CALIFORNIA STATE UNIVERSITY, NORTHRIDGE

Modeling of Gallium Nitride MESFETs at High Temperatures

A graduate project submitted in partial fulfillment of the requirements

For the degree of Master of Science in

Electrical Engineering

By

FNU Syed Zabiullah

May 2015

ii

The graduate project of FNU Syed Zabiullah is approved:

Professor Dr. Matthew Radmanesh Date

Professor Dr. Kourosh Sedghisigarchi Date

Professor Dr. Somnath Chattopadhyay, Chair Date

California State University, Northridge

iii

Acknowledgement

I would like to express my sincere gratitude and appreciation to everyone who

made this thesis possible. Most of all, I would like to thank my project coordinator, Dr.

Somnath Chattopadhyay for his guidance in achieving my thesis objective. It was an

honor getting the privilege to work under his supervision. I would also like to thank my

other committee members, Dr. Matthew Radmanesh and Dr. Kourosh Sedghisigarchi for

providing their valuable suggestions.

I would also like to thank the Department of Electrical and Computer Engineering

for providing the facilities to complete this project.

Finally, I would like to express my love and gratitude to my parents; for their

understanding & endless love, through the duration of my studies.

iv

Table of Contents

Signature Page .................................................................................................................... ii

Acknowledgement ............................................................................................................. iii

List of Figures ................................................................................................................... vii

List of Tables ................................................................................................................... viii

ABSTRACT ....................................................................................................................... ix

Chapter 1 Introduction .........................................................................................................1

Chapter 2 Overview of GaN Material ..................................................................................7

2.1 Gallium Nitride properties: ....................................................................................... 7

2.2 Energy- Band Structure............................................................................................. 8

2.2.1 Band structure of Zinc Blend GaN: ................................................................... 8

2.2.2 Band structure of wurtzite GaN: ........................................................................ 9

2.2.3 Temperature dependence of band gap energy: ................................................ 10

2.2.4 Band gap energy Vs Temperature for Wurtzite structure of GaN ................... 10

2.2.5 Band gap energy vs Temperature for Wurtzite GaN: ...................................... 11

2.2.6 Band gap energy vs Temperature for zinc blende GaN on MgO substrate: .... 12

2.2.7 Band gap energy vs temperature of zinc blende GaN with Si substrate: ......... 12

2.3 Intrinsic carrier concentration ................................................................................. 13

2.4 GaN Crystal Structure ............................................................................................. 15

2.5 Various charge effects in GaN: ............................................................................... 18

2.5.1 Piezoelectric effect on GaN: ............................................................................ 18

2.5.2 Polarization charge effect: ............................................................................... 19

2.6 Drift velocity versus electric field: ......................................................................... 21

2.7 Growth process of GaN: ......................................................................................... 22

v

2.8 Why the SiC, Si and sapphire are used for GaN? ................................................... 24

2.9 Growth defects and process induced defects of GaN: ............................................ 25

2.9.1 Native Point Defects: ....................................................................................... 25

2.9.2 Interstitials and Antisites Defects: ................................................................... 26

Chapter 3 Ion Implantation ................................................................................................28

3.1 Ion Implantation ...................................................................................................... 28

3.1.1 Ion implantation equipment: ............................................................................ 30

3.2 Impurity distribution equation: ............................................................................... 31

3.3 Annealing: ............................................................................................................... 34

3.4 Fabrication process of MESFET:............................................................................ 35

Chapter 4 Physics of MESFET ..........................................................................................38

4.1 MESFET: ................................................................................................................ 38

4.2 Working of MESFET:............................................................................................. 39

4.2.1 Types of MESFETS and its operations:........................................................... 39

4.3 MESFET Characteristics: ....................................................................................... 41

4.3.1 I-V Characterisctics: ........................................................................................ 41

4.3.2 Operating Regions in MESFET: ...................................................................... 42

4.4 MESFET applications in various fields: ................................................................. 43

Chapter 5 Theory and Calculations....................................................................................45

5.1 I-V characteristics Of GaN MESFET: .................................................................... 45

5.2 Trans-conductance of GaN MESFET: .................................................................... 46

5.3 Temperature dependence of GaN properties: ......................................................... 47

Chapter 6 Results and Discussion ......................................................................................48

6.1 Temperature versus current: ................................................................................... 48

6.2 I-V characteristics: .................................................................................................. 49

vi

6.3 I-V characteristics for different active channel thickness (a): ................................ 50

6.4 Transconductance by varying temperature: ............................................................ 51

Chapter 7 Conclusion .........................................................................................................53

References ..........................................................................................................................54

APPENDIX A ....................................................................................................................66

APPENDIX B ....................................................................................................................68

vii

List of Figures

Figure 2.1 Energy band diagram for Zinc Blend GaN........................................................ 8

Figure 2.2 Energy band diagram of wurtzite GaN .............................................................. 9

Figure 2.3 Excitation energies vs Temperature plot ......................................................... 11

Figure 2.4 Band gap (eV) vs Temperature (K) plot .......................................................... 11

Figure 2.5 Temperature (T) vs Band gap (eV) plot .......................................................... 12

Figure 2.6 Band energy vs Temperature plot for zinc blende GaN with Si as substrate .. 13

Figure 2.7 Intrinsic carrier concentration vs Temperature ................................................ 15

Figure 2.8 The correlation between lattice constant of zinc blende and wurtzite and band

energy gap for various materials and their related alloys ................................................. 16

Figure 2.9 Structures of atoms for zinc blend (a), wurtzite (b), rocksalt (c) .................... 17

Figure 2.10 Drift velocity vs electric field for GaN.......................................................... 22

Figure 2.11 Principle of MOVCD process ....................................................................... 23

Figure 2.12 Formations of Energies at Fermi Level for Native Point Defects ................. 26

Figure 3.1 (a) Doping by diffusion, (b) Doping by ion implantation ............................... 29

Figure 3.2 Schematic of medium current ion implanter ................................................... 30

Figure 3.3 Schematic for the ion range ............................................................................. 33

Figure 3.4 Boron implanted atom distribution .................................................................. 34

Figure 3.7 Steps involving MESFET fabrication ............................................................. 37

Figure 4.1: Schematic representation of Gallium Nitride MESFET................................. 38

Figure 4.2: E-MESFET ..................................................................................................... 40

Figure 4.3: Depletion MESFET ........................................................................................ 40

Figure 4.4: Typical (I-V) characteristics of MESFET ...................................................... 41

Figure 4.5: I-V chadracteristics in a linear or active region ............................................ 42

Figure 4.6: Drain-source current vs drain-source voltage in saturation region ................ 43

Figure 5.1: Gallium Nitride MESFET shown in a cross-sectional view .......................... 45

Figure 6.1 Variation of current with change in temperature ............................................. 48

Figure 6.2: Ids versus Vds plot by giving different gate source voltage Vgs ...................... 49

Figure 6.3: Ids versus Vds plot for different active channel thickness. .............................. 50

Figure 6.4 Variation of Transconductance with Temperature: ......................................... 51

viii

List of Tables

Table 1.1 Physical properties of various semiconductor materials ..................................... 2

Table 2.1 Properties of various materials ........................................................................... 7

Table 2.2: Lattice constants and unit cell parameters for GaN, AIN, InN ....................... 18

Table 5.1: GaN parameters at different temperature: ....................................................... 47

ix

ABSTRACT

Modeling of Gallium Nitrate MESFETs at High Temperatures

By

FNU Syed Zabiullah

Master of Science in Electrical Engineering

GaN shows an extreme promising material showing the properties of wide

bandgap, high electron velocity and high breakdown voltage with low thermal generation

rate, excellent thermal conductivity and high radiation resistance for high power and high

frequency amplifier.

An analytical model of GaN MESFET has been developed to simulate the

temperature dependent drain current and transconductance. The drain current shows

small variation in the current due the temperature transition from 300 K to 500 K. The

transconductance also exhibits very insignificant change due to temperature variation

from 300 K to 500 K. In order to understand the device performance at 300 K, the drain

current has been computed for different gate-source voltage. The drain current clearly

shows the linearity regime, non-linear regime and saturation regime to justify the validity

of the model. Further, the drain current has been evaluated for different active channel

thickness to justify the desired pinch-off voltage. The computed results show that GaN

MESFET shows incredible thermal stability at extreme high temperatures.

1

Chapter 1 Introduction

In recent years a greater interest has been paid to the wide band-gap materials

such as Gallium Nitride (GaN) [1] due to its low thermal generation rate and high

breakdown field as it has a potential in high power [2], high temperature and microwave

frequency application. GaN is being used in high frequency electronic devices and these

devices are commercialized. Because of gallium nitride’s incredible properties, wide

band gap which cause high electric field breakdown gives GaN potential in high power

device area and are used for military purposes [3-4].

The wide band gap materials such as GaN, SiC typically has an order of

magnitude greater when compared to the other conventional semiconductors [5]. The

band gap energies of these materials are multiple times greater than that of conventional

semiconductors namely Si, GaAs, InP. The wide band-gap materials can be operated at

high voltage supply because of high breakdown field (Ec) which is due to their wide band

gap (Eg). GaN material has an ability to withstand at high operating temperatures and

accepts improved radiation hardness. High thermal conductivity of GaN plays an

important role because most of the electronic devices are projected for high power

applications and the ability to extract heat caused due to dissipated energy results the

better performance of the device [6]. Silicon and Gallium Nitride has almost similar

thermal conductivity but the thermal conductivity of SiC is multiple times higher than

that of GaN and Si. The thermal conductivity of Gallium Nitride was calculated to be 130

W/mK [7].

Wide band-gap materials are capable of making lesser noise than conventional

semiconductors and thus GaN is encouraged in ultra-violet range in producing high

2

sensitive detectors. For a doping convergence of 1 ×1017

, the hypothetical low field

electron portability of GaN is about 1500 cm2/vs, which is higher than the qualities for

any of the SiC poly-sorts [8]. Gallium Nitride material has high saturation velocity of

about with a breakdown electric field of 4 V/cm which is favorable for the

microwave applications in the conduction structure of GaN [9]. Though wide band gap

semiconductors have relatively low mobility, but they also have very high values for the

saturation velocity, which is reached at high electric fields that can easily be supported

[10].

Some of the physical properties can be described as shown in Table 1.1:

Table 1.1 Physical properties of various semiconductor materials [12]

Table 1.1 shows various properties of different materials of which band gap

energy is one of them. The band-gap energy (Eg) for Gallium Nitride (GaN) at a

temperature of 300 was found to be 3.4 eV which is much higher when compared to

the other semiconductor materials. Thus, GaN is preferred as a material in electronic

3

devices [13].

The performance of high power and high frequency devices totally depend on the

material characteristics such as conduction efficiency, switching speed, cost, size of

material and breakdown voltage. These characteristics determine the power density and

frequency of the device [14]. Gallium Nitride (GaN) has indicated great attributes

towards electronic and optical devices at high temperatures, high frequencies and high

power. By using GaN material many different varieties of electronic devices have been

modeled which offers high performance in microwave frequencies when compared to Si

and GaAs devices [15].

Gallium Nitride (GaN) metal semiconductors field effect transistors (MESFET)

was developed first in the year 1993 and from then various researches has been carried

out. GaN MESFETs were developed to substitute power MOSFETs in applications where

power conversion efficiency and switching speeds are important [16]. GaN MESFET has

its applications in various aspects such as military, aerospace, Radars etc. GaN MESFETs

are receiving more awareness as it has a structure which is simple to analyze when

compared to other complicated transistors such as high electron mobility transistors

(HEMT) [17].

Analytical modeling has been conducted on GaN MESFETs various times,

though significant experimental work is available [18]. In recent researches it has been

reported GaN MESFET is encouraging in power performance. In a research, the current

device performance exhibited a power density of 2.2 W/mm with a power added

efficiency of 27% at VDS = 30V and VGS = 2V at 2GHz [19]. In some other research

conducted on the GaN based MESFET, device showed a high frequency of 10 GHz with

4

power density of 2.7 W/mm [20]. In a research conducted on GaN MESFET based device

a cut-off frequency of 900 MHz and an output power of 51 W with 78 % power added

efficiency was shown [21]. In another GaN MESFET device 10W output power with a

power added efficiency (PAE) of 34% at = 48V and a cut off frequency of 700 MHz

and maximum frequency of 1.8 GHz was achieved [22]. A 0.8µm x 150µm GaN

MESFET has been reported with a cut off frequency of 6.5 GHz and a maximum

frequency of 14GHz. These are in lateral agreement with their measured values

of 6 and 14 GHz using a technique called Volterra-series technique [23], where the 1-dB

compression point and output-referred third-order intercept points are 16.3dBm and

22.2dBm, respectively. In this case a constant channel temperature of 300K is assumed

whereas some other researchers have achieved cut off frequency ) of 20 GHz and a

maximum frequency of 50 GHz [24]. Hence the above measurements show the

high frequency performance of GaN material which was discussed at the beginning.

In a research, GaN MESFET based device showed a performance of 2GHz cutoff

frequency with power density of 2.2 W/mm and had an associated power added

efficiency of 27% at [25]. In another research, the threshold

voltage for a GaN MESFET was found to be in a range of 4 V to 20 V with maximum

drain current which went up to 300 mA/mm and transconductance values of up to 60

mS/mm. This was measured for a device with 100 µm gate length which created potential

performance for high frequency applications [26].

In a research conducted on a DC and microwave performances of GaN MESFET

using ICP-RIE, a small signal RF performance was measured using a network analyzer

from 1GHz to 35 GHz at VDS =20 v and VGS=-0.5 v. The cut-off frequency was measured

5

as 28 GHz and the maximum frequency was measured as 55 GHz [27].

For a non-surface-depleted GaN MESFET, it has been found that the maximum

trans-conductance ) was 244 mS/mm and the maximum cut-off frequency 230 GHz,

with a maximum output power of 2.66 W/mm [28]. In a GaN based MESFET device

research, cutoff frequency ( was measured to be 6.35 GHz and maximum frequency

( was found to be 10.25 GHz in a 0.1 µm gate-length zinc blende crystal structure

[29]. In this case GaN MESFET showed a maximum cut-off frequency of 220 GHz and

trans-conductance of 210 mS/mm [30].

In a GaN MESFET research the output power of 230W and a cut-off frequency

( ) of 30 GHz for a gate length of 0.25 µm was found [31]. With a drain current of 500

mA at = 40 V and = 0 V GaN MESFET device was fabricated and this device

resulted in a cut-off frequency of 8 GHz, trans-conductance ) of 93mS/mm and an

output power of 4W/mm with a power added efficiency of 50% and a gain 20dBm. These

results were better than SiC MESFET simulation by the same researcher [32]. During

another research a GaN MESFET device was fabricated with = 15.6 GHz and =

7.2 GHz, transconductance of 164 mS/mm with a PAE of 38% at = 3.5V [33].

Gallium Nitride (GaN) has been fabricated on HEMTs. A research was conducted

for a Sapphire GaN/AlGaN based HEMT devices which had a 1 nm aluminum nitride

(AlN) interlayer at a room temperature and a mobility of 1780 . An electron sheet

carrier density of which exhibited a power density of 4.9 W/mm, a

linear gain of 14 dB and a PAE beyond 32 % are obtained at 10 GHz with a gate width of

1 mm were accomplished [34]. A research on GaN HEMT device with Silicon Carbide

(SiC) as a substrate, a maximum power added efficiency greater than 56% while

6

maintaining output power of 205 Watts with a cutoff frequency of 1.2 GHz and

maximum frequency of 1.4 GHz was found[35]. A research was carried out on a AlGaN

mole fraction HEMT structure on Semi-insulating SiC substrates. This resulted in an

output power of 103 W with a high power density of 5.2 W/mm and power added

efficiency (PAE) of 35.3% [36]. A research on AlGaN/GaN power HEMT in sapphire

substrate showed an output power density of 1.1W/mm with PAE of 20.1%. A cutoff

frequency ( ) of 36 GHz and maximum frequency ( ) of 70 GHz was achieved. In

this case, gate-to-drain breakdown voltage up to 230V and channel current greater than

300 was obtained [37]. Some researchers have obtained the transconductance of

68mS/mm with maximum frequency of approximately 31 GHz and a cutoff frequency of

1.8 GHz with an RF power of 84 mW/mm. In this case maximum drain to source current

density was approximately 174 mA/mm for a 1400 mm wide gate AlGaN/GaN HEMT

with = -1.1V and = 6V [38-39].

7

Chapter 2 Overview of GaN Material

2.1 Gallium Nitride properties:

Nitrides have magnificent physical properties that make them particularly

attractive towards solid state devices. The wide band-gap materials have low dielectric

constants with a high thermal conductivity. Group III nitrides display decent

characteristics at high temperatures [40].

The extensive band quality could perhaps repress disengagement development

and enhance unwavering quality in examination to other II-VI and III-V materials.

Moreover the nitrides are impervious to chemical etching and ought to permit GaN-based

devices to be worked in bad situations [41]. These properties may prompt devices with

prevalent dependability. Gallium nitride (GaN) has great mobility yet is constrained by

low thermal conductivity and inaccessibility of GaN substrates. Correlation of Different

Wide Band Gap Materials is exhibited in Table 2.1.

Table 2.1 Properties of various materials [42]

8

2.2 Energy- Band Structure

2.2.1 Band structure of Zinc Blend GaN:

Figure 2.1 Energy band diagram for Zinc Blend GaN [43]

Figure 2.1 depicts the energy band diagram for gallium nitride with zinc blend as

crystal. Energy band gap (Eg) in the band structure shows that it has a value of 3.2 eV in

the -valley is measured through the conduction band minima and valence band maxima

at k (wave vector) = 0. The energy band gap in X-valley is defined as Ex and has a value

of 4.6 eV. L-valley has a band gap designated as EL comprising a value of 4.8 to 5.1 eV.

The value of Es0 is 0.02 eV and is called split-off band in the valence band.

9

2.2.2 Band structure of wurtzite GaN:

Figure 2.2 Energy band diagram of wurtzite GaN [44]

Above Figure 2.2 depicts the energy band diagram for gallium nitride with zinc

blend as crystal. The energy band-gap (Eg) with a value of 3.39 eV in the -valley is

measured through the conduction band minima and valence band maxima at k (wave

vector) = 0. The energy band gap in A-valley is defined as EA and has a value of 4.7-5.5

eV. L-valley has a band gap designated as EM-L comprising a value of 4.5 to 5.13 eV. The

value of Es0 0.08 eV and is called split-off band in the valence band.

10

2.2.3 Temperature dependence of band gap energy:

The temperature dependent energy band gap can be calculated with the help of

following equation [45],

(2.1)

Where, Eg is energy band gap at temperature T (in degrees kelvin) and Eg (0) is band gap

energy at K and has a value of 3.47 eV for wurtzite crystal and a value of 3.28 eV for

zinc blende GaN.

Temperature dependence energy band gap can also be calculated with the help of

Varshni expression [46] is given by,

(2.2)

Where, the value of energy band gap at 0 K is given as 3.427 eV.

2.2.4 Band gap energy Vs Temperature for Wurtzite structure of GaN

From above we know that the energy band gap of wurtzite GaN at 0 is 3.47

eV. Energy band gap for the temperatures below 295 K is expressed by the equation [47],

(2.3)

Where T is in kelvin and the value of band gap energy Eg, at 300K is calculated

to be 3.44 eV and Eg (T) temperature dependent excitation energy band gap. This can be

represented graphically in a Figure 2.3 as shown below.

11

Figure 2.3 Excitation energies vs Temperature plot [48]

Figure 2.3 plot shows that the temperature is low at high excitation energy. As the

temperature increases, the value of excitation energy decreases exponentially. It

decreases from 3.505 eV to 3.44 eV when temperature increases from 0 to 300K.

2.2.5 Band gap energy vs Temperature for Wurtzite GaN:

Figure 2.4 Band gap (eV) vs Temperature (K) plot [49]

12

Gallium Nitride samples by using different techniques were grown on different

substrates such as SiC, Si and sapphire [50]. From the Figure 2.4, it shows that band gap

energy for wurtzite GaN gradually decreases as the temperature is increased, which

means that band gap energy is inversely proportional to the temperature.

2.2.6 Band gap energy vs Temperature for zinc blende GaN on MgO substrate:

Zinc blende GaN film was grown on the magnesium oxide (MgO) substrate.

When the temperature of the substrate was increases the energy band gap decreases from

3.3 eV to 3.23 eV for a temperature range of 0 to 300K. This can be presented in the

Figure 2.5 below.

Figure 2.5 Temperature (T) vs Band gap (eV) plot [51]

2.2.7 Band gap energy vs temperature of zinc blende GaN with Si substrate:

When a zinc blende GaN films was grown on silicon (100) substrates, the dependencies

were extracted by using two different theoretical models from pseudo electric function.

13

Figure 2.6 Band energy vs Temperature plot for zinc blende GaN with Si as

substrate [52]

In the above Figure 2.6, the band gap energy is decreased with increase of the

temperature when GaN growth was made on the Si substrate.

2.3 Intrinsic carrier concentration

Intrinsic carrier concentration is the concentration of free carriers which are

created in the valence and conduction bands because of the thermal excitation of the

carriers in both conduction and valence band. It is designated as ni or Ni. It is defined as

the equal number of electrons in the conduction band and equal number of holes in the

valence band in intrinsic material [53]. Higher band gap materials have lower intrinsic

carrier concentration because the thermal excitation of carriers is difficult for the higher

band gap material such as GaN. Intrinsic carrier concentration plays an important role in

14

inheriting quality of GaN as wide band gap properties. Intrinsic carrier concentration can

be calculated with the help of following equation [54],

(2.4)

Where, Nc and Nv are effective density of states in conduction and valence band

respective, Eg is the band gap energy, T is the temperature in Kelvin and KB is Boltzmann

constant having a value constant value

The effective density of states in the conduction band (Nc) which can be expressed as,

For Zinc blende structure (

)

(2.5)

For Wurtzite structure (

)

(2.6)

is the effective density of states in the Valance band which can be valued by

below equation:

For Zinc blende structure

(2.7)

For Wurtzite structure

(2.8)

“Intrinsic carrier concentration depends on the temperature and can be evaluated

from the following plot.”

15

Figure 2.7 Intrinsic carrier concentration vs Temperature [55]

Figure 2.7 shows that the intrinsic concentration for both zinc blende and

wurtzite GaN reaches to the value of 10-9

cm-3

at room temperature and the intrinsic

carrier concentration linearly increases with high temperature. The intrinsic carrier

concentration of GaN at 850ok is approximately 10

10cm

-3, which is almost the same as

silicon at 300 K. Hence, the property of intrinsic carrier concentration shows that the

GaN is having more withstanding potentiality in high temperature environment compared

to silicon and GaAs [56]. Zinc Blende GaN structure has higher intrinsic carrier

concentration when compared to the wurtzite GaN.

2.4 GaN Crystal Structure

Generally Gallium Nitride (GaN) is crystalized by either zinc blende crystal or by

wurtzite structure. The modifications of GaN, AIN, InN by zinc blende or wurtzite are

identical but has some kind of significant differences [57].

16

Zinc blende and wurtzite are very closely related crystallographically in many

aspects. Because of the immediate and wide band gap these crystals cover the energy

spectrum range extending from infrared rays to ultraviolet rays. The semiconductor

materials of III-gathering nitride have been exceptionally appealing to the application of

high-power devices and light discharging devices of short-wavelength [58]. The Figure

2.8 shows the correlation between √ of lattice constant for zinc blende or lattice

constant a for wurtzite and band gap energy of InN, AlN, GaN and their related

compounds.

Figure 2.8 The correlation between lattice constant of zinc blende and wurtzite and

band energy gap for various materials and their related alloys [59]

Normally, the crystal structure of GaN and other related semiconductor materials,

including AlN, InN and ZnO is wurtzite (WZ) type of hexagon. These crystals possess

similar tetrahedral atomic coordination of nearest-neighbor with the structure of cubic

zinc blende (ZB) type. The stacking sequence of WZ structure is

AaBbAaBbAaBb…along the axis of [0001] and the stacking sequence of ZB structure

17

is AaBbCcAaBbCc…along the axis of [111], where Aa, Bb, Cc represent the three

types of cation and anion location in the lattice of triangle on the planes of (0001) and

(111). This is are demonstrated by Figure 2.9.

Figure 2.9 Structures of atoms for zinc blend (a), wurtzite (b), rocksalt (c) [60]

If stacking sequence is the factor which discriminates the structure of zinc blende

and the wurtzite then, c/a=1.633 will exist between wurtzite structure lattice constants.

18

The crystal lattice parameters of various materials can be shown in the table

below,

Table 2.2: Lattice constants and unit cell parameters for GaN, AIN, InN [61]

2.5 Various charge effects in GaN:

2.5.1 Piezoelectric effect on GaN:

Piezoelectric is created by combining epitaxial growth which is performed in the c

plane [0001] orientation of wurtzite crystal structure of GaN. The associated electrostatic

charge densities had influenced many properties namely electric field, carrier distribution

and some of the optical and electric properties of nitride materials and their devices [62].

Some results of positional dependence of the piezoelectric polarization, piezoelectric

charge distribution and conduction band potential profile for several possible

approximations are determined. In GaN quantum well (QW) hetero structures are

strongly affected by structural imperfections.

19

2.5.2 Polarization charge effect:

Gallium Nitride materials generally exist in the wurtzite phase because of

which it has strong polarization properties in C-direction. The ball and stick model of

GaN in the basal plane and the associated polarization in the crystal and these

polarizations charges occur on each unit cell when it is in a classical mode. The

summation of internal polarization is null in the crystal after leaving a charge of ± at

each end of the crystal forms a dipole [63]. The screening dipole which is the result of

placing equal and opposite charges at or close to the charges of polarization dipole is

created because of the unscreened dipole, which creates a non-sustainable dipole

moment.

In Gallium Nitride (GaN) the polarization charge density ( ) leads

to an electric field , which is expressed by the following equation [64],

=

1.6 MV/cm (2.9)

Where,

is the polarization charge density,

is the electric field,

is charge

This dipole charge results in a voltage across the material in a crystal of thickness

d = 1 , and this voltage is given by the equation [65],

= .d=160V (2.10)

Where,

is the voltage,

20

is the electric field,

d is the thickness of crystal

This brings up the issue how the charges that form a screening dipole. They could

emerge from counter particles which is present in the atmosphere. This is most likely the

case for mass polar materials utilized as a part of ceramic industry [66]. This is not likely

the situation for epitaxial GaN thin films, since these films can be made in an

environment free of counter particles, for example in a MBE reactor. This creates inquiry

of whether screening of counter particles is conceivable without outside counter particles.

The accompanying examination addresses this issue [67].

Considering, a lightly doped n-type GaN sample in the initial stages of growth.

GaN is hetero-epitaxially grown on sapphire, Si or SiC substrates rather the GaN

substrate due to its lack in availability. The material at the substrate and thin film

interface is highly defective and therefore capable of trapping mobile charges. The effect

of the background n-type doping on the electric field profile within the material is

assumed to be negligible when compared to the electric field generated by the

polarization charges [68]. The effects of surface states on the electrical properties of the

material can be ignored. Both of these effects will be considered later.

In the absence of surface states, as the material becomes thicker the electric field

in the material (given by the slope of the conduction and valence band) will remain

constant until the valence band crosses the Fermi level. The thickness of the film ( at

which this occurs is given by [69].

(2.11)

21

Where, = 3.4 eV is the bandgap of GaN. Once d > , holes begin to

accumulate at the surface (created by generating across the gap), leading to an equal

electron concentration which drifts to the substrate-epi interface (the GaN N-face),

creating a screening dipole. The magnitude of the screening charge increases

continuously with epitaxial layer thickness. The evolution of the screening charge with

distance is obtained by recognizing that the maximum voltage across the structure is the

band gap of the material [70],

| | (

) d (2.12)

=

(2.13)

As d , , or in other words for very thick samples the polarization

dipole is fully screened.

2.6 Drift velocity versus electric field:

Drift velocity in semiconductors is the velocity of the charge carriers under the

influence of electric field. In Figure 2.10 we can see the relationship between the drift

velocity and the electric field for zinc blende and wurtzite gallium Nitride structures.

22

Figure 2.10 Drift velocity vs electric field for GaN [71]

In the Figure 2.10, curve 1 shows how the drift velocity changes when the electric

field is applied for wurtzite structure which is applied in the direction (1010). Drift

velocity increases till certain point and the gradually decreases from 220 kV/cm for

wurtzite structure. Curve 2 shows how drift velocity behaves by increasing the electric

field along (100) direction in the zinc blende structure. Drift velocity increases when

electric field is increased and goes up to 2.6x107cms

-1 for 200 kV/cm of electric field and

then further increase in electric field decreases drift velocity gradually.

2.7 Growth process of GaN:

The hetero structures of GaN and AlGaN/GaN have epitaxially been grown on

different substrates like sapphire, spinel, 6H-SiC, 2H-SiC, Si, and recently on a bulk AlN

and GaN [72]. The Metal- Organic Vapor Phase Epitaxy is a typical technique of GaN

growth. The epitaxial layers are deposited using low pressure MOCVD over basal plane

sapphire substrates in most GaN based devices. Triethylgalium, triethylaluminum and

ammonia as the precursors for ‘Ga’, ‘Al’ and ‘N’ are used for a typical MOCVD growth.

23

The APA Optics group reports a typical growth pressure and temperature of 76 torr and

1000 oC. The two metal organics have a typical flow in the range of 1 to 10 and 1.5 to 0.6

moles/min, respectively. The deposited GaN layers are highly resistive with a carrier

density well below 1015

cm-3

. Using silicon (Si) as the dopant, the insulating GaN layers

can be doped n-type. The quality of the epitaxial GaN depends on the quality of the

substrates and this is shown by the studies of transport properties. All this implies a

considerable interest in the development of bulk GaN crystals for homo epitaxy. In

Warsaw, (Poland) under the direction of Professor Sylvester Porowski, a pioneering

effort in high-pressure bulk growth of GaN is underway. A square centimeter or little

more is typical crystal size. These epitaxial layers have no interface detected and with the

dislocation density below the detection limit and making them an excellent quality.

Figure 2.11 shows the principle involved in MOCVD-process.

Figure 2.11 Principle of MOVCD process [73]

Lateral Epitaxial Overgrowth (LEO) is recently gaining high attention. This

allows production of GaN films with the density of up to 4 orders of magnitude smaller

than for GaN films grown on sapphire and 6H-SiC substrates. The studies of threading

24

dislocations in GaN films have been investigated in the LEO-grown GaN films. There is

a dramatic drop in the leakage current in GaN-based p-n junctions and GaN/AlGaN

hetero-junction field-effect transistors grown by LEO as a result of the dislocation

density. Molecular Beam Epitaxy (MBE) is one other technique of the epitaxial growth of

GaN. GaN layers grown by MBE are similar in quality to the layers grown by MOCVD

[74]. Thick layers of GaN are important for potential applications of GaN-based materials

in power devices and are yielded by HVPE. HVPE technique was used recently for the

epitaxial growth of AlN/AlGaN/GaN hetero structures on SiC substrates. The fabrication

of quantum dots is one interesting emerging direction in the epitaxial growth of GaN,

AlN, and InN materials. Having electron density higher than 1019

cm-3

, 54 N-type GaN

can be obtained. The highest reported hole concentration in p-GaN was around 1018

cm-3

(using Mg as an acceptor) causing p-doping to remain a serious problem. The ionization

energy of this acceptor is quite high (160 meV) so that less than 1% of Mg acceptor is

activated at room temperature is the reason for this behavior [75].

2.8 Why SiC, Si and sapphire are used for GaN?

Gallium Nitride can be manufactured on lot of substrates such as Si, SiC, AIN,

MgO and various others. Before choosing a substrate there are a lot of criteria to go

through such as lattice coincidence, lattice matching, thermal expansion coefficient

(TEC), surface chemistry, temperature stability, conductivity, cleavability, availability,

price. The first MBE developed GaN LED on Si in 1998 which showed that silicon can

be considered as a substrate material for GaN development. A seed layer or buffer layer

to accommodate the lattice mismatch between the substrate and the epi-layer is used for

the GaN growth on sapphire, SiC or Si. The 6H–SiC, 4H–SiC and 3C–SiC substrates for

25

GaN growth has the effect of surface pre-treatment by exposure. This work proposed a

possibility that p-type doping was achievable in GaN on Si and mechanisms could be

found out. In recent years researches have been carried out around there and even from an

optimistic GaN layers on Si are very nearly similar to GaN layers on SiC.

The deposited GaN film was found to be polycrystalline, after the nitration of

Silicon carbide. The development of the seed layer will bring about non-stoichiometric

synthesis at flat temperatures and additionally processes a heightened thickness of defects

in the structure, along these variations. This also brings down the restraint between

Silicon/AlN interfaces. The least resistance utilizing a flat level temperature has been

indicated in LEDs of GaN on Silicon [76].

2.9 Growth defects and process induced defects of GaN:

There could be many defects associated to GaN grown in different substrate.

Most common defects are mismatch of lattice constant, thermal expansion coefficient and

dislocation. There are many other defects such as inversion domain, stacking mismatch

boundaries, micro pipes or nanopipes or voids and surface pits. These defects will cause

the periodicity of the crystal to be dislocated over distances of several atomic diameters.

This will affect the electronic and optoelectronic properties of the device. Dislocation

defects cause rapid recombination of holes with electrons without conversion of their

available energy into photons. This causes heating up of the crystal and making electronic

and optoelectronic devices malfunction [77].

2.9.1 Native Point Defects:

The native defects inside the materials will affect the optical properties and

26

electrical properties of these materials. These defects also cause annealing in the

materials. Vacancies, interstitials, and anti-sites are the different forms these defects can

take. The interaction of isolated native defects causes the formation of complex defects.

Figure 2.12 shows the energy formation at the different levels of the formation energy

(eV).

Figure 2.12 Formations of Energies at Fermi Level for Native Point Defects [78]

2.9.2 Interstitials and Antisites Defects:

The minor cross section consistent in GaN and the expansive size between Ga and

N molecules cause imperfections regularly. Under certain conditions some of the

imperfections might shape yet in extremely little focuses on the other hand. Development

of energies of the Ga interstitial (GaI) and huge cross section relaxations are expedited by

the imposing size of the Ga particles. Large portability of GaN even at room temperature

27

intimates that GaN is trapped by some different deformities and does not exist in GaN as

a confined negative aspect in equilibrium.

28

Chapter 3 Ion Implantation

3.1 Ion Implantation

Ion implantation is a process in which a gas is ionized, and then ions are accelerated

by high electric field. These ions are injected into the target wafer to hundreds of nano

meter in depth [79]. The idea of ion implantation was first proposed by Shockley in the

year 1954, but this process came into mass production only after 1970. Prior to ion

implantation, doping was achieved by diffusion into the bulk silicon from gaseous source

above surface, or pre-deposited chemical source on wafer surface. This diffusion

approach lacked the flexibility and control required. Hence ion implantation process

gained popularity as it had introduced the dopant atoms. With the help of particle

accelerator technology, modern ion implanters have been developed. Their energy spans

100eV to several MeV. Ions are injected few nm’s to several microns in depth range,

where implantation is always followed by thermal activation at 600-1100 . Some of the

typical ion implantation parameters are as follows,

o Ion: P, As, Sb, B, ln, O

o Dose: 1011

-1018

cm-2

o Ion Energy: 1- 400 KeV

o Uniformity and reproducibility: +-1%

o Temperature: room temperature

o Ion flux: 1012

-1014

cm-2

s-1

Ion implantation has very precise dose control. The ion implanter forms a simple

electric circuit. Significant accuracy in the implanted dose can be maintained by

monitoring the current in the circuit. By assuming a current sensitivity of nA, and

minimum required implantation time of 10 seconds doses as low as 1011

cm-2

can be

29

measured. This process is done in high vacuum and hence it’s a very clean process

step. In ion implantation beside the dose control, peak depth and spread range can

also be controlled which is way better then diffusion process.

Figure 3.1 (a) Doping by diffusion, (b) Doping by ion implantation

Figure 3.1 shows comparative doping process by diffusion (top) and doping by ion

implantation (bottom) and it shows how precisely doping is done in ion implantation.

Some of advantages of ion implantation are,

o It is a low temperature process,

o wide selection of masking materials,

o less sensitive to surface cleaning procedures,

o Very fast and complex profiles can be achieved by multi-energy implants.

30

3.1.1 Ion implantation equipment:

Figure 3.2 Schematic of medium current ion implanter [80]

Figure 3.2 shows a simplified schematic that demonstrates the significant components

of medium-current ion implanter. The ion source begins with a proper molecular species

and converts into ions. Ions are accelerated and afterwards enter the mass analyzer for ion

determination. The analyzer is usually sensitive enough to differentiate the adjacent mass

numbers and the exit beam of desired implant ions is selected depending on the charge to

mass ratio of the ions. Ions goes through a final acceleration because of which ion beam

will be marginally electrostatically deflected so as to separate it from the neutral atoms

that have formed. By using electrostatically, mechanically or combination of both the

beam is scanned all over the wafer surface. Moreover, an electron source may be close to

the wafer to surge the surface with the electrons and from preventing a charge build up on

insulating surfaces such as Silicon oxide and silicon nitride. If this charge buildup is not

eliminated, it will be severe enough to cause gate oxide failure because of electrical

31

breakdown from gate to substrate through oxide. Some of the functions of various parts

of ion implanter are as follows:

1. Ion source: It usually operates at a subsequently high voltage (25 Kv) and

converts the electrically neutral dopant atoms in the gas phase into the plasma

ions and undesired species Sources such as arsine, phosphine, diborane can be

sputtered in ion sources.

2. Mass Spectrometer: In this, a magnet bends the ion beam into a right angle and

selects the desired impurity ion and removes undesired species. Ions which are

selected are passed through an aperture.

3. Accelerator: Adds energy to beam up to 5 MeV.

4. Scanning system: x-axis and y-axis deflection plated are used for scanning the

beam all over the wafer for the formation of uniform implantation of desired dose.

The beam is prevented in such a way that neutral particles are prevented from

hitting the target.

3.2 Impurity distribution equation:

Each ion in the ion implantation travels in some random path as it has to penetrate

the target. Hence, it loses its energy because of nuclear and electronic stoppage. The

doses used in implantation are generally higher than 1012

ions/cm3. Trajectories of the

ions can be predicted with the help of statistical means. By composing both lateral and

vertical motions the average total path length is determined which is called as range R.

The projected range Rp is the average depth of implanted ions. By using Gaussian

32

distribution of implanted ions, the depth can be approximated with standard deviation p

(or Rp). The ion concentration N(x), at depth x is given by the expression [81],

(3.1)

Where,

Np is the peak concentration,

Rp is projected range

p is standard deviation

If the total implanted dose is , by integrating the above equation we get the

expression for peak concentration Np which can be given as [82],

√ (3.2)

Generally, moments are considered to characterize the arbitrary distribution.

a) Dose, is considered as the zeroth moment.

b) The projected range Rp is considered as the normalized first moment.

c) The second moment is the standard deviation p.

d) The third moment is considered to be skewness , which is a measure of

asymmetry of the distribution. If the skewness is positive than the peak of the

distribution is placed closer to the surface other than projected range. Typically

the value of skewness is 0.

e) The last and fourth moment is kurtosis which is expressed by Kurtosis

indicates the top flatness of the distribution which is 3 for true Gaussian

distribution.

The above parameters can be illustrated schematically with the help of the figure below,

33

Figure 3.3 Schematic for the ion range [83]

In the Figure 3.1 i.e., (a) it is clear that the total path length R is longer than the

projected Rp. The bottom part (b) shows the stopped atom distribution is two-dimensional.

There are lots of different distributions which have been employed to give more

precise fit to moments of ion implantation which is possible using a Gaussian of which

the most important is Pearson IV fit. The fitted distributions for energies between 30 KeV

and 800 KeV is compared for experimental boron profiles under non channeling

conditions in the figure given as,

34

Figure 3.4 Boron implanted atom distribution [83]

Figure 3.4 shows that as the energy increases, the boron profiles become more

negatively skewed and hence deviate more significantly from a typical Gaussian.

Heavier ions such as arsenic have positive skewness for low energies which decrease

very slow but can be negative for some higher energy. Skewness nature can be elaborated

by increased electronic stoppage for faster moving ions.

3.3 Annealing:

Once the ion implantation is completed there are defects present on the wafer. A

process called annealing is necessary for restoring back the crystal lattice structure and to

activate implanted dopant ions electrically. Ions which has been doped must be placed on

their regular substitutional lattice sites. In old traditions furnace annealing was used for

annealing at a temperature of 600 and upwards for few minutes to hours. After

completing furnace annealing at 600 , it can leave some of the defects on the surface

which needs a another higher temperature for annealing [84].

35

Annealing process called rapid thermal annealing (RTA) has been applied more

recently in which arc and halogen lamps are used. This process is used for higher

temperatures greater than 1000 , for shorter anneal durations which is in seconds. Using

the same RTA equipment spike annealing is carried out which is applied to minimise the

diffusion. The dwell time is zero at maximum temperature for spike annealing which uses

rapid up and down rates.

Annealing processes are carried out in a heat balance regime where the

equilibrium between power deposited and lost power is maintained. This results in a

steady state heat balance throughout the wafer with a time scale equivalent to t>10-2

s.

Flash annealing is one of the type of annealing where a short pulse (10-6

<t<10-2

s) will

rapidly raise the temperature which comes out of a flash lamp known as thermal flux

regime. Pulsed layers are capable of producing a rapid heat of the surface layers with

times of 10-11

to 10-6

s which is known as adiabatic regime and effects the near surface

only. With the help of pulsed lasers it is possible to regrow the surface region by liquid

phase epitaxy or in the sub melt region by solid phase epitaxy.

Generally in the device production most common annealing is either spike or

rapid thermal annealing. But for shallower junctions different annealing methods such as

laser annealing comes into picture.

3.4 Fabrication process of MESFET:

There is a standard operating procedure followed for fabricating a MESFET. Steps

involving the fabrication of MESFET are as follows [85]:

o Intially the wafer is inspected and cleaned.

o Gallium Nitride cap is deposited by process called reactive sputtering.

36

o Positive resist is used for the channel implantation.

o Deep etching of gallium nitride is done by alignment registration process.

o Stripping and ashing is done on oxygen plasma.

o Using a positive resist source and drain are implanted by resist patterning.

o Ion implantation for the device source and drain regions is done.

o Resist the stripping and ashing of O2 plasma.

o Using the rapid thermal annealing, ion implants should be annealed.

o Resist patterning for ohmic contact formations.

o Ethcing of gallium nitride for the formation of ohmic contacts.

o Depositing GaN metal for ohmic contacts to source and drain using d-beam

evaporation and patterning by using process called litoff technique.

o Thermal heating is done on ohmic contact.

o Schottky gate is formed by resisting the pattern of etched nitride.

o Etching for forming Schottky gate.

o Metal depostion for schottky gate formation using e-beam lift-off technique.

Basically, fabricating of GaN is done by four mask ,double ion implanatation which

can be seen in the figure below:

37

Figure 3.7 Steps involving MESFET fabrication [86]

38

Chapter 4 Physics of MESFET

4.1 MESFET:

MESFET is a shortened form for metal-semiconductor field effect transistor. It is

a unipolar device where the current conduction happens by flow of majority carriers

only. MESFET can be either n-type or a p-type. In an n-type MESFET current

conduction is due to flow of electrons, while in a p-type MESFET holes cause the current

conduction. MESFET comprises of a conducting channel through which the device

conducts electricity. This channel is positioned between source and drain contacts, as

illusttrated in Figure 4.1 below. The flow of free carriers, and consequently the current

through the channel is controlled by modifying the gate voltage. This results in the

thickness of the consumption layer underneath the metal contact. The Schottky barrier is

a potential enegy barrier for electrons formed st metal-semiconductor junction. Schottky

barriers have rectifying characteristics, suitable for use as a diode.

Figure 4.1: Schematic representation of Gallium Nitride MESFET [87]

39

4.2 Working of MESFET:

Figure 4.1 shows a MESFET which includes 3 terminals, called as gate, source

and drain. A semi-protecting GaN substrate is utilized underneath the conduction

channel. The n-doped area, which acts as a channel can be framed in two ways, by ion

implantation or by developing an epitaxial layer. As mentioned before ion implantation

includes ion dispersion in the slight n-doped layer, epitaxial growth is a methodology

where crystals are developed in a specific introduction over another crystal. [88]. If both

crystals are of the same material, the methodology is known as homoepitaxy, and if the

materials are different, it is known as heteroepitaxy. n+ doped area are embedded on both

sides of the n-doped channel and are termed source and drain. Metal contacts are then set

on top of the gate, source and drain forming three unique terminals for a MESFET. The

gate metal and n-doped material forms a Schottky barrier [89].

4.2.1 Types of MESFETS and its operations:

There are two types of MESFETs as explained beloe:

Enhancement MESFET:

In an n channel MEFET the device remains switched off and the channel region is

maturely covered by depletion region completely. This depletion region is narrowed so

that the channel region gets expanded. This facilitates the flow of carriers. A junction

between the channels is forward bias and gate is made by applying positive voltage to the

gate terminal. The device conducts with the increase in channel width allowing the

current to flow. [90].

40

Figure 4.2: E-MESFET [91]

Depletion MESFET:

In an n-channel depletion MESFET (as shown in Figure 4.3), the depletion width

is varied by varying voltage at the gate terminal. Applying a negative voltage at the gate-

to-source causes the depletion width to expand and make the channel width narrow,

obstructing the flow of carriers. As a result the junction between the gate and the drain

becomes reverse biased. If the depletion region is expanded such that it completely

blocks the channel, or pinches-off` the channel, the resistance of the channel from source

to drain becomes large, causing the MESFET to be turned off like a switch. Applying a

positive gate-to-source voltage minimizes depletion width and allows the channel size to

increase again turning the MESFET ON.

Figure 4.3: Depletion MESFET [92]

41

4.3 MESFET Characteristics:

4.3.1 I-V Characterisctics:

Current-Voltage characterisctic of MESFET is almost similar to that of MOSFET

and JFET. The ideal characteristics of a MESFET is shown in the below Figure 4.4:

Figure 4.4: Typical (I-V) characteristics of MESFET [93]

Figure 4.4 shows a typical drain current (Ids) with respect to drain source voltage

(Vds) characteristics. we realize that the drain current is additionally a capacity of gate-

source voltage (Vgs) so a singular curve. The Figure 4.4 shows the reliance of drain

current (Ids) in drain source voltage (Vds) for a specific quality of gate-source voltage

(Vgs). Above Figure 4.4 shows the I-V characteristics of an enhancement type MESFET.

In addition there is an alternate mode of operation in MESFET which is referred to as the

breakdown mode where extra drain source voltage is applied.

For operating a MESFET in a depletion mode a voltage has to be applied at the

gate terminal. By applying extra negative voltage at the increases depletion region and

the junction is reverse biased. The drain gets completely exhausted, in the event that

continue expanding the negative voltage at gate terminals Hence there is no flow of

42

current and leads to threshold voltage which can be defined as the voltage completely

deplete the fully doped channel layer [94]. Figure 4.4 shows that Id value decreases as the

gate source voltage decreases further increasing negative voltage on the gate terminal will

stop the channel completely. In this way it is clear that threshold voltage of the Figure 4.4

is near to the lowest Vgs curve.

4.3.2 Operating Regions in MESFET:

MESFET is operated in different regions, which can be illustrated as follows:

Linear Region: In the linear operating region the voltage Vds is expected to be very

small. Hence the current and voltage in this region behave in a linear fashion. Therefore

the drain current Ids is proportional to the drain source voltage Vds, when Vds is in a low

range [95].

Figure 4.5: I-V chadracteristics in a linear or active region [96]

43

Saturation Region: In the linear region, drain-source current Ids is directly proportional

to the source drain voltage Vds but after further increasing the voltage Vds there is not that

much change in the drain-source current Ids. Therefore a saturation drain current is

achieved when source-drain voltage equals the drain voltage(ie, Vds=Vd) . This depletes

the channel length resulting an increase in the drain current Id.

Figure 4.6: Drain-source current vs drain-source voltage in saturation region [97]

4.4 MESFET applications in various fields:

Various fabrication methods have been applied for fabricating MESFET for use in

different variety of semiconductor systems. Of this some of the main applications of

MESFET for numerous purposes such as:

o Military applications, where MESFET is applied in various secured

communicating equipment.

o As there is an increase in the telecom industry now a days MESFET is playing an

important role in manufacturing of low power RF amplifiers which is reducing the

manufacturing costs.

o In the high frequency applications for example RADAR and satellite

communication MESFET is an important electronic device.

44

o In the microwave links MESFET can be used as a power amplifier for the output

stages.

o It is also used as a power oscillator in some areas and had a wide application in

commercial optoelectronics. [98]

45

Chapter 5 Theory and Calculations

The cross-sectional view of gallium nitride MESFET is shown in Figure 5.1. For the

purpose of high temperature performance an offset gate structure is considered.

Figure 5.1: Gallium Nitride MESFET shown in a cross-sectional view [99]

5.1 I-V characteristics Of GaN MESFET:

The drain current equation can be calculated to be,

(

)

(

)

(5.1)

Where,

Ids = Drain-source current

Idss = Drain current at zero gate voltage

Vds = Drain-source voltage

Vth = Threshold voltage

46

Vgs = gate-source voltage

T = Temperature in kelvin

T0 = Room temperature which is 300k

The drain current at zero gate voltage can be defined by following equation,

[

[ ( )]]

(5.2)

Where,

ha = Depletion region width

Ifc = Full saturation current

Vp = Pinch-off voltage

Qa = Conducting channel charge

Nd = Donor concentration

Vbi = Built in voltage

Vgs = gate-source voltage

5.2 Trans-conductance of GaN MESFET:

The quality of a device is mainly determined by trans-conductance. The equation

of trans-conductance is given by following equation,

(

)

(

)

( ) (

) (5.3)

Where,

gm = trans-conductance

47

Ids = Drain-source current

Vgs = gate-source voltage

Vth = Threshold voltage

Vds = Drain-source voltage

5.3 Temperature dependence of GaN properties:

Gallium Nitride (GaN) properties such as band-gap energy, intrinsic carrier

concentration and permittivity can be calculated with help of equations (2.2), (2.4)

respectively for different temperatures and can be shown in Table 5.1

Table 5.1: GaN parameters at different temperature:

Temperature

(K)

Band-gap energy (Eg)

(eV)

Intrinsic carrier

concentration (ni) (cm-3) Permittivity ( )

300 3.348 7.657x10-10

7.9650x10-13

400 3.298 0.0261 8.0446x10-13

500 3.242 1000.634 8.1243x10-13

600 3.181 1.254x106 8.2039x10

-13

700 3.114 2.232x108 8.2836x10

-13

800 3.045 1.133x1010

8.3632x10-13

48

Chapter 6 Results and Discussion

A physics based analytical model of GaN based MESFET has been developed to

study the temperature effect on drain current and transconductance. The intrinsic carrier

concentration shows a value in the order of 1x10-9

cm-3

at 300K whereas the value of

silicon and GaAs materials show in the order of 1010

cm-3

and 106cm

-3. Hence, the GaN

based device shows no detrimental performance at the high temperature range of 800k -

900K. Hence the some electrical parameters such as I-V characteristics and

transconductance have been computed and the temperature effect on the device

performance has been established through the following results. The analytical model

incorporates the temperature dependence intrinsic carrier concentration, bandgap energy,

permittivity of GaN material and detailed properties are shown in Table 3.1.

6.1 Temperature versus current:

Figure 6.1 Variation of current with change in temperature

49

The Figure 6.1 shows a plot of drain current versus temperature for different gate-source

voltage of Vgs = 0V, -2V and -4V with constant drain-source voltage of Vds = 25V,

channel doping concentration of Nd = 7x1017

cm-3

, substrate doping of Na = 1x1015

cm-3

,

gate length of L = 0.25x10-4

cm, device width of Z = 100x10-4

cm and active channel

thickness of a = 0.25x10-4

cm. Different drain currents are found to be 1.98 A, 1.76 A and

1.52 A at 300K for the gate-source voltage Vgs = 0V, -2V and -4V, respectively. The

drain currents are observed to be exponentially dropped to the approximate value of 0.7

A, 0.86 A and 0.96 A, when the temperatures reaches tot 500K. Hence, the value of the

drain current does not change significantly due to the change of temperature from 300K

to 500K. This graph has been generated by using the Equation (5.1).

6.2 I-V characteristics:

Figure 6.2: Ids versus Vds plot by giving different gate source voltage Vgs

50

The Figure 6.2 presents a graph of drain current (Ids) versus drain-source voltage

(Vds) for different gate-source voltage of Vgs = 0V, -2V, and -4V with channel doping

concentration of Nd = 7x1017

cm-3

, substrate doping of Na = 1x1015

cm-3

, gate length of L

= 0.25x10-4

cm, device width of Z = 100x10-4

cm and active channel thickness of a =

0.25x10-4

cm. The drain currents of 1.5A for different Vgs clearly show linearity up to

Vds = 20V, whereas the non-linearity of average current range from 1.65A to 2.4A is

observed for the drain-source voltage range of 20V to 50V. Three currents for different

Vgs become saturated at 2.65A, 2.55A and 2.45A, when the drain-source voltage appears

to 100V. This plot has been generated using the Equation (5.1) to find the I-V

characteristics at 300K.

6.3 I-V characteristics for different active channel thickness (a):

Figure 6.3: Ids versus Vds plot for different active channel thickness.

51

The Figure 6.3 exhibits a graph of drain current (Ids) versus drain-source voltage

(Vds) for different active channel thickness of a = 0.2x10-4

cm, 0.25x10-4

cm, 0.3x10-4

with channel doping concentration of Nd = 7x1017

cm-3

, substrate doping of Na = 1x1015

cm-3

, gate length of L = 0.25x10-4

cm, device width of Z = 100x10-4

cm and constant gate

to source voltage of Vgs = 0 V. The drain currents clearly show the linearity, non-linearity

and saturation regimes. The plot shows that the maximum current is obtained for large

active thickness of 3x10-4

cm. The pinch-off voltage is found in the order of 35V, 25V

and 15V for the active channel thickness of 3x10-4

cm, 2.5x10-4

cm and 2x10-4

cm

respectively.

6.4 Transconductance by varying temperature:

Figure 6.4 Variation of Transconductance with Temperature:

52

The Figure 6.4 displays a plot of transconductance versus temperature for

different drain-source voltages of Vds = 50V and 100V with active channel thickness of a

= 0.25x10-4

cm and channel doping concentration of Nd = 7x1017

cm-3

, substrate doping

of Na = 1x1015

cm-3

, gate length of L = 0.25x10-4

cm, device width of Z = 100x10-4

cm and

constant gate to source voltage of Vgs = -2 V. The transconductance for both drain-source

voltages of Vds = 50V and 100V exponentially decreases with increasing the temperature

in the range of 300k to 500k. It is evident from the plot that the transconductance reduces

by the factor of 0.04S and 0.021S for Vds = 50V and 100V due to the increase of

temperature from 300 K to 500 K. The mobility degradation with temperature is main

responsible for the reduction of transconductance in high temperature. The reduction of

transconductance at high temperature primarily degrades the frequency response of GaN

MESFET devices.

53

Chapter 7 Conclusion

An analytical model of GaN MESFET has been developed to simulate the

temperature dependent drain current and transconductance. The drain current drops to

1A, 0.9 and 0.82 for gate-source voltage Vgs = 0V, -2V and -4V for a temperature

variation from 300 K to 500 K. The transconductance also falls with a factor of 0.04S and

o.021S for the temperature variation from 300 K to 500 K. All I-V characteristics clearly

show the linearity regime, non-linear regime and saturation regime to justify the validity

of the model. The computed results show that the drain current and transconductance

have very insignificant variation on the device performance. Hence, GaN MESFET

shows incredible thermal stability at extreme high temperatures. The scope of the

research shows tremendous potential for developing high temperature stable FET using

GaN material. This will be a very attractive arena for withstanding at high temperatures,

harsh environment suitable to military, aerospace and space exploration.

54

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66

APPENDIX A

Ids=Drain current

Idss=Drain current at zero gate voltage

Vds=Drain-source voltage

Vth=Threshold voltage

Vgs=gate-source voltage

T=Temperature in kelvin

T0=Room temperature which is 300k

(α)= constant

(γ) =constant

(λ) = constant

ha=Depletion region width

Ifc=Full saturation current

Qa=Conducting channel charge

Nd=Donor concentration

Vbi=Built in voltage

Vth=Threshold voltage

z=base width

Vp=pinch off voltage

67

q=electron charge

L=gain length

a=active layer depth

Rg=total resistance

Rs=Source series resistance

68

APPENDIX B

Matlab code for temperature versus current:

clear all;

clc;

close all;

Eg0 = 3.427;

na = 9.39*10^-4;

nb = 772;

K = 1.38*10^-23;

Nc0 = 4.3*10^14;

Nv0 = 8.9*10^15;

q = 1.602*10^-19;

Nd = 3*10^17;

Na = 1*10^15;

Es0 = 9*8.85*10^-14;

Xs = 10^-4;

Xv = 98*10^2;

a = 0.25*10^-4;

Vs = 2.8743*10^7;

z = 100*10^-4;

Rs = 160;

Vgs = 0;

Vds = 25;

alpha = 1.5858;

gamma = -0.0553;

Y=0.249;

To = 300;

Rg = 10;

L = 0.25*10^-4;

A = 14.7*10^2;

bn = 0.87;

W = 0.06;

T = 310:10:500;

for i = 1:20

Eg = Eg0 - (na*(T(i)^2)/(T(i) + nb));

Nc = Nc0*(T(i))^(3/2);

Es = Es0*(1 + Xs*(T(i) - To))

Vp = q*Nd*(a^2)/(2*Es)

69

Vsat = Vs-(Xv*T(i))

Nv = Nv0 *(T(i))^(3/2);

ni = ( Nc^(1/2)) *(Nv^(1/2)) *( exp((-q*Eg)/(2*K*T(i))))

A1 = (K*T(i))/q

A2 = log((Nd*Na)/(ni*ni))

Vbi = A1*A2

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds));

B = Vgs/(Vth + (gamma*Vds));

Ids(i) = Idss *(1 + (Y*Vds))*(To/T(i))^(3/2)*((1 - B)^2)*tanh(C);

end

plot(T,Ids*5,'r'), xlabel('temperature(k)'),ylabel('drain current(a\mm)'),title('Variation of

temperature with drain current ')

hold on

Vgs = -2

for i = 1:20

Eg = Eg0 - (na*(T(i)^2)/(T(i) + nb));

Nc = Nc0*(T(i))^(3/2);

Es = Es0*(1 + Xs*(T(i) - To))

Vp = q*Nd*(a^2)/(2*Es)

Vsat = Vs-(Xv*T(i))

70

Nv = Nv0 *(T(i))^(3/2);

ni = ( Nc^(1/2)) *(Nv^(1/2)) *( exp((-q*Eg)/(2*K*T(i))))

A1 = (K*T(i))/q

A2 = log((Nd*Na)/(ni*ni))

Vbi = A1*A2

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds));

B = Vgs/(Vth + (gamma*Vds));

Ids(i) = Idss *(1 + (Y*Vds))*(To/T(i))^(3/2)*((1 - B)^2)*tanh(C);

end

plot(T,Ids*5,'b'), xlabel('temperature(k)'),ylabel('drain current(a\mm)'),title('Variation of

temperature with drain current ')

hold on

Vgs = -4;

for i = 1:20

Eg = Eg0 - (na*(T(i)^2)/(T(i) + nb));

Nc = Nc0*(T(i))^(3/2);

Es = Es0*(1 + Xs*(T(i) - To))

Vp = q*Nd*(a^2)/(2*Es)

Vsat = Vs-(Xv*T(i))

71

Nv = Nv0 *(T(i))^(3/2);

ni = ( Nc^(1/2)) *(Nv^(1/2)) *( exp((-q*Eg)/(2*K*T(i))))

A1 = (K*T(i))/q

A2 = log((Nd*Na)/(ni*ni))

Vbi = A1*A2

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds));

B = Vgs/(Vth + (gamma*Vds));

Ids(i) = Idss *(1 + (Y*Vds))*(To/T(i))^(3/2)*((1 - B)^2)*tanh(C);

end

plot(T,Ids*5,'g'), xlabel('temperature(k)'),ylabel('drain current(A)'),title('Variation of

temperature with drain current ')

hleg=legend ('Vgs=0v','Vgs=-2v','Vgs=-4v');

grid on

72

Matlab code current versus voltage for different Vgs: clear all;

clc;

close all;

Eg0 = 3.427;

na = 9.39*10^-4;

nb = 772;

K = 1.38*10^-23;

Nc0 = 4.3*10^14;

Nv0 = 8.9*10^15;

q = 1.602*10^-19;

Nd = 7*10^17;

Na = 1*10^15;

Es0 = 9*8.85*10^-14;

Xs = 10^(-4);

Xv = 98*10^2;

a = 0.25*10^-4;

Vs = 2.8743*10^7;

z = 100*10^-4;

Rs = 160;

alpha = 1.5858;

gamma = -0.0553;

Y=0.249;

To = 300;

T=300;

Eg = Eg0 - (na*(T^2)/(T + nb));

Nc = Nc0*(T)^(3/2);

Es = Es0*(1 + Xs*(T - To));

Vp = q*Nd*(a^2)/(2*Es);

Vsat = Vs-(Xv*T);

Nv = Nv0 *(T)^(3/2);

ni = sqrt ( Nc *Nv * exp((-q*Eg)/2*K*T));

Vbi = (K*T/q)*(log(Nd/ni)-log(Nc/Nd));

Vth = Vbi - Vp;

Qa = Nd * sqrt ( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

73

ha = 2 + (Rs* Ifc/Vp);

Vgs = 0;

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

Vds = (0:1:100)

for i=10

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds(i)));

B = Vgs/(Vth + (gamma*Vds(i)));

Ids = Idss *(1 + (Y*Vds(i)))*(To/T)^(3/2)*((1 - B)^2)*tanh(C);

end

plot(Vds,Ids*5,'r'), xlabel('Drain to Source Voltage'),ylabel('Drain

Current'),title('Variation of temperature with drain current ')

hold on

Vgs = -2;

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

Vds = (0:1:100)

for i=10

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds(i)));

B = Vgs/(Vth + (gamma*Vds(i)));

Ids = Idss *(1 + (Y*Vds(i)))*(To/T)^(3/2)*((1 - B)^2)*tanh(C);

end

plot(Vds,Ids*5,'b'), xlabel('Drain to Source Voltage'),ylabel('Drain

Current'),title('Variation of temperature with drain current ')

hold on

Vgs = -4

;

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

74

Vds = (0:1:100)

for i=10

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds(i)));

B = Vgs/(Vth + (gamma*Vds(i)));

Ids = Idss *(1 + (Y*Vds(i)))*(To/T)^(3/2)*((1 - B)^2)*tanh(C);

end

plot(Vds,Ids*5,'g'), xlabel('Drain to Source Voltage'),ylabel('Drain Current (A)'),title('Ids

vs Vds characteristics ')

hleg=legend ('Vgs=0v','Vgs=-2v','Vgs=-4v');

grid on;

75

Matlab Code for current versus voltage for different active channel thickness:

clear all;

clc;

close all;

Eg0 = 3.427;

na = 9.39*10^-4;

nb = 772;

K = 1.38*10^-23;

Nc0 = 4.3*10^14;

Nv0 = 8.9*10^15;

q = 1.602*10^-19;

Nd = 7*10^17;

Na = 1*10^15;

Es0 = 9*8.85*10^-14;

Xs = 10^-4;

Xv = 98*10^2;

Vs = 2.8743*10^7;

z = 100*10^-4;

Rs = 160;

alpha = 1.5858;

gamma = -0.0553;

Y=0.249;

To = 300;

T=900;

Eg = Eg0 - (na*(T^2)/(T + nb))

Nc = Nc0*(T)^(3/2);

Es = Es0*(1 + Xs*(T - To))

a = 0.2*10^-4;

Vp = q*Nd*(a^2)/(2*Es);

Vsat = Vs-(Xv*T);

Nv = Nv0 *(T)^(3/2);

ni = sqrt( Nc *Nv * exp((-q*Eg)/2*K*T))

Vbi = (K*T/q)*(log(Nd/ni)-log(Nc/Nd));

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

76

ha = 2 + (Rs* Ifc/Vp);

Vgs = 0;

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

Vds = (0:1:100)

for i=10

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds(i)));

B = Vgs/(Vth + (gamma*Vds(i)));

Ids = Idss *(1 + (Y*Vds(i)))*(To/T)^(3/2)*((1 - B)^2)*tanh(C);

end

plot(Vds,Ids*5,'r'), xlabel('Drain to Source Voltage'),ylabel('Drain

Current'),title('Variation of temperature with drain current ')

hold on

a = 0.25*10^-4;

Vp = q*Nd*(a^2)/(2*Es);

Vsat = Vs-(Xv*T);

Nv = Nv0 *(T)^(3/2);

ni = sqrt( Nc *Nv * exp((-q*Eg)/2*K*T));

Vbi = (K*T/q)*(log(Nd/ni)-log(Nc/Nd));

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Vgs = 0;

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

Vds = (0:1:100)

for i=10

77

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds(i)));

B = Vgs/(Vth + (gamma*Vds(i)));

Ids = Idss *(1 + (Y*Vds(i)))*(To/T)^(3/2)*((1 - B)^2)*tanh(C);

end

plot(Vds,Ids*5,'b'), xlabel('Drain to Source Voltage'),ylabel('Drain

Current'),title('Variation of temperature with drain current ')

hold on

a = 0.3*10^-4;

Vp = q*Nd*(a^2)/(2*Es);

Vsat = Vs-(Xv*T);

Nv = Nv0 *(T)^(3/2);

ni = sqrt( Nc *Nv * exp((-q*Eg)/2*K*T));

Vbi = (K*T/q)*(log(Nd/ni)-log(Nc/Nd));

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Vgs = 0;

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

Vds = (0:1:100)

for i=10

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds(i)));

B = Vgs/(Vth + (gamma*Vds(i)));

Ids = Idss *(1 + (Y*Vds(i)))*(To/T)^(3/2)*((1 - B)^2)*tanh(C);

end

78

plot(Vds,Ids*5,'g'), xlabel('Drain to Source Voltage'),ylabel('Drain

Current'),title('Variation of temperature with drain current ')

hleg=legend ('a=0.2*10^-4','a=0.25*10^-4','a=0.3*10^-4')

grid on

79

Matlab code for transconductance versus temperature:

clear all;

clc;

close all;

Eg0 = 3.427;

na = 9.39*10^-4;

nb = 772;

K = 1.38*10^-23;

Nc0 = 4.3*10^14;

Nv0 = 8.9*10^15;

q = 1.602*10^-19;

Nd = 7*10^17;

Na = 1*10^15;

Es0 = 9*8.85*10^-14;

Xs = 10^-4;

Xv = 98*10^2;

a = 0.25*10^-4;

Vs = 2.8743*10^7;

z = 100*10^-4;

Rs = 160;

Vgs = -2;

alpha = 1.5858;

gamma = -0.0553;

Y=0.249;

To = 300;

Rg = 10;

L = 0.25*10^-4;

A = 14.7*10^2;

bn = 0.87;

W = 0.06;

T = 310:10:500;

for i = 1:20

Vds = 50;

Eg = Eg0 - (na*(T(i)^2)/(T(i) + nb));

Nc = Nc0*(T(i))^(3/2);

Es = Es0*(1 + Xs*(T(i) - To))

Vp = q*Nd*(a^2)/(2*Es)

Vsat = Vs-(Xv*T(i));

80

Nv = Nv0 *(T(i))^(3/2);

ni = sqrt( Nc *Nv * exp((-q*Eg)/2*K*T(i)));

Vbi = (K*T(i)/q)*(log(Nd/ni)-log(Nc/Nd));

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds));

B = Vgs/(Vth + (gamma*Vds));

Ids = Idss *(1 + (Y*Vds))*(To/T(i))^(3/2)*((1 - B)^2)*tanh(C);

D = (2*alpha*Vds)/(Vgs-Vth-(gamma*Vds));

E = Vgs-Vth-(gamma*Vds);

gm(i) = 2*Ids*(To/T(i))*((sinh(D-1))/(E*sinh(D)));

end

plot (T,gm,'r'), xlabel ('temperature (k)'), ylabel('Transconductance'), title('Variation of

temperature with drain current ')

hold on

for i = 1:20

Vds = 100;

Eg = Eg0 - (na*(T(i)^2)/(T(i) + nb));

Nc = Nc0*(T(i))^(3/2);

Es = Es0*(1 + Xs*(T(i) - To));

81

Vp = q*Nd*(a^2)/(2*Es);

Vsat = Vs-(Xv*T(i));

Nv = Nv0 *(T(i))^(3/2);

ni = sqrt( Nc *Nv * exp((-q*Eg)/2*K*T(i)));

Vbi = (K*T(i)/q)*(log(Nd/ni)-log(Nc/Nd));

Vth = Vbi - Vp;

Qa = Nd * sqrt( (2 *Es*Vp)/(q*Nd));

Ifc = q * z* Qa * Vsat;

ha = 2 + (Rs* Ifc/Vp);

Idss = (Ifc/2)*(ha - ((ha^2 - (4/Vp)*(Vp-(Vbi + Vgs)))^(1/2)));

C = (alpha*Vds)/(Vgs - Vth - (gamma*Vds));

B = Vgs/(Vth + (gamma*Vds));

Ids = Idss *(1 + (Y*Vds))*(To/T(i))^(3/2)*((1 - B)^2)*tanh(C);

D = (2*alpha*Vds)/(Vgs-Vth-(gamma*Vds));

E = Vgs-Vth-(gamma*Vds);

gm(i) = 2*Ids*(To/T(i))*((sinh(D-1))/(E*sinh(D)));

end

plot (T,gm,'b'), xlabel ('temperature (k)'),ylabel('Transconductance'),title('Variation of

temperature with trans-conductance ')

hleg=legend ('Vds=50v','Vds=100v')

grid on;