design and growth of aluminum nitride/gallium nitride high electron mobility field effect transistor

Lakehead University

Engineering 4969 YB Degree Project

Design and Growth of Aluminum

Nitride/Gallium Nitride High Electron

Mobility Field Effect Transistor

Presentation Date

April 4, 2013

Report Submission Date

March 29, 2013

Supervisor/Advisor

Dr. Dimiter Alexandrov

Group Members

Aleksandar Aleksandrov (# 0501660)

Joey Mercier (# 0502424)

Ericson Rede (# 0491931)

ENGI-4969-YB Electrical Engineering Dept. Lakehead University

- i -

Abstract

Design and Growth of Aluminum Nitride/Gallium Nitride High Electron Mobility

Field Effect Transistor

By: Aleksandar Aleksandrov, Joey Mercier, Ericson Rede

The use of transistors has evolved the way humans live their lives. The

advancements in technology enabled by this device far outreach its minimal physical

dimensions. The problem with some current technologies however, is the limit in

high-frequency operation predominantly at higher microwave frequencies. At

these very high frequencies, transistor behaviors are harder to predict and power

output is lacking, therefore the scarcity in newer technologies is potentially

foreboding. High Electron Mobility Transistors (or HEMTs) have great operating

characteristics at high frequencies, with GaN (Gallium Nitride) semiconductors

potentially leading the way due to their expected low costs (as compared to other

semiconductors with similar properties) and important material properties. This

report will focus on the design and growth of such a device with N-type Aluminum

Gallium Nitride, intrinsic Gallium Nitride (N-AlGaN/GaN), with an InGaN buffer

layer to form a double heterojunction high electron mobility field effect transistor.


- ii -

Table of Contents

Abstract ........................................................................................................................ i

Table of Figures ......................................................................................................... v

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

List of Equations ....................................................................................................... ix

List of Acronyms ........................................................................................................ x

1. Introduction ......................................................................................................... 1

1.1 Objective.......................................................................................................... 1

1.2 Description of Materials ................................................................................. 1

1.2.1 Gallium Nitride (GaN) ............................................................................. 2

1.2.2 Aluminum Nitride (AlN) .......................................................................... 2

1.2.3 Indium Nitride (InN) ................................................................................ 2

1.3 The High Electron Mobility Transistor (HEMT) ............................................ 3

1.3.1 Field Effect Transistors and HEMT characteristics ................................. 3

1.3.2 Heterojunctions and Basic Semiconductor Physics ................................. 6

1.3.3 Basis of Operation .................................................................................... 8

1.3.4 Physical Nature ...................................................................................... 14

1.4 Two-Dimensional Electron Gas (2DEG) ...................................................... 16

1.5 Application of HEMT Devices....................................................................... 19

1.6 Potential Economical and Societal Impacts.................................................. 20

2. Design of the HEMT ......................................................................................... 23

2.1 Electron Band Diagrams and Resulting Heterojunctions ............................... 23

2.2 Growth ............................................................................................................. 30

2.3 Doping and Metal Deposition.......................................................................... 31

2.4 Final Device Structure ..................................................................................... 34


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3. Theory of Experimental Measurements ......................................................... 36

3.1 Overview........................................................................................................ 36

3.2 Theory............................................................................................................ 36

3.2.1 Atomic Force Microscope ...................................................................... 36

3.2.2 X-Ray Diffraction .................................................................................. 38

3.2.3 Scanning Electron Microscope............................................................... 39

3.2.4 Hall-Effect .............................................................................................. 39

4. Experimental Results ........................................................................................ 42

4.1 AFM Measurements ...................................................................................... 42

4.1.1 Sample #1 (2012-11-22) ........................................................................... 42

4.1.2 Sample #2 (2012-12-12) ........................................................................... 42

4.1.3 Sample #3 (2012-12-19) ........................................................................... 43

4.1.4 Discussion .............................................................................................. 43

4.2 XRD Measurements ....................................................................................... 44

4.2.1 Discussion .............................................................................................. 44

4.3 SEM Measurements ....................................................................................... 46

4.3.1 Sample #1 (2012-11-22) ........................................................................... 46

4.3.2 Sample #2 (2012-12-12) ........................................................................... 48

4.3.3 Sample #3 (2012-12-19) ........................................................................... 49

4.3.4 Discussion ............................................................................................. 50

4.4 Hall-Effect Measurements ............................................................................. 51

4.4.1 Sample #1 (2012-11-22) ........................................................................... 51

4.4.2 Sample #2 (2012-12-12) ........................................................................... 52

4.4.3 Sample #3 (2012-12-19) ........................................................................... 53

4.4.4 Discussion .............................................................................................. 53

5. Conclusion and Future Work .......................................................................... 55

5.1 Future Work and Limitations ........................................................................ 55

5.2 Conclusion ..................................................................................................... 56


- iv -

6. References .......................................................................................................... 57

Appendix A Microwave Frequency Bands ...........................................................A

Appendix B Binary and Ternary Semiconductor Properties .......................... B.1

Appendix C Overview of Local Diffusion ..........................................................C.1

Appendix D Quantum Tunneling .......................................................................D.1


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Table of Figures

FIGURE 1: SIMPLE OVERVIEW OF DIFFUSION [2] ........................................................... 4

FIGURE 2: OUTPUT POWER DENSITY VS. FREQUENCY [3] ............................................. 5

FIGURE 3: THE MINIMUM NOISE FIGURE (NF,MIN) FOR GAAS AND GAN HEMTS AS A

FUNCTION OF FREQUENCY (WITH ID = 100 MA/MM, L = 150NM) [1] .................... 5

FIGURE 4: THE ANDERSON MODEL ............................................................................... 6

FIGURE 5: OVERVIEW OF A 2DEG AT THE HETEROINTERFACE [7] ................................ 9

FIGURE 6: ELECTRON MOBILITY IN THE 2DEG AND BULK OF MATERIALS [4] ............. 9

FIGURE 7: VOLTAGE (VDS) TO DRAIN CURRENT (IDS) RELATIONSHIP WITH DIFFERENT

GATE VOLTAGES (VGS) AND TWO VALUES OF DOPED LAYER THICKNESS (DD) (AL

CONCENTRATION IN ALGAN [IE: X] = 0.2) [7] ................................................. 10

FIGURE 8: VOLTAGE (VDS) TO DRAIN CURRENT (IDS) RELATIONSHIP WITH DIFFERENT

GATE VOLTAGES (VGS) AND TWO VALUES OF AL CONCENTRATION IN ALGAN

(IE: M = X) [7] ..................................................................................................... 11

FIGURE 9: VARIATION OF THE ELECTRONIC DENSITY OF THE 2DEG WITH ALUMIMUM

CONCENTRATION = 0.25, INTRINSIC LAYER THICKNESS OF 3NM AND DIFFERENT

DOPED LAYER THICKNESSES [8] ......................................................................... 12

FIGURE 10: TYPICAL VALUES OF TRANSCONDUCTANCE FOR HEMT DEVICES [4] ..... 13

FIGURE 11: PHYSICAL STRUCTURE OF THE HEMT DESIGNED .................................... 14

FIGURE 12: DISLOCATION DENSITY AS A FUNCTION OF LATTICE MISMATCH RELATIVE

TO GAN [1] ......................................................................................................... 15

FIGURE 13: CONDUCTION BAND EDGE VS. DEPTH AS A FUNCTION OF POLARIZATION 17

FIGURE 14: SPONTANEOUS AND PIEZOELECTRIC POLARIZATION VECTORS IN AL1-X

GAXN AND GAN [16] .......................................................................................... 17

FIGURE 15: NET POLARIZATION INDUCED CHARGES AT INTERFACES OF AL1-X GAXN

AND GAN [16] .................................................................................................... 18

FIGURE 16: BAND DIAGRAM FOR AL1-XGAXN/GAN HEMT AS BARRIER THICKNESS

GROWS [16] ......................................................................................................... 18

FIGURE 17: COST PROJECTION FOR VARIOUS TYPES OF GAN DEVICES [15] ............... 22

FIGURE 18: ANDERSON MODELS FOR GAN AND ALN ................................................ 23


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FIGURE 19: SHEET RESISTANCE OF ALXGA1XN/GAN HETEROSTRUCTURES AS A

FUNCTION OF ALUMINUM CONTENT X [1] ....................................................... 24

FIGURE 20: SHEET CARRIER CONCENTRATION IN ALXGA1XN/GAN

HETEROSTRUCTURES AS A FUNCTION OF ALUMINUM CONTENT X [1] ............. 25

FIGURE 21: ANDERSON MODEL OF ALGAN (DOPED) AND GAN (UNDOPED) ............... 26

FIGURE 22: BAND DIAGRAM OF THE N-ALGAN/GAN HETEROJUNCTION ................... 27

FIGURE 23: ANDERSON MODELS FOR GAN AND INGAN ............................................ 28

FIGURE 24: BAND DIAGRAM FOR THE GAN/INGAN HETEROJUNCTION ...................... 29

FIGURE 25: BAND DIAGRAM FOR THE N-ALGAN/GAN AND GAN/INGAN DOUBLE

HETEROJUNCTION ............................................................................................... 29

FIGURE 26: GENERAL OVERVIEW OF IDEAL EPITAXIAL GROWTH (NO MISMATCH OR

DEFECTS) [2] ....................................................................................................... 30

FIGURE 27: DIFFERENCES BETWEEN OHMIC AND SCHOTTKY CONTACTS [11] ............ 33

FIGURE 28: ENERGY BAND DIAGRAMS FOR (A) SCHOTTKY JUNCTION FOR N-TYPE SI,

(B) SCHOTTKY CONTACT WITH QUANTUM TUNNELING FOR N++AND (C) OHMIC

CONTACT FOR P+WITH METAL [9]........................................................................ 33

FIGURE 29: FINAL STRUCTURE OF THE HEMT (NOT TO SCALE) .................................. 35

FIGURE 30: AFM MEASUREMENTS FOR SAMPLE #1 ................................................... 42



FIGURE 33: XRD MEASUREMENTS FOR SAMPLE #1.................................................... 44



FIGURE 36: SEM SIDE VIEW OF SAMPLE #1 (X60K) ................................................... 46

FIGURE 37: SEM SIDE VIEW OF SAMPLE #1 (1) (X220K) ........................................... 46

FIGURE 38: SEM SIDE VIEW OF SAMPLE #1 (2) (X220K) ............................................ 46

FIGURE 39: SEM SIDE VIEW OF SAMPLE #1 (X250K) ................................................. 46

FIGURE 40: SEM SURFACE VIEW OF SAMPLE #1 (X60K) ............................................ 47

FIGURE 41: SEM SURFACE VIEW OF SAMPLE #1 (X110K) .......................................... 47

FIGURE 42: SEM SURFACE VIEW OF SAMPLE #1 (X400K) ......................................... 47



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FIGURE 45: SEM SIDE VIEW OF SAMPLE #2 (X130K) ................................................ 48






FIGURE 51: SEM SIDE VIEW OF SAMPLE #3 (X220K) ................................................ 49





FIGURE 56: CURRENT VS VOLTAGE AND CURRENT VS RESISTANCE PLOTS FOR SAMPLE

#1 ....................................................................................................................... 51

FIGURE 57: HALL EFFECT MEASUREMENT RESULTS FOR SAMPLE #1 ......................... 51


#2 ....................................................................................................................... 52



#3 ....................................................................................................................... 53


FIGURE 62: PRINCIPLE OF OPERATION OF AFM [24] .................................................. 37

FIGURE 63: XRD BEAM ON A CRYSTALLINE LATTICE [19]......................................... 38

FIGURE 64: HALL-EFFECT IN A SEMICONDUCTOR [18] ............................................... 40

FIGURE 65: ENERGY BAND STRUCTURE OF GAN [6] ................................................. B.1

FIGURE 66: ENERGY BAND STRUCTURE OF ALN [6] .................................................. B.2

FIGURE 67: ENERGY BAND STRUCTURE OF INN [6] ................................................... B.2

FIGURE 68: GENERAL OVERVIEW OF LOCAL DIFFUSION WITH SILICON [2] ............... C.1

FIGURE 69: OVERVIEW OF QUANTUM TUNNELING THROUGH A BARRIER [18] ..........D.1

FIGURE 70: EFFECT OF BARRIER WIDTH ON QUANTUM TUNNELING [18] ..................D.2


- viii -

List of Tables

TABLE 1: FREQUENCIES OF EXPERIMENTAL WIDE BANDGAP FETS [3] ........................ 4

TABLE 2: PROPERTIES OF SUBSTRATES USED FOR HEMT DEVICES [1] ...................... 15

TABLE 3: OHMIC CONTACT MATERIALS AND PROPERTIES OF OHMIC CONTACTS ON

GAN [1] .............................................................................................................. 34

TABLE 4: SUMMARY OF XRD RESULTS ...................................................................... 45

TABLE 5: SUMMARY OF HALL-EFFECT MEASUREMENTS ............................................ 54

TABLE 6: MICROWAVE FREQUENCY BANDS .................................................................A

TABLE 7: PROPERTIES OF MATERIALS AT 300K [6] (CALCULATIONS ACHIEVED WITH

FORMULAS FROM [1]) ......................................................................................... B.1

TABLE 8: DENSITY OF STATES IN CONDUCTION BAND AND DOPING CONCENTRATION

FOR SEMICONDUCTORS ...................................................................................... B.3

TABLE 9: ADDITIONAL INFORMATION ON VARIOUS MATERIAL INTERFACES [1] ....... B.3


- ix -

List of Equations

(1.1) NOISE FIGURE ....................................................................................................... 6

(1.2) ELECTRON EFFECTIVE MASS ................................................................................ 8

(1.3) ELECTRON ENERGY AS A FUNCTION OF PROPAGATION VECTOR ........................... 8

(1.4) TRANSCONDUCTANCE OF A TRANSISTOR ............................................................ 13

(1.5) SHEET DENSITY OF POLARIZATION INDUCED CHARGES ..................................... 17

(1.6) MAGNITUDE OF ELECTRIC FIELD AT ALGAN/GAN INTERFACE .......................... 18

(1.7) GAUSS' LAW ....................................................................................................... 19

(2.1) BANDGAP DISCONTINUITY APPROXIMATION FOR BINARY COMPOUNDS ............ 23

(2.2) INTERPOLATION OF ALXGA1-XN CONDUCTION BAND ENERGY ........................... 24

(2.3) QUADRATIC INTERPOLATION OF ALXGA1-XN BANDGAP ENERGY ...................... 25

(2.4) ALXGA1-XN/GAN CONDUCTION BAND DISCONTINUITY APPROXIMATION .......... 26

(2.5) ALXGA1-XN/GAN VALENCE BAND DISCONTINUITY APPROXIMATION ................ 26

(2.6) INTERPOLATION OF INXGA1-XN CONDUCTION BAND ENERGY ............................ 28

(2.7) QUADRATIC INTERPOLATION OF INXGA1-XN BANDGAP ENERGY ........................ 28

(2.8) INXGA1-XN/GAN CONDUCTION BAND DISCONTINUITY APPROXIMATION ........... 28

(2.9) INXGA1-XN/GAN VALENCE BAND DISCONTINUITY APPROXIMATION ................. 28

(2.10) DONOR IMPURITY DOPING CONCENTRATION APPROXIMATION FOR ALXGA1-XN

........................................................................................................................... 32

(2.11) INTERPOLATION OF ALXGA1-XN DENSITY OF STATES ....................................... 32

(2.12) GAN DENSITY OF STATES ................................................................................ 32

(2.13) ALN DENSITY OF STATES ................................................................................. 32

(3.1) BRAGG'S LAW ..................................................................................................... 38

(3.2) LORENTZ FORCE EQUATION ............................................................................... 39

(3.3) HALL COEFFICIENTS IN SEMICONDUCTORS ......................................................... 40


- x -

List of Acronyms

2DEG

3DEG

AFM

Al

AlGaN (or )

AlN

CMOS

ELO

eV

FET

GaAs

GaN

HEMT

InGaN (or )

JFET

MBE

MESFET

MOCVD

MOSFET

SEM

Si

SiC

SiO2

UV

XRD

Two-Dimensional Electron Gas

Three-Dimensional Electron Gas

Atomic Force Microscope

Aluminum

Aluminum Gallium Nitride

Aluminum Nitride

Complementary Metal Oxide Semiconductor

Epitaxial Lateral Overgrowth

Electron Volts

Field Effect Transistor

Gallium Arsenide

Gallium Nitride

High Electron Mobility Transistor

Indium Gallium Nitride

Junction Field Effect Transistor

Molecular Beam Epitaxy

Metal Semiconductor Field Effect Transistor

Metal-Organic Chemical Vapor Deposition

Metal Oxide Semiconductor Field Effect

Transistor

Scanning Electron Microscope

Silicon

Silicon Carbide

Silicon Dioxide

Ultraviolet Light

X-ray diffraction


[This page was left blank intentionally.]


Introduction 1

1. Introduction

1.1 Objective

The objective of this project is to design and grow a high electron mobility field

effect transistor using different types of nitride semiconductors. The HEMT is to be

designed primarily with different gallium nitride compounds such as gallium nitride

itself, aluminum nitride (or aluminum gallium nitride), and indium gallium nitride.

All of the aforementioned semiconductors are to be grown together to form a high

electron mobility transistor. This introductory section of the report will deal with a

description of the materials used (physical and quantum) and provide an introduction

into the mechanisms of operation behind the HEMT (most notably the two

dimensional electron gas). It will also cover possible economical and societal

impacts of the HEMTs using nitride semiconductors.

The second section of the report will deal with the design of the HEMT, and how it is

grown and doped. This section will provide insight into the double heterojunction

structure, along with the equations for doping and will explain the reasoning behind

the chosen levels of impurities. This section will also briefly discuss growth

methods, with an emphasis on epitaxial growth.

The third and fourth sections will include the experimental results and the meaning

of those results respectively. They will describe the methodology used for the

experiment and provide information on the theory and testing process.

In the final section, a brief overview of future work will be explored, along with

conclusions obtained from doing this experiment.

1.2 Description of Materials

Crystal Structures for Electronic Applications, in the group III-N semiconductors,

can be found in three common crystal structures: Wurtzite, Zincblende, and Rock salt.


Introduction 2

At room temperature GaN, AlN, and InN are found in the wurtzite structure [1]. The

properties of the materials used in this report can found in Appendix B.

1.2.1 Gallium Nitride (GaN)

GaN band structure is currently thought to be a direct bandgap across the entire alloy

range, and its wide band gap of 3.4 eV allows the fabrication of high quantum

efficiency light emitters, high power and high frequency devices [21]. It has low

dielectric constants with high thermal conductivity pathways, and high melting

temperatures. Also, its resistance to chemical etching makes it suitable in harsh

environment operations. GaN is used in all device layers requiring fast carrier

transport with high breakdown voltage. It is incorporated in most ohmic contact

layers in any devices [1].

1.2.2 Aluminum Nitride (AlN)

AlN is the most important binary material in the III-N material family for electronic

applications, after GaN. It has high bandgap energy and high activation energy. Its

mass density is much smaller than in GaN or InN; thermal expansion and Vickers

hardness of AlN are relatively similar to those of GaN. AlN is an attractive substrate

material because its high thermal conductivity is better than that of any other

semiconductor apart from BN, SiC, and diamond. The low-field electron mobility of

AlN is found to be 135 cm2 V

1 s

1 at room temperature and at a doping

concentration of 1017cm3. The electron high-field transport in wurtzite yields a

very high critical field of 450 kV cm1, and the peak velocity in the bulk is found to

be 1.7 107 cm s1

at a doping concentration of 1 1017 cm3

. With a high-bandgap

energy of 6.2eV at room temperature, it possesses a great range to modify the value

of GaN to AlN on the bandgap of Al1-xGaxN [1].

1.2.3 Indium Nitride (InN)

InN and other compounds such as InxGa1xN and InxAl1xN so far are not

extensively used in electronic devices. A bulk electron mobility of 3,570 cm2 V

1 s

1

at 300 K, and 5,100cm2 V1

s1

at 300 K can be achieved. Also, an electron mobility


Introduction 3

of 1,200 cm2 V

1 s

1 and a sheet carrier concentration of 1.2 10

14 cm

2 have been

obtained at the interface InN/AlN. InxAl1xN/GaN is important, because the

polarization-induced charge is a much stronger function of the material composition

x than in the AlGaN/GaN material system [1].

1.3 The High Electron Mobility Transistor (HEMT)

GaN HEMTs are currently the most widespread and most advanced electronic nitride

devices. They make full use of heterostructures and the advantageous breakdown and

transport properties of undoped GaN [1]. Before explaining the operation of the

HEMT, the details and physics behind the operation of field effect transistors should

be known, as it will facilitate the understanding of this more exotic quantum

device.

1.3.1 Field Effect Transistors and HEMT characteristics

Field Effect Transistors (or FETs, for short), get their name from the effects that

occur when a field is applied to a certain semiconductor structure [2]. Earlier FETs

were of a homogeneous structure, meaning that such devices (such as MOSFETs,

JFETs, MESFETS, etc) where predominantly composed of one material. The

differences stemmed not from the selection of material (mostly Silicon), but rather in

the doping of this material. Doping is the term used to describe a process where

impurities are inserted into the lattice of the semiconductor (most commonly

interstitially, or in between the atoms of the lattice) typically by diffusion (see

below figure) or by ion implementation. As it can be seen from this figure, impurity

atoms move from an area of greater concentration (above the semiconductor lattice)

to an area of less concentration during diffusion (inside the semiconductor lattice).

The concentration gradient is the driving force of diffusion [2]. The longer this

process occurs, the more doped the semiconductor will become. If the atom

impurities are donors, the semiconductor is referred to as n-type, whereas acceptor

impurities produce a p-type semiconductor.


Introduction 4

Figure 1: Simple Overview of Diffusion [2]

In usual methodology, diffusion is performed on a single type of semiconductor,

usually leading to the creation of different p and n regions. This is the basis of

operation of most common solid-state devices (their exact operation will not be

discussed in this report). The issue with most common electronic devices, however,

is their behavior at higher microwave frequencies (see Appendix A for a list of

microwave frequencies). At these frequencies, the speed and output power of these

devices is usually suboptimal, and these shortcomings are what helped pave the way

for other forms transistors, such as HEMTs, utilizing promising materials with wide

band gaps and heterostructures [3]. The following table shows the cutoff frequencies

(fT) and the maximum frequency of oscillation (fmax) of different wide bandgap FETs

(with respect to gate length L):

FET Type L (m) fT (GHz) fmax (GHz)

SiC 0.45 22 50 SiC 0.5 13.2 42 AlGaN/GaN 0.05 110 140 AlGaN/GaN 0.12 101 155 AlGaN/GaN 0.25 50 100

*Latest year of data: 2001 Table 1: Frequencies of Experimental Wide Bandgap FETs [3]

Lattice Atoms

Impurity Atom

Legend

Diffusion


Introduction 5

It is obvious that high frequencies can be achieved using GaN/AlGaN HEMT

technology. Initial studies where performed mostly on GaAs and Si, but after nearly

30 years, these materials are approaching their theoretical limits [3]. The following

figure illustrates the power density of different types of HEMT devices with respect

to frequency, and it can easily be seen that AlGaN/GaN has by far the best power

density:

Figure 2: Output Power Density vs. Frequency [3]

And with all of these seemingly remarkable advantages, noise performance is still

relatively comparable to GaAs, as can be seen in the figure below [1]:

Figure 3: The Minimum Noise Figure (NF,min) for GaAs and GaN HEMTs as a Function of Frequency (with

ID = 100 mA/mm, L = 150nm) [1]


Introduction 6

Noise figure is the is the power ratio of the Signal to Noise Ratios (SNR) of the

output to that of the input, and can be mathematically expressed by referring to the

following equation:

(

) (1.1)

This proves that a lower noise figure is better, which is again quite advantageous

given the increase in power performance of the AlGaN/GaN HEMT. This, among

the other desirable characteristics mentioned (and surely other ones), has led the way

for research in nitride semiconductors, which was initially held back due to problems

with the mismatch between substrates and GaN (which lead to a significant amount

of defects in the growth phase ie: there was no ideal substrate) [4].

1.3.2 Heterojunctions and Basic Semiconductor Physics

The main idea behind the HEMT lies within its structure: unlike common devices,

HEMTs are built using different semiconductors (for the actual structure of the

HEMT designed, refer to section 1.3.4), which form heterojunctions at the interface

between these different materials. The device designed in this report has two

interfaces of different semiconductor material; therefore it is known as a double

heterojunction structure. Before getting into the effect of the heterojunction,

knowledge of the Anderson model for energy bands is needed. A typical Anderson

model (or the electron affinity model) is depicted in the figure below:

Figure 4: The Anderson Model

Evac

Ec

Ei

Ev

F

12

3


Introduction 7

In this figure, Evac stands for the vacuum energy level, which is used as the

reference level and has an energy of 0 eV. This level is of importance to lattice

structured crystalline materials because electrons above this value of energy are no

longer bound to the solid (they can move freely throughout space). This implies that

electrons below this level are bound to the atoms of the lattice. Ec stands for

conduction band (the energy level where electrons can move freely from atom to

atom), F stands for the Fermi level (the level at which there is a 50% probability of

electron presence, as guided by the Fermi-Dirac distribution function [3]), Ei for the

intrinsic Fermi level, and finally, Ev is for the valence band. The intrinsic Fermi

level is at the middle of the bandgap (usually known as Eg a gap where there are no

energy levels for elections/holes), which is in between Ec and Ev (denoted as 3 in

the figure). The level at which Ec is located is known as the electron affinity, which

is denoted by 1 in the figure. The work function is denoted as 2 in the figure,

and is the average amount of work required for an electron to get to the vacuum level

(it is the difference between Evac and F). When a semiconductor is intrinsic (or not

doped), the Fermi level F and Ei are the same. As a semiconductor becomes

extrinsic (or doped), the Fermi level deviates from Ei. If the Fermi level is above Ei,

then the semiconductor is known as an n-type material, and conversely, if F is below

Ei, the semiconductor is a p-type material. The Anderson model is revered for its

simplicity and for the amount of insight it gives into the mechanisms of rather

complex quantum behaviors such as heterojunctions, but unfortunately it is not the

most accurate method at predicting band offsets since it assumes idealities [3]. Other

methods such as energy band structures are much more accurate [2], but much more

complex and will not be overly discussed in this report. Refer to Appendix B for the

energy band structures of GaN, AlN, and InN respectively (there is no concise

structure for AlGaN or InGaN as of yet). The energy band gap used in the simplified

Anderson model can be taken from the energy band structure at the point where the

propagation vector, denoted k, (which implies quantum theory is used rather than

conventional theory; that is, the electron is treated as an electromagnetic wave rather

than a particle) is zero [2].


Introduction 8

The band structure also helps explain the change in electron effective mass. When

an electron moves through a crystal structure (such as a semiconductor), its change in

velocity can only be explained by a change in its effective mass, which is governed

by the following equation:

[

]

(1.2)

Where is Plancks constant, and it is multiplied by the inverse of the second

derivative of the energy band structure function E(k). It must be noted that the

effective mass is not linked with quantity of matter (which is itself constant and

unalterable), but rather, it is connected with the inertia of an electron (or how easily it

can move through a lattice) [2]. The above equation is only pertinent if used in

conjunction with the following equation:

(1.3)

Where v is the velocity. The above equation implies that at a certain energy level,

if the effective mass of an electron goes down, in order to keep the equation true, the

velocity of that electron must go up, which indicates that the electrons mobility goes

up as well [2]. This behavior is very important and is the reason behind the high-

speed operation of the HEMT, and will be discussed in greater detail later in the

report. The actual heterojunctions will be discussed in section 2 of this report.

1.3.3 Basis of Operation

The basis of operation of the HEMT will be briefly discussed; for more information

on the operation of the HEMT, refer to section 1.4 that deals with the in depth details

of the 2DEG. As mentioned previously, the driving force behind the HEMT is the

heterojunction. The figure below shows such a junction and shows the effect of such

an interface the creation of a two-dimensional electron gas (2DEG).


Introduction 9

Figure 5: Overview of a 2DEG at the Heterointerface [7]

The 2DEG is a triangular quantum well that prevents electron scattering such as in a

3DEG. The effect is increased mobility in two directions (which is why it was

named 2DEG). Additionally, the electrons are confined in the 2DEG in discrete

quantum states. This allows for much greater mobility of electrons as compared to

the bulk of a material [3]. The figure below compares typical values of electron

mobility through the bulk of a material and through the 2DEG:

Figure 6: Electron Mobility in the 2DEG and Bulk of Materials [4]

It is quite clear that there is an approximate four to fivefold increase in mobility in

the 2DEG. This is what allows for high-speed operation of the HEMT. The main

reason for this was introduced in the previous section with the concept of effective

mass for the electrons. Since when in the 2DEG, the electrons are confined to move

only in two directions, their movement through that channel is greatly streamlined,


Introduction 10

which has the effect of decreasing their effective mass. As mentioned above, there

are discrete energy states in the 2DEG, which implies that if an electron occupies

such a discrete energy state and its effective mass goes down (or is low), its velocity

(or corresponding mobility) must increase [2]. This generally explains the reasoning

behind the high electron mobility in the 2DEG as compared to the bulk of the

material (where the effective mass is higher), and the above figure substantiates this

claim.

The HEMT has a very similar connection scheme as regular field effect transistors

(eg: MOSFETs, MESFETs, etc), that is, it has a drain, a source, and a gate. The

former two are typically Schottky contacts, while the latter is typically an Ohmic

contact (more information on the contacts in section 2.3) [8]. Its operation is also

quite similar to that of other transistors as is its voltage to current relationship.

However, as with most common transistors, material composition and the layer

thickness in the structure of the device play a key role in these relationships. The

following two figures display the typical relationship between the current (IDS) and

the drain voltage (VDS) for given values of gate voltage (VG) in an AlGaN/GaN

HEMT with different doped-layer thickness (dd) and percent concentration x of Al

in (denoted m in the figure), respectively [7]:

Figure 7: Voltage (VDS) to Drain Current (IDS) Relationship with Different Gate Voltages (VGS) and Two

Values of Doped Layer Thickness (dd) (Al concentration in AlGaN [ie: x] = 0.2) [7]


Introduction 11

Figure 8: Voltage (VDS) to Drain Current (IDS) Relationship with Different Gate Voltages (VGS) and Two

Values of Al concentration in AlGaN (ie: m = x) [7]

From the first figure it is obvious that a thicker doped layer results in more drain

current. This is most likely attributed to the fact that the extrinsic layer contains

more free electrons, and the thicker it is, the more of these free electrons are in the

entire structure of the device, thus increasing current [7]. It can be seen in the second

figure that an change in m (previously named x), or Al composition in AlGaN,

has an effect on the drain current; that is, an increase in m induces an increase in

drain current with all else constant. This is due to the strong band discontinuity

caused by the higher concentration of Al, which in turn affects the 2DEG and the

concentrations contained therein, which ultimately leads to a greater current [7]. It

can be argued that the voltage-current characteristics of the HEMT are practically

identical to that of common FET devices; however, there is one major difference.

Whereas the drain current reaches saturation due to the pinch off of the channel in

FETs, in HEMTs, the drain current saturation is due to the saturation of the 2DEG

(no more holes/room for additional electrons), and there is never a pinch off of the

channel [2].

Again, it can be seen that the current voltage characteristics of the HEMT is similar

to other field effect transistors, however, unlike other devices such as MESFETs, the


Introduction 12

gate voltage in HEMTs has different effects on the device. The gate voltage in

HEMTs has the effect of altering carrier density in the 2DEG, whereas channel

height remains essentially the same [3]. As the gate voltage is increased in the

negative direction, the 2DEG becomes more and more depleted, until there are no

more free electrons in the heterostructure (this would be the cutoff voltage). When

the gate voltage is above this threshold value and a positive potential is applied from

the drain to source, the 2DEG electrons move from the source to the drain, and thus,

a current flows from drain to source [3]. As discussed above, the gate voltage alters

the carrier density in the 2DEG in the HEMT, which explains the variations with the

voltage and drain current with respect to different values of gate voltages, as shown

in the figures above. The following figure depicts the effect of gate voltage on the

2DEG.

Figure 9: Variation of the Electronic Density of the 2DEG with Alumimum Concentration = 0.25, Intrinsic

Layer Thickness of 3nm and Different Doped Layer Thicknesses [8]

It can be seen that the gate voltage has a significant effect on the electronic density of

the 2DEG, which explains why increasing the gate voltage has the effect of

increasing the drain current (if there are more electrons, more current will flow with

the same applied potential at the drain).


Introduction 13

As discussed above, GaN is a wide band semiconductor. This interesting material

property leads to high breakdown voltage, which means that GaN can sustain a high-

applied voltage, making it very useful for high-power, RF (and microwave)

operations [3].

Another very important characteristic of a transistor is its transconductance [2]. The

transconductance can be mathematically expressed with the following expression:

|

(1.4)

By inspecting the equation it can be seen that the transconductance is a ratio of

change in current to that of voltage, and is an important tool for circuit analysis [2].

A high transconductance generally means high current gain for small changes in

voltage. The figure below illustrates typical values of transconductance for HEMT

devices [4]:

Figure 10: Typical Values of Transconductance for HEMT Devices [4]

It can be seen that the HEMT shows very great and promising characteristics and is

therefore a very desirable device to be used at higher frequencies.


Introduction 14

1.3.4 Physical Nature

The HEMT designed in this report has five layers: a substrate (sapphire), InGaN,

GaN, and finally, AlGaN. The general physical structure is shown in the figure

below:

Figure 11: Physical Structure of the HEMT Designed

Substrates, often overlooked, are one of the most important parts of any device. A

substrate whose lattice that matches the semiconductor grown on to of it will greatly

improve device performance. If there is some mismatch between the two lattices,

there is a much greater probability of defects and imperfections during the growth

phase. Other important factors such as thermal conductivity, electrical isolation,

price, along with mechanical and chemical properties must all be considered when

selecting a substrate [1]. All these properties can in turn affect device performance.

To substantiate this claim, the following figure can be consulted, which gives an

overview of the relationship between lattice mismatch and dislocation densities:


Introduction 15

Figure 12: Dislocation Density as a Function of Lattice Mismatch Relative to GaN [1]

It can be seen from the above figure that the best options are GaN and ELO (epitaxial

regrowth techniques [stands for epitaxial lateral overgrowth] used to lower defect

concentration [1]) in terms of lattice mismatch and dislocation density. It can also be

seen that although sapphire has a much higher mismatch with GaN than SiC, their

dislocation densities are very similar. The following table summarizes all pertinent

properties mentioned above for various substrates:

Table 2: Properties of Substrates Used for HEMT Devices [1]

Therefore, one of the best substrates is silicon carbide, or SiC, due to its low

mismatch, very high thermal conductivity, and very good electrical isolation


Introduction 16

properties [1]. However, price must also be factored into the equation, which are

substantially high for SiC. Due to the advancements in technologies for growths and

such, sapphire is becoming a much more viable option to use as a substrate, and it

this is the main reason it was used.

The InGaN layer is included in the device in order to give the HEMT its first

heterojunction. This layer is known as a buffer layer, and the purpose of this first

interface between the two dissimilar semiconductors is to provide a form of energy

known as excitons [2]. This will be covered in greater detail in section 2.1.

Grown on top of the InGaN are the intrinsic GaN and extrinsic AlGaN layers, which

are the layers that serve the most important function in the HEMT, since they form

and house the 2DEG. The rationale behind using undoped GaN and doped AlGaN

will be discussed in section 2.3.

1.4 Two-Dimensional Electron Gas (2DEG)

This section is devoted entirely to the driving force behind the HEMT operation: the

2DEG. Electrons in the conduction band of molecules of a structure form a sort of a

gas, which can be known as a three-dimensional electron gas (or 3DEG). In this

case, the electron scattering is at a maximum as they can travel in any direction, with

their effective mass depending on the direction of travel [2]. In the 2DEG, the

electrons can only travel in two-directions, which greatly optimizes mobility and

corresponding velocity. The formation of this channel is therefore of great interest,

and will be explained herein.

While in most semiconductor carriers the 2DEG originates from the n-type dopants

within the barrier, the AlGaN/GaN materials built in polarization field is strong

enough to induce the formation of the 2DEG [1]. The polarization is both

spontaneous and piezoelectric: the spontaneous one is due to the fact that AlN, and

GaN bonds are highly ionic and each carry a strong dipole; the lattice constants a0

and c0 for GaN are slightly larger than those of AlN, and this results in a tensile

strained Al1-xGaxN layers grown in GaN, which causes piezoelectric polarization due


Introduction 17

to the deformation of the AlGaN layer [16]. The figure below shows a relationship

between the conduction band edge and the depth as a function of different types of

polarization:

Figure 13: Conduction Band Edge vs. Depth as a Function of Polarization

Since the total polarization in the Al1-xGaxN is larger, because of spontaneous

and piezoelectric polarization, as shown in the figure below, the overall result is a net

positive sheet charge at the Al1-xGaxN/GaN interface [1,16].

Figure 14: Spontaneous and piezoelectric polarization vectors in Al1-x GaxN and GaN [16]

The equation below shows the sheet density of the polarization-induced charges:

(1.5)

Where D1 and D2 are electric displacement vectors, and P1 and P2 are the

polarization vectors on either side on either side of the intersecting plane with normal


Introduction 18

vector n. The figure below shows the net polarization and the direction of the electric

field in the Al1-xGaxN layer:

Figure 15: Net polarization induced charges at interfaces of Al1-x GaxN and GaN [16]

The equation below represents the magnitude of the electric field [16]:

| |

| | (1.6)

The interface sheet charges formed in the heterojunction both, due to polarization

and not free charge carriers, and the induced electric field, allow the formation of the

2DEG. That is, an electron on the Al1-xGaxN surface increases its electronic potential

linearly with the Al1-xGaxN thickness, which causes the bands in the Al1-xGaxN layer

to slant upwards towards the free surface due to polarization induced field [3]. The

figure below shows that the thickness of the barrier increases the valence band, as it

moves upward from t1 to t2, past the Fermi level, causing electrons from the valence

band to go into the heterojuntion interface, which is the most energetically favorable

location, inducing polarization and 2DEG [16].

Figure 16: Band diagram for Al1-xGaxN/GaN HEMT as barrier thickness grows [16]


Introduction 19

Before going further in the explanation of band bending, a basic understanding of

Guass Law is useful. Gauss Law constitutes one of the fundamental laws of

electromagnetism, and it states that the total electric flux through any closed surface

is equal to the total charge enclosed by that surface [17], and can be mathematically

expressed through the following equation:

(1.7)

Where D electric flux density (or electric field) and is the volume charge. If a

Gauss surface is drawn around the entire system, the net charge is zero. However,

since there was a transfer of electrons from the Al1-xGaxN into GaN, there is a

positive charge in Al1-xGaxN because of the ionized donors that balance the negative

charge due to electron transfer. Therefore, as an electron moves from Al1-xGaxN to

GaN, it sees a negative charge that acts to raise its energy, causing the Al1-xGaxN

band to bend upwards. Similarly, as an electron moves from GaN to Al1-xGaxN, it

sees a net positive charge due to the presence of ionized donors in Al1-xGaxN, which

reduces its energy and causes its band to bend downwards. Thus, a conduction band

discontinuity occurs and this forms a notch, or well-like potential, in the conduction

band of the GaN, known as the 2DEG. In the HEMT design in the report, the 2DEG

is in fact a triangular quantum well.

1.5 Application of HEMT Devices

High Electron Mobility Transistors (HEMT) is fairly new component in the

electronics world, but they are quickly taking over and being used in many

applications that require high gain and low noise at very high frequencies. Initially

these transistors were meant to be used to increase the speed of a circuit, but after

being used in applications, researchers found out that HEMTs reduce the effects of

noise at very high frequencies [1]. HEMTs are found in many different types of

electronic equipment such as; cell phones, satellite television receivers, microwave

and millimeter wave communications, radars, radio transmission and so on. Due to

its great characteristics; high gain, high power added-efficiency, higher output power,


Introduction 20

and better low noise performance, the HEMT is best choice for high power

applications [1]. At such high frequencies the operation of the device is separated in

few different band frequency groups due to the need of different characteristics that

can change with higher frequencies. Some of these bands are; L-Band and S-Band

(1-3 GHz), C-Band (4-8 GHz), X-Band (8.2-12.4 GHz), Ku-Band (12.4-18 GHz), K-

Band (18-26 GHz) and MM-Wave Frequencies are above 30 GHz for the complete

list of microwave frequency band, kindly refer to Appendix A. For all these different

bands a slight structural adjustment is needed depending on what the application

desires. For example, devices that operate in the L-Band Frequency need higher

impedance and reduced thermal memory effect, on the other hand we have a HEMT

that is built for applications that use the X-Band Frequencies which require high-gain

and high-efficiency while maintaining high-speed [1]. By applying slight changes to

the structure of the transistor these needed characteristics can be modified for better

result in each application. In the previous sections of this report we have explained

HEMT based on AlGaN/GaN, here are some useful applications of this particular

transistor. X-band applications include transmit-receive modules for naval and

airborne phased array radars. For these devices power-added efficiency is very

important for both the device and system. By using a modified version of the

AlGaN/GaN HEMT we are able to focus mostly on the efficiency of the component

and make it a very good choice for these circuits. For devices that operate in the C-

band frequencies (4-8 GHz ), most important qualities of the transistor are being able

to operate at high power and high temperature that is combined with high PAE [1].

1.6 Potential Economical and Societal Impacts

Although technical and theoretical research forms the bulk of this report, the

economical and societal analyses are also a very important portion of any experiment,

helping determine the viability, survivability and conceivable evolution of the

experiment over the coming years, and therefore cannot be overlooked. Since this

experiment contains no immediate environmental impact, this topic was deemed

irrelevant and was not included in the report.


Introduction 21

The potential economical impacts of utilizing nitride semiconductors (GaN, InN,

AlN, AlGaN, InGaN) to build HEMTs (and other transistors) are quite promising.

Due to the advantages of GaN (and nitride devices in general) mentioned above, it

seems inevitable that technological advancements in microelectronics be intertwined

with the advancements in this technology. According to [12], the GaN market is

forecasted to rise from near zero in 2011 to exceeding $1 billion in 2021. This

implies that there will be much more research and development in GaN (or even

nitride) devices, such as HEMTs. This new market is particularly attractive in the

microelectronic scene, since tapping into a rising market can yield economical

benefits to not only individual corporations, but to an economy as a whole.

Additionally, using low-cost substrates such as sapphire (as compared to silicon-

carbide) produces a greater worth to the overall HEMT design due to its lower costs

of production and similar operating characteristics (this was initially unviable due to

the lack in epitaxial technologies for growth on sapphire). It can then be argued from

the arguments above that the most of the potential economic impacts from using GaN

HEMTs are positive.

The major drawback of using GaN HEMTs rather than Silicon devices is the initial

cost associated with those devices. According to the economics, the worth for the

transistor does not outweigh its production costs (the substrates are quite expensive,

and so are the growth methods). An alternate means of this is to grow GaN on Si

substrates, and is currently being done by [13], which, according to them, will yield

tremendous savings in production costs. Additionally, an independent research firm

(Lux Research) found that gallium nitride substrates could still displace cheaper

silicon by offering 360% to 380% better performance [15].

Another seemingly viable option is the use of GaN itself as a substrate. According to

LUX research, bulk Gallium Nitride costs will fall 60% by 2020, leading to more

efficient devices [15]. The following figure depicts some results obtained by this

firm:


Introduction 22

Figure 17: Cost Projection for Various Types of GaN Devices [15]

It can be seen that as of today, GaN on Si is the most viable option, but with increase

in technologies, GaN on GaN will become feasible cost-wise in the future, maybe

one day replacing current sapphire and SiC substrates.

The societal impacts of advancements in HEMTs are also paramount to integrated

circuits and microelectronics. So far in the microelectronic scene, Moores Law

(number of transistors on integrating circuits double approximately every two years)

seemed be proven true, but with reducing size, power scaling has also become an

issue [14]. New IC chips cannot become much smaller without having more

expensive means to dissipate power (since lowering operating voltage can no longer

be done without deteriorating device performance) additional costs that would not

be beneficial. Using the properties of the HEMT (high mobility, high breakdown

voltage), one could reap the rewards of small devices without sacrificing too much

performance [14]. It can then be seen that the many professionals seem to agree that

the societal and economical benefits of HEMT design and research is positive.


Design of the HEMT 23

2. Design of the HEMT

2.1 Electron Band Diagrams and Resulting Heterojunctions

The HEMT designed in this report uses GaN and AlGaN semiconductors to form the

heterointerface, but before AlGaN can be used, the properties of AlN must be fully

known. The figure below illustrates the Anderson model for GaN and AlN (not to

scale), with the values for the levels given in Appendix B.

Figure 18: Anderson Models for GaN and AlN

It can be seen that both materials have different bandgaps, and these discontinuities

are at the heart of the operation of the HEMT. This bandgap discontinuity is the

result of the conduction and valence band offsets, and the three are usually related

together (for binary compounds) by the following equation [3]:

(2.1)

The conduction band discontinuity is found by subtracting the electron affinity of

both materials together, and the valence band discontinuity can be found by altering

the above equation when both other discontinuities are known [3]. Since AlGaN is

used, and not AlN, obtaining an Anderson model for this material is paramount.



Fortunately, most parameters for ternary compounds are determined through the

interpolation of the values from its composite binary compounds (since research to

their actual structure is still at an infant stage) therefore AlN and GaN can be used

to determine the properties of AlGaN. The approximate conduction band can be

obtained by interpolating using both GaN and AlN bands with respect to their

percent concentrations, as is displayed in the equation below [2] and is included in

Appendix B:

(2.2)

In order to find the bandgap of AlGaN, the value of x (or percent concentration of

Aluminum) in must known. This value is of great importance to the

operation of the HEMT. The concentration affects the amount of band bending that

occurs in the conduction band and therefore affects the operation of the device [7].

Additionally, the Aluminum content must be selected with two other important

factors taken into account: a good balance of sheet resistance and sheet carrier

concentration is desired [1]. The following figure illustrates the relationship between

the sheet resistance and Aluminum content in AlGaN:

Figure 19: Sheet Resistance of AlxGa1xN/GaN Heterostructures as a Function of Aluminum Content x [1]



It can be seen that without using an interlayer, the higher the concentration of

Aluminum, the lower the sheet resistance in the 2DEG (doping also lowers the sheet

resistance more on this later in the report).

Another important factor that cannot be overlooked is sheet carrier concentration in

the 2DEG. The Aluminum content of AlGaN also plays a crucial role determining

this concentration [1], as is depicted by the figure below:

Figure 20: Sheet Carrier Concentration in AlxGa1xN/GaN Heterostructures as a Function of Aluminum

Content x [1]

It can be seen upon inspection of both figures above that a higher Aluminum content

yields good sheet carrier concentration and good sheet resistance. According to this

information, the Aluminum content as chosen to be 0.5. This should also produce a

greater band discontinuity between the GaN and AlGaN interface, as stated per [3]

(Appendix B). Additionally, it was discussed in section 1 of the report that a higher

Al concentration yields higher sheet density of the 2DEG and therefore higher

mobility/current. The bandgap for AlGaN is a function of x, and can be computed

using a quadratic interpolation of both AlN and GaN values as shown in the

following equation [1]:

(2.3)

Where the last term is the bowing factor (constant), which is either -0.7 or -1.3 [1].

Once the bandgap is known, the conduction and valence band discontinuities can be



found by using the following two equations [1] (the results of all these calculations

are included in Appendix B):

(2.4)

(2.5)

It can be seen that using a ternary compound (AlGaN) complicates the computations

slightly as compared to only using binary compounds (AlN and GaN). Now that all

the levels for AlGaN are known, the Anderson model can be constructed for this

material, and can be seen in the figure below:

Figure 21: Anderson Model of AlGaN (doped) and GaN (undoped)

It can be seen that the AlGaN is an extrinsic semiconductor in this figure, and this is

in fact an accurate depiction, since the HEMT is composed of intrinsic GaN and

doped (n-type) AlGaN. The actual doping scheme will be thoroughly discussed in

section 2.3.

Once the two semiconductors are brought together, their Fermi levels become

aligned horizontally throughout the entire structure. To obtain this condition, the

band diagram of the AlGaN must be pulled down and the GaN lifted up while

pinning the conduction and valence band edges at the heterojunction [3]. This occurs

because when both materials come in contact, the electrons from the n-type material

tend diffuse to the undoped material (since there is a higher concentration in the n-

type material). The process continues until equilibrium is reached [3], and the final

result of this union is depicted in the figure below.



Figure 22: Band Diagram of the N-AlGaN/GaN heterojunction

It is obvious that with a heterostructure, the Anderson model is quite different then

with a homogeneous structure, and this is the motivation behind the quantum effects

of the HEMT, as explained earlier.

The heterojunction of the GaN and InGaN interface is not as important as the

AlGaN/GaN one for the simple fact that the 2DEG (and corresponding conducting

channel of the device) is contained in the interface of the latter semiconductors. The

InGaN/GaN heterojunction is simply used to introduce excitons to the GaN

semiconductor, as previously mentioned in section 1 (it is a buffer layer). An exciton

is the bound state of an electron and a hole that can move freely inside the

semiconductor that is, it is the combination of the two charges and it can move

throughout the lattice. Although the exciton is electronically neutral, it is still a

transport of energy, which is akin to increasing the electron/hole (or energy)

concentration inside the HEMT and corresponding 2DEG channel [2]. This more

abstract explanation can be simplified by simply saying that the InGaN is used in

order to add energy in the form of holes and electrons to the GaN layer, without

having to dope the semiconductor.

Now that the purpose of the InGaN is known, its properties can be found in a very

similar manner than with AlGaN; equation 2.2 is modified in order to find the

conduction band energy of InGaN:



(2.6)

Moreover, the percent composition x of must be known in order to

proceed with the calculations. The value of x is not as important as with the

case, and should be kept low in order to achieve lattice match between

InGaN and GaN [1] (chosen to be 0.1). Hence, equation 2.3 can also be modified in

order to quadratically interpolate the bandgap energy of InGaN (where the bowing

factor is constant at -1.4 [1]):

(2.7)

Now that the bandgap and conduction band energies are known, the valence band

and corresponding band discontinuities can be determined (the results are included in

Appendix B)1:

(2.8)

(2.9)

With these values computed, the Anderson model can now be constructed for InGaN,

and is depicted in the following figure:

Figure 23: Anderson Models for GaN and InGaN

GaN was included into the figure in order to quantitively and visually compare the

two semiconductors, and it can be seen that their bandgaps and energy levels are very

1 It must be advised that experimental band values for InGaN are not well

documented as of yet, therefore theoretical results could not be adequately compared

with any published experimental data



similar; therefore it can be easily rationalized that the union of these two materials

yields the following approximate heterojunction:

Figure 24: Band Diagram for the GaN/InGaN Heterojunction

Finally, when the entire device is considered as a whole, the presence of the two

heterojunctions gives the double heterojunction structure, as is approximated by the

figure below:

Figure 25: Band Diagram for the N-AlGaN/GaN and GaN/InGaN Double Heterojunction

The above figure depicts the proposed structure of the HEMT device designed in this

report.



2.2 Growth

There are many types of growth methods for semiconductor technologies, the

prominent ones being epitaxy, molecular beam epitaxy (MBE), metal organic-

chemical vapor deposition, and so on. It does suffice to say that MOCVD is achieved

at a much higher temperature than MBE, and MBE enables the growth of very

precise interfaces that improve transport properties [1]. However, the physics behind

these growth methods is rather complex and will not be explained in this report. This

report will simply introduce the concepts behind epitaxial growth, the fundamentals

of which can be used to understand the other techniques. The figure below illustrates

an ideal case of epitaxial growth:

Figure 26: General Overview of Ideal Epitaxial Growth (no mismatch or defects) [2]

The growth is referred to as ideal because in the case presented in the above figure,

there is a perfect match between the substrate and semiconductor, and there are no

imperfections such as dislocations (lattice misalignment) or point defects (vacancies,

interstitial atoms). It does, however, give a general idea of the process of epitaxial

growth. Epitaxial growth is a process where a crystal structure (or lattice) is formed

on top of another crystal structure. To achieve this method of growth, everything

must be placed in a vacuum to assure optimal temperature, pressure, and contents. A

substrate (or semiconductor structure) is first inserted inside the vacuum, followed by

Substrate Lattice Atoms

Epitaxial Layer Lattice Atoms

Legend

Epitaxial Growth



ions of the wanted layer. These ions will then bond themselves to the substrate,

following the substrates lattice structure, layer after layer [2]. This is why mismatch

is important: if there is a high percentage of mismatch between the two layers, high

strain will be present during the growth, which can lead to the aforementioned

imperfections, among other undesirable effects. This growth is repeated sequentially

for each different semiconductor layer.

2.3 Doping and Metal Deposition

As previously stated on numerous occasions in the design of the HEMT, intrinsic

GaN is used with extrinsic AlGaN. One of the main reason behind using undoped

GaN is to not impede electron mobility throughout the channel (or 2DEG) [1].

Adding impurities into the semiconductor could create potential barriers to the flow

of electrons through the lattice. Additionally, using undoped GaN is essential for the

formation of the 2DEG, as mentioned in the previous section (no doping required to

achieve a 2DEG due to the strong polarization fields in AlGaN/GaN interface) [16].

Using intrinsic GaN also simplifies the design process.

Unlike GaN, AlGaN is doped in the HEMT. This doping was done in order to

achieve a good balance between greater electron concentrations in the 2DEG and

lower sheet resistance without the use of an AlN interlayer [1]. Also, since the

channel is located inside the GaN portion of the heterointerface, the impurities

cannot impede electron mobility. Additionally, as it was seen in section 1, by using

doped AlGaN, greater currents are achieved for the same values of gate voltage. The

optimal doping concentration of AlGaN is obtained by inspection of the materials

energy levels: it is desired to have the Fermi level of AlGaN above the conduction

band of GaN and close to enough to the conduction band of AlGaN. These

conditions are desired in order to obtain a 2DEG even when no potential is applied

(ie: at least one discrete energy state of quantum well in the conduction band be

above the Fermi level of the heterostructure) [2]. The following equation describes

an approximation on how the doping concentration can be obtained:



[

] (2.10)

Where Nc is the density of states in the conduction band, k Boltzmanns constant

( - ), and T is the temperature in Kelvin. The temperature is assumed

to be 300K and the density of states in the conduction band is obtained by

interpolating values from GaN and AlN using the following equation:

(2.11)

Furthermore, values for density of states for both binary compounds were obtained

from the following equations coming from [6]:

(2.12)

(2.13)

The calculated values can be found in Appendix B of the report. As previously

mentioned, the Fermi level of AlGaN was chosen to be above the conduction band of

GaN, and with equation 2.10, a rough approximation for doping concentration of

AlGaN was calculated and included in Appendix B2.

Although the GaN portion of the HEMT is said to be intrinsic, the semiconductor is

highly doped at the interface with the metal (termed n+ doping). The n-type doping

is to create the formation of an ohmic contact between the GaN and the metal (Al).

When a metal and a semiconductor come in contact, their Fermi levels align and

band bending occurs in the semiconductor. If this band bending yields no barrier to

the electrons in the conduction band or holes in the valence band, the interface is

called an ohmic contact. However, if the converse is true (a barrier exists to the

electrons in the conduction band or holes in the valence band), the contact is known

as a Schottky barrier and operates in a similar way as a pn junction [2]. However, if

the width of this Schottky barrier is kept to a minimum, the electrons/holes can

tunnel through the barrier, which is a phenomenon termed quantum tunneling (can

only be understood and explained if the electron is modeled to behave like an

2 The doping concentration calculated is used more as a guideline and is not an exact

value (due to all the rough approximations used)



electromagnetic wave rather than a particle [2]). This quantum tunneling has the

effect of making the Schottky contact behave more like an ohmic contact, since

electrons effectively tunnel through the barrier [2]. The following figure depicts the

two types of contacts that arise in a metal-semiconductor interface (the first being a

Schottky contact, and the other being a Schottky with quantum tunneling or ohmic

contact) it can be seen that the barrier width in the bottom figure is lower than the

barrier width in the upper figure:

Figure 27: Differences Between Ohmic and Schottky Contacts [11]

The n+ pockets in GaN are used to assure quantum tunneling occurs at the interface

between the Al contact and the GaN semiconductor. For more information on

quantum tunneling, refer to Appendix D. A more general layout of metal-

semiconductor interface can be seen in the following figure:

Figure 28: Energy Band Diagrams for (a) Schottky Junction for n-type Si, (b) Schottky Contact with

Quantum Tunneling for n++and (c) Ohmic Contact for p+with metal [9]

The n+ pockets can be created by local diffusion, a process that is briefly explained

in Appendix C [2]. The deposition of Al on the HEMT is achieved in a very similar



way as local diffusion (steps 1 thru 6 are practically identical), but instead of doping,

metal is applied to the structure and then annealed at high temperatures [1]. The

following table lists typical values of annealing temperatures and contact resistances

for different types of metals and the type of doping required for GaN:

Table 3: Ohmic Contact Materials and Properties of Ohmic Contacts on GaN [1]

The work functions of different types of metals can be found in [10] and therefore

were not included in this report.

2.4 Final Device Structure

The previous sections all covered the design of the HEMT. The reasons for selecting

each material and for performing the particular growths, depositions, and doping

were explained in detail. Finally, this brief section is dedicated to the final device

structure. Section 1.3.4 gave an idea of the physical nature of the device, which is

the main structure of the HEMT. The figure below illustrates the actual shape of the

HEMT designed. It can be seen that it is very simple and that it resembles that of a



MOSFET device, but instead of a dielectric, a ternary semiconductor is used

(AlGaN) at the gate. The drain, source, and gate terminals are labeled D, G, and S,

respectively. As mentioned previously, the metal contacts are Al, and the figure

shows an approximate location of the 2DEG at the GaN/AlGaN interface. It should

be noted that the figure does not accurately depict the devices physical dimensions

to scale; it does not show the actual size of the layers, of the n+ pockets, of the metal

contacts, or of the substrate. Typically, the AlGaN layer should be approximately

200 300 3, while the GaN layer can be in the micrometer range ( ) [16].

The size of the buffer layer should be kept low but be high enough as to no hinder

device performance [1].

Figure 29: Final Structure of the HEMT (not to scale)

3

Sapphire

InGaN

GaN

N-AlGaN

n+ n+

metal

metal metal

2DEG

D G S


Theory of Experimental Measurements 36

3. Theory of Experimental Measurements

3.1 Overview

The experiments were conducted in the MEAglow semiconductor lab at Lakehead

University4. Unfortunately, current technologies and processes at this facility do not

allow the entire fabrication of the HEMT designed in this report (much more testing

and research must be done on the growth and such), but three separate samples of

thin GaN on InN were grown on sapphire substrates. The following subsections

discuss brief theory behind the operation of the measurements taken on the three

samples. Results were obtained from Atomic Force Microscopy (AFM), X-Ray

diffraction (XRD), Scanning Electron Microscopy (SEM), and Hall effect

measurements (for the actual results, please refer to section 4).

3.2 Theory

3.2.1 Atomic Force Microscope

The Atomic Force Microscope is a very high-resolution type of scanning, which is

used to visualize the surface of a given sample in the range of nanometers. It is based

on measuring the force acting between a fine tip and a sample. The tip is attached to

the free end of a cantilever and it scans very closely to the sample. Then attractive or

repulsive forces acting on the cantilever will result in positive or negative bending.

The bending is detected by a laser beam that reflects to a photo detector and creates a

signal that is sent to a PC and by the help of appropriate software an image of the

sample is created [24]. The following figure shows the typical arrangement of AFM:

4 MEAglow: Migration Enhanced Afterglow a hybrid system that utilizes

principles of both MBE and MOCVD to grow nitride semiconductor devices with

plasma



Figure 30: Principle of Operation of AFM [24]

The AFM has three modes of operation; Contact Mode, Non-Contact and Tapping

Mode. In contact mode the tip makes a slight contact with the edge of the sample

surface to sense the surface and create the image. In this mode the tip of the

cantilever is very important to be soft enough to be able to be deflected by very small

force to avoid damage to the sample [24]. Non-contact mode uses attractive force

region, which minimizes the contact between the tip and the sample (also a

Proportional, Integral, and Derivative (PID) controller is used) [2]. Silicon based tips

are mostly used for this mode. In tapping-mode the cantilever is oscillating close to

its resonance frequency, which generates an electronic feedback loop to make sure

that the oscillation amplitude is constant at all times. The forces acting between the

sample and the tip will cause change in oscillating amplitude and also change in

resonant frequency and phase of the cantilever. The image of the sample is created

by the phase changes. In this mode the amount of contact to the sample is very low,

which causes in less damage to the sample. Silicon based tips are used in tapping-

mode.

Even if AFM gives a good idea of surface conditions, when there is something of

interest on the surface, SEM is used to quantify what is actually present at this region

of interest. Additionally, the aforementioned software used in conjunction with



AFM can provide RMS surface roughness, and values under 9-10nm typically

indicate a smooth surface [2].

3.2.2 X-Ray Diffraction

X-ray diffraction is method of analysis used in crystalline materials; A. W. Hull

conceptualized it in the early 1900s. Hull stipulated in his paper that every

crystalline substance has a unique diffraction pattern and, in a mixture of substances,

each produces its pattern independently of others (it can be seen as a fingerprint to

a substance) [19]. The theory behind x-ray diffraction can be understood with the

help of Braggs Law, which is the following equation:

(3.1)

Where d is the spacing between diffracting planes, is the incident angle, n is

any integer, and is the wavelength of the beam. These values are better understood

with the help of the following image:

Figure 31: XRD Beam on a Crystalline Lattice [19]

When an X-ray beam is projected into a lattice (as seen in the image above), the

electrons from the atoms will oscillate at the frequency of the incoming beam. This

will cause destructive interference (the combining electron waves are out of phase

with each other) in almost all directions [19]. In some directions (according to

Braggs Law), there will be constructive interference since the atoms in a lattice are

usually in a predefined structure. The X-ray reflections occur at angle with respect

to the incident beam, and generate a reflected beam at an angle 2 from the incident



beam. The angles and such are determined by the arrangement of the unit-cell of the

atoms in the lattice and arrangement of the lattice itself [19].

With this theory, when a compound semiconductor is analyzed by XRD, a curve can

be generated with the help of hardware (the x-ray device) and software. The

corresponding curve should have peaks at a certain angle 2 that identifies the type

of semiconductor present. Furthermore, the areas under those peaks are related to the

amount of each semiconductor present in the sample, ie: a thicker layer of

semiconductor should have a higher peak [19].

3.2.3 Scanning Electron Microscope

The scanning electron microscope (SEM) uses a focused beam of high-energy

electrons, which interact with the electrons on the sample to produce a detailed

topography of the samples surface, chemical composition, crystalline structure and

orientation of materials. It can detect specimens in high vacuum, low vacuum and in

environmental SEM specimens can be observed in wet conditions while achieving a

resolution of 25 angstrom (0.25 nm) [22]. The electron beam dissipates energy,

producing different signals that give information of the characteristics of the material.

These signals include secondary and backscattered electrons, which are commonly

used for imaging samples; secondary electrons are suited for s

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