concentration  is the ionized acceptor concentration  is the dielectric permittivity   is the intrinsic Fermi potential  is the surface charge density Ea is the applied field   25 Fn is the electron quasi-Fermi energy Fp is the hole quasi-Fermi energy   is the electron current density vector  is the hole current density vector  is the electron recombination rate  is the hole recombination rate  is the electron mobility  is the hole mobility  is the electron diffusivity  is the hole diffusivity Medici employs the finite element method to solve the 5 basic equations above such that the area of the simulated device is discretized into a simulation grid. This discretization process yields a set of coupled nonlinear algebraic equations, which are then calculated for a number of grid points with the different potentials and carrier concentrations. This set of coupled nonlinear algebraic equations must be solved by a nonlinear iteration method. There are two iteration methods available in Medici namely, solutions will be carried out over the entire grid until a self-consistent potential () and carrier concentrations (, ) are achieved. Once the potential and carrier concentrations have been calculated at a given bias, it is possible to obtain the quasi-Fermi levels (Fn and Fp) and the hole and electron currents ( and ).  For accurate results, Medici incorporates a number of physical models such as recombination, impact ionization, bandgap narrowing, band-to-band tunneling, mobility,   26 Fermi-Dirac and Boltzmann statistics. [9] Arbitrary device geometries can be simulated. The user can define types of material, regions, impurity concentrations and electrodes for a specific device structure and simulation process. A summary of processes in Medici to yield a solution is shown in figure 3.1.  3.2 Diamond Parameters Diamond is still new compared to other traditional semiconductors such as silicon (Si) and gallium arsenide (GaAs). Hence, its material parameters are not readily available in Medici like the others. In order to perform simulations of diamond devices, it is required that proper values of diamond parameters have been input into Medici for the accuracy of the results. Fortunately, Medici allows users to define new materials arbitrarily. The rest of this chapter discusses the models and parameters that are used for diamond throughout the Medici simulations in this project.  3.2.1 Bulk Properties Since 1797 when diamond was discovered as pure carbon, many of its bulk properties were investigated and the values published. [4, 5, 6] From table 3.1, silicon carbide (SiC), gallium nitride (GaN) and diamond are considered wide bandgap semiconductors with diamond being the widest. Wide bandgap semiconductors have higher thermal stability and breakdown field compared to silicon, the most popular semiconductor. This means wide bandgap semiconductors can withstand higher field strength intrinsically without the breakdown of the material.     27 Property Si GaAs 4H-SiC GaN Diamond Bandgap Energy, Eg (eV) 1.1 1.4 3.2 3.4 5.47 Electric Breakdown Field, Ec (MV/cm) 0.3 0.4 3 5 20 Electron Mobility, µn (cm2/V·s) 1450 8500 900 2000 4500 Hole Mobility, µp (cm2/V·s) 480 400 120 200 3800  1.5 0.55 3.7 1.3 24 Dielectric constant, r      11.9 13.1 10.1 9 5.5 Saturated Electron Drift Velocity, (x107 cm/s)  1  1 2 2.2 2.7 Table 3.1: Bulk Properties of Diamond Compared to Si, GaAs, 4H-SiC and GaN at 300K [4, 5, 6]   In terms of carrier mobilities, diamond also possesses very high values for both electrons and hole. This is beneficial for electronic devices that require fast response and operate at high frequency. Even though the electron mobility of GaAs surpasses that of diamond, the hole mobility is significantly less. So while GaAs is suitable for some high-speed electronics such as mobile phones and satellite communication, there are many other high-energy and high-temperature applications which diamond is more promising. Moreover, this is especially true for high power electronic devices that suffer from high generation of heat. Since the thermal conductivity of diamond is high, it can better conduct the heat away from the active device region of heat generation.   3.2.2 Incomplete Ionization Model To make electronic devices out of diamond; it is doped so that the material is more conductive. The problem of dopant activation originates from the wide 5.45 eV bandgap of diamond and the large ionization energies of dopants in the material. Phosphorus and boron are known donor and acceptor species in diamond and exhibit activation energies of 590 and 360 meV respectively. As shown in figure 3.2, the dopant levels for n-type and p-  28 type diamond are rather deep which effect the thermal excitation of the carriers at room temperature. From the Pearson and Bardeen approximation, the activation energy in the freeze-out region is a function of temperature and impurity concentration. [11] The parameters and equations in [11] have been verified and plotted as shown in figure 3.3, the number of ionized impurity carriers increases with the increasing temperature. This model has been input in the subsequent Medici simulations.  Figure 3.2: N-type and P-type dopant levels in single-crystal diamond   Figure 3.3: Ionized impurity carriers versus temperature in single-crystal diamond   29 3.2.3 Temperature-and-impurity-dependent Mobility Model  At the beginning of the study, the concentration dependent mobility model from [11] was implemented in Medici for the simulations (equation 3.6). However, as experimental data from the Hall measurement became available. The first model in equation 3.6 was no longer used. All of the results presented in this dissertation are based on the Hall measurement values, which were manually entered into Medici files. For completion, a brief description on the first model from [11] is given below. This model was developed from concentration-dependent Hall and time-of-flight (TOF) hole mobility values reported in [24, 25] for heavily boron-doped diamond, which yielded the following empirical expression:  where  is the doping dependence mobility. The terms , , , , , , ,  are fitting factors obtained from the data in [26].   More recently, researchers in our group have conducted Hall measurements on several of our boron doped diamond samples grown in our lab and the results are shown in figure 3.5. [27] A tabulated data set of doping concentration and the associated hole and electron mobilities was created based on the findings in [27]. This set of data replaced the first model. The simulation results presented in the next chapters are based on this data set whose values are shown in table 3.2 below.    30  Figure 3.5: Hall measurements of boron doped diamond samples [27]   -                                            Table 3.2: Hall Mobility Data Obtained from Hall Measurement of  the Actual Diamond Samples Grown in MSU Lab [27]    31 3.2.4 Impact Ionization Model  Impact ionization is a process that occurs in high electric fields. It is an important phenomenon for power device design as it governs the breakdown voltage (VBR) of the device. When energetic particles scatter due to a high electric field, this gives excess energy and allows some electrons to be excited into the conduction band. As a result, new electron-hole pairs are created. This process can occur when the particles gain at least the threshold energy for ionization (Ei) from the electric field. The impact ionization rates  (for holes) and (for electrons) are defined as the number of electron-hole pairs generated by the carriers traveling unit distance along the direction of electric field. Empirically, the impact ionization rates can be shown [28, 29] as follows:   and  are fitting parameters and E is the electric field through the semiconductor layer [5]. The fitting parameters are An=4.62x105, Bn=7.59x106, Cn=1.0, Ap=1.93x105, Bp=4.41x106, and Cp=1.0. [34]  When impact ionization happens in high electric field region, it can free bound electrons, which also accelerate to velocities that can liberate additional electrons during collisions of particles. This process is called avalanche breakdown at which point the current in a semiconductor will become extremely high [33]. It is crucial to determine VBR to approximately quantify the blocking capability of diamond power devices in reverse bias. Thus, this model is also included in the Medici simulations.     32 3.2.5 Metal Contacts to Diamond Ohmic and Schottky contact are implemented as simple Dirichlet boundary conditions [9]. Medici calculates the surface potential, , at the metal-semiconductor interface by the following equation:  where Eg is the bandgap energy,  is the electron affinity of the semiconductor, Nc and Nv are the electron and hole density of state, respectively, and WORKFUNC is the value of the metal work function used at the contact. All of these values are listed in table 3.3 for diamond. The temperature, T, and the applied voltage, Vapplied, in equation 3.8 are the values that can be specified for each simulation. The constant values for the electron charge is q = 1.6 x 10-19 C and Boltzmann constant k =8.62 x 10-5 eV/K.  3.3 Summary of Diamond Parameters for the Simulations in this Study  All of the diamond physical parameters that were used in the simulations in this study are listed in table 3.3.          33 Diamond Parameters Symbols in Medici Symbols in Dissertation Values Units Bandgap at Room Temperature EG300 Eg 5.47 eV Relative Permittivity PERMITTI  5.7  Affinity AFFINITY  1.3 eV Electron Density of State NC300 Nc 1 x 1020  cm-3 Impact Ionization Coefficients (for electrons) AN An 4.62 x 105 cm-1 " BN Bn 7.59 x 106 V/cm " CN Cn 1  Activation Energy (for electrons) EB0 EA,n 0.59 eV Degeneracy Factor (for electrons) GB ga 2  Ionization Fitting Factor  (for electrons) ALPHA  3.1 x 10-8  " BETA  200  " GAMMA  1  Hole Density of State NV300 Nv 1 x 1020 cm-3 Impact Ionization Coefficients (for holes) AP Ap 1.93 x 105 cm-1 " BP Bp 4.41 x 106 V/cm " CP Cp 1  Activation Energy (for holes) EB0 EA,p 0.36 eV Degeneracy Factor(for holes) GB ga 4  Ionization Fitting Factor (for holes) ALPHA  3.037 x 10-8  " BETA  200  " GAMMA  0.95  Workfunction for (Al) WORKFUNC m,Al  4.3 eV Workfunction for (Au) WORKFUNC m,Au  5.2 eV Table 3.3: Diamond Material Parameters Used in All the Simulations of this Work  [5,9,11 and 34]         34 CHAPTER 4  SCHOTTKY DIAMOND DIODE DESIGN AND SIMULATION  Despite the rather simple structure of the Schottky diodes, their simulations can provide meaningful information. Since the mechanisms of charge transport in a basic p+/p- Schottky diode are identical to multi-layer structures, the knowledge from these simulations serves as the building block for performance optimization in more complicated devices. In this chapter, basic Schottky diode theory that matters to high power applications is introduced. It is followed by the forward bias and reverse bias simulations. Results from the use of field plate structures to control the electric field and increase the breakdown voltage is also reported.   4.1 Schottky diode fundamentals A Schottky diode has a metal-semiconductor interface which creates a junction known in theory as the Schottky barrier. The structure of a Schottky diamond diode consists of a thin layer of heavily doped diamond on top of a lightly doped layer. Although with different levels of concentration, both layers are doped by boron, which makes this a p+/p- type structure. There are two electrodes, one on the top and the other on the bottom of the structure. The electrode on the p+ layer forms an Ohmic contact; while the electrode on the p- layer forms a Schottky contact. The structure is shown in figure 4.1.   35  Figure 4.1: Structure of Schottky diamond diode   Unlike PN-junction diodes which are discussed in Chapter 5, Schottky diode is a majority-carrier device. This means for the structure in figure 4.1, the forward current is only due to hole injection from the semiconductor. There can be negligible minority carrier injection which makes the storage of excess minority charge omissible. Thus, Schottky diodes can operate at higher frequency than PN-junction diodes. In figure 4.1, the interface between the p- diamond to Schottky contact exhibits a rectifying current-voltage (IV) characteristic. The interface between p+ diamond and Ohmic contact exhibits a linear IV characteristic. It behaves like a low resistance Ohmic contact. The band diagrams are depicted in figure 4.2 for the moment before the metal and semiconductor are brought into contact (top left inset), after they are in contact and in equilibrium (top right inset), when the forward bias is applied (bottom left inset) and when the reverse bias is applied (bottom right inset).    36 Before contact     In equilibrium      Forward bias       Reverse bias  Figure 4.2: Band diagram of Schottky diode        37 4.1.1 Design Parameters in Power Devices  Figure 4.3: Block of semiconductor (left);  Electric field distribution in the drift region in reverse bias (right)   The understanding of the relationship between each design parameter starts by the following derivation. Looking at a block of semiconductor in figure 4.3 the left inset, the conductivity () through the block and resistivity () is given by definition as in equation 4.1 where J is the current density and E is the electric field.    38 Also, by definition the resistivity is the resistance (R) times the cross-sectional area per unit length (WD) as given in equation 4.2. Note that WD is also used to refer to the length of drift layer.  On the right inset of figure 4.3, the electric field distribution in the drift region (p-) for reverse bias is shown when the maximum electric field (Emax) equals to the critical breakdown electric field (EC). The critical breakdown electric field is a physical parameter for each semiconductor material before avalanche breakdown takes place. The carrier concentration can be optimized such that Emax reaches Ec and the drift region is depleted entirely as shown in figure 4.3 (right inset). The breakdown voltage (VBR) is the area under the electric field curve in figure 4.3, which can be written out as in equation 4.3.  e slope of the electric field plot is determined as shown in figure 4.3, so it can be written in equation 4.4 the relationship between the electric field at the depletion region.  where q is the electron charge, NA is the doping concentration in the drift region, and s is the permittivity of the region. Combining equations 4.3 and 4.4, the doping concentration can be determined as written in equation 4.5.     39 By definition, the specific on-resistance (Ron,sp) is an inherent property of a material and is defined by the resistance offered by the unit cross-sectional area of the material when voltage is applied.  Back to equation 4.2, with basic knowledge of electric theory it follows that  where p is the mobility of holes. Equation 4.6 represents the ideal case when the drift region in reverse bias is fully depleted. Combining equations 4.5 and 4.6, the ideal specific on-resistance can also be written as:  Through equations 4.3 - 4.7, the relationship between the design parameters including NA, VBR, WD and Ron,sp are clearly stated. The electric field varies as NA. Ron,sp is inversely proportional to the electric field. VBR increases with WD but is inversely proportional to NA. These understandings will be important when the simulation results are observed.  There are four basic processes for carrier transport in the forward bias as shown in figure 4.4. Each process is indicated by the arrow showing the location in the band it occurs. These are (1) thermionic emission, (2) tunneling, (3) recombination and  (4) diffusion. They can take place at the same time, but usually one process dominates. Since for p+/p- Schottky diodes, there is only one type of charge carriers and that is hole; the recombination process can be ignored for now. Note that this is also called a unipolar device when there is only one type of charge carriers, either holes or electrons but not both, in the device.    40  Figure 4.4: Four basic transport processes in forward bias: (1) thermionic emission  (2) tunneling (3) recombination and (4) diffusion   The tunneling process where carriers travel through the barrier is often the case for Ohmic contacts and heavily doped (>1020 cm-3) semiconductors. For moderately doped semiconductors operating at moderate temperature (like room temperature), the thermionic emission process dominates. Due to the difference in workfunctions, a barrier forms naturally at a metal-semiconductor interface. In the forward bias, the applied voltage allows carriers to travel over the lowered barrier. The injection current based on thermionic emission is represented by the Richardson-Dushman equation as follows. (Note that detailed derivation of this equation can be found in chapter 3 in Physics of Semiconductor Devices by Sze.) [35]     41 where A* is the Richardson constant, T is the temperature in Kelvin, V is the applied voltage in V,  is the barrier height of semiconductor in V, k is the Boltzmann constant, q is the  Furthermore, there are various numerical models that approximate the amount of charge transport in the semiconductor devices based on certain assumptions. All the differences come from the type of materials (insulating or semiconductor), dimensions of the device, trapping effects and etc. In any case, the I-V relation of semiconductor devices often follows a universal power law of the form I m. The conduction regime varies depending on the value of the exponent m. In the Ohmic conduction regime, m = 1, and the current density J varies linearly with applied voltage V. The Ohmic conduction can be approximated by a simple drift current as shown in the following equation.  where q is the electronic charge, n is the density of the carriers,  is the mobility of the carriers, and W is the thickness of the drift layer.           42 4.1.2 Space Charge Limited Conduction (SCLC)  Figure 4.5: Band diagram of Schottky diamond diode in SCLC regime  There is a special situation when the current is controlled by the gradient of charge carriers (space charges) at a certain forward bias. When the density of the injected carriers is large as shown in figure 4.5, the space charge effect occurs, and these injected carriers influence the electric-field profile. In other words, with sufficient forward bias the density of injected carriers is much larger than the equilibrium acceptor levels. This generally happens when the ionization acceptor level is low. The local field, caused by the surplus carriers, yields a large gradient of carrier density and it is responsible for driving the current to the electrode. [36] So the current through a device is limited by the surplus space charges. There is no significant de  43 excess free-electron or free-hole concentration, ninjected, becomes large enough to be noticeable. When ninjected becomes comparable to n0 (thermal equilibrium free electron concentration), the space-charge-limited (SCL) mechanism becomes noticeable, and the current voltage characteristics change.  The situation is depicted in figure 4.5. The bands bend down due to over-compensated acceptor level. [37] This current is referred to as a space-charge limited current (SCLC). Mott-Gurney Law is an analytical theory describing the SCLC. It assumes that the electric field at the charge-injecting interface is zero. If the electric field exists at the interface, it is assumes to be neutralized by the field in the opposite direction generated by the injected p-type free carriers. The Mott-Gurney Law is derived as follows: With sufficient forward bias,  it can be approximated that  where  is the charge density, and p is the hole concentrations. The Poisson equation becomes independent of doping concentration in this region:  where again E is the electric field. In the lowly doped region with large enough forward bias, the drift current becomes much larger than diffusion current. So the total current can be approximated to the drift current only:  Combining equations 4.12 and 4.13:     44 Integrate from  assuming  by separating variables yields:   Integrate from  with  yields:  Therefore, the Mott Gurney equation is    SCLC is still part of the ordinary current-voltage characteristics of a majority carrier device in forward bias. Specifically, it describes the case of charge transport by the electric field from the surplus carriers of a highly doped region into another with much lower doping. From the assumptions made in the derivation of SCLC equation, it is evident that the equation holds only for devices in which the entire lowly doped region can be swept over by holes from p+ region. [37] Hence, such devices have to be thin. The simulations in the following section show that a Schottky diamond diode does produce SCLC under certain design parameters. Furthermore, when those design parameters vary, the forward conduction changes from SCLC to Ohmic regime.  4.2 Simulation Setup for Schottky Diamond Diodes Since Medici allows users the freedom to create arbitrary structures to simulate, for all of the simulations in this entire chapter the p+ layer was 6 m wide and 1 m thick with   45 the doping concentration of 1020 cm-3. The p- layer was also kept at 6 m wide. Both contacts were 0.1 m thick and 5 m wide  offsetting by 0.5 m from the left and right edge of diamond substrate. The design parameters that affect the performance of Schottky diodes were studied in this section of simulations. These parameters are:  The p- layer thickness, W (m)   The p- layer doping, NA (cm-3)  Operating temperature, T (K)  4.2.1 Schottky Diamond Diode Simulations in Forward Bias The I-V characteristics can give some insights about the transport mechanisms of a diamond Schottky diode. The set-up structure for the simulations is displayed in figure 4.1 and the basic parameters are stated in section 4.2. The thickness of p- layer, W, was studied first and the results are shown in figures 4.6, 4.7 and 4.8. For these results, the doping concentration in p- layer was 1 x 1016 cm-3 with the compensation of 1 x 1014 cm-3 to mimic the actual synthesized doped diamond. The temperature was set to 300 K (room temperature).     46  Figure 4.6: I-V Characteristic of Schottky diamond diode at 300K and p- was 1x1016 cm-3 for different thicknesses of the p- layer   The first information from the I-V plot of Schottky diode simulations is that at the bias of 2.0 V the current started to increase above 100 A/cm2 and this point is taken as the on) of the diode. For all the different thicknesses of the p- layer, Von was the same at 2.0 V. Next, the Mott Gurney equation (eq. 4.17) when W = 1 m was plotted in figure 4.7 (with the SCLC label) along with the simulations of different thicknesses on the semi-log plot. This is a quick check to see if the diamond model parameters compiled in Chapter 3 agreed with the SCLC theory. Figure 4.7 shows that the simulation result at 1 m agreed quite well with equation 4.17. It is apparent that the model of Schottky diamond diode   47 produced the forward conduction that matched the SCLC theory as the curves followed each other very closely.   Figure 4.7: Semi-log plot of current density versus forward bias voltage of Schottky diamond diode simulations at 300K and p- was 1x1016 cm-3 for different thicknesses of p- layer  Finally, the log(J) versus log(V) plot in figure 4.8 allows us to observe the power law relationship, J m., and m can be calculated. When m = 2, J and V relationship followed the Mott-Gurney Law and SCLC was observed. When m = 1, the transport mechanism was in Ohmic regime. In figure 4.8, when the thickness of the lowly doped layer was 1 current density curve follows the same gradient as the theoretical SCLC. As the thickness of the lowly doped layer (W) increased, the gradient of the current density curves decreased towards m = 1, the value of Ohmic conduction. It can be observed that the effect of SCLC was less and less as the thickness increased in figure 4.8. This matches with the   48 expectation, as it was more difficult for the charges to sweep through the thicker layer according to equation 4.16.  Figure 4.8: Log plot of current densities versus voltage of  Schottky diamond diode simulations at 300K and p- was 1x1016 cm-3       49  Figure 4.9: Log plot of current densities versus voltage of Schottky diamond diode simulations for varying thickness and temperature based on p- = 1x1016 cm-3  When coupled in the effect of SCLC with layer thickness and temperature, the results are shown in figure 4.9. Again as expected, as the thickness and the temperature increased the conduction became more Ohmic. This is also shown in figure 4.10, which is the plot of - layer (drift layer) with varying temperature. The alues were calculated between the forward voltages of 5-10 V. Here, it can be conclu with increasing layer thickness and temperature.   50 Thus, the effect of SCLC became less and less (m became closer to 1) with thicker devices and high operating temperature.   draft layer thickness W  Furthermore, the forward conduction was affected by the doping concentration in the p- layer and this is shown in figure 4.11 (which is the simulation when the p- layer was  2 m at 300K). Increase in the doping concentration, NA, resulted in higher current density. However, the effect of the doping variation on SCLC was less prominent compared to that from the d between 1.8  1.95 for the curves in figure 4.11 when measured between 5  10 V.      51  Figure 4.11: Log plot of current density versus voltage at 300K and p- = 2 m thick   Therefore, in the forward conduction the design parameter that affected SCLC the most was the thickness of the device. Operating temperature and doping concentration still had some effects but they were less prominent than the thickness of the device.         52 4.2.2 Schottky Diamond Diode Simulations in Reverse Bias  According to equation 4.5, the impurity doping concentration (NA) is the key parameter that affects the breakdown voltage. Hence, it is the design parameter that is discussed first in the reverse bias regime.  Figure 4.12: Schottky diode structure and dimension  for easy electric field comparison    53  Figure 4.13: Electric field versus drift layer when biased at VBR   The structure of Schottky diamond diode for simulations in reverse bias remained the same as shown in figure 4.1. However, figure 4.12 is also given which is just the rotated version of figure 4.1, so that comprehending the electric field plot in figure 4.13 is easier. Note one difference between figure 4.1 and 4.12 in that x=0 is defined at a different location. For figure 4.12, x=0 is at the p+/Ohmic contact interface. Figure 4.13 shows the plot of electric field versus device dimension from x=0 to x=6 m for the Schottky diode simulation at 300 K and drift layer is 5 m thick when biased at VBR. The values of VBR, Ron,sp and Emax for each NA are also listed in table 4.1.       54 -    -                 Table 4.1: Breakdown Voltages, Specific On-resistance and Maximum Electric Field of Schottky Diamond Diode Simulations at 300 K and Drift Layer, p-, was 5 m.   Figure 4.14: Semi-log plot of current versus voltage in the reverse bias at 300 K  As explained earlier in section 4.1, the area under the electric field versus dimension plot equals to VBR. The area under the yellow curve in figure 4.13 which belongs to NA =   55 3x1016 cm-3 appears larger compared to the area under the red curve for NA = 1x1017 cm-3. This agrees with the values of VBR measured from the simulations and shown in table 4.1 such that the breakdown voltage of the lower doped drift layer was higher.  This is as expected according to equation 4.5. Also displayed in figure 4.14 is the semi-log plot of current (A/m) versus voltage in the reverse bias of the structure in figure 4.12 at 300 K. When the drift layer doping was 1x1016 cm-3, the breakdown voltage was 1950 V. The breakdown voltage reduced to 1180 V as the drift layer doping increased to 3x1016 cm-3.  The results are also listed in table 4.1   Figure 4.15: Electric field versus drift layer dimension at 300 K at 1000 V reverse bias  Furthermore, figure 4.15 presents another set of results based on slightly different structural dimensions. The p+ layer was 2 m thick while the p- (drift) layer was 7 m. Doping concentration in the p+ layer remained the same as the previous simulations. For the p- layer, the doping concentration was varied from 1x1015 to 1x1018 cm-3. At 300 K, the   56 electric filed for each p- doping concentration was plotted for the same 1000 V reverse bias. The results showed the rise in the maximum value of the electric field (Emax) with increasing doping concentration in the drift layer. Viewing the results from figures 4.13, 4.14 and 4.15 and table 4.1 together, it can be concluded that the electric field varied proportionally as the drift layer doping concentration; while the breakdown voltage was inversely proportional to the electric field and the doping concentration.  This conclusion agreed with the theory in equations 4.4 and 4.5. Results on the variation in operational temperatures are reported in figures 4.16, 4.17 and 4.18. Regardless to the change in the temperatures always resulted in slightly greater breakdown voltage.    57  Figure 4.16: Breakdown voltage versus doping concentration of  Schottky diamond diode with drift layer (p-) of 5 m thick      58  Figure 4.17: Breakdown voltage versus p- layer thickness  when p- doping was fixed at 1x1016 cm-3    59  Figure 4.18: Breakdown voltage versus temperature for varying p- layer thickness  when p- doping was fixed at 1x1016 cm-3   The relationship between breakdown voltage and drift layer thickness is reported in figure 4.17. It was seen that the thicker drift layer yielded a higher breakdown voltage based on the simulations at the doping level of 1x1016 cm-3, which agreed with equation 4.3. In figure 4.18, the breakdown voltage increased with temperature. The mobility was greatly reduced at higher temperature, with that the peak electric field rose and in turns the higher breakdown voltage resulted.      60  Figure 4.19: Specific on-resistance versus breakdown voltage when p- layer thickness was fixed at 5 m and p- doping was fixed at 1x1016 cm-3  The reverse bias blocking capability relates to the forward bias performance via the specific on-resistance and breakdown voltage relationship theoretically stated in equation 4.7 and the agreeing results are plotted in figure 4.19. The specific on-resistance rose with increasing breakdown voltage as predicted by equation 4.7. This presents a trade-off in the design of Schottky diodes since normally one would like to increase the voltage blocking capability while minimizing the forward loss.    61 4.3 Schottky Diamond Diode with Field Plate Structures  The effect of high electric field at the edge of Schottky metal contact is exemplified by the simulation results reported in figure 4.20. The simulation of the structure shown in figure 4.20 where the Schottky contact only extended half way across the simulated structure showed the field concentrates higher at the edge of the contact. At 400 V reverse bias, the field at the edge of the Schottky contact was 1.4x107 V/cm, which was higher than the field in the middle of the contact, which was 5.2x106 V/cm.   Figure 4.20: Simulation setup and results of electric field vectors in the device  at 400 V reverse bias, 300 K   Adding a field plate made of aluminum oxide (dielectric constant, = 9.1) to the Schottky barrier as shown in figure 4.21 reduced the high field edge termination problem. Results are reported in table 4.2 and figure 4.21. Both field plate thicknesses yielded improved results in terms of electric field at the edge of the Schottky contact and   62 breakdown voltage. Between the two thicknesses, the thinner field plate of 0.5 m gave slightly better results.  Figure 4.21: Electric field at the edge and middle of Schottky contact without field plate (left); with 1.0 m thick field plate (middle); with 0.5 m thick field plate (right)                 Table 4.2: Electric field at the Edge of Schottky Contact and Breakdown Voltage  at 700 V Reverse Bias When Varying Thickness of Field Plate was Used   4.4 Summary of Chapter To summarize this chapter, the following points were deduced from the simulations of Schottky diamond diode with variations in design parameters:   63 - In the forward conduction the thickness of the device was the most prominent design parameter that would affect the current flow the most. Raising the temperature encouraged more ionization of charges, so the forward conduction improved. Changing the doping concentration did not impact the result as much if space limit current was occurring, however if ohmic conduction was dominating then the doping concentration was important.  - In reverse bias the doping concentration was the most prominent design parameter. Changing the thickness of the device would affect the result until the depletion width equaled the drift layer thickness, after which VBR would not vary. Raising the temperature did not provide much effect.  - Adding field plate structures made of high dielectric constant material reduced the high electric field at Schottky contact edges. Hence, greater breakdown voltage could be achieved.              64 CHAPTER 5  COMPARISON OF DIAMOND DIODE DESIGNS  This chapter presents the simulation results of the PN-junction and merged diamond diodes. The basic operational mechanism of the different structures and their attributes are first introduced. The results from different diode designs are then compared. The chapter is organized into the following sections including (1) PN-junction diamond diode with consideration of the basic operation of PN-junction diodes, simulation of PN-junction diamond diodes, and performance comparison of Schottky and PN-junction diamond diodes and (2) merged diamond diodes with consideration of basic operation of merged diode structures, simulation of merged diamonds and comparison of Schottky, PN-junction and merged diamond diodes.  5.1 PN-junction Diamond Diode  Unlike the Schottky barrier formed by a semiconductor-to-metal interface, a PN-junction is formed by bringing two semiconductor materials with dissimilar Fermi energies together. The PN-junction structure performs like a rectifier, but due to its semiconductor-to-semiconductor interface, its operational mechanisms are different from the ones seen in Schottky diamond diode in the previous chapter. In fact the physics in the forward conduction is more complicated in PN-junction diode as it is a minority carrier device in which movements of both electrons and holes take place.      65 5.1.1 Basic Operation of PN-junction Diode The basic operational mechanism of a PN-junction is depicted in figure 5.1. When p-type and n-type semiconductors are brought in contact, initially some diffusion occurs when some free electrons in the n-region move across the interface (leaving behind some positive donor ions) to combine with the holes in the p region yielding some negative acceptor ions. This results in the area near the junction of the p and n type material having a space charge built up, which is called the depletion region. The space charge region with its electric field prevents any further electron transfer in the equilibrium. In forward bias, the applied voltage will cause the electrons to diffuse across the depletion region to the p-type region and holes to diffuse across the depletion region to the n-type region. Electrons and holes also can partially recombine in the depletion region. In reverse bias, electrons and holes are pulled away from the junction. The depletion region width increases. Breakdown occurs when the applied voltage creates an electric field large enough that impact ionization occurs.    66  Figure 5.1: Basic operations of a PN-junction diode [39]    Because there are movements of holes and electrons in the drift region for PN-junction diodes, the resistance in the area is lowered and changing depending on the amount of forward bias applied. Hence, at higher forward bias the current density is normally large when compared to Schottky diode at higher voltage. This is called conduction modulation, which is the process that Schottky diode is lacking.  When either side of the semiconductor is much more heavily doped, p+/n or n+/p, the situation is referred to as a one-sided abrupt junction. The depletion region primarily extends into the lightly doped region; any extension into the highly doped area can be  In equilibrium Forward bias Reverse bias   67 neglected. Detailed theoretical derivations and explanations about PN-junction diodes can be found in chapter 2 of Physics of Semiconductor Devices by Sze. [35]  For the n+/p- junction in the simulations in the next section, ND >> NA and the depletion width is given in equation 5.1. The built-in potential and breakdown voltage are given in equations 5.2 and 5.3 respectively. [35]    where s is permittivity of the semiconductor (diamond in this case), k is the Boltzmann constant, T is the temperature, q is the electric charge, Emax is the peak electric field, ND is the donor impurity concentration, NA is the acceptor impurity concentration, and ni is the intrinsic carrier concentration. Equations 4.3  4.7 are also applicable for the PN-junction structure. [35] The built-in potential in equation 5.2 is larger than the barrier potential in Schottky diodes. As a result, higher turn-on voltage is to be expected.  5.1.2 Structure Setup and Simulation of PN-junction Diamond Diode The structure of the PN-junction diode used in all of the simulations in this chapter is shown in figure 5.2. It looks similar to the structure in figure 4.1 for Schottky diode simulations. The difference was the thin and heavily doped layer is n-type with the concentration of 1 x 1020 cm-3 and thickness of 1 m. Phosphorus was assumed as the n-type dopant and its parameters which were necessary for the simulations are listed back in   68 chapter 3. The lowly doped layer is p-type and was 5 m thick. Two ohmic contacts were formed; one was placed on top of the n+ layer while the other was on the bottom side of p- layer. Both were 100 nm thick, and 5 m long. (Note that Medici assumes the  2-dimensional structure has 1 m depth into the page for figure 5.2).  Figure 5.2: Setup structure of PN-junction diode   The structure in figure 5.2 was simulated by varying the operating temperature from 300 to 600 K and the doping concentration in the p- layer (NA) from 1x1016  2.5x1017 cm-3. The values of breakdown voltages (VBR) and the calculated specific on-resistance (Ron,sp) from the I-V plots of the simulation results are listed in table 5.1. Similar to the Schottky diamond diode, as the operating temperature rose the incomplete ionization effect became less, resulting in higher current density in the forward bias as seen in the J-V plot in figure 5.3. Also when keeping the operating temperature fixed at 450 K and only varying NA, the current densities increased with the level of doping concentration as shown in figure 5.4. In figure 5.5, the specific on-resistance decreased with increasing doping level, which agreed with equation 4.6.   69  -      -   -   -                             Table 5.1: Results of PN-junction Diamond Diode Simulations  (structure displayed in figure 5.1) with Varying Temperature and Doping Concentration   Figure 5.3: J-V plot of a PN-junction diamond diode  when NA in p- layer was 1x1017 cm-3 and 5 m thick    70   Figure 5.4: J-V plot of a PN-junction diamond diode  when p- layer was 5 m thick and operating temperature was 450K   Figure 5.5: Specific on-resistance versus doping concentration  in the drift layer of PN-junction diode   71 In the reverse bias, the values of peak electric field (Emax) measured at 450 K were recorded at the breakdown voltage. When the drift layer doping was 1x1016 cm-3, Emax was 5.57x106 V/cm. When doping was increased to 1x1017 cm-3, Emax went up to 6.24x106 V/cm. This also agreed with the theoretical equation 4.4 since increasing drift layer doping resulted in higher peak electric field at breakdown in the reverse bias. This led to the results in figure 5.6. Since the breakdown voltage was inversely proportional to the peak electric field, the breakdown voltage decreased with increasing p- layer (drift layer) doping concentration as shown in figure 5.6.  Figure 5.6: Breakdown voltage versus drift layer doping concentration of  a PN-junction diamond diode based on 5-m thick drift layer      72  Figure 5.7: Specific on-resistance versus breakdown voltage of  PN-junction diamond diode at 300 K   The specific on-resistance of PN-junction diode versus the blocking capability is plotted in figure 5.7. The result matched the expectation based on the theoretical derivation in equation 4.7. This suggests that higher voltage blocking capability comes with greater power loss.  5.1.3 Performance Comparison of Schottky and PN-junction Diamond Diode In this section, the simulation results between the two types of diodes are compared. Depicted in figure 5.8 is a plot of current density versus voltage in the forward bias of the Schottky and PN-junction diodes - both of which had the p- layer doping concentration of 1 x 1017 cm-3 and thickness of 5 m at 450 K. It can be observed that the turn-on voltage (Von) was approximately 2 V for Schottky diode and 4.8 V for PN-junction   73 diode. This was as expected since the Schottky barrier height between metal and semiconductor was lower. Thus, lower built-in potential was required to transport carriers. However, the PN-junction diode conducted more current as a result of high carrier injection.   Figure 5.8: Comparison of the turn-on voltages (Von) of Schottky and  PN-junction diodes at 450 K based on NA of 1 x 1017 cm-3 and p- was 5 m thick     74  Figure 5.9: Comparison of Ron,sp of PN junction and Schottky diamond diodes    Additionally, a comparison between the specific on-resistance (Ron,sp) of Schottky and PN-junction diodes are plotted in figure 5.9. Again, Ron,sp was calculated by determining the differential resistance from the current density versus voltage data obtained from the simulation output multiplied by the area of the contact area through which the current flowed (which was 5 m x 1 m) . The differential resistance was calculated around the forward voltage of 10 V. Since PN-junction diodes produced higher current as seen in figure 5.8, intuitively they had lower loss in the forward conduction.     75  Figure 5:10 Semi-log plot of current versus voltage in reverse bias of Schottky and  PN-junction diamond diodes at 450 K and drift layer doping of 4x1017 cm-3   As for the reverse bias, the PN-junction diamond diodes were expected to perform better and they did when comparing the simulation results shown in figure 5.10. Additionally, figure 5.11 also displays the breakdown voltage versus doping concentration in the drift layer of Schottky and PN-junction diamond diodes at 300 K and 450 K. The peak electric field at breakdown of PN-junction and Schottky diodes are reported in table 5.2. For the same doping concentration, the field peaked higher in PN-junction diodes and this accounted for its better voltage-blocking attribute.   76  Figure 5.11: Breakdown voltage versus p- layer doping concentration of  Schottky and PN-junction diamond diodes based on  p- layer of 5 m thick and operating temperatures at 300 K and 450 K  - -                Table 5.2: Peak Electric Field at Breakdown of  PN-junction and Schottky Diode at 450 K        77 5.2 Merged Diamond Diode 5.2.1 Basic Operation of Merged Diode Structures  Incorporating the best operating attributes of Schottky and PN-junction diodes into one discrete device have many benefits and it has been previously done with other wide bandgap materials. [40] The structure of the proposed merged diode design is depicted in figure 5.12. It can be thought of as putting a Schottky diode in parallel with the PN-junction diodes.   Figure 5.12: Structure of merged diode design   At low forward bias, the merged diode will start to conduct and current will flow through the Schottky contact. So it incorporates the low turn-on voltage attribute from the Schottky diode that offers lower potential barrier to current flow. Under reverse bias conditions, depletion regions formed at the n+/p- interface spread out and intersect under the area where the Schottky contact is placed as depicted in figure 5.13. This depletion region establishes a potential barrier under the Schottky contact that can reduce the high field in the area.    78  Figure 5.13: The intersection of depletion regions in merged diamond diode  under reverse bias  5.2.2 Structure Setup and Simulation of Merged Diamond Diode  Figure 5.14: Merged diode setup for simulations    79  The structural setup of merged diode for simulations is exemplified in figure 5.14. The doping concentration in p+ layer (NA) was 1 x 1020 cm-3. Boron was used for p-type doping. Phosphorus was used for the n+ regions and the concentration was 1 x 1020 cm-3. The dimension of each n+ region was 1 m thick while the width varied depending on the spacing width between them. Since the spacing is the area where the depletion regions from each n+/p- interface would merge, it became one of the design parameters in the simulations. A Schottky contact was placed on top of this spacing area, it was 100nm thick. An Ohmic contact on the p+ layer was 100 nm thick and 5 m wide, while the ones on the n+ regions had the same thickness but the width varied according to the spacing. Three values of the spacing width were simulated, the dimension of n+ width, the Schottky contact above the spacing, and the Ohmic contacts above the n+ regions were configured as shown in figure 5.15.  Figure 5.15: Dimension configurations of merged diode dimensions   It should be noted that the surface area that current flowed through for merged diodes was different from that of the Schottky and PN-junction diodes. In fact, for the three dimension configurations shown in figure 5.15, the surface area of current flow was different. This is important when the specific on-resistance was calculated. For the results   80 reported in the next sections, the specific on-resistance was determined by obtaining the differential resistance from the current density versus voltage plot where the voltage was about 10 V then multiplied by each surface area of the Schottky contact.  5.2.3 Comparison of Schottky, PN-junction and Merged Diamond Diodes  Values of breakdown voltage, turn-on voltage and specific on-resistance from different diode designs are reported in table 5.3 based on the simulation at 450 K and the drift layer doping of 1x1017 cm-3. At a quick glance at table 5.3, the merged diodes had low turn-on voltage like the Schottky diode and higher voltage blocking capability like the PN-junction diode.     - -         -     -     -    Table 5.3: Breakdown Voltage, Turn-on Voltage and Specific On-resistance for  PN-junction, Schottky and Merged Diamond Diodes Simulated at  450 K and Drift Layer Doping of 1x1017 cm-3  Among the merged diodes, the structure that had 1- the highest breakdown voltage. The breakdown voltage dropped as the spacing width increased. The   81 1- the lowest specific on-resistance. Smaller area of the PN-junctions yielded higher resistance. This can be interpreted that the smaller spacing allowed the depletion regions formed by each p-/n+ interface to merge more easily. The situation is depicted in figure 5.16 through the electric field vector at each biasing. At equilibrium (0 V), as indicated by the empty field vector in the drift region, no current was flowing yet. At the forward bias of 10 V, field vectors existed through out the drift region indicating current flow. In the reverse bias of -180 V, the longer field vectors indicated higher field values, which were located in the depletion regions at the p-/n+ interface. The depletion regions intersected in the spacing area (below the Schottky contact) forming a potential barrier as indicated by the line enclosing the field vectors. No field vectors existed below the potential barrier. The high electric field that conventional Schottky diodes experience at breakdown was reduced by this mechanism allowing the merged diode to have larger voltage blocking capability.   Figure 5.16: Electric field vector of the merged diode with 2-of 1x1017 cm-3 and simulated at 450 K    82  Figure 5.17: Forward conduction of Schottky, PN junction and merged diamond diode simulated at 450 K and drift layer doping of 1x1017 cm-3  (the inset is zoomed in on the x and y axes)  Looking at the inset of figure 5.17, the merged diodes and Schottky diode started to conduct before the PN-junction diode. It was seen that the currents by the merged diodes followed the trend of the Schottky diode from 2 V up until 5 V. As previously reported, the Schottky diode turned on at 2 V while the PN-junction diode turned on at 5 V. Above 5.5 V, the merged diode currents increased significantly especially for the 1-and they no longer looked similar to that of the Schottky diode. This can be explained that as forward voltage increased, the p-/n+ junction began to inject some minority carriers into the drift region in p- layer. The resistance in the drift region was lessened due to the presence of the minority carriers. As a result, more current was flowing. This process is   83 called conductivity modulation when increasing number of carriers lowers the drift layer resistance allowing more current to flow. [40]  5.3 Summary of Chapter Simulations of PN-junction diodes yielded agreeable results to the theory. They provided higher voltage blocking capability and higher forward current than the Schottky diodes. Although being a minority carrier device, the reverse recovery time between the on and off state would not be as fast as the Schottky diodes. The merged diode structure combined the low turn-on voltage of the Schottky diode and high breakdown voltage of the PN-junction diode. However, the performance depended greatly on the structure design particularly the spacing width between the interfaces (p-/n+) that form depletion regions.     84 CHAPTER 6  CONCLUSION AND FUTURE RESEARCH  6.1 Conclusion of Findings This study developed a set of diamond physical parameters with the most up-to-date models in the literature and from the measurements of the experimental work at Michigan State University. Models for incomplete ionization, temperature-and-impurity dependent mobility, and impact ionization, along with diamond bulk parameters were included for this compilation, which was used for device simulations of diamond diode designs.  In this study, the design parameters for diamond diodes included the doping concentration in the drift layer, thickness of the drift layer, operational temperature, and spacing width between depletion regions when applicable.  Diode performance metrics for high power, high voltage and high temperature applications included the breakdown voltage, turn-on voltage, and specific on-resistance. Three different structures of diamond diodes were simulated versus changes in the design parameters. These structures were the Schottky, PN-junction and merged Schottky/PN-junction diodes. The design parameters affect the performance metrics of each diode structure as follows. In Schottky diamond diodes, the thickness and doping level of the drift layer are the most prominent design parameters in the forward conduction. The space-charge-limited conduction (SCLC) current was observed in the forward bias when the drift layer thickness was thin. The forward current entered the Ohmic conduction regime as the drift layer thickness increased. The increase in operational temperature also caused the forward   85 conduction to become more Ohmic. The specific on-resistance reduced as the doping concentration and temperature increased. Higher temperature enabled more carriers to be ionized, while higher doping concentration also gave more carriers in the drift region. Both of these effects reduced the series resistance in the drift layer.   As for the reverse bias performance of the Schottky diamond diodes, the drift layer doping concentration has the highest impact. The doping concentration inversely affected the breakdown voltage - causing the reduced breakdown voltage as the doping increased. The larger thickness of the drift layer caused the peak electric field at breakdown to increase yielding higher breakdown voltage. The thin aluminum oxide field plate reduced the high field associated to the edge termination problem of the Schottky contact. The field plate thickness of 0.5 m yielded the most improved result by lowering the field and giving the significant increase in breakdown voltage.   In the PN-junction diamond diodes, the same trend of the design parameter effects on the performance metrics was observed. The breakdown voltage had the inverse relationship with the drift layer doping concentration; while its relationship to temperature was positive. The specific on-resistance varied as the doping concentration and opposite to the temperature.  The performance comparison from the simulations between the Schottky and PN-junction diamond diodes matched their conventional and well-known attributes in both directions of conduction. In the forward bias, the turn-on voltage by the Schottky diamond diodes was lower than that of the PN-junction diamond diodes. This agrees with the known fact that the barrier potential of Schottky diodes is lower than the built-in potential of PN-junction diodes. However, the Schottky diamond diodes produced more forward loss, as   86 their specific on-resistances were larger resulting in the much lower current density at the higher conducting voltage. This stems from the fact that Schottky diodes are unipolar device that lack the high carrier injection condition from the process of carrier recombination and generation seen in bipolar devices like PN-junction diodes. Conventionally, PN-junction diodes have higher voltage blocking capability when compared to Schottky diodes. This results from the higher field at breakdown of the PN-junction structure. In the simulations of this study, the PN-junction diamond diodes yielded the higher breakdown voltages than the values produced by the Schottky diamond diodes  agreeing with the convention. Additionally, the higher breakdown voltage for PN-junction diodes are due to the elimination of the edge effect found in the Schottky diodes. The merged diamond diodes combined the benefits of the Schottky and PN-junction diamond diodes. As seen in the reverse bias of the PN-junction diodes, the merged diamond diodes also produced high voltage breakdown capability. This was achieved from the intersection of the depletion regions, which created the potential barrier that reduced the electric field at its Schottky contact resulting in the high breakdown voltage. The turn-on voltage of the merged diamond diodes was low like that of the Schottky diamond diodes because its forward conduction path involved the Schottky barrier. As the forward voltage reached pass the higher turn-on voltage of the PN-junction diamond diodes, the merged diamond diodes started to deviate from the trend of Schottky diamond diodes and produced higher current density due to conductivity modulation. The performance of the merged diamond diodes depended greatly on the spacing width between the interfaces that form depletion regions. The performance deteriorated as the spacing width widened.     87 6.2 Future research For the high voltage, high power and high temperature applications of diamond devices, further study on the aspects not covered in this study are required.  These aspects are the following: 1. Extend the performance metrics to include the leakage current since it can give high power loss especially as the temperature increases. This can be done by plotting the J versus V characteristic of the simulation results similar to figure 4.14 and 5.10. The leakage current densities can then be observed and compared for different cases of design structures.  2. Model the forward current of the PN-junction diamond diodes. In particular, determine the design parameters that affect the ideality factor and the high injection regime. Similar methods that were used for the study of the forward current in Schottky diamond diodes in chapter 4 can be used. 3. Fabricate diamond diodes based on the simulated designs and compare the performance outcomes. Ultimately, a physical diamond device that is working as predicted is the goal.  4. Improve the carrier mobility database as more experimental results become available especially at high temperatures. The theoretical models indicate the lower rate of carrier mobility at higher temperature due to carrier scattering.  As more doped diamond samples in p-type and n-type become available, the Hall measurement method can be used to measure the mobilities at various temperatures.  The data can be from in-house measurements or gathered from the literature when available.    88 5. Apply the findings to the design and simulation of diamond field effect transistors (FETs). The findings from diamond diode simulations serve as the fundamentals from which more complicated diamond devices can be achieved.                        89            APPENDICES              90 APPENDIX A: Input File of Schottky Diamond Diode     (p- = 1x1017 cm-3; 450 K)  TITLE Schottky Diamond Diode p-/p+  MESH  SMOOTH=1  X.MESH  WIDTH=6.0 N=10 Y.MESH   DEPTH=1.0 H1=0.1 Y.MESH      DEPTH=5.0 H1=0.2  REGION  NAME=SUB  DIAMOND  ELECTR  NAME=Anode X.MIN=0.8 X.MAX=5.2 TOP  ELECTR  NAME=Cathode X.MIN=0.8 X.MAX=5.2 BOTTOM   PROFILE     P-TYPE  N.PEAK=1E17 UNIFORM  OUT.FILE=DDT1 PROFILE     N-TYPE N.PEAK=1E14 UNIFORM PROFILE     P-TYPE  N.PEAK=1E20 X.MIN=0.0 WIDTH=6.0 Y.MIN=0 Y.JUNC=1.00  MATERIAL  DIAMOND PERMITTI=5.7  EG300=5.47 AFFINITY=1.3   AN=4.62E5  +BN=7.59E6  CN=1.0  AP=1.93E5  BP=4.41E6  CP=1.0 NC300=1E20 NV300=1E20 +TAUP0=1E-9   IMPURITY    NAME=N-TYPE REGION=SUB GB=2   EB0=0.59   ALPHA=3.1E-8     BETA=200   +GAMMA=1      HDT.MIN=3E19    HDT.MAX=3E20  IMPURITY    NAME=P-TYPE REGION=SUB GB=4   EB0=0.36   ALPHA=3.037E-8   BETA=200   +GAMMA=0.95   HDT.MIN=3E19    HDT.MAX=3E20  CONTACT    NAME=Cathode WORKFUNC=4.3 CONTACT    NAME=Anode  WORKFUNC=7.2  COMMENT mobilities by Dr. Hogan's Hall Measurements COMMENT MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20) COMMENT at 300K HOLE=(930, 820, 800, 150, 39)   ELECTRON=(540, 380, 270, 120, 8) COMMENT at 450K HOLE=(310, 250, 230, 90, 32)    ELECTRON=(560, 420, 300, 180, 140) COMMENT at 600K HOLE=(130, 100, 98, 56, 24)     ELECTRON=(590, 520, 490, 475, 470)     MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20)  + HOLE=  (310, 250, 230, 90, 32) + ELECTRON= (560, 420, 300, 180, 140) + PR.TABLE   PLOT.2D  GRID TITLE="Grid" FILL SCALE DEVICE=POSTSCRIPT PLOT.OUT=DiT1.ps   91 REGRID      DOPING LOG RATIO=2 SMOOTH=1 IN.FILE=DDT1  PLOT.2D     GRID TITLE="Doping Regrid" FILL SCALE DEVICE=POSTSCRIPT +PLOT.OUT=DiT2.ps  MODELS      SRH AUGER CONMOB INCOMPLE HIGH.DOP ENERGY.L IMPACT.I +TEMPERAT=450  SYMB        NEWTON CARRIERS=2  SOLVE   INITIAL SOLVE   V(Anode)=0 SOLVE   V(Anode)=5 SOLVE   V(Anode)=10 SOLVE   V(Anode)=200 ELEC=Anode VSTEP=-7 NSTEP=400  PLOT.1D   E.FIELD X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=6.0 TITLE="EFvsDist" +PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGEF.ps  PLOT.1D   Y.LOGARI Y.AXIS=I(Anode)  X.AXIS=V(Anode) POINTS COLOR=2 TITLE="IV +Schottky REV 450K" DEVICE=POSTSCRIPT PLOT.OUT=DiT6HogCom.ps  PLOT.1D   POTENTIA X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=6.0 TITLE="PoTentail" +PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGPP.ps  PLOT.1D   Y.LOGARI HOLES X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=3.0 +TITLE="Holes" PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGHoles.ps  SOLVE     V(Anode)=-5 ELEC=Anode VSTEP=0.5 NSTEP=50 PLOT.1D   Y.AXIS=I(Anode)  X.AXIS=V(Anode) POINTS COLOR=2 TITLE="IV Schottky FWD +450K" PRINT DEVICE=POSTSCRIPT PLOT.OUT=DiT3HogCo.ps                 92 APPENDIX B: Input File of Schottky Diamond Diode with Field Plate     (p- = 1x1017 cm-3; 450 K)  TITLE Diamond Test1 Field Plate p/p+  MESH  X.MESH  WIDTH=1.0 H1=0.5 X.MESH      WIDTH=1.0 H1=0.1 X.MESH      WIDTH=0.5 H1=0.25 X.MESH      WIDTH=1.0 H1=0.1 X.MESH      WIDTH=2.5 H1=0.5 COMMENT Y.MESH NODE=1 L=-1.0 COMMENT Y.MESH NODE=11 L=0 Y.MESH  NODE=1 L=-0.5 Y.MESH  NODE=6 L=0 Y.MESH      WIDTH=0.5 H1=0.025 Y.MESH      WIDTH=4.5 H1=0.10 Y.MESH      WIDTH=1.0 H1=0.20  REGION  NAME=SUB  DIAMOND REGION      OXIDE X.MIN=0 X.MAX=3 Y.MIN=-0.5 Y.MAX=0  ELECTR  NAME=Anode  X.MIN=1.5 X.MAX=3.0 TOP  ELECTR      NAME=Anode2  X.MIN=3.001 X.MAX=6.0 Y.MAX=0.0 ELECTR  NAME=Cathode  BOTTOM   PROFILE  P-TYPE N.PEAK=1E17 UNIFORM  OUT.FILE=DDT2 PROFILE     P-TYPE  N.PEAK=1E20 Y.JUNC=1.0 Y.MIN=5.0 Y.MAX=6.0  X.MIN=0.0 +WIDTH=6.0 XY.RATIO=0.75   MATERIAL  DIAMOND PERMITTI=5.7  EG300=5.47 AFFINITY=1.3   AN=4.62E5  +BN=7.59E6  CN=1.0  AP=1.93E5  BP=4.41E6  CP=1.0 NC300=1E20 NV300=1E20 +TAUP0=1E-9   MATERIAL  OXIDE PERMITTI=9.1    IMPURITY    NAME=P-TYPE REGION=SUB GB=4   EB0=0.36   ALPHA=3.037E-8  BETA=200  +GAMMA=0.95   HDT.MIN=3E19   HDT.MAX=3E20    CONTACT   NAME=Cathode WORKFUNC=7.2 CONTACT    NAME=Anode  WORKFUNC=4.3 CONTACT   NAME=Anode2   WORKFUNC=4.3   93 COMMENT mobilities by Dr. Hogan's Hall Measurements COMMENT MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20) COMMENT at 300K HOLE=(930, 820, 800, 150, 39)   ELECTRON=(540, 380, 270, 120, 8) COMMENT at 450K HOLE=(310, 250, 230, 90, 32)    ELECTRON=(560, 420, 300, 180, 140) COMMENT at 600K HOLE=(130, 100, 98, 56, 24)     ELECTRON=(590, 520, 490, 475, 470)     MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20)  + HOLE=  (310, 250, 230, 90, 32) + ELECTRON= (560, 420, 300, 180, 140) + PR.TABLE   PLOT.2D  GRID TITLE="Grid" FILL SCALE DEVICE=POSTSCRIPT PLOT.OUT=DiT2.ps  REGRID      DOPING LOG RATIO=2 SMOOTH=1 IN.FILE=DDT2  PLOT.2D     GRID TITLE="Doping Regrid" FILL SCALE DEVICE=POSTSCRIPT PLOT.OUT=DiT2.ps  MODELS      SRH AUGER CONMOB INCOMPLE IMPACT.I HIGH.DOP TEMPERAT=450  SYMB             NEWTON CARRIERS=2  SOLVE INITIAL SOLVE V(Cathode) = 0  COMMENT   SOLVE V(Cathode) =-5 ELEC=Cathode VSTEP=1 NSTEP=25  SOLVE V(Cathode)=50 ELEC=Cathode VSTEP=-7 NSTEP=150  COMMENT SOLVE V(Cathode)=0 ELEC=Cathode VSTEP=-7 NSTEP=100  PLOT.1D   E.FIELD X.START=3.0 X.END=3.0 Y.START=-1.0 Y.END=6.0 TITLE="EF -700V-+Bias" PRINT DEVICE=POSTSCRIPT PLOT.OUT=DiT2EF.ps  PLOT.1D   E.FIELD X.START=1.5 X.END=1.5 Y.START=-1.0 Y.END=6.0 TITLE="EF -700V-+Bias" PRINT DEVICE=POSTSCRIPT PLOT.OUT=DiT2EF1.ps  PLOT.1D   E.FIELD X.START=0.75 X.END=0.75 Y.START=-1.0 Y.END=6.0 TITLE="EF -700V-+Bias" PRINT DEVICE=POSTSCRIPT PLOT.OUT=DiT2EF2.ps  PLOT.1D   E.FIELD X.START=1.75 X.END=1.75 Y.START=-1.0 Y.END=6.0 TITLE="EF -700V-+Bias" PRINT DEVICE=POSTSCRIPT PLOT.OUT=DiT2EF3.ps  PLOT.2D  JUNCTION DEPLETION SCALE TITLE="E-field Vector Struc3" +DEVICE=POSTSCRIPT PLOT.OUT=DiT2EFC.ps    94 VECTOR     E.FIELD  PLOT.2D   BOUND JUNC DEPL FILL SCALE TITLE="Potential Contours at -700V Struc3" +DEVICE=POSTSCRIPT PLOT.OUT=DiT2CC.ps  CONTOUR  POTENTIA  PLOT.1D Y.AXIS=I(Cathode)  X.AXIS=V(Cathode) POINTS COLOR=2 TITLE="Log IV Struct3" +PRINT DEVICE=POSTSCRIPT PLOT.OUT=DiT2b.ps  EXTRACT IONIZATI                      95 APPENDIX C: Input File of PN-junction Diamond Diode     (p- = 1x1017 cm-3; 450 K)  TITLE PN-junction Diamond Diode p-/n+  MESH  X.MESH  WIDTH=6.0 N=10 Y.MESH   WIDTH=1.0 H1=0.10 Y.MESH                          WIDTH=5.0 H1=0.20   REGION  NAME=SUB  DIAMOND   ELECTR  NAME=Anode X.MIN=0.8 X.MAX=5.2 TOP  ELECTR  NAME=Cathode X.MIN=0.8 X.MAX=5.2 BOTTOM    PROFILE P-TYPE  N.PEAK=1E17 UNIFORM  OUT.FILE=DDT1 PROFILE N-TYPE N.PEAK=1E14 UNIFORM PROFILE   N-TYPE  N.PEAK=1E20 X.MIN=0.0 WIDTH=6.0 X.CHAR=6 Y.MIN=0.0 Y.JUNC=1.0 PROFILE   P-TYPE  N.PEAK=1E20  Y.MIN=5.0 Y.JUNC=5.5 X.MIN=0 X.MAX=6  MATERIAL  DIAMOND PERMITTI=5.7  EG300=5.47 AFFINITY=1.3   AN=4.62E5  +BN=7.59E6  CN=1.0  AP=1.93E5  BP=4.41E6  CP=1.0 NC300=1E20 NV300=1E20 +TAUP0=1E-9   IMPURITY    NAME=N-TYPE REGION=SUB GB=2 EB0=0.59 ALPHA=3.1E-8 BETA=200 +GAMMA=1 HDT.MIN=3E19 HDT.MAX=3E20  IMPURITY    NAME=P-TYPE REGION=SUB GB=4   EB0=0.36   ALPHA=3.037E-8  BETA=200  +GAMMA=0.95   HDT.MIN=3E19 HDT.MAX=3E20  CONTACT   NAME=Cathode  CONTACT    NAME=Anode   COMMENT mobilities by Dr. Hogan's Hall Measurements COMMENT MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20) COMMENT at 300K HOLE=(930, 820, 800, 150, 39)   ELECTRON=(540, 380, 270, 120, 8) COMMENT at 450K HOLE=(310, 250, 230, 90, 32)    ELECTRON=(560, 420, 300, 180, 140) COMMENT at 600K HOLE=(130, 100, 98, 56, 24)     ELECTRON=(590, 520, 490, 475, 470)     MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20)  + HOLE=  (310, 250, 230, 90, 32)   96 + ELECTRON= (560, 420, 300, 180, 140) + PR.TABLE   PLOT.2D  GRID TITLE="Grid" FILL SCALE DEVICE=POSTSCRIPT PLOT.OUT=DiT1.ps  REGRID      DOPING LOG RATIO=2 SMOOTH=1 IN.FILE=DDT1  PLOT.2D     GRID TITLE="Doping Regrid" FILL SCALE DEVICE=POSTSCRIPT +PLOT.OUT=DiT2.ps  MODELS      SRH AUGER CONMOB INCOMPLE HIGH.DOP ENERGY.L IMPACT.I +TEMPERAT=450  SYMB             NEWTON CARRIERS=2  SOLVE INITIAL  SOLVE V(Cathode)=0 COMMENT SOLVE     V(Cathode)=-5 ELEC=Cathode VSTEP=5 NSTEP=30 COMMENT PLOT.1D   Y.AXIS=I(Cathode)  X.AXIS=V(Cathode) POINTS COLOR=2 TITLE="IV +PN 1E16 5um Compensated 450K" PRINT DEVICE=POSTSCRIPT +PLOT.OUT=DiT3HogCo.ps  COMMENT PLOT.1D   E.FIELD X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=6.0 TITLE="EFvsDist" PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGEF.ps COMMENT PLOT.1D   POTENTIA X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=6.0 TITLE="PoTentail" PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGPP.ps COMMENT PLOT.1D   Y.LOGARI HOLES X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=6.0 TITLE="Holes" PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGHoles.ps  SOLVE V(Cathode)=10 ELEC=Cathode VSTEP=-9 NSTEP=400 PLOT.1D  Y.LOGARI Y.AXIS=I(Cathode)  X.AXIS=V(Cathode) POINTS COLOR=2 TITLE="IV +PN 350K" DEVICE=POSTSCRIPT PLOT.OUT=DiT3HogPN.ps  PLOT.1D   E.FIELD X.START=3.0 X.END=3.0 Y.START=0.0 Y.END=6.0 TITLE="EFvsDist" +PRINT DEVICE=POSTSCRIPT PLOT.OUT=TGEF.ps            97 APPENDIX D: Input File of Merged Diamond Diode     (p- = 1x1017 cm-3; 450 K; spacing = 1 m)  TITLE        Diamond Merged N+/P-/P+ Diode  COMMENT      Specify a rectangular mesh  MESH         SMOOTH=1   COMMENT     Specify the width of the mesh and the spacing is 0.125 micron  X.MESH       WIDTH=6.0  H1=0.25   Y.MESH       N=1    L=0  COMMENT      Specify the spacing between y=0 and y=2.5um is 0.125um for P- Y.MESH       DEPTH=5.0  H1=0.25   COMMENT      Specify the spacing between y=2.5 and y=3um is 0.25um for P+ Y.MESH       DEPTH=1.0  H1=0.5   COMMENT      Eliminate  all nodes between y=1.1um and y=2um  ELIMIN       COLUMNS  Y.MIN=5.1   REGION       NAME=SUB DIAMOND  COMMENT      Electrode definition  ELECTR       NAME=Ohmic  X.MIN=1.0 X.MAX=5.0 BOTTOM  ELECTR      NAME=Left X.MIN=0.4 X.MAX=1.8 TOP ELECTR       NAME=Right X.MIN=4.2 X.MAX=5.6 TOP ELECTR       NAME=Mid X.MIN=2.7 X.MAX=3.3 TOP  COMMENT      Specify impurity profiles and fixed charge  PROFILE      P-TYPE  N.PEAK=1E17  UNIFORM OUT.FILE=MDEX1DS  PROFILE      N-TYPE  N.PEAK=1E14 UNIFORM PROFILE      P-TYPE  N.PEAK=1E20  Y.MIN=5.0 Y.JUNC=5.5 X.MIN=0 X.MAX=6 PROFILE      N-TYPE  N.PEAK=1E20  Y.JUNC=1.0  X.MIN=0.0  WIDTH=1.5    XY.RAT=1.0 PROFILE      N-TYPE  N.PEAK=1E20  Y.JUNC=1.0  X.MIN=4.5  WIDTH=1.5    XY.RAT=1.0   MATERIAL  DIAMOND PERMITTI=5.7  EG300=5.47 AFFINITY=1.3   AN=4.62E5  +BN=7.59E6  CN=1.0  AP=1.93E5  BP=4.41E6  CP=1.0 NC300=1E20 NV300=1E20 +TAUP0=1E-9   IMPURITY    NAME=N-TYPE REGION=SUB GB=2 EB0=0.59 ALPHA=3.1E-8 BETA=200 +GAMMA=1 HDT.MIN=1E15 HDT.MAX=1E21    98 IMPURITY    NAME=P-TYPE REGION=SUB GB=4   EB0=0.36   ALPHA=3.037E-8  BETA=200  +GAMMA=0.95   HDT.MIN=1E15    HDT.MAX=1E21  CONTACT    NAME=Left   CONTACT    NAME=Right  CONTACT    NAME=Ohmic  CONTACT    NAME=Mid  WORKFUNC=4.3  COMMENT mobilities by Dr. Hogan's Hall Measurements COMMENT MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20) COMMENT at 300K HOLE=(930, 820, 800, 150, 39)   ELECTRON=(540, 380, 270, 120, 8) COMMENT at 450K HOLE=(310, 250, 230, 90, 32)    ELECTRON=(560, 420, 300, 180, 140) COMMENT at 600K HOLE=(130, 100, 98, 56, 24)     ELECTRON=(590, 520, 490, 475, 470)     MOBILITY DIAMOND CONCENTR=(6.5E15, 3.1E16, 2.5E17, 6E18, 2E20)  + HOLE=  (310, 250, 230, 90, 32) + ELECTRON= (560, 420, 300, 180, 140) + PR.TABLE   PLOT.2D      GRID  TITLE=" Initial Grid"  FILL  SCALE  +           DEVICE=POSTSCRIPT PLOT.OUT=GRID.ps   COMMENT      Regrid on doping  REGRID       DOPING  LOG  RATIO=2  SMOOTH=1  +            IN.FILE=MDEX1DS   PLOT.2D      GRID  TITLE="Doping Regrid"  FILL  SCALE  +           DEVICE=POSTSCRIPT PLOT.OUT=REGRIDDOPING.ps   MODELS      SRH AUGER CONMOB INCOMPLE IMPACT.I TEMPERAT=450 SYMB             NEWTON CARRIERS=2  SOLVE    V(Ohmic)=-5 ELEC=Ohmic VSTEP=1 NSTEP=30  PLOT.1D   Y.AXIS=I(Ohmic)  X.AXIS=V(Ohmic) POINTS COLOR=2 TITLE="Merged Di Diode +1um sep" PRINT DEVICE=POSTSCRIPT PLOT.OUT=MED1.ps  SOLVE    V(Mid)=0 V(Left)=0 V(Right)=0 V(Ohmic)=1 ELEC=Ohmic VSTEP=-7 NSTEP=300  PLOT.1D   Y.LOGARI Y.AXIS=I(Ohmic)  X.AXIS=V(Ohmic) POINTS COLOR=2 TITLE="Log +Merged Di Diode 1um sep" PRINT DEVICE=POSTSCRIPT PLOT.OUT=MED2.ps      99            BIBLIOGRAPHY               100 BIBLIOGRAPHY  [1] International Energy Agency (IEA), World Energy Outlook 2013: Renewable energy outlook, www.iea.org. 2013.   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