Fabrication and characterization of AIGaN gan HEMTs

Chapter 1
Introduction

1.1

Review on III-V semiconductor transistors

The radio frequency (RF) semiconductor market is ever increasing due to the exploding
development of cellular phones and satellite communications. The bulk of this market has
been occupied by Si and GaAs. This however is likely to change in the near future as two
other semiconductors emerge with greater capabilities. They are SiC and GaN [1], [2].
The comparison of GaN with the other materials is shown in Figure 1.1 [1-5]: all
semiconductors, which are candidates for the RF applications are schematically indicated
in a frequency-power diagram. For some semiconductors (Si, GaAs), this represents the
current situation while for others (SiC, GaN) it represents the expected one in the near
future. On the high frequency side, InP-based materials take advantage of small effective
mass and high mobility to achieve record frequencies. On the low frequency side, Si
prevails for moderate powers. Owing to the success of SiGe [6], the Si industry is now
extending towards higher frequencies, about 2.5 GHz. SiC is performing well for high
power and low frequency, but is, however, limited to frequencies of a few giga-hertz
(GHz) only [1].

1


GaN is in competition with SiC on its low frequency side and with GaAs on its low
power/high frequency side (see Figure 1.1). Thanks to breakthroughs in technology that
improve the thermal management (wafer fusion and flip chip, etc.) [7, 8], all technologies
are moving towards higher power where heat dissipation is a prevailing barrier for
optimum performance.

RF Output Power
50W
SiC
GaN
Si
10W

SiGe

GaAs
InP

1 GHz

10 GHz

100 GHz

Frequency

Figure 1: Semiconductor materials for RF electronics. RF power is plotted against Frequency [1-5].

The domain of RF applications is wide and in rapid growth. As new applications emerge,
there is a continuous shift towards higher frequencies. On the low frequency side, Si and
GaAs benefit from the exponential development of cellular phone (0.8 and 1.9 GHz) [9].
At high frequencies, satellite and terrestrial communications (1.6, 2.5, 5.2, 23, 28 GHz)
[9] and military applications (X-band, 8 to 12 GHz) represent a strong potential for
development of GaN [9]. Applications at higher frequencies such as anticolliding radar
(76 GHz) can also be implemented using GaN and InP [9].
The cost of RF systems depends on the power and frequency of use. As the frequency

increases, the difficulty to coherently add the individual powers coming from different
transistors increases. Dephasing has to be accounted for by a proper design and addition
of passive elements such as capacitors can take up to three-quarter of the area on the
wafer. As a result, high frequency high power modules are expensive. In addition, a
2


cooling system is usually required as high power applications generate substantial heat
that deteriorates the device performance.
The advantage of III-V semiconductors, which feature wide bandgaps, is tremendous.
They provide a larger RF power per unit area, which simplifies the design, and also, they
work well at elevated temperatures, which allows reduced peripherals for cooling. The
power generated in each transistor under a large bias makes the impedance and power
matching between different stages easier. This is especially so for the AlGaN/GaN
transistor which has a characteristic impedance three times larger than its counterpart,
AlGaAs/GaAs [21]. Thus, it is expected that using GaN rather than conventional III-V
compounds such as GaAs will lead to the same performance at a lower price, or to a
higher performance at a competitive price due to ease of design.
The advantage of GaN over SiC is the possibility of making heterostructures. Such
heterostructure has been demonstrated to produce two-dimensional electron gas (2DEG)
at the heterojunction, and this makes possible several novel devices that can operate at
frequencies beyond the capability of SiC. This is due to the mobility of the 2DEG at
about 3 times higher than the carriers in SiC metal-semiconductor FETs, (MESFETs)
[10]. Also, the 2DEG permits low resistance and low noise performance not possible in
SiC. The state-of-the-art performance of MODFETs can be summarised by the following
data collected from different devices: the average saturation drain-source current is about
1 A/mm in virtue of a large 2DEG sheet carrier density (1013cm-2) that is possible by the
very large conduction band offset at the AlGaN/GaN interface [2], [11]. The
transconductance can reach 270 mS/mm (for a 0.7µm gate length high electron mobility
transistor (HEMT)) [12] and the highest unity-gain bandwidth (ft) and unity-power gain

bandwidth (fmax) could reach 67 and 140 GHz [13], respectively. Extremely high
breakdown voltage of 100V has been recorded, and power density of 10W/mm at 10 GHz
has been attained due to good thermal management [14]. Up to now, the best solution for
good thermal management has been the usage of bulk SiC as a substrate as it has a very
high thermal conductivity constant of about 3 W/Kcm (10 times that of sapphire) [31]. It
is crucial to note that the highest temperature drop occurs at the first micron below the

3


channel region. However, in order to obtain a decent quality GaN, it is necessary to grow
more than one micron of GaN on the substrate (SiC or sapphire) [1]. As a result, the good
thermal conductivity of SiC is not fully exploited.
In the arena of high temperature electronic applications, until recent times, electronics
was kept far away from heat sources. A temperature of up to 200°C was usually allowed
simply because silicon-on-insulator (SOI) can work up to this temperature [37].
Semiconductors such as GaAs and InP, in general have low thermal conductivity, hence
limiting operations at high power where much heat is dissipated due to large current flow,
and this can drastically degrade performance. III-nitride semiconductor transistors
however, have found their way to excel in performance over these materials as they are
several times more thermal conductive than their counterparts. Domains of application
include aerospace, automotive and terrestrial and high power transmitters in wireless
communications. In general, the substrate conductivity is not an issue and both SiC and
sapphire are well adapted. There have been many demonstrations of GaN transistors
working in high temperature [15, 16]. A peak electron drift velocity of 1 x 107 cm/s at
750K and 3 x 107 cm/s at room temperature was demonstrated. [15]. Presented also were
the results of the DC and RF measurements showing that these devices can operate at
least up to 300°C.

1.2

Current Issues

Field-effect transistors fabricated using the AlGaN/GaN heterostructure offer the
potential to produce a class of devices with excellent DC and RF performance. Although
the physics of the 2DEG that forms at the heterojunction is not completely understood at
this time, it is clear that the sheet charge density is very high and of the order of 1013
cm-2, which is a factor of ten higher than that for the AlGaAs/GaAs 2DEG. The sheet
charge density is higher than would be expected from the standard 2DEG theory, which
indicates that additional physical effects are probably involved. Several explanations for
this phenomenon using arguments such as spontaneous polarization and piezoelectric

4


polarization have been proposed [17]. The 2DEG at the AlGaN/GaN heterojunction has
excellent charge transport characteristics and the saturation velocity has a magnitude of
about 3 x 107 cm/s [2]. Room temperature mobility was found to be in the range of 1200
to 2000 cm2/Vs [18]. The combination of high sheet charge density and good transport
characteristics, has resulted in high current capability for the transistor. This is in fact
observed in AlGaN/GaN MODFETs where maximum channel current of over 1 A/mm is
routinely obtained in experiments [19, 20]. Table 1.1 summarises the key material
parameters [21] for AlGaAs/GaAs, 4H SiC and AlGaN/GaN transistors. It can be seen
that with large energy bandgap, high breakdown voltage, high saturation velocity and
good thermal conductivity, SiC and AlGaN/GaN devices have shown to be more
promising candidates for high power and high frequency operations.
Table 1.1: Summary of key material parameters for AlGaAs/GaAs, 4H SiC and AlGaN/GaN transistors
[21].

Metric

AlGaAs/GaAs

4H SiC

AlGaN/GaN

Energy Bandgap (eV)

1.43 for GaAs

3.2

3.4 for GaN

12.5

10.0

9.5

2-3 x 1012

N/A

1-5 x 1013

4

20

33

8500

N/A

2000

Saturation electron velocity (x107 cm/s)

1.0

2.0

3.0

Thermal conductivity (W/cm K)

0.53

4

1.3

Dielectric constant
Maximum sheet charge concentration (cm-2)
Breakdown field (V/cm) (x105)
2DEG mobility (cm2/Vs)

Piezoelctric coefificients (C/m2)
e31

0.093

e33

-0.185

-0.36
0.2

1.0

GaN-based transistors have also set state-of-the art performance for high output power
density and have the potential to replace GaAs-based transistors for a number of high
power applications [22]. The underlying reasons for the advances made with GaN
devices again stemmed from the material properties inherent in the GaN-based material
system. One of the key advantages is the high breakdown field of the wide bandgap GaN
5


and its relative materials such as AlGaN. This breakdown field is about 3.3 MV/cm,
much higher that that of GaAs of 0.4 MV/cm. With such parameter, high drain bias
operation is then possible due to high breakdown voltage. Together with the high output
current driving capabilities, GaN-based transistors with high power output will then
become viable.
In high frequency applications, GaN has a very high saturation/peak velocity, and this is
critical for achieving high cut off frequencies, and therefore is competitive with GaAs.
Although the mobility of carriers in GaN is about 4 times lower than that of GaAs, it is

sufficient for high frequency operations as the critical mobility for optimum RF power
performance is approximately 500 cm2/Vs. [23] Moreover, the sheet charge-mobility
product is higher owing to the high sheet charge concentration in the AlGaN/GaN 2DEG.
This is vital for the development of low noise and high frequency transistors. Another
important property of GaN-based materials is the ability to utilise bandgap engineering in
the design of device structures. Modulation doped field effect transistor (MODFET)
which utilises heterojunction design can result in higher sheet carrier concentrations,
higher mobilities, better charge confinement, higher peak saturation drain currents, higher
breakdown voltages, higher cutoff frequencies, etc. This is in view of exploiting the
advantages of spontaneous and piezoelectric polarization induced sheet charge and the
growth of low defects AlGaN barrier layers with high aluminium mole fractions. With
this combination of high frequency operation, high breakdown voltage, and high drain
current, GaN is an excellent candidate for high power microwave operations.
Currently, numerous GaN-based MODFETs especially AlGAN/GaN, have been
fabricated by researchers and the device performance was investigated. These included
small signal microwave performance, dc performance, power performance, etc.
A comparison of the cutoff frequency versus gate length reported by several
organisations was compiled by C. Binari [24]. It was found that the cutoff frequency has
an approximate negative proportion relationship with the gate length. In the report of C.
Binari, the gate length ranges from 0.15 µm to 1 µm and the ft ranges from 15 GHz (for 1

6


µm) to 67 GHz (for sub-micron gate lengths). The highest reported values for ft and fmax
are 67 and 140 GHz, respectively [13]. Refinements and optimization in material
structure and device design can actually be done to produce an overall improvement in
the AlGaN/GaN MODFET small signal performance.
Recent intensive research on AlGaN/GaN MODFETs grown on sapphire substrate has
resulted in a steady increase in power density from 1.1 W/mm at 2 GHz [25] to 1.5-1.57

W/mm at 4 GHz [26, 27] and 1.7 W/mm at 10 GHz [28]. The best power density ever
reported is for HEMTs grown on a semi-insulating 4H-SiC substrate with 10 W/mm at 10
GHz and 4.1 W/mm at 16 GHz [29]. Total power results have also been pushed up to 7.6
W/mm achieved at 4 GHz for HEMTs grown on sapphire and flip-chip mounted on AlN
heat sinks [30]. Such improvement has partially resulted from an increased understanding
and application of the piezoelectric effect at the AlGaN/GaN interface that induces large
sheet carrier concentrations, and also the of use of bandgap engineering to design and
grow HEMT structures with larger Al mole fractions to allow a large sheet charge
concentration to coexist with a higher carrier mobility [2]. Gates with high Schottky
barrier height have also been fabricated, yielding a high gate-drain reverse breakdown
voltage of more than –80V [32]. This is a result of using high Al mole fraction to
effectively suppress thermionic gate leakage current at elevated temperature operations.
GaN-based FET structures offer the potential of not only high power and high-speed
operation, but also high temperature. This is found to be beyond those of Si and GaAs,
which have operated up to 400 °C [33] and 500 °C [34], respectively. However, to date,
the operation of GaN-based FETs has only been reported up to 750 °C for doped-channel
(DC) AlGaN/GaN HFET [35], but none has been made for undoped channel HFETs up
to such high temperatures. It has been proposed that AlGaN/GaN doped channel, DCHFETs performs better than undoped channel AlGaN/GaN HFETs at elevated
temperatures because of a decrease in ionised impurity scattering [15]. This is due to a
larger carrier concentration at the 2DEG, which acts to screen off the ionized impurity
scattering from the AlGaN barrier layer. It was found by Binari et al. [36] that for the

7


doped-channel AlGaN/GaN HFET, an increase in temperature led to an increase in drain
current. However, this phenomenon might not be true for undoped channel HFETs.
1.3

Motivation and Objectives of Current Project

It is clear at this juncture that the GaN-based devices such as the AlGaN/GaN HEMT has
many properties that make them attractive for high power microwave applications, and
their performance is greatly dependent on the fabrication process, device structure and
material parameters. In order to realize high performance AlGaN/GaN HEMTs for high
power and high frequency applications, it is crucial to first develop and optimize a good
fabrication process that is reproducible and cost effective. Development and optimization
of fabrication processes such as the formation of ohmic contacts with very low specific
contact resistance, and the laying of reliable gate metals with high Schottky barrier
heights and low leakage currents are important. This is because good ohmic and Schottky
contacts allow devices to deliver high output current at low knee voltage with low gate
leakage current, which are needed for high power applications. High frequency
measurements differ from those at low frequency, and it can only be realized by
fabricating devices with dimensions specific to GHz probing. Hence, designing a set of
high frequency photomask is necessary.
To our best of knowledge, there have not been many reports on the simulation of
AlGaN/GaN HEMTs. It is important to assess and quantify the performance that is
realistically achievable in AlGaN/GaN HEMTs by studying optimal device geometry and
material parameters. Through simulations, we can investigate the feasibility of possible
new device structure designs to improve device performance, before implementing these
appropriate designs and material parameters to actual wafer growth and fabrication of
HEMT devices. In this way, we can save time and money by achieving as close to the
required dc or rf performance without going through the process of trial and error on
actual fabricated wafers. Significant improvements in the quality and performance of the
AlGaN/GaN system can then be realized in this way.

8


It is therefore our objective to first, study the fabrication process of ohmic and Schottky

contact formation on the AlGaN/GaN HEMT structure. We aim to achieve a low specific
contact resistance of the order of 10-7 Ωcm2 or lower, an improvement from 10-6 Ωcm2
achieved by other research groups [85-87]. We shall be investigating the possibility of
using surface treatment on the wafer and also etching procedures to achieve our
objective. We are also studying methods to obtain Schottky diodes on AlGaN/GaN
devices with minimal reverse leakage current, high barrier heights and good thermal
stability. Till this date, little has been done in this area of research and information on
thermal stability of Schottky contact on AlGaN/GaN HEMTs has not been published. It is
then our aim to fabricate AlGaN/GaN HEMT devices for dc measurements and
characterization before going into the designing of a set of photomask for high frequency
and high power measurements. With the importance of simulation as mentioned earlier,
we shall extend our study into the potential of AlGaN/GaN HEMTs by running
simulations of a possible new AlGaN/GaN HEMT device structure and compare it with
the performance of HEMTs with conventional device structure reported in literature.
1.4

Outline of Thesis

Chapter 1 has presented an introduction to the current status of the research and
development of the AlGaN/GaN HEMT. It has also spelt out the importance of the
current project and the objective we hope to achieve at the end. In Chapter 2, the
fundamentals of the GaN related materials and the theory of the AlGaN/GaN HEMT are
described. The experimental procedures for the fabrication of ohmic contact, Schottky
contact and AlGaN/GaN HEMTs are presented along with their characterizations in
Chapter 3. In addition, the performance is discussed. The design of photomasks suitable
for the making of HEMTs for high frequency and/or high power applications is
considered in Chapter 4. Chapter 5 shows the simulation results of a new AlGaN/GaN
HEMT structure that may surpass the performance of existing conventional device
structures reported in literature. Last but not least, Chapter 6 presents the conclusions
from the current work and some of the possible avenues for furthering the current

research work.

9


Chapter 2
Theoretical study of GaN related
semiconductors and devices

2.1

Introduction

In this chapter, the material study of some nitride-based semiconductors is presented. It
includes the crystal structure, the chemical, electrical and mechanical properties of
materials such as GaN, AlN and AlGaN. It also introduces the basic device structure of
the AlGaN/GaN HEMT and its properties and characteristics such as the formation of the
2DEG, the piezoelectric effect and the carrier transport mechanism. Finally, the
measurement techniques for specific contact resistance and the Schottky barrier height
are presented.

2.2

Crystal Structures of Nitrides

Wurtzite (Wz), zincblende (ZB) and rocksalt structures are the three common crystal
structures shared by group-III nitrides. Under ambient conditions, the thermodynamically
stable structure is wurtzite for bulk AlN, GaN and InN. The zincblende structure for GaN
and InN has been stabilized by epitaxial growth of thin films on {011} crystal planes of
cubic substrates such as Si, MgO, and GaAs. In these cases, the intrinsic tendency to

form the wurtzite structure is overcome by topological compatibility. The rocksalt, or

10


NaCl, structure can be induced in AlN, GaN and InN under very high pressures. The
wurtzite structure has a hexagonal unit cell and thus two lattice constants, c and a. It
contains six atoms of each type and consists of two interpenetrating Hexagonal Close
Packed sublattices, each with one type of atom, offset along the c axis by 5/8 of the cell
height.
The zincblende structure has a unit cell containing four group III elements and four
nitrogen elements. The position of the atoms within the unit cell is identical to the
diamond crystal structure. Both structures consist of two interpenetrating face-centred
cubic sublattices, offset by ¼ of the distance along a body diagonal. Each atom in the
structure may be viewed as positioned at the center of a tetrahedron, with its four nearest
neighbours defining the four corners of the tetrahedron.
There are some similarities between the wurtzite and zincblende structure. In both cases,
each group-III atom is coordinated by four nitrogen atoms, and conversely, each nitrogen
atom coordinated by four group-III atoms. The main difference between these two
structures lies in the stacking sequence of the closest packed diatomic planes. For the
wurtzite structure, the stacking sequence of the (0001) plane is ABABAB in the <0001>
direction, while the stacking sequence of the (111) plane in a zincblende structure is
ABCABC in the <111> direction.
A stick and ball representation of wurtzite structure is depicted in Figure 2.1. The
wurtzite and zincblende structures differ only in the bond angle of the second-nearest
neighbour, (see Figure 2.2).

11

Figure 2.1: A stick and ball diagram of a hexagonal structure.

Figure 2.2: Stick and ball stacking model of crystals with wurtzite (a) an zincblende (b) orientations.

As shown clearly, the stacking order of the wurtzite along the [0001] c direction is
ABAB, meaning a mirror image but no in-plane rotation with the bond angles. In the
zincblende structure along the [111] direction there is a 60° rotation which causes a
stacking order of ABCABC, Figure 2.2b. The wurtzite polytypes of GaN, AlN and InN
form a continuous alloy system whose direct bandgaps range from 1.9 eV for InN, to 3.4
eV for GaN, to 6.2 eV for AlN. Thus, the III-nitrides could potentially be fabricated into

12


optical devices, which are active at wavelengths ranging from the red well into the
ultraviolet.

2.3

Gallium Nitride

2.3.1

Chemical Properties of GaN

Since the first synthesized GaN in 1932, a large body of information has repeatedly
indicated that GaN is an exceedingly stable compound with a large bandgap and exhibits
significant hardness. It is this chemical stability at elevated temperatures combined with
its hardness that has made GaN an attractive material for high temperature and high
power electronics. While the thermal stability of GaN allows freedom of hightemperature processing, the chemical stability of GaN presents a technological challenge.

Conventional wet etching techniques used in the semiconductor processing have not been
very successful for GaN device fabrication. For example, Maruska and Tietjen [38]
reported that GaN is insoluble in H2O, acids, or bases at room temperature, but does
dissolve in hot alkali solutions at very slow rate. Pankove [39] noted that GaN reacts with
NaOH forming a GaOH layer on the surface, prohibiting wet etching of GaN. To
circumvent this difficulty, he developed n electrolytic etching technique for GaN. Lowquality GaN has been etched at reasonably high rates in NaOH [40, 41], H2SO4 [42],
H3PO4 [43-45]. Although these etches are useful for identifying defects and estimating
their densities in GaN films, they are not very successful for the fabrication of devices.
Well-established chemical etching processes are required for the device-technology
development. Promising possibilities are the various dry-etching processes under
development, and reviewed by Mohammad et al. [46].

13


2.3.2

Thermal and Mechanical Properties of GaN

In the hexagonal wurtzite structure, GaN has a molecular weight of 83.728 g/mol. At
300K, the lattice parameters of this semiconductor are a0 = 3.1892 ± 0.0009 Å and c0 =
5.1859 ± 0.0005 Å. However, for the zincblende polytype, the calculated lattice constant
based on the measured Ga-N bond distance in the wurtzite GaN is a = 4.503 Å. The
measured lattice constant of this polytype varies between 4.49 and 4.55 Å, indicating that
the calculated value lies within acceptable limits [47]. A high-pressure phase transition
from the wurtzite to the rocksalt structure has been predicted and observed
experimentally. The transition point is 50 Gpa and the experimental lattice constant in the
rocksalt phase is a0 = 4.22 Å. Table 2.1 compiles the known properties of wurtzite GaN.
Table 2.1. List of the known properties of Wurtzite and zincblende GaN.

Wurtzite Polytype
Bandgap energy

Eg (300K) = 3.42 eV

Eg (4K) = 3.505 eV

Temperature coefficient

dEg/dT = -6.0 x 10-4 eV/K

Pressure coefficient

dEg/dP = 4.2 x 10-3 eV/kbar

Lattice constant

a = 3.189 Å

c = 5.185 Å

Thermal expansion

∆a/a = 5.59 x 10-6 /K

∆c/c = 3.17 x 10-6 /K

Thermal conductivity

κ = 1.3 W/cmK

Index of refraction

n(1eV) = 2.35

Dielectric constant

εr = 10.4

Electron effective mass, me

0.22m0

Hole effective mass, mp

>0.8m0

n(3.42eV) = 2.85

Zincblende polytype
Bandgap energy

Eg(300K) = 3.2—3.3 eV

Lattice constant

a = 4.52 Å

Index of refraction

n(3eV) = 2.9

It is interesting to note that the lattice constants of GaN grown with higher growth rates
was found to be larger. When doped heavily with Zn [48], and Mg [49] a lattice
14


expansion occurs because at high concentrations, the group-II element begins to occupy
the lattice sites of the much smaller nitrogen atoms.
Measurements made over the temperature range of 300-900 K indicates the mean
coefficient of thermal expansion of GaN in the c plane to be ∆a/a = 5.59 x 10-6 K-1.
Similarly, measurements over the temperature ranges of 300-700 K and 700-900 K,
indicates the mean coefficient of thermal expansion in the c direction to be ∆c/c = 3.17 x
10-6 K-1 and 7.75 x 10-6 K-1, respectively [38]. Sheleg and Savastenko [50] reported a
thermal expansion coefficient near 600 K, perpendicular and parallel to the c-axis, of
(4.52 ± 0.5) x 10-6 K-1 and (5.25 ± 0.05) x 10-6 K-1, respectively.
Sichel and Pankove [51] measured the thermal conductivity of GaN for the temperature
range of 25-360 K. The room temperature value of the thermal conductivity κ = 1.3
W/cmK is a little smaller than the predicted value of 1.7 W/cmK [52]. Other thermal
properties of Wz-GaN have been studied by a number of researchers. The specific heat of
Wz-GaN at constant pressure (Cp) is given by [53]
Cp (T) = 9.1 + (2.15 x 10-3 T) [cal/mol K].
2.4

(2.1)

Aluminum Nitride

AlN exhibits many useful mechanical and electronic properties. For example, hardness,
high thermal conductivity, resistance to high temperature and caustic chemicals, make

AlN an attractive material for electronic packaging applications. The wide bandgap is
also the reason for AlN to be touted as an insulating material in semiconductor device
applications. Piezoelectric properties make AlN suitable for surface-acoustic-wave device
applications [54]. However, the majority of this semiconductor stems from its ability to
form alloys with GaN producing AlGaN and allowing the fabrication of AlGaN/GaN
based electronic and optical devices, the latter of which could be active from the green
wavelength into the ultraviolet.

15


2.4.1 Thermal and Chemical Properties of AlN
When crystallized in the hexagonal wurzite structure, the AlN crystal has a molar mass of
20.495 g. It is an extremely hard ceramic material with a melting point higher than
2000°C. The thermal conductivity κ of AlN at room temperature has been predicted at ≈
3.2 W/cmK [55, 56], and values of κ measured at 300 K are 2.5 [57] and 2.85 W/cmK
[58]. The measured thermal conductivity as a function of temperature is plotted in Figure
2.3.

Figure 2.3: Thermal conductivity of single crystal AlN. (Ref: 57)

The thermal expansion of AlN is isotropic with a room-temperature value of 2.56 x 10-6
K-1. The thermal expansion coefficients of AlN measured by Yim and Paff [59] have a
mean value of ∆a/a = 4.2 x 10-6 K-1 and ∆c/c = 5.3 x 10-6 K-1. The equilibrium N2-vapour
pressure above AlN is relatively low compared to that above GaN, which makes it easier
to be synthesized. Similar to GaN but even more so, AlN exhibits an inertness to many
chemical etches. The surface chemistry of AlN was investigated by Slack and McNelly
[60] and it indicated that the AlN surface grows and oxide 50-100 Å thick when exposed
to ambient air for about a day. However, this oxide layer was protective and resisted
further decomposition of the AlN samples.

16


Table 2.2. List of the known properties of Wurtzite and zincblende AlN
Wurtzite polytype
Bandgap energy

Eg (300K) = 6.2 eV

Eg (5K) = 6.28 eV

Lattice constant

a = 3.112 Å

c = 4.982 Å

Thermal expansion

∆a/a = 4.2 x 10-6 /K

∆c/c = 5.3 x 10-6 /K

Thermal conductivity

κ = 3.2 W/cmK

Index of refraction

n(3eV) = 2.15 ± 0.05

Dielectric constant

ε = 8.5 ± 0.2

n(3.42) eV = 2.85

Zincblende polytype
Bandgap energy

Eg (300K) = 5.11 eV

Lattice constant

a = 4.38 Å

2.4.2

Electrical Properties of AlN

Electrical characterization on AlN has been limited to just resistivity measurements and
not other measurements such as mobility because of some of its inherent properties.
These include low intrinsic carrier concentration, and deep level defects and impurity
energy levels. Kawabi et al. [61] conducted such a test and found the resistivity, ρ, of
transparent AlN single crystals to be 1011 – 1013 Ωcm. However, impure AlN crystals
which, showed a bluish colour due to the presence of Al2OC, have much lower
resistivities of 103 – 105 Ωcm.
The insulating nature of these AlN films has hindered meaningful studies on the electrical
transport properties. However, with the availability of refined growth techniques, AlN is

presently grown with much improved crystal quality and shows both n- and p-type
conductions. Edwards et al.[61] and Kawabe et al.[62] carried out some Hall
measurements on p-type AlN and found a rough estimate of the hole mobility to be, µp =
14 cm2 /Vs at 290 K.

17


2.5

Aluminum Gallium Nitride (AlGaN) alloy

Good k nowledge of the compositional dependence of the barrier and well materials is a
requirement in attempts to analyze heterosturctures in quantum wells and superlattice. In
the nitride system, a wide scope of possible options is available for the construction of
such structures. The barriers formed can be materials such as AlGaN or GaN; while
depending on the barrier material, the wells can be constructed of GaN or InGaN layers.
The energy bandgap of AlxGa1-xN may be expressed by
Eg(x) = xEg(AlN) + (1-x)Eg(GaN) – bx(1-x),

(2.2)

Where Eg(GaN) = 3.4 eV, Eg(AlN) = 6.2 eV, x is the Al mole fraction, and b is the
bowing factor which until now has controversial values. Yoshida et al. [63] concluded in
their studies that as the Al mole fraction increases, the energy bandgap of AlxGa1-xN
deviates upwards from a graph of Eg vs x when b = 0. This implied a negative value for
the bowing factor, b. In contrast, Koide et al. [64] observed that the bowing factor is
positive as they concluded a downward deviation that is opposite to that of Yoshida.
The resistivity of unintentionally doped AlGaN increases rather rapidly with increasing
Al mole fraction, so much so that AlGaN becomes almost insulating for Al fraction

exceeding 20%. As the Al mole fraction increases from 0 to 30%, the n-type carrier
concentration drops from 1020 to 1017 cm-3, and the mobility increases from 10 to 30
cm2/Vs. An increase in the native defect ionization energies with increasing Al mole
fraction may be the explanation for this variation. It is still not known how the dopant
atoms such as Si and Mg respond to the variation of the AlN mole fraction in AlGaN.
AlGaN with Al mole fraction as high as 50-60% is dopable by both n-type and p-type
impurity atoms. Until now, a low Al mole fraction of about 15% is sufficient for good
optical field confinement.

18


2.6

Substrates for Nitride Epitaxy

Of the many challenges faced in the research of GaN, one of the major difficulties is the
lack of a suitable material that is lattice matched and thermally compatible with GaN.
GaN, AlN and InN have been grown primarily on sapphire, most commonly the (0001)
orientation. In addition, III-nitrides have also been grown on Si, SiC, InP, ZnO, TiO2, and
LiGaO2.

2.7

The AlGaN/GaN High Electron Mobility Transistor

2.7.1

The structure of the conventional n+ - AlGaN/GaN HEMT

The cross section of a conventional HEMT is shown in Figure 2.4. The source and drain
contacts and the gate metallization are analogous to those in either Si-MOS or the
compound semiconductors, such as GaAs MESFET devices. The epitaxial layer structure
of the AlGaN/GaN HEMT grown and fabricated is illustrated in Figure 2.5. The device is
grown on a AlN buffer layer to reduce the lattice mismatch of 49% between the GaN
channel layer and the sapphire substrate. The layers grown, from bottom to top are, a
sapphire substrate, an AlN buffer layer, an undoped GaN “channel layer”, an undoped
AlGaN “spacer layer”, a n-doped AlGaN “donor layer” and finally an undoped AlGaN
“cap layer”. The role of each layer will become apparent in this section. The thickness of
individual layers and their doping have a direct influence on the device properties and the
performance of the HEMT. The gate lengths and the source-drain distance may vary
according to speed, application, and yield requirements.

19


Gate

Source

Drain

+

n AlGaN

Undoped AlGaN

Undoped GaN

2DEG

AlN

Sapphire Substrate

Figure 2.4: Schematic of a conventional AlGaN/GaN HEMT

EF
2DEG
100Å

Gate
Metal

n+-AlGaN
Donor Layer

AlGaN
Spacer
Layer

GaN Channel
Layer

Al2O3
Substrate

Figure 2.5: Epitaxial layer structure and conduction band diagram for a HEMT under positive gate bias.

20


2.7.2

Heterostructures in Semiconductors

In conventional semiconductor devices, only one type of semiconductor material is used
in the fabrication of the devices. Control of current flow is achieved by creating a
junction within the device structure. Such device is called a homostructure, and one such
example is Si-based metal-oxide-semiconductor (MOS), or the bipolar-junction transistor
(BJT). If more than one semiconductor is used, causing a change in the energy bands
within the structure, this type of devices is termed a heterostructure. The ability to
customize the energy-band structure adds flexibility to the design of new devices based
on doping and material variations in the various layers. These changes in the energy band
provide an additional means, independent of doping and applied external fields, to control
the flow and distribution of the charge carriers throughout these devices.
When two semiconductor materials with different bandgaps are joined together to form a
heterojunction, discontinuities in both the conduction and valence band edges occur at the
heterointerface. For the HEMT, the wide-bandgap material, for example AlGaN, is ndoped with Si donors. The added charges bend the band edges and create a triangular
potential well in the conduction-band edge of the lower bandgap material, for example,
GaN. Electrons accumulate in this well and form a sheet charge analogous to the
inversion channel in an SiO2/Si MOS structure. The thickness of this channel is typically
only 100 Å, which is much smaller than the de Broglie wavelength of the electrons in
GaN which is given by λ = h/(2mn*kT)1/2. Hence the electrons are quantized in a twodimensional system at the interface, and so the channel of the HEMT is called a twodimensional electron gas (2DEG). An advantage to such a device structure is the physical
separation between the donors and the electrons in the channel layer, thus reducing the
impurity Coulombic scattering and, therefore, enhances the mobility as well as the
effective velocity of the electrons under the influence of an electric field.

21

2.7.3 Equations for the Two-dimensional Electrons as the current carriers.
Within the framework of the effective mass approximation, the electronic subband energy
levels, Ei, and the corresponding envelope wavefunction are the solutions of the
Schrödinger equation given by Stern et al. [65]:
[T – eV(z)] ψ(x,y.z) = Eψ(x,y,z)

(2.3)

where T is the kinetic energy operator, and V(z) is the electrostatic potential which in
turn is found from the solution of the Poisson equation:

ρ ( z)
d 2V ( z )
=−
2
ε
dz

(2.4)

with the boundary conditions:
dV ( z )
= 0,
dz

as z → ± ∞

(2.5)

dV ( z )
dz

(2.6)

and

εA

dV ( z )
dz

z=d −

=εB

z = d1+

Here εA and εB are the static dielectric constants of the barrier and the channel layers,
respectively. ρ(z) is the charge density in both the depletion layer and the channel layer:

ρ(z) = e[n(z) – p(z) + NA – ND]

(2.7)

where n(z) and p(z) are the densities of the electrons and holes, and NA and ND are the
densities of the ionized donors and acceptors, respectively.

22

Since the electrostatic potential, V(z), given by equation (2.4), is only a function of the z
coordinate, the envelope function ψ(x,y,z) can be written as (Stern et. al):

ψ(x,y,z) = ξi(z)exp(iθz)exp(ikxx + ikyy)

(2.8)

where kx and ky are the x and y components of the wavevectors measured relative to the
band edge, θ is the superlattice wavevector, and ξi(z) is the solution of Schrödinger
equation which describes the one-dimensional bound motion:

η2 d 2
−
− eV ( z ) ξ i ( z ) = E i ξ i ( z )
2m z dz 2

(2.9)

where the boundary conditions are:

ξi(z) = 0

for z = ± ∞.

(2.10)

Here mz is the principal effective mass for the electron motion perpendicular to the
interface. The two-dimensional free motion of the electrons can be described by the

Schrödinger equation:

−

η2 ∂ 2
η2 ∂ 2
−
exp(ik x x + ik y y ) = E x , y exp(ik x x + ik y y )
2m x ∂x 2 2m y ∂y 2

(2.11)

where mx and my are the principal effective masses for the motion parallel to the
interface, obtained from the bulk masses (Stern et. al). Each eigenvalue Ei of (2.9) is the
bottom of a continuum of energy levels called a ‘subband’. The subbands can be grouped
into ladders with respect to the bulk conduction band minimum from which they
originate. Each subband energy level is found from the solution of (2.9) and is given by:

23


E i (k ) = E i +

2 2
η2 k x2 η k y
+
2m x
2m y

i = 0, 1, 2,...

(2.12)

representing the subband energy levels arising from the conduction valley with the
electron mass mz for the motion perpendicular to the interface. Equation (2.12) states that
a continuum of the allowed states is associated with the subband level Ei, which implies
the model of the two-dimensional electron gas (2DEG) as well as the concept of 2D
subbands.
In order to progress further from the solution of equations (2.3) and (2.4) to determine the
band bending, one has to specify the electrostatic potential. Once V(z) is specified, one
must solve the Schrödinger equation (2.3) and the Poisson equation (2.4) self-consistently
(Stern et al). One can, however, find a satisfactory physical picture for some limiting
cases. The simplest cases are illustrated in Figure 2.6a, representing an infinite square
well (e.g. (AlGaN/GaN/AlGaN heterostructure), and 2.6b, representing a triangular
(asymmetric) well (e.g., (AlGaN/GaN) heterostructure).
V(z)

V(z)

∞

∞

∞
i=2

i=2
i=1

i=1

i=0

i=0
Z

-LZ
(a)

0

LZ

Z

0
(b)

Figure 2.6: Schematic diagram showing eigenenergies and wavefunctions for (a) an infinite square well and
(b) a triangular well.

24


(i) Infinite square well
- eV(z) = 0

for –Lz < z < Lz

(2.13a)

- eV(z) = ∞

for |z| > Lz

(2.13b)

Since wavefunction must vanish at z = ± Lz the Bohr-Sommerfeld quantization
conditions yields (Landau et al.) [66]:

Lz
− Lz

dz =

ηπ (i + 1)

(2.14)

2m z E i

which gives:

Ei =

η2 π 2
(i + 1) 2
2
8m z L z

i = 0, 1, 2,...

(2.15)

(ii) Asymmetric triangular well
-eV(z) = eFsz

for z ≥ 0

(2.16a)

-eV(z) = ∞

for z < 0

(2.16b)

where Fs is the effective electric field at the interface.
Then the Bohr-Sommerfeld quantization condition gives (Landau et. al):

∞
0

1

( E i − eFs z ) 2 dz =

ηπ (i + 3 / 4)
2m z

(2.17)

and the solution of this equation gives the energy levels quantized in the z-direction as:

25