CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

A COMPREHENSIVE MODEL OF FREQUENCY DISPERSION OF NITRIDE MESFET

A graduate project submitted in partial fulfillment of the requirements For the degree of Master of Science in Electrical Engineering

By Rumman Raihan

August 2018

Copyright by Rumman Raihan 2018 ii

The graduate project of Rumman Raihan is approved:

…………………………………….. ……………. Dr. Sembiam Rengarajan Date

……………………………………. …………….. Dr. Jack Ou Date

……………………………………… …………… Dr. Somnath Chattopadhyay, Chair Date

California State University, Northridge iii ACKNOWLEDGEMENT At the very beginning, I would like to express my best and foremost gratitude towards Dr. Somnath Chattopadhyay for his help and guidance not just in this project, but also throughout my entire Graduate study period. He opened the door of his vast knowledge towards me and I am very much thankful to him for letting me work under his supervision. I also forward my gratitude towards Dr. Sembiam Rengarajan and Dr. Jack Ou to be on the graduate committee and spending their valuable time to guide me throughout the project. I express my love and gratitude to my mother and my family, my uncle Mr. Mohammad Islam and his family for their mental and financial support.

iv DEDICATION This work is dedicated to my departed father Mr. K. M. Nur-ul-Alam (may his soul rest in peace) and my loving mother Mrs. Nilufa Akter.

v TABLE OF CONTENTS COPYRIGHT PAGE..……………………………………………………………...... ii SIGNATURE PAGE..….…………………………………………………………...... iii ACKNOWLEDGEMENT…………………………………………………...... iv DEDICATION...... v TABLE OF CONTENTS..………………………………………………………...... vi LIST OF FIGURES...... …………………………………………………...... viii LIST OF TABLES...... ix ABSTRACT....………………………………………………………………………..…...x CHAPTER 1 1.1 INTRODUCTION ……………………………………………………………...…….1 1.2 FREQUENCY PERFORMANCE BETWEEN GaN AND SiC DEVICES …………3 1.3 SWITCHING PERFORMANCE BETWEEN GaN AND SiC DEVICES …………..5 1.4 POWER PERFORMANCE BETWEEN GaN AND SiC DEVICES …………...... 8 1.5 GaN SUBSTRATE PREFERANCES ...... 9 1.5.1 Sapphire ...... 10 1.5.2 SiC...... 11 1.5.3 Silicon...... 11 1.5.4 Diamond...... 11 1.6 GaN IN OPTOELECTRONIC DEVICES...... 11 1.7 ADVANTAGES OF GALLUIM NITRIDE MATERIAL ……...... 11 1.8 COMPARISON OF FETS...... 13 1.9 APPLICATIONS OF GALLIUM NITRIDE DEVICES…………………………….14 1.9.1 Point of load converters.…………………………………………………...14 1.9.2 Monolithic motor drive.……………………………………………………14 1.9.3 Discrete motor drive.……………………………...... ………………....14 1.9.4 Automotive applications…………………………………………………...14 vi 1.10 RADIATION EFFECT ON GaN...... 14 1.10.1 Damage in GaN for different types Radiations...... 15 1.10.2 Comparison of radiation hardness between GaN and SiC...... 16 CHAPTER 2 2.1 GALLIUM NITRIDE MATERIAL PROPERTIES………………………………....18 2.2 FUNDAMENTAL PROPERTIES………………………………………………...... 19 2.3 BAND STRUCTURE...... 20 2.4 ENERGY BAND GAP...... 22 2.5 ENERGY BANDGAP VERSUS LATTICE CONSTANT COMPARISON...... 23 2.6 INTRINSIC CARRIER CONCENTRATION...... 23 2.7 P-N JUNCTION BUILT-IN POTENTIAL...... 25 CHAPTER 3 3.1 GALLIUM NITRIDE MESFET DEVICES...... 26 3.2 GaN MESFET PLANER STRUCTURE...... 26 3.3 OPERATION OF GAN MESFET DEVICES...... 27 3.4 BREAKDOWN VOLTAGE...... 28 3.5 ON-STATE RESISTANCE...... 29 CHAPTER 4 4.1 TRAPPING EFFECT...... 32 4.2 TRAPPING EFFECT ON I-V CHARACTERISTICS...... 35 4.3 TRAPPING EFFECT ON TRANSCONDUCTANCE...... 37 4.4 RESULT AND DISCUSSION...... 38 CHAPTER 5 CONCLUSION...... 42 REFERENCES...... 43 APPENDIX-CODES...... 47

vii LIST OF FIGURES Figure 1.1 Areas of applications for silicon, gallium nitride and silicon carbide...... 4 Figure 1.2 Drift velocity versus applied electric field of different ...... 6 Figure 1.3 Drain current versus Drain to source voltage plot for FETs made with different semiconductors...... 7 Figure 1.4 Comparison of switching performance among Si, SiC, GaN, GaAs...... 7 Figure 1.5 Bandgap versus lattice constants for IV-IV, III-V and II-VI materials ...... 10 Figure 1.6 Output characteristics for SiC and GaN devices before and after radiation.....16 Figure 1.7 Drain current vs gate to source voltage plot GaN and SiC devices before and after radiation...... 17 Figure 2.1 GaN wurtzite and zincblende structure...... 18 Figure 2.2 Band structure of wurtzite GaN...... 20 Figure 2.3 Band structure of zincblende GaN...... 21 Figure 2.4 GaN crystal structure...... 21 Figure 2.5 Energy bandgap vs temperature for Si, SiC and GaN...... 22 Figure 2.6 Energy bandgap versus lattice constant...... 23 Figure 2.7: Intrinsic carrier concentration versus temperature...... 24 Figure 2.8 Built in potential vs temperature...... 25 Figure 3.1: Planer structure of a GaN MESFET (simulated)...... 26 Figure 3.2: Comparison of Depletion and Enhancement mode MESFET ...... 28

Figure 3.3 Resistance is a lateral junction MESFET...... 29 Figure 4.1 A MESFET structure...... 32

Figure 4.2 I-Vds graph...... 39

Figure 4.3 gm vs Vgs plot for different Vds...... 40

Figure 4.4 gm vs Vgs plot for different channel thickness...... 41

viii LIST OF TABLES Table 1.1 Physical properties of different semiconductors...... 12 Table 1.2 Comparison between different GaN FETs...... 13 Table 2.1 fundamental properties comparison...... 19

ix ABSTRACT

A COMPREHENSIVE MODEL OF FREQUENCY DISPERSION OF GALLIUM NITRIDE MESFET

By

Rumman Raihan

Master of Science in Electrical Engineering

A physics based analytical modeling for Gallium Nitride (GaN) MESFET has been developed in this project to calculate drain to source current versus drain to source voltage and the transconductance with and without traps centers using MATLAB software. The drain-bias dependence of trapped carrier concentration has been calculated and incorporated in drain current and transconductance to study the traps behavior on drain current and transconductance. The drain current has been developed by two sets of equations for non-saturation and saturation current components and two current equations have been merged by optimizing different physical parameters. Hence, the current clearly shows linear and non-linear properties to validate the device performance. The transconductance has been derived from the derivative of saturated drain current function to gate-source voltage for constant drain-source voltage. The threshold voltage has been determined from the gate-source voltage, when the transconductance is equal to zero. The transconductance has been also determined for various active channel thicknesses, which reflects the device frequency performance.

x CHAPTER 1 1.1 INTRODUCTION: The search for the perfect replacement of silicon and GaAs in the semiconductor industry has been going on for more than three decades. Gallium nitride and silicon carbide are the most promising candidates. These two materials are ahead of the others to be used in high voltage circuits, higher frequency (like mm-wave and THz) devices, high temperature environment [1]. GaN material shows a lot of advantages over silicon and GaAs. GaN material shows higher breakdown voltage, high electron saturation velocity, high radiation resistance, high temperature operation, high critical electric field, high chemical resistance with direct and wide bandgap properties. GaN material has wider spectrum coverage in optoelectronics area starting from infrared and ending at ultraviolet due to direct bandgap properties. Gallium nitride material is already being used in optoelectronics and electronics devices, but these materials also suffer the effect of trap centers due to material defects which significantly reduces device performance. In this project, a device physics based analytical model is described. This model incorporates trap center effects on the drain current (ID) versus drain to source voltage (VDS) characteristics and on transconductance (gm) and gate to source voltage (VGS). Gallium nitride MESFET devices have been reported to be used for high RF power devices [2, 3]. GaN material shows high electron saturation velocity in the order of 3x107cm/s. A MESFET with 65% power aided efficiency (PAE) was reported the cut-off frequency in the range of 500-600 MHz with 9.2 mW output power [4]. Another research work on GaN FET showed 51.1W delivered power with 79% PAE while the cutoff frequency was obtained as 900MHz [5]. Some other research work showed the output power in the order of 10W with 34% PAE at 48V and about 700MHz cutoff frequency. Another research work presented the transconductance in the order of 68mS/mm while the cutoff frequency and maximum frequency were obtained in the range of 1.8 GHz and 31GHz respectively, while the RF power showed 84mW/mm for a 1400mm wide gate AlGaN/GaN HMET [6]. Gallium nitride device has been fabricated for applications too. A research work reported to achieve power density in the order of 32W/mm and 12W/mm using GaN device [7]. Some semiconductor industries at Japan have been reported to achieve power over 150W at [8] while having 2GHz cutoff frequency. In this work power density and PAE was reported in the order of 6W/mm and 74% respectively. Using a 0.3µm long and 2x50µm width gate, cutoff and maximum frequency has been achieved to be 6.35GHz and 10.25GHz respectively in [9]. In another research work, a GaN MESFET has been reported with maximum frequency of 15.6 GHz, transconductance 164mS/mm, PAE 38% and drain to source voltage is 3.5V [10]. It was also been reported in another research work that a GaN MESFET was used to achieve 500mA drain current, 40V drain to source voltage, 8GHz cutoff frequency, 92mS/mm transconductance, 4W/mm power with 50%efficiency, and 20dBm gain [11]. 1 Gallium nitride MESFET was fabricated by MOVPE to form a channel of 0.25pm length on a GaN layer with high resistance [12]. This fabricated device showed transconductance of 20mS/mm. Another MESFET with the gate width of 100µm has been reported having RF power of 200W which has cutoff frequency of 11GHz, 2.2W/mm power output density, 27% PAE [13]. A simulation of GaN FET with gate length 0.3µm, gate width 2x50µm, gate to the source spacing 1µm, source to drain spacing 2.3 µm was reported [14]. The research work reported a cutoff frequency of 11GHz. GaN MESFETs can also be produced with longer channel [15]. The longer channel device reported some interesting results. The cutoff frequency was found to be around 11.6GHz. For AlGaN-GaN MOS-HFET the value of the cutoff frequency was 16.4 GHz on SiC substrate while 18.2 GHz on sapphire substrate. When the doping concentration was raised, cutoff frequency also increased. It was also reported that when the gate length was 0.25µm, the threshold voltage Vth was -3.7V. At 298K, fmax was reported to be in the order of 56GHz, comparing to a GaN MESFET, it was found that it had lower Vth and higher transconductance. GaN is a suitable candidate in both high voltage circuits and MHz to GHz even THz frequency devices. Both MESFET and HEMT devices show promising results. In case of high temperature and stress, a GaN FET was reported having 8.7W/mm output power at 7.9GHz frequency [16]. The recorded temperature for this research work was 740degree Celsius. Another research shows that two power amplifiers were designed using SiC MESFET and GaN HEMT devices. They cover the frequency band 0.7 to 1.8GHz. The SiC MESFET worked at Vd = 48V and its output power was 41.3dB with 32% PAE. The GaN amplifier works at Vd = 48V and its output power was 40dBm with 34% PAE. SiC amplifier showed better performance than GaN device 10W [17]. Device performance also depends on crystal structure. A research work was conducted to show that for a zinc blende device, cutoff frequency and transconductance were found in the order of 220GHz and 210 mS/mm respectively, but the fabricated with wurtzite crystal had different performance rating. The cutoff frequency was found to be 160GHz and transconductance was found to be158mS/mm [18]. In both cases, gate length was 0.1µm. Another research work reported a microwave Doherty power amplifier using GaN MESFET NPTB00025[38]. The cutoff frequency was obtained as 1GHz while the output power, PAE and supply voltage was 25W, 69.8% and 20V respectively. Two class D-1 amplifier which were designed using GaN MESFET was reported in [19]. For both amplifiers, operating frequency was 900MHz while output power was 20.7 and 51.1Watt respectively. Another GaN MESFET NPTB00025 class E wideband microwave PA was reported to obtain bandwidth in the order of 500-600MHz while output power, PAE and supply voltage were 9.2W, 65% and 18V respectively [20]. It was reported by another research work that another GaN device achieved RF power density in the order of 30-40 2 W/mm while maximum frequency was 200GHz [21]. Some other research work reported to obtain 2.2 W/mm power density at 2GHz with a GaN MESFET [22] . In that work, PAE, VDS and VGS has been reported as 27%, 30V and -2V respectively. To select the most promising material for higher RF power applications like THz devices, one should look for a potential semiconductor delivering high power conversion efficiency, high cutoff frequency, high maximum frequency, wide range of operating temperature, high reliability and low cost. Considering all materials, GaN is a very potential candidate to replace silicon and . Due to critical electric field, SiC and GaN MESFET and HEMT devices have very high- density power attributes. They also have higher breakdown voltage than silicon and gallium arsenide. This quality makes them qualified for military and commercial applications too. 1.2 FREQUENCY PERFORMANCE BETWEEN GaN AND SiC DEVICES Different semiconductor material has different industries and users. In CMOS industry, silicon is very reliable as a semiconductor. On the other hand, silicon carbide is already being used in high rectifying voltage devices which are usually designed for working in hotter environment than silicon and gallium arsenide devices. Gallium nitride has the properties to be used as a replacement. It has the potential in both CMOS and high temperature high voltage situations. The following picture shown in Figure 1.1 gives an idea about the areas of applications of different materials.

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Figure 1.1 Areas of applications for silicon, gallium nitride and silicon carbide The frequency applications can be discussed in following four sections. For minimum voltage and low frequency category, the frequency resides between 100kHz to 10MHz and the voltage lies between 50V to 650V. Consumer appliances, household electronics, lighting, portable switching power supply electronics falls into this category. This is a justified category for silicon devices, because silicon has a lot less switching and conduction loss in the previously mentioned frequency and voltage. The operating temperature is also low for these devices. So, for this category, silicon outperform gallium nitride transistors. For high voltage (like 200V and over) and low frequency category, silicon MOSFET experiences higher on resistances. Both GaN and SiC has the potential to replace silicon in this section. Both semiconductors have the following properties, higher thermal conductivity, higher breakdown voltage. It makes them compatible in this kind of situation, but SiC devices have the edge because of comparatively lower production cost and availability. 4 For low voltage and high frequency applications like wireless chargers, cellular communications. usually work between 10MHz to 5GHz and 50V to 600V. This is an area in which GaN has a lot of potential to succeed. Silicon experiences very high switching loss at 2.5MHz to 5MHz at about 500 V and beyond. On the other hand, this area of applications is not compatible with SiC devices because of their bulky designs. So GaN devices can take the lead here. There is something that is needed to be mentioned very much. At low voltage and high frequencies (2GHz to 5GHz), silicon transistors have shown their greatest performance in integrated circuit technology. They are easy to design and fabricate, very dependable in performance, and most of all, very cheap to make. So, to shine in CMOS and IC industry, GaN still must go a long way to outperform silicon. Silicon and SiC devices do not work reliably in high frequency situations. Applications which works between 20kV to 25kV and 15MHz to 20 MHz, like AM and FM radio towers, HV rectifiers, aircrafts, military equipment are mostly designed with GaN devices.

1.3 SWITCHING PERFORMANCE BETWEEN GaN AND SiC DEVICES: SiC and GaN being wide bandgap semiconductors, have the advantage over silicon and GaAs devices in reaching a higher peak voltage. In case of switching, high power and short pulses, these wide bandgap semiconductors show real potential. A study has been done in which showed a detail comparison among different material made FETs’ switching efficiency [23]. GaAs also has wider bandgap than silicon. Its carrier mobility (µ) value is also better. Even though GaAs is not preferred because it loses its electron properties in a strong electric field due to negative differential mobility. Both SiC and GaN has risen to the occasion and shows better performance than silicon and GaAs. When any semiconductor is introduced to an electric field, the carriers experiences force which in magnitude, is equal to the multiplication of the charge itself and the applied electric field (F=q*E). Due to this fore, the charge achieve acceleration towards the direction of the field. In the meantime, the carrier also goes through collisions with other carries and the lattice itself. As a result, the charge achieves velocity. The magnitude of the velocity varies with variation of the electric field. It is called carrier drift velocity.

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Figure 1.2 Plot of drift velocity versus applied electric field of different semiconductors. Due to different material properties, for the same electric field, different semiconductors show different drift velocity. Figure 1.2 shows a velocity versus electric field plot for four different types of semiconductor materials [24]. The plot shows that Si, SiC and GaAs experience velocity saturation before the electric field increases to 1*105 V/cm. But GaN does not achieve saturation even when the electric field is increased to 3*105 V/cm. For fast switching, pulsed power applications, crystal defects also limit device performance from which SiC and GaN suffers a lot. So, in that work, a comparison of electrical properties between silicon, SiC, GaN and 4H-SiC was performed as showed in figure 1.3 and 1.4. In wurtzite GaN, trapping happens mostly in thick layers. Because of these defects, both GaN and SiC are not more suitable than 4H-SiC. The following figure 1.3 and 1.4 can give some light in this topic [23]. In this work, FETs which are made of Silicon, Silicon Carbide. Gallium Arsenide and Gallium Nitride are compared in the basis of hold off voltage and switching performances. Deep level effects were also considered. This consideration changed some electrical properties.

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Figure 1.3 Drain current versus Drain to source voltage plot for FETs made with different semiconductors.

Figure 1.3 shows a graph of drain current (IDS) vs drain to source voltage (VDS) for FETs fabricated with different semiconductors. The drain current for the FET fabricated from SiC is a lot lower than other three FETs. It is concurred from this figure that SiC has the best breakdown voltage than the others.

Figure 1.4 Comparison of switching performance among Si, SiC, GaN, GaAs devices

7 Figure 1.4 shows the VDS versus transient time graph for FETs for the previously mentioned FETs. This study shown above proves that for the same amount of transient time, the drain to source voltage is a lot lower for GaN and GaAs FETs than the other two. So, the switching speed for these two (GaN and GaAs) will be a lot faster than the others (SiC and Si). So, in the previously mentioned case, there is no material best for both characteristics. But considering faster switching speed, GaN has the best figure of merit. Another study was done for switching devices needed for electrical vehicles [25]. Since these devices are going to be used in vehicles, there are some things needed to be considered in this sector like reliability of the device, cost of production, highest operating temperature etc. Diamond was ranked number one followed by silicon. the third to fifth positions were secured by different compositions of silicon carbide. Gallium arsenide and nitride were the last two. Although diamond has been ranked as number one, due to larger bandgap and inherent quality, its research and development as a semiconductor material is still in a very early stage. Silicon devices are at number two, showing how advanced the silicon technology is, despite having all the disadvantages, still ranked better than all the other candidates except diamond. Then comes the silicon carbide materials, which are ranked batter than both GaAs and GaN. The most complying reason behind this is, SiC technology is more advanced because of its more advanced research and commercialization. Besides, Gallium is not a cheap material as silicon, which increases the cost. So, for fast switching, SiC takes the edge over GaN. 1.4 POWER PERFORMANCE BETWEEN GaN AND SiC DEVICES: Power semiconductor devices usually refers to devices which works with high power load. Both GaN and SiC has great future in this industry but is very important to mention that silicon insulated-gate bipolar transistors (IGBTs) has already made a massive effect on power devices. IGBTs has the advantages of having better durability to overloads, better parallel current distribution, lower on-state and switching loss, low thermal impedance and lower input capacitance. Because of these properties, IGBTs saves a lot more power than other semiconductor devices. In the last three decades the use of IGBTs has saved a lot of electricity and gasoline. It was reported that in the last 25 years 73,000 Tera Watt hours electricity and 1.5 trillion pounds gasoline was saved by IGBTs which resulted in the reduction of carbon emission by 100 trillion pounds [26]. There is no reason to stop there. After the introduction of wide bandgap semiconductors, a new era of modern technology has opened. By 2013 SiC devices were reported to achieve revenue of over 95 million dollars [26]. Although SiC devices have become more developed due to earlier research and industrialization of Schottky power rectifiers, GaN 8 devices are also experiencing a very rapid growth. They are very useful in making high power and high frequency devices. Both SiC and GaN has turned over a new leaf towards power semiconductor devices. Research shows that GaN devices work very well to block voltages from 200V to 600V. For higher voltages, SiC is more preferred as it loses less power and can work at higher frequency than existing silicon devices. It has some other advantages too. It reduces the size of passive devices and output filters which results in increased efficiency. But the main issue with wide bandgap semiconductors is its increased cost over silicon technology. SiC devices has the edge in this sector over GaN too. It is important to mention that continuous research has caused tremendous development for GaN too. Lots of research are going on to reduce cost overall.

1.5 GaN SUBSTRATE PREFERANCES: Figure 1.4 shows a bandgap versus lattice constant graph for an extended number of IV- IV, III-V and II-VI compound materials. This figure helps to predict the amount of mismatch in lattice structure between the semiconductor and underlying substrate. If the difference between the lattice constant values of the semiconductor and the substrate is small, there will be less lattice mismatch. Lattice mismatch causes defects in the epitaxial film which increases resistivity, reduces electron or hole mobility and minority carrier lifetime.

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Figure 1.5 Bandgap versus lattice constants for IV-IV, III-V and II-VI materials

To grow GaN on a wafer, a few materials has already been used, sapphire, Si, SiC, GaAs and diamond are some of them. The substrates and their advantages or disadvantages are briefly described below.

1.5.1 Sapphire:

Aluminum oxide (Al2O3) as single crystal structure is commonly known as sapphire too. It was the first material ever as substrate for GaN. Until today, it is the most popular substrate for GaN. But it has a lot if issues too. Lattice mismatch is about 15% between them. It raises high defect density in epitaxial film, which causes a lot of problems. It hampers heat conductivity, carrier mobility and minority carrier lifetime. So, the overall device performance goes down.

10 1.5.2 Silicon Carbide: SiC has smaller lattice mismatch than sapphire, so heat conduction is better. Device structure is also simpler than sapphire. But it has its own disadvantages too. growing GaN epitaxy on silicon carbide is not easy. The wetting is very low between these two compounds. Sometimes an AlGaN buffer layer is introduced to solve this issue, but it raises unwanted device resistance. 1.5.3 Silicon: Silicon is very cheap, and it is found everywhere. So, it is also widely used as substrate. But till now, both sapphire and SiC shows better performance as substrate than silicon. Silicon has high lattice constant. The thermal coefficient also matches poorly. Sometimes when GaN is grown on Si, silicon created silicon nitride which is amorphous in nature and it is highly unwanted. But being cheap and always available, a lot of Light Emitting Diode and High Electron Mobility Transistors are being fabricated on silicon. 1.5.5 Diamond: Diamond was first used as substrate in 2003. It conducts thermal energy the most among all materials discussed. The developed process for diamond substrate is, first GaN is grown in silicon, then the silicon is removed. Then it is replaced with CVC diamond. Recent research has made the diamond thickness more improving the stiffness and strength of the device.

1.6 GALLIUM NITRIDE IN OPTOELECTRONIC DEVICES: Because of direct bandgap properties, optoelectronics industry adopted GaN long time for making lasers and other devices. The first ever Light Emitting Diode made from GaN reported in a work was grown on silicon which experienced a lot of optical loss [27]. Later, a nitride distributed bragg reflector was described which reduces some optical loss [28]. In some cases, silicon on insulator substrate is also used to reduce loss. 1.7 ADVANTAGES OF GALLUIM NITRIDE MATERIAL: Since the 1950s, silicon has been used in semiconductor technology because of having some advantages over other materials like germanium, selenium. Some of the advantages were being more reliable, easy to fabricate and use, cost efficient etc. and it is easily noticeable that all these advantages has come from the basic material properties of silicon. If any new material is needed to be chosen as a replacement or successor of silicon, the material needs to outperform silicon in case of material properties. Hence a table is produced here comparing some physical properties of silicon (Si), silicon carbide (SiC), gallium nitride (GaN) and gallium arsenide (GaAs). [29]

11 Parameter SiC Silicon GaN GaAs Critical field 2.2MV/cm .23MV/cm 3.3MV/cm 4·105 V/cm Electron mobility 950cm2/V.s 1400cm2/V.s 1500cm2/V.s 8500 cm2/V.s Thermal 3.8W/cm.K 1.5W/cm.K 1.3W/cm.K 0.55 W/cm.K conductivity Band gap 3.2eV 1.1eV 3.3eV 1.521eV Permittivity 9.7 11.8 9 12.9 Table 1.1 Physical properties of different semiconductors To consider a suitable replacement of silicon, the new material needs to be a better conduction property. To obtain high voltage density, the breakdown voltage needs to be higher too. It would be another advantage if it is possible to fabricated devices smaller than the ones made with silicon. The switching efficiency is expected to be better than silicon devices. The devices need to be operable in harsh condition. If it is cheap to fabricate, it would be another great advantage. All these properties heavily depend on their own material properties. Both GaN and SiC has better numbers than silicon and hence can outperform silicon in every aspect. Both are suitable candidates to replace silicon. Gallium nitride has wider bandgap comparing to silicon, gallium arsenide and silicon carbide. Also because of the stronger electric field per unit area, gallium nitride outperforms silicon in power conversion too. It has higher electron mobility which is needed to fabricate faster operating devices. Gallium nitride shows the property of having higher efficiency and lower switching loss due to low output capacitance and fast recovery time. It has better electric conductivity and a small dielectric constant. It has a higher melting point and can withstand higher physical strain. It can operate at higher voltages and its leakage current is also significantly lower than silicon. It performs best in case of high frequency and high switching operations too, but for high power operations, silicon carbide holds the key to be the best candidate because of having higher thermal conductivity than silicon and gallium nitride.

12 1.8 COMPARISON OF GALLIUM NITRIDE FETS: Gallium nitride has been used to fabricate several types of FETs as well as HEMT devices. The list includes MESFETs, MISFETs, , MODFETs/HFETs. A MISFET is a special kind of inverted HFET which has a dielectric insulator between gate metal and channel. MODFET uses a channel which is separate from charge supplying layers to prevent gate leakage and current collapse. It can minimize impurity scattering and enhance mobility. JFET uses a p-n junction rather than a metal gate to control the gate turn on voltage better than other devices. The following table shows a comparison among some of the GaN FETs [30].

Device MESFET MISFET JFET MODFET Structure GaN channel / AlGaN / GaN n-GaN i- or n-GaN metal gate channel/insulator channel/p- channel/ / metal gate GaN gate AlGaN barrier gate Gate formation Schottky gate Metal gate on Ohmic contact Schottky gate on GaN dielectric to p-GaN gate on AlGaN channel insulator barrier Advantages Simple Low gate Variable and High electron structure leakage, high high gate turn velocity, high turn on voltage on voltage current Disadvantages Low electron Extra gate bias Low electron Very velocity, low needed to velocity, low complicated current compensate for current, hard layer growth piezoelectric to make short fields gate Table 1.2 Comparison between different GaN FETs In MESFET higher maximum drain current is produced with thick doping channel and higher doping density. In this case, getting the pinch-off voltage becomes very hard. The channel thickness is also kept to an acceptable limit because of not being able to change the threshold voltage to a randomly big value. The usual channel thickness is kept between 200 to 600nm. The channel is usually doped to the average of 1017 cm-3. This way it is possible to gain a pinch-off characteristics and average mobility. Although comparing with MODFET MESFET has lower current, MESFET fabrication processes is way easier than MODFET and a lot cheaper. When compared to GaN MESFET and GaN HEMT devices, HEMT devices also outperforms MESFET devices in some cases, but MESFET a way simpler structure than HEMT which makes it more useful than other devices.

13 1.9 APPLICATIONS OF GALLIUM NITRIDE DEVICES: Since it was possible to grow GaN layers in Si substrates in 1990, GaN devices have been experiencing very rapid development. It has been reported that high voltage GaN lateral transistors has been fabricated with low and prespecified on resistance [31]. Now they are also commercially available. A few applications of GaN devices are mentioned below. 1.9.1 Point of load converters: Point of load converters are used to reduce the 12volt bus lad to 1volt DC used in the chips in the servers. These are operated at a very high frequency to keep passive components as small as possible. It has been found in [32] and [33] using GaN HEMT devices improve the efficiency by 4% comparing to silicon. 1.9.2 Monolithic motor drive: GaN HFET technology makes it possible to make lateral devices to make a monolithic motor control chip [34]. On a 20W power level, 93% efficiency is achieved which is 1% higher than IGBT/PiN diode. This make the motor drive more compact. 1.9.3 Discrete motor drive: A comparison between Si IGBT and GaN HFET for 400B DC bus has been reported in a research work [35]. Although no efficiency was not found on full load, 1% efficiency was found on light load. The cascode Si MOSFET is used as fly back diode. This approach makes GaN HFET being able to work at 100kHz which Si IGBT cannot. This is one of the most important advantages. 1.9.4 Automotive applications: Although SiC devices are widely used in this sector nowadays, GaN has a lot of potential there too. GaN HEMT has very low on resistance and it can work on quite a high temperature. A simulation was reported that projects that GaN inverter could reduce power lossy 10 times than a Si IGBT inverter [36]. 1.10 RADIATION EFFECT ON GALLIUM NITRIDE: GaN is a very strong material with a lot of potential to be used in electronic and space industry. It has been reported in that GaN is stronger than GaAs [37]. In this study, GaN does not degrade when GaAs starts to do so. Rather, it can withstand one to two times higher radiation than GaAs. The reason behind this strength of GaN is having a stronger bond than GaAs.

14 1.10.1 Damage in GaN for different types Radiations: Proton damage: Exposure to proton radiation has a significant effect on GaN devices. In case of HEMT devices, proton radiation damages the 2D electron gas. Different nonionizing energy loss is the cause of the damage. A research work reported the damage on AlGaN/GaN devices of proton fluence of 1014 /cm2 while the energy was 1.8 MeV [38]. The research reported that at saturation, drain to source current was reduced from 260 milliampere per millimeter to 100mA/mm. It also reported that transconductance was also reduced from 80 milliSiemens per millimeter to 26 milliSiemens per millimeter. GaN devices which were exposed to proton radiation in the amount of 1.8 MeV was reported in another work [39]. The finding of this research work was very interesting. It reported that devices grown under ammonia rich condition gets more damaged in proton radiation than the devices grown under gallium or nitrogen rich condition. In general, proton damaged HEMT devices showed good pinch-off characteristics but poor drain current characteristics. The effects on proton radiation on GaN LED devices was also been reported [40]. Some InGaN Multi Quantum Well (MQW) LED devices (emission wavelength 410 nm to 525 nm) were exposed to 40MeV proton radiation with the doses of 5*109 /cm2 to 5*1010 /cm2. The research work reported that after irradiation, electroluminescence intensity was reduced by 15% to 20% while reverse breakdown voltage was increased by 1-2V. Gamma-ray damage: A research work reported the effects of gamma-rays on GaN HEMTs [37]. Devices were exposed towards 600Mrad gamma rays. Breakdown voltage was increased while threshold voltage became more negative. In addition, 20% to 30% reduction in the value of transconductance was also reported in this work. The effects of gamma rays on GaN LEDs was also been reported [40]. Some InGaN MQW LED devices (emission wavelength 410 nm to 525 nm) were exposed to 150 to 2000Mrad gamma radiation. There was very minimum change of turn on voltage, but reverse breakdown voltage did not change at all. Light intensity decreased by 20% after 150Mrad and by 75% AFTER 2Grad doses. Neutron damage: Current vs voltage characteristics of GaN devices change after being exposed to neutron radiation. A study on the changes of GaN LEDs after neutron irradiation was reported [37]. After 1.6 neutron radiation the light intensity became almost zero. MQW LEDs were exposed to 9.8MeV neutron radiation at the dose of 5.5*1011 /cm2. Neutron irradiation caused displacements in lattice structures which resulted in significant reduction in forward current. Electron damage: Electron irradiation introduces trapping effects in the quantum wells which changes the value of conductivity of the material. The ionization energies of the previously mentioned interface traps are 100meV and 190meV. In addition, the radiation also creates traps inside the bandgap. The acceptor and hole traps are created near Ec - 1.1eV and Ev +0.9eV respectively [39]. In case of LED devices, the required electron dose 15 to observe the change in microcathodoluminescence was 1015 /cm2 of 10MeV electrons. The change in electrical properties were observed after doses of 1016 /cm2 [39]. In case of HEMT devices, 1015 /cm2 of 10MeV electron dose reduced the electron mobility by the factor of two. Gate and drain-source current were both observed increasing. The research work reported that less than 1MeV electron radiation increased transistor channel drain to source current [37]. It was also reported in [37] that the device stared annealing right after the radiation and was almost completely recovered after 72 hours. The following Figure reported radiation damage from different types of radiation on different type of GaN materials with different dopant concentration [39]. It also reported carrier removal time, defect levels and defect production rate for various radiation type.

1.10.2 Comparison of radiation hardness between GaN and SiC: In [38] a performance comparison between a 1700V SiC power MOSFET C2M1000170D device and a second gen. 200V enhancement mode GaN HEMT EPC2012 device is reported, both before and after they are exposed to 4.5MeV electron irradiation.

Figure 1.6 Output characteristics plot for SiC and GaN devices before and after radiation.

The left plot shows output characteristics ID vs VDS of the SiC MOSFET both before and after being exposed to radiation. The process was repeated for two different Total Irradiation Doses (TIDs) of 1kGy and 5kGy. The right plot shows drain current vs drain to source voltage characteristics of the second device both before and after being exposed to radiation. The TID was 2000kGy in this case. Both processes were done at room temperature, 300K.

16

Figure 1.7 Drain current vs gate to source voltage plot GaN and SiC devices before and after radiation.

The left plot shows change in transfer characteristics ID vs VGS of the SiC MOSFET both before and after being exposed to radiation. The right plot shows change in transfer characteristics of the second device both before and after being exposed to radiation. Both processes were done at room temperature, 300K. Both processes were done for four different Total Irradiation Doses (TIDs) of 1kGy, 5kGy, 20kGy and 200kGy.

17 CHAPTER 2 2.1 GALLIUM NITRIDE MATERIAL PROPERTIES: Material properties vary from silicon to III-V and III- nitride materials. Hence GaN is compared with other semiconductor materials. GaN devices can be fabricated on different kinds of substrates, i.e. sapphire, silicon carbide, silicon, diamond etc. In the fabrication process an extra aluminum nitride layer is grown over GaN layer to increase electron mobility. Silicon has almost reached its potential limit as the primary semiconductor used in the industry. Among all other emerging materials, GaN and SiC has made more progress than the others. Gallium nitride (GaN) is preferred for high-voltage and high-frequency (HF) applications while silicon carbide has been chosen for high power and high temperature situations. It is not always true, various high power GaN devices are already in the industry while SiC devices are also used in high frequency devices. Gallium nitride is a compound material made from gallium (atomic number 31). GaN can be found in two forms in nature, they are called wurtzite and zincblende. Both cases, a gallium atom bonds with 4 nitrogen atoms. Pictures of GaN wurtzite and zincblende structures are shown below.

Figure: 2.1 GaN wurtzite and zincblende structure.

18 Both GaN structure is very stable with strong piezoelectric properties. Although, it is possible to make both p type and n type material with silicon or magnesium, p type GaN fabrication is hard and costly, so it is usually doped as n type material. Crystal defects increase electric conductivity too. 2.2 FUNDAMENTAL PROPERTIES: To justify the use of a material as a good semiconductor, there are some fundamental properties needed to be looked at. Some of them are bandgap, dielectric constant, electron affinity, mobility, ionization coefficient, thermal conductivity, intrinsic carrier concentration, built in potential etc. The following table 2.1 compares some fundamental properties of gallium nitride with silicon and 4H-SiC at 300K.

Properties unit 4H-SiC Si GaN Eg eV 3.26 1.11 3.44 ε 9.7 11.7 8.9 k W/cmK 3.7 1.5 1.3 Breakdown V/cm 22 x105 2x105 35 x105 electric field Electron affinity eV 3.8 4.05 4.1 Room temp. elec. cm2/V.s 900 1360 2000 mobility Mobility of hole cm2/V.s 120 480 30 at room temp. Conduction band cm-3 1.23x1019 2.8x1019 2.3x1018 density state Valence band cm-3 4.58x1018 1.04x1019 4.6x1018 density satate Table 2.1 Semiconductor fundamental properties comparison.

19 2.3 BAND STRUCTURE: The band structure of wurtzite GaN is shown in figure 2.2 [29]. The energy bandgap between conduction band minimum and valence band maximum is at the Γ valley. There the bandgap(Eg) is 3.39V. At A valley bandgap EA is 4.7 to 5.5eV. At M-L valley EM-L is 4.5 to 5.3 eV. Spin off band Eso is 0.008eV and crystal energy Ecr is 0.04eV.

Figure 2.2 Wurtzite bandgap structure

20 The zincblende GaN bandgap structure is shown in figure 2.3 [29]. The bandgap at Γ valley is 3.2 eV. At <100> orientation, at X valley, Ex is 4.6eV. At <111> orientation, at L valley, EL is 4.8 to 5.1 eV. Eso is 0.02 eV.

Figure 2.3 Band structure of zincblende GaN GaN wurtzite structure

Figure 2.4 GaN crystal structure 21 In Figure 2.4, the wurtzite crystal structure for GaN has been shown. Wurtzite crystals are made of unit cells which are hexagonal in shape. There are two lattice layers. One is gallium and the other in nitrogen. These two lattice layers form wurtzite structure together. The lattice offset between two lattices is 5/8C. Being made by two lattice layers, wurtzite has two atomic planes, each for gallium and nitrogen. They pair in (0001) direction. At that time, they are stacked in “ababab” sequence. This sequence makes two consecutive gallium, or two consecutive nitrogen layers stay directly on top of each other, aligned. 2.4 ENERGY BAND GAP: Both gallium nitride and silicon carbide have bigger bad gap than silicon, hence labeled as wide bandgap semiconductor. The bandgap of any semiconductor goes down as the temperature rises. The relation between the energy bandgap and temperature can be found from the following graph [26]

Figure 2.5 Energy bandgap vs temperature comparison Figure 2.4 shows that the bandgap for wide bandgap semiconductors are almost 3 times bigger than silicon, justifying their name as wide bandgap semiconductor. Both create less carriers at the depletion region and create a lot smaller leakage current in the bulk. Gallium nitride and silicon carbide also makes higher possible in high voltage rectifiers which reduces leakage current. In MESFET and HFET, the higher Schottky barrier helps controlling threshold voltage.

22

2.5 ENERGY BANDGAP VERSUS LATTICE CONSTANT COMPARISON:

Figure 2.6 Energy bandgap versus lattice constant. In Figure 2.5 several nitride semiconductors have been plot using their corresponding bandgap energy and lattice constant. Area ‘a’ shows that GaN has a lattice match with AlInGaN, while bandgap energy is different. Area ‘b’ shows that AlInGaN with bandgap=2.75eV, while net interfacial polarization charge is varied. 2.6 INTRINSIC CARRIER CONCENTRATION: Intrinsic carrier concentration refers to the total number of electron and holes in an intrinsic, un-doped, pure semiconductor. The pair of electron and holes are generated by thermal energy and the number is increased with temperature. The following equation expresses intrinsic carrier concentration.

-[Eg.(T)/2kT] ni = √푛. √푝 = √푁푐. √푁푣. e ...... (2.1)

23 Where, Eg refers to the bandgap, T refers to absolute temperature, Nc refers to the conduction band state density, Nv refers to the valance band state density and k refers to Boltzmann’s constant. Using the equation, the following intrinsic carrier concentration versus temperature graph has been calculated [26].

Figure 2.7 Carrier concentration. vs temperature.

It clearly depicts that the ni of GaN or 4H-SiC are a lot lower than silicon. Here ni refers to carrier concentration of the pure semiconductor. Wider bandgap is the reason behind this. At 298K, the intrinsic carrier concentration of silicon is 1.38x1010 cm-3. But the intrinsic carrier concentrations of 4H-SiC and GaN are extremely low in value, they are in the range of 2.5x10-10 cm-3 and 9.8x10-12 cm-3 respectively [26]. The low value of intrinsic carrier concentration of SiC and GaN show promise to fabricate device to withstand high temperature. When there is presence of states in the bandgap, bulk surface generation current is high. In case of wide bandgap semiconductor, surface generation current is a lot lower, almost negligible. Mesoplasmas is an electrical phenomenon which causes a high density electrical current in the semiconductor causing the ultimate destruction of the device. Mesoplasmas were first observed by Thronton and Simmons in collector junction in 1958 [41]. It was reported that the high current occurred at the collector was varying with the variation of the reverse bias 24 voltage and increasing function of frequency. It has also been reported as second breakdown phenomenon. Later Schaft and French found out all kinds of transistor can experience mesoplasmas if enough current goes through them [42]. Mesoplasmas appear as bright red spot in the device, clearly visible to the naked eye. The brightness increases with the current. It has also been reported that the red spot moves within the device with the change of the current [41]. It was also reported that the amount of current which turns on the mesolplasmas phenomenon, is a function of frequency of the ac condition. The creation of mesoplasmas is also related to intrinsic carrier concentration. So mesoplasmas is very unlikely to occur in either one of the two discussed wide bandgap semiconductors. 2.7 P-N JUNCTION BUILT-IN POTENTIAL: The built-in potential of a semiconductor in specific temperature can be calculated using the following formula.

- + 2 Vbi = (kT/q)ln((NA .ND )/ni ...... (2.2)

Here, NA- and ND+ are two impurity concentrations of the two sides. The change of the built-in potential with the change of temperature for silicon 4H-SiC and GaN is shown in 35 -6 the following plot [26]. NA-. ND+ is assumed as 10 cm .

Figure 2.8 Built in potential vs temperature At room temperature, Vbi for GaN is 3.40V, 4H-SiC is 3.23V. Both are much higher than silicon which is only 0.88V.

25 CHAPTER 3 3.1 GALLIUM NITRIDE MESFET DEVICES: The acronym MESFET stands for ‘Metal Semiconductor Field-Effect Transistor’. The main difference between MOSFET and MESFET is there is no oxide layer underneath the gate in MESFET. But the field aided channel is formed in MOSFET whereas the channel in MESFET is physically formed. Wide bandgap semiconductors exhibit a special property which makes them very useful in high voltages. They have very low resistance in the drift region. High voltage unipolar devices are developed more because of their switching speed than bipolar devices. The inversion layer mobility is very low in MOSFET devices. So, both MESFET and JFET have good merit to be used as unipolar switching devices. In wide bandgap semiconductors, it is possible to dope the drift region with higher doping concentration. In silicon, it is not possible because in Si JFET the breakdown voltage is limited by the resistance in drift region. 3.2 GaN MESFET PLANER STRUCTURE:

Figure 3.1: Planer structure of a GaN MESFET (simulated) In Figure 3.1 a planer structure of GaN MESFET has been showed. The device is fabricated on semi insulating GaN substrate, length of the source and drain terminal is 0.5 µm. The length of the gate is 0.3 µm. the thickness of the layer is 0.2 µm.

26 3.3 OPERATION OF GAN MESFET DEVICES: GaN MESFET has the same working principle as MOSFET, with two types of operation mode, i. depletion mode and ii. enhancement mode

Depletion mode MESFET In depletion mode MESFETs, the depletion region is not extended up to the p-type substrate. So, the channel is not pinched off. Depletion mode MESFETs are also known as ‘Normally-On’ devices, since they are conductive even when the gate to source voltage is zero. To turn off these devices, negative gate to source voltage (VGS) is needed to be applied so the depletion region pinches off the channel. Depletion mode devices are used mostly in logic-based circuits.

Enhancement mode MESFET In enhancement mode MESFETs, the depletion region is so enhanced that it pinches off the channel without any voltage applied at the gate. Enhancement mode devices are also known as ‘Normally-Off’ devices since they are not on at zero voltages. If there is positive voltage is applied at the gate, it shrinks the depletion region. This shrinkage makes the channel conductive again. There is a disadvantage of enhancement mode devices. The MESFET gate is Schottky metal and the positive voltage which is needed to be applied at the gate to turn on the MESFET puts the Schottky diode to forward bias too. This causes a large current flow in the device would cause more power consumption. Enhance mode MESFETs are mostly used in switching devices.

27

Figure 3.2: Comparison of Depletion and Enhancement mode MESFET Figure 4.2 compares the drain current versus gate to source voltage between a depletion mode and an enhancement mode device. It shows that, one device is turns on at - 0.8V(depletion mode) and the other one turns on at 0.0V (enhancement mode). So the depletion mode device experiences pinch off in the negative gate voltage. Hence, even there is no voltage applied at the gate, VGS = 0, depletion mode devices are ‘On’. 3.4 BREAKDOWN VOLTAGE: Breakdown voltage is directly related to crystal configuration, lattice structure, critical electric field. GaN breakdown voltage is much higher than silicon. In [27] the breakdown voltage has been approximated as

1 VBD ≈ ωd . EBD (3.1) 2

ωd = εe . ε0 .EBD/ qNd

Here,

VBD is breakdown voltage,

ωd is width of the drift region,

EBD is critical electrical field for breakdown, 28 εe is relative permittivity of GaN,

ε0 is absolute permittivity, q is 1.6x10-19 C,

Nd refers to donor concentrations. To get the same breakdown voltage, a GaN device would be a lot smaller than a silicon device. The Smaller device causes smaller parasitic components. So GaN shows better switching characteristics. On the other hand, higher critical electric field makes GaN perform better in high voltages, causing low leakage currents.

3.5 ON-STATE RESISTANCE:

3.3 Resistance is a lateral junction MESFET To calculate the on-state resistance, channel resistance, FET region resistance, drift region resistance, and substrate region resistance is needed to be calculated first. Channel resistance can be calculated by

(퐿푐ℎ+ 훼푊푝).푝 RCH = 휌푑 (3.2) (푇푐ℎ−푊푔−푊푝) 29 Where,

RCH is channel resistance, ρd is resistivity, Lch is channel length, α is a constant that depends on charge carriers spreading from the channel to FET, p is cell pitch, Tch is channel thickness, Wg is zero bias depletion width at gate Wp is zero bias depletion width at P+ region. The previous two can be evaluated by the following

Wg = √(2. εe. VbiG)/ √(q.Nd)

Wp = √(2. εe VbiP)/ √(q.Nd)

Where,

VbiG is built in voltage for metal semiconductor gate

+ VbiP built in voltage for P junction

εe is substrate permittivity

Nd refers to the concentration of doping Resistance of the FET region can be calculated 푝 RFET = 휌푑(푇푐ℎ + 푇푝 − 푊𝑔 )( ) (3.3) 푊푓−푊푝

Where,

RFET is resistance of the FET region,

+ Tp is P region thickness,

Wf is zero bias depletion width at FET region

30 Drift region resistance can be calculated as

2푝 2푝 RD = ρd ( )ln( )+ ρd(t-s- 푊푝) (3.4) 푊푓−푊푝 푊푓−푊푝 Where,

RD is the drain region resistance, t refers to the thickness of drift area under P+ area, s refers to width of the same region. N+ substrate resistance is calculated here,

Rsubs = ρsubs . tsubs

Where,

Rsubs is substance resistance,

ρsubs is substance resistivity, tsubs is substance thickness. So, the on resistant will be,

Rop,sp = RCH + RFET + RD + Rsubs. (3.5) Where,

Rop,sp is specific on resistance,

RCH is channel resistance,

RFET is FET region resistance,

Rsubs substrate resistance.

31 CHAPTER 4 4.1 TRAPPING EFFECT: GaN grows trap centers both in epitaxial layers and surface [28]. Epitaxial layer traps occur from impurities, dopants, defects and dislocations. Surface trap centers come from piezoelectric polarization of nitride layer growth. The trapping effect causes a lot of problems for GaN semiconductors. It causes frequency dispersion, significant current reduction and decreases efficiency. GaN being a wide bandgap semiconductor, its trapping effects are very much needed to be modelled and mitigated. In this work, the effect of traps on drain current and transconductance has been discussed. A MESFET Is made with a conductive channel with two ohmic contacts, one on each side, each working either a source or a drain. The contact in which positive voltage is applied is called drain and the other one is called source. When negative voltage is applied at the source, electron starts to inject from source to drain. So, the carriers are originating in the source where the drain is acting as a sink for the carriers. The gate which is made with schottky metal is placed on top of the conduction channel. The depletion region forms right under the gate. The depletion region controls the carrier flow from whereas the size of the depletion region depends on the magnitude of voltage applied at the gate. So, a MESFET actually works as a Voltage Controlled Resistor (VCR). The resistance is controlled by controlling the size of the depletion layer by varying the voltage applied at the gate.

Figure 4.1 A MESFET structure 32 In Figure 4.1 a n-channel depletion mode MESFET structure is shown. The gate length which is also known as channel length is denoted as L. Channel width is shown as Z. At any arbitrary position in the channel, the width of the depletion layer and channel opening are denoted as h and b. y1 and y2 are the width of the depletion layer at the source and the drain end of the gate respectively. Since the device is in depletion mode, even if the voltage at the gate terminal (Vgs or only VG) is zero, if any voltage is applied at the drain terminal (Vds or only VD), current (Id) will inject from the drain to the source through the channel. When Vds is high enough, drain current will saturate which is expressed as IDsat. The current - voltage characteristics and transconductance of a long channel (channel length L is greater than channel depth a) MESFET device are presented below [43]. At first, a few assumptions are considered, 1. gradual channel approximation 2. abrupt depletion layer and 3. constant mobility. The direction along the channel is considered x direction and the direction from device surface to the substrate is considered y direction. The n- channel is considered to be uniformly doped in order to avoid complexity. The analytical model has been developed considering the gradual channel approximation i.e. depletion layer varies only along the x direction (along the channel). One-dimensional Poisson equation can be expressed as

2 ⅆ 푣 ⅆE푦 휌(푦) − 2 = = (4.1) ⅆ푦 ⅆ푦 휀푠 where,

휌(푦) is charge density and equals to 푞푁퐷 q is the charge of a carrier

ND is dopant concentration

E푦 is the strength of the electric field in the y direction

휀푠 is permittivity of gallium nitride So, the equation becomes,

2 ⅆ 푉 푞푁퐷 − 2 = (4.2) ⅆ푦 휀푠

At x distance from the source, the depletion layer width can be expressed using the following formula using abrupt junction expression.

1/2 h = {2 * 휀푠 * [ V(x) + VG + Vbi ] / q ND } (4.3) 33 Where,

Vbi is the built-in voltage and can be expressed as

Vbi = (kT/q) ln (ND /ni) (4.4) V(x) is the voltage at x distance from the source Also, q is the charge of a carrier

ND is the dopant concentration.

Depletion widths at the source and drain end are y1 and y2 respectively and they can be expressed as

1/2 y1 = {2 * 휀푠 * [ VG + Vbi ] / q ND } at x = 0(source end of the channel) (4.5)

1/2 y1 = {2 * 휀푠 * [ VD + VG + Vbi ] / q ND } at x = L (drain end of the channel) (4.6) To cause pinch off, the depletion layer width needs to be maximum wide to block the channel flow. The maximum width for y2 can be a. The voltage when pinch off occurs is called pinch off voltage and it can be expressed as the following.

2 VP = V( y2 = a) ≡ q * ND * a / 2휀푠 (4.7) The current density towards x direction can be calculated from the ohmic law

Jx = σ(x) ℰ푥 (4.8) or,

Jx = q * ND * µ *ℰ푥 (4.9) where,

Jx is the density of the current along the direction of the channel

ℰ푥 is the electric field in the x direction and can be expressed as the following, ⅆ푉 ℰ = − (4.10) 푥 ⅆ푥 µ is carrier mobility which is assumed independent from the effect of the electric field. So the drain current can be found as the following

ⅆ푉 ID = q * ND * µ *( ) (푎 − ℎ)푍 (4.11) ⅆ푥 34 or

ID * 푑푥 = 푍 * µ * q * ND * (푎 − ℎ)* 푑푉 (4.12) The drain voltage differential 푑푉 can be found using equation 4.2

푞푁 푑푉 = 퐷 ℎ 푑ℎ (4.13) 휀푠 If the value of 푑푉is put into the drain current equation, and integrate it for the whole channel length (from x=0 to x=L) the following equation is formed,

1 푦2 푞푁퐷 퐼퐷 = ∫ 푍휇푞푁퐷 (푎 − ℎ) ℎ 푑ℎ (4.14) 퐿 푦1 휀푠 or,

2 2 3 푍휇푞 푁퐷푎 3 2 2 2 3 3 퐼퐷 = [ 2 (푦2 − 푦1 ) − 3 (푦2 − 푦1 )] (4.15) 6휀푠퐿 푎 푎 So, the current equation now becomes

2 2 3 푍휇푞 푁퐷푎 3/2 3/2 3/2 ID = { 3 VD / VP -2 [ ( VD + VG + Vbi ) - ( VG + Vbi ) ]/ VP } (4.16) 6휀푠퐿

To calculate the maximum or saturated current, we can put y2 equals a in equation 4.15.

3/2 3/2 IDsat = IP [ 1 – 3 ( VG + Vbi )/ VP + 2 ( VG + Vbi ) / VP ] (4.17) The saturation voltage will be calculated from

2 푞푁퐷푎 푘푇 푁퐷푁푎 VDsat = VP – VG – Vbi = – VG - 푙푛 ( ) (4.18) 2휀 푞 푛2 푠 푙̇ From equation 4.16 transconductance can be found

2푍휇푞푁퐷 gm ≡ (푦 − 푦 ) (4.18) 퐿 2 1

4.2 TRAPPING EFFECT ON CURRENT-VOLTAGE CHARACTERISTICS: Trapping effect on current voltage characteristics has been formulated like the following in some research work [44].

Electron mobility(µ0) in the MESFET can be expressed like the following,

푇 푥 휇 ( ) −휇 푚푎푥 300 푚푖푛 휇0 = + α (4.19) 푇 푦 푁 1+( ) ( 퐷 ) 300 푁푟푒푓

35 + ND refers to the concentration of impurity at ionized condition,

µmax and µmin are maximum and minimum mobility,

Nref is reference concentration, x, y are temperature variable. Electron mobility can also be expressed using electric field, µ(E) = v(E) / E (4.20) Where,

퐸 휃 퐸 휂 휇1퐸+휇1퐸( ) +푣푠푎푡( ) 푣(퐸) = 퐸0 퐸1 (4.21) 퐸 휃 퐸 휂 1+( ) +( ) 퐸0 퐸1

E0 and E1 are factors which influences maximum velocity 휃 is is a factor which influences maximum electric field η determine how steep v(E) would be at saturated state. Thermal conductivity is calculated from

-3/2 K(Ṭ) = K0 (Ṭ/300) (4.22)

K0 depends on the concentration of the dopant.

2 K0=a0+a1log Nd + a2(log Nd) (4.23) When gate bias is applied, depletion layer is formed right under the gate. But because of trapped carriers, depletion layer also forms at the channel-buffer interface. Considering this effect along with velocity saturation, drain current was expressed by the following equations [44],

2 2 3 3 3 3 푛푐 3(푢푑−푢0)− 2(푢푑−푢0)− 2(푢푡푑−푢푡0)∕√(1+ ) 푁푇 ID(VG, VD) = Ip 2 2 When VD < VDsat 1+푍(푢푑−푢푑) (4.24) and

IDsat=qNavsatWaγ(1-us) When VD > VDsat (4.25) Here,

2 2 3 Ip = q .nc .µ0.Wa / 6.ε.L

2 Vp = q.nc.a / 2.ε 36 2 Z = q.nc. µ0.a / 2.ε . L . vsat

1 2⋅휀 푉퐺+푉푏푖 푢0(푉퐺) = √ (푉퐺 + 푉푏𝑖) = √ 푎 푞푛푐 푉푃

1 2⋅휀 푉퐷+푉퐺+푉푏푖 푢ⅆ(푉퐺 ,푉퐷) = √ (푉퐷 + 푉퐺 + 푉푏𝑖) = √ 푎 푞푁퐷 푉푃

1 2⋅휀 푉푡푏푖 푢푡0(푉퐺) = √ (푉푡푏𝑖) = √ 푎 푞푛푐 푉푃

1 2⋅휀 푉퐷+푉푏푖 푢푡ⅆ(푉퐺 ,푉퐷) = √ (푉퐷 + 푉푡푏𝑖) = √ 푎 푞푛푐 푉푃

푘푇 2 Vtbi = ln (nc . NT / ni ) 푞 Where,

NT refers to concentration of the occupied trap centers, ni refers to carrier concentration of the intrinsic semiconductor, ε refers to dielectric constant of GaN, k refers to Boltzmann constant, T refers to absolute temperature,

µ0 refers to carrier mobility on low field, a refers to channel thickness W refers to device width, L refers to the length of the gate, γ is used as the saturation constant, vsat refers to the velocity of carrier at saturation, nc refers to the concentration of the electron in the channel.

4.3 TRAPPING EFFECT ON TRANSCONDUCTANCE: The transconductance considering the trapping effect can be calculated using the following formula [44]

푎1+2푎2푉퐺 gm`` = qvsatWaNt0β exp[-β(VD – VDon)] (4.26) 1+푎1+2푎2푉퐺 37 Where,

NT is trapped carrier concentration

NT = Nt0 exp (-β (VDS – VDon)) (4.27)

VDon is drain voltage at the start onset of detrapping process

2 VDon = a0 + a1VG + a2VG Where, a0 is 6.4V a1 is 0.84

-1 a2 is 0.0055V

4.4 RESULT AND DISCUSSION: The physics based analytical model of GaN MESFET for trapping effect has been developed to study the effect of trap centers on drain current and transconductance. In order to visualize the traps effects, MATLAB simulations have been performed. The 17 -3 channel doping concentration (ND) of 5x10 cm and channel thickness (a) of 0.5 µm in the drift region of GaN MESFET were considered. A detailed discussion of traps effects on I-V characteristics and transconductance has been discussed below with the appropriate results.

38

Figure 4.2 Drain current ID versus drain to source voltage VDS graph

The Figure 4.2 shows a plot of drain current versus drain-source voltage for different gate- source voltage with traps effect and without traps effect. I-V characteristic shows clearly both linear and saturated region. The pinch-off voltage was found in the order of 1V and it is acceptable with the considered value of active channel depth. The drain current has been evaluated by merging two separate drain current equations for non-saturation and saturation conditions. The determination of drain current shows the validity of the merging of two set of equations by showing the current in linear and non-linear regimes. The saturation current for VGS = 0V without and with traps effect is found to be in the order of 19 mA and 18.5 mA. The saturation current for VGS = -2V without and with traps effect is observed in the order of 15 mA and 14.5 mA. The drain current has been plotted by using the Equation (4.24) and (4.25).

39

Figure 4.3 transconductance gm versus gate to source voltage VGS plot for different VDS

The Figure 4.3 presents a plot of transconductance gm versus source voltage VGS for different drain-source voltage VDS = 10V and 20V. The transconductance exponentially increases up to VGS = 0V and VGS = 10V for drain-source voltage VDS = 10V and 20V. When VDS = 10V, the saturation transconductances have been found in the order of 0.2 siemens and 0.14 siemens respectively without and with traps effect for VGS = 2.5V. When VDS = 20V, the saturation transconductances have been found in the order of 0.2 siemens and 0.14 siemens respectively without and with traps effect for VGS = 12.5V. The threshold voltage from the plot has been found in the order of -15V and -5V for drain-source voltage VDS = 10V and 20V respectively. The threshold voltage remains same without and with traps effects due to subthreshold current. The transconductance has been plotted by using the Equation (4.26).

40

Figure 4.4 transconductance gm vs gate to source voltage VGS plot for different channel thickness

The Figure 4.4 displays a plot of transconductance gm versus source voltage VGS for different channel thickness of 0.8µm and 0.1 µm with/without traps effects. The transconductance exponentially increases up to VGS = 5V and further linearly increases up to VGS = 9V for drain-source voltage VDS = 10V and channel thickness of 0.8µm. The transconductance exponentially increases up to VGS = 10V and further linearly increases up to VGS = 14V for drain-source voltage VDS = 10V and channel thickness of 0.1µm. The saturation transconductances for VGS = 9V have been found in the order of 3 siemens and 2 siemens respectively without/with traps effect for 0.8µm channel thickness. The saturation transconductances for VGS = 14V have been found in the order of 3 siemens and 2 siemens respectively without/with traps effect for 0.1µm channel thickness.The threshold voltage from the plot has been found in the order of -5V and -0V for different channel thickness 0.8µm and 0.1 µm, while the drain-source voltage was kept in the order of VDS = 10V. The threshold voltage more or less remains same without and with traps effects due to subthreshold current. The value of the transconductance is higher for channel thickness of 0.8µm and it is evident from the Equation 4.26. The transconductance has been plotted by using the Equation (4.26).

41 CHAPTER 5 CONCLUSION

A physics based analytical modeling of GaN MESFET has been developed to study the trapping effect on drain current and transconductance using MATLAB software. The drain- bias dependence of trapped carrier concentration has been calculated and incorporated in drain current and transconductance to study the traps effects on drain current and transconductance. The drain current has been evaluated by merging two separate drain current equations for non-saturation and saturation conditions. The determination of drain current shows the validity of the merging of two set of equations by showing the current in linear and non-linear regimes. The drain current has been optimized by active channel depth, pinch-off voltage and different non-saturation and non-saturation physical parameters. The optimized drain current clearly shows linear and non-linear properties to validate the device I-V characteristics. The drain current for VGS = 0V and -2V increases up to 19 mA and 15 mA under no trap condition, whereas the drain currents for VGS = 0V and -2V stay up to 18.5 mA and 14.5 mA under trap condition. Transconductance under saturation condition has been found in the order of 0.2 siemens and 0.14 siemens for VDS = 10V and 20V. The extracted threshold voltage from the plot was found -15V for VDS = 10V and -5V for VDS = 20V. This research work claims a future research scope to understand the transition of threshold voltage for depletion and enhancement mode device depending on the nature of traps center.

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46 APPENDIX-CODES IV (with and without trap) % Drain current GaN MESFET device clc clear all % Electron Charge q=1.60218e-19; % Electron Mobility in GaN Un = 440; % Width of the MESFET device W = 1000e-4; % Length of the MESFET device L = 1e-4; % Gate Length a = 0.5e-4; % Energy Gap Eg= 3.2; % Boltzmann Constant k=1.3807e-23; % Temperature T=300; % Dielectric Constant Eo= 8.9; % Doping Concentrations Na = 1e15; Nd = 5e17;

47 % Fitting parameters for calculating the trap concentration a0 =6.4; a1 = 0.85; a2 = 0.0055; beta = 0.36; Nto = 3.5e15 % Dielectric Constant with vacuum E= Eo*8.854e-14; % Conduction Band concentration Nc = 3.25e15*sqrt(T*T*T) % Valency Band concentration Nv = 4.8e15*sqrt(T*T*T) % intrinsic carrier concentration ni = sqrt(Nc*Nv)*exp(-(Eg*q)/(2*k*T)) % Calculating Thermal voltage Vt = (k*T)/q % Saturation voltage Vsat = 0.72 % Plotting Drain Current Vs Drain Voltage for vg = [0 -2] %nc=5e17; Vds = 0:1:30 Vdon = a0+(a1*vg)+(a2*vg^.2) Nt = Nto*exp(-beta*(Vds-Vdon)) %Nt=1 nc=Nd-Nt;

48 % Calculating built in voltage Vbi = Vt*log(Na*Nd/ni^2) Vp = Vbi-(a^2*q*Nd/(2*E)) ip = (q*q*nc.*nc*Un*W*a*a*a)/(6*E*L) % Calculating the fitting parameters uo = sqrt((Vbi-vg)/Vp) ud = sqrt((Vds-vg+Vbi)/Vp) vtbi = (k*T/q).*(log((nc.*Nt)./(ni*ni))) uto = sqrt(vtbi./Vp) utd = sqrt((Vds+vtbi)/Vp) Z = (q*nc*uo*a^2)/(2*E*L*Vsat) % Calculating the drain current Id = ip.*((3.*(ud.^2-uo.^2))-(2.*(ud.^3-uo.^3))-(2*(utd.^3- uto.^3)./(sqrt(1+(nc./Nt)))))./(1+Z.*(-ud.^2+uo.^2)*10^-2); plot(Vds,Id*10,'--') xlabel('Drain Voltage') ylabel('Drain Current') title('Drain Voltage(V) Vs Drain Current(mA) in GaN MESFET') %legend('Vgs =-2 ','Vgs = 0') hold on end for vg = [0 -2] nc=Nd Vds = 0:1:30 Vdon = a0+(a1*vg)+(a2*vg^.2) Nt = Nto*exp(-beta*(Vds-Vdon)) %Nt=1

49 % Calculating built in voltage Vbi = Vt*log(Na*Nd/ni^2) Vp = Vbi-(a^2*q*Nd/(2*E)) ip = (q*q*nc*nc*Un*W*a*a*a)/(6*E*L) % Calculating the fitting parameters uo = sqrt((Vbi-vg)/Vp) ud = sqrt((Vds-vg+Vbi)/Vp) vtbi = (k*T/q)*(log((nc*Nt)/(ni*ni))) uto = sqrt(vtbi/Vp) utd = sqrt((Vds+vtbi)/Vp) Z = (q*nc*uo*a^2)/(2*E*L*Vsat) % Calculating the drain current Id = ip*((3*(ud.^2-uo.^2))-(2*(ud.^3-uo.^3))-(2*(utd.^3- uto.^3)./(sqrt(1+(nc./Nt)))))./(1+Z*(-ud.^2+uo.^2)*10^-2); plot(Vds,Id*10,'color',rand(1,3)) xlabel('Drain Voltage(V)') ylabel('Drain Current(mA)') title('Drain Current(mA) Vs Drain Voltage(V)) %legend('Vgs =-2 ','Vgs = 0') hold on end xlim([0 6]) legend('Vgs = 0 with trap ','Vgs =-2 with trap ','Vgs = 0 without trap','Vgs =-2 without trap ','L = 1µm','Z = 1000 µm','a = 0.5 µm','ND = 5e17 cm-3','Location', 'NorthWest')

50 gm vs Vgs for different Vds (with and without trap) clc; clear all; q=1.60218e-19; k=1.3807e-23; Eg=3.4; to=300; eo=8.9; es=8.85418e-14; e=eo*es; Nc=4.35e14*sqrt(to*to*to); nv=8.9e15*sqrt(to*to*to); ni=sqrt(Nc*nv)*exp(-(Eg*q)/(2*k*to)); Un=440; Nd=1e17; w=1000e-4; d=0.5e-4; L=1e-4; vsat=2.7e7; for Vds=[10,20]; Nto=3.5e16; Nt=Nto*exp(-0.112*Vds); nc=Nd-Nto; %Nto=1e17; a0 =6.4; a1 = 0.85;

51 a2 = 0.0055; alpha = 0.36; Vgs=-20:0.1:20; VdsONset=a0+(a1.*Vgs)+(a2.*Vgs.*Vgs); gm1=q*vsat*w*d*nc*alpha; gm21=a1+(2*a2.*Vgs); gm22=1+gm21; gm2=gm21./gm22; gm3=Vds-VdsONset; gm4=exp(-alpha*gm3); gm=gm1.*gm2.*gm4; plot(Vgs,gm,'--') hold on ylim([0,0.2]) xlim([-20 20]) %axis([-25 0 0 0.025 ]) nc=Nd; gm1=q*vsat*w*d*nc*alpha; gm21=a1+(2*a2.*Vgs); gm22=1+gm21; gm2=gm21./gm22; gm3=Vds-VdsONset; gm4=exp(-alpha*gm3); gm=gm1.*gm2.*gm4; plot(Vgs,gm) hold on end 52 xlabel('Gate-source Voltage (V)') ylabel('Transconductance(Siemens)') title('Transconductance Vs Gate Voltage') legend('Vds=10 with Trap','Vds=10 without Trap','Vds=20 with Trap','Vds=20 without Trap','Location', 'NorthWest')

gm vs channel thickness clc; clear all; q=1.60218e-19; k=1.3807e-23; Eg=3.4; to=300; eo=8.9; es=8.85418e-14; e=eo*es; Nc=4.3e14*sqrt(to*to*to); nv=8.9e15*sqrt(to*to*to); ni=sqrt(Nc*nv)*exp(-(Eg*q)/(2*k*to)); Un=440; Nd=1e17; w=1000e-4; L=6e-4; vsat=2.7e7; Vds=10

53 Nto=3.5e16; Nt=Nto*exp(-0.112*Vds); %Nto=1e17; a0 =6.4; a1 = 0.85; a2 = 0.0055; alpha = 0.36; Vgs=-20:0.1:20; VdsONset=a0+(a1.*Vgs)+(a2.*Vgs.*Vgs); for d=[0.8e-4,0.1e-4] nc=Nd-Nto; gm1=q*vsat*w*d*nc*alpha; gm21=a1+(2*a2.*Vgs); gm22=1+gm21; gm2=gm21./gm22; gm3=Vds-VdsONset; gm4=exp(-alpha*gm3); gm=gm1.*gm2.*gm4; plot(Vgs,gm,'--') hold on nc=Nd; gm1=q*vsat*w*d*nc*alpha; gm21=a1+(2*a2.*Vgs); gm22=1+gm21; gm2=gm21./gm22; gm3=Vds-VdsONset;

54 gm4=exp(-alpha*gm3); gm=gm1.*gm2.*gm4; plot(Vgs,gm) hold on end ylim([0,3]) xlabel('Gate-source Voltage(V)') ylabel('Transconductance(Siemens)') title('Transconductance Vs Channel Thickness') legend('d=0.8 microns with trap','d=0.8microns without Trap','d=0.1 microns with trap','d=0.1 microns without trap','Location', 'NorthWest')

55