Download - Design and Growth of Aluminum Nitride/Gallium Nitride High Electron Mobility Field Effect Transistor
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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)
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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.
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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
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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 31: AFM MEASUREMENTS FOR SAMPLE #2 ................................................... 42
FIGURE 32: AFM MEASUREMENTS FOR SAMPLE #3 ................................................... 43
FIGURE 33: XRD MEASUREMENTS FOR SAMPLE #1.................................................... 44
FIGURE 34: XRD MEASUREMENTS FOR SAMPLE #2.................................................... 44
FIGURE 35: XRD MEASUREMENTS FOR SAMPLE #3.................................................... 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
FIGURE 43: SEM SURFACE VIEW OF SAMPLE #1 (X500K) .......................................... 47
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FIGURE 44: SEM SIDE VIEW OF SAMPLE #2 (X110K) ................................................. 48
FIGURE 45: SEM SIDE VIEW OF SAMPLE #2 (X130K) ................................................ 48
FIGURE 46: SEM SIDE VIEW OF SAMPLE #2 (X150K) ................................................. 48
FIGURE 47: SEM SURFACE VIEW OF SAMPLE #2 (X60K) ............................................ 48
FIGURE 48: SEM SURFACE VIEW OF SAMPLE #2 (X110K) .......................................... 49
FIGURE 49: SEM SURFACE VIEW OF SAMPLE #2 (X350K) .......................................... 49
FIGURE 50: SEM SIDE VIEW OF SAMPLE #3 (X120K) ................................................. 49
FIGURE 51: SEM SIDE VIEW OF SAMPLE #3 (X220K) ................................................ 49
FIGURE 52: SEM SIDE VIEW OF SAMPLE #3 (X250K) ................................................. 50
FIGURE 53: SEM SURFACE VIEW OF SAMPLE #3 (X20K) ............................................ 50
FIGURE 54: SEM SURFACE VIEW OF SAMPLE #3 (X130K) .......................................... 50
FIGURE 55: SEM SURFACE VIEW OF SAMPLE #3 (X150K) .......................................... 50
FIGURE 56: CURRENT VS VOLTAGE AND CURRENT VS RESISTANCE PLOTS FOR SAMPLE
#1 ....................................................................................................................... 51
FIGURE 57: HALL EFFECT MEASUREMENT RESULTS FOR SAMPLE #1 ......................... 51
FIGURE 58: CURRENT VS VOLTAGE AND CURRENT VS RESISTANCE PLOTS FOR SAMPLE
#2 ....................................................................................................................... 52
FIGURE 59: HALL EFFECT MEASUREMENT RESULTS FOR SAMPLE #2 ......................... 52
FIGURE 60: CURRENT VS VOLTAGE AND CURRENT VS RESISTANCE PLOTS FOR SAMPLE
#3 ....................................................................................................................... 53
FIGURE 61: HALL EFFECT MEASUREMENT RESULTS FOR SAMPLE #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
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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
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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
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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
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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.
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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
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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.
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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
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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]
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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
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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].
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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).
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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,
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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]
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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).
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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.
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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:
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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
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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
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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]
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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,
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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.
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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:
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
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.
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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.
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Design of the HEMT 24
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]
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
Design of the HEMT 25
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
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
Design of the HEMT 26
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.
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Design of the HEMT 27
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:
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
Design of the HEMT 28
(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
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ENGI-4969-YB Electrical Engineering Dept. Lakehead University
Design of the HEMT 29
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.
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Design of the HEMT 30
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
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Design of the HEMT 31
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:
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Design of the HEMT 32
[
] (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)
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Design of the HEMT 33
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
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Design of the HEMT 34
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
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Design of the HEMT 35
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
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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
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Theory of Experimental Measurements 37
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
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Theory of Experimental Measurements 38
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
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Theory of Experimental Measurements 39
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