805
The III–V nitride semiconductors, gallium nitride,
aluminium nitride, and indium nitride, have
been recognized as promising materials for
novel electronic and optoelectronic device
applications for some time now. Since informed
device design requires a firm grasp of the
material properties of the underlying electronic
materials, the electron transport that occurs
within these III–V nitride semiconductors has
been the focus of considerable study over the
years. In an effort to provide some perspective
on this rapidly evolving field, in this paper
we review analyses of the electron transport
within these III–V nitride semiconductors. In
particular, we discuss the evolution of the field,
compare and contrast results obtained by different
researchers, and survey the current literature.
In order to narrow the scope of this chapter,
we will primarily focus on electron transport
within bulk wurtzite gallium nitride, aluminium
nitride, and indium nitride for this analysis.
Most of our discussion will focus on results
obtained from our ensemble semi-classical threevalley Monte Carlo simulations of the electron
transport within these materials, our results
conforming with state-of-the-art III–V nitride
semiconductor orthodoxy. Steady-state and
transient electron transport results are presented.
We conclude our discussion by presenting some
recent developments on the electron transport
within these materials.
The III–V nitride semiconductors, gallium nitride
(GaN), aluminium nitride (AlN), and indium nitride
(InN), have been known as promising materials for
novel electronic and optoelectronic device applications
for some time now [33.1–4]. In terms of electronics, their wide energy gaps, large breakdown fields,
high thermal conductivities, and favorable electron
transport characteristics, make GaN, AlN, and InN,
and alloys of these materials, ideally suited for novel
33.1
Electron Transport Within
Semiconductors and the Monte Carlo
Simulation Approach ...........................
33.1.1 The Boltzmann Transport
Equation ..................................
33.1.2 Our Ensemble Semi-Classical
Monte Carlo Simulation Approach
33.1.3 Parameter Selections for Bulk
Wurtzite GaN, AlN, and InN.........
33.2 Steady-State and Transient Electron
Transport Within Bulk Wurtzite GaN, AlN,
and InN ..............................................
33.2.1 Steady-State Electron Transport
Within Bulk Wurtzite GaN ...........
33.2.2 Steady-State Electron Transport:
A Comparison of the III–V Nitride
Semiconductors with GaAs .........
33.2.3 Influence of Temperature
on the Electron Drift Velocities
Within GaN and GaAs.................
33.2.4 Influence of Doping
on the Electron Drift Velocities
Within GaN and GaAs.................
33.2.5 Electron Transport in AlN ............
33.2.6 Electron Transport in InN............
33.2.7 Transient Electron Transport .......
33.2.8 Electron Transport: Conclusions...
33.3 Electron Transport Within III–V
Nitride Semiconductors: A Review .........
33.3.1 Evolution of the Field ................
33.3.2 Recent Developments ................
33.3.3 Future Perspectives ...................
33.4 Conclusions .........................................
References ..................................................
806
807
808
808
810
811
812
812
815
816
818
820
822
822
822
824
825
826
826
high-power and high-frequency electron device applications. On the optoelectronics front, the direct nature
of the energy gaps associated with GaN, AlN, and
InN, make this family of materials, and its alloys,
well suited for novel optoelectronic device applications
in the visible and ultraviolet frequency range. While
initial efforts to study these materials were hindered
by growth difficulties, recent improvements in material quality have made the realization of a number of
Part D 33
Electron Trans
33. Electron Transport Within the III–V Nitride
Semiconductors, GaN, AlN, and InN:
A Monte Carlo Analysis
806
Part D
Materials for Optoelectronics and Photonics
Part D 33.1
III–V nitride semiconductor-based electronic [33.5–9]
and optoelectronic [33.9–12] devices possible. These
developments have fueled considerable interest in these
III–V nitride semiconductors.
In order to analyze and improve the design of III–V
nitride semiconductor-based devices, an understanding
of the electron transport that occurs within these materials is necessary. Electron transport within bulk GaN,
AlN, and InN has been examined extensively over the
years [33.13–32]. Unfortunately, uncertainty in the material parameters associated with GaN, AlN, and InN
remains a key source of ambiguity in the analysis of
the electron transport within these materials [33.32].
In addition, some recent experimental [33.33] and theoretical [33.34] developments have cast doubt upon
the validity of widely accepted notions upon which
our understanding of the electron transport mechanisms within the III–V nitride semiconductors, GaN,
AlN, and InN, has evolved. Another confounding matter is the sheer volume of research activity being
performed on the electron transport within these materials, presenting the researcher with a dizzying array
of seemingly disparate approaches and results. Clearly,
at this critical juncture at least, our understanding of
the electron transport within the III–V nitride semiconductors, GaN, AlN, and InN, remains in a state of
flux.
In order to provide some perspective on this rapidly
evolving field, we aim to review analyses of the electron
transport within the III–V nitride semiconductors, GaN,
AlN, and InN, within this paper. In particular, we will
discuss the evolution of the field and survey the current
literature. In order to narrow the scope of this review,
we will primarily focus on the electron transport within
bulk wurtzite GaN, AlN, and InN for the purposes of this
paper. Most of our discussion will focus upon results
obtained from our ensemble semi-classical three-valley
Monte Carlo simulations of the electron transport within
these materials, our results conforming with state-of-theart III–V nitride semiconductor orthodoxy. We hope that
researchers in the field will find this review useful and
informative.
We begin our review with the Boltzmann transport
equation, which underlies most analyses of the electron
transport within semiconductors. The ensemble semiclassical three-valley Monte Carlo simulation approach
that we employ in order to solve this Boltzmann transport equation is then discussed. The material parameters
corresponding to bulk wurtzite GaN, AlN, and InN are
then presented. We then use these material parameter
selections and our ensemble semi-classical three-valley
Monte Carlo simulation approach to determine the nature of the steady-state and transient electron transport
within the III–V nitride semiconductors. Finally, we
present some recent developments on the electron transport within these materials.
This paper is organized in the following manner.
In Sect. 33.1, we present the Boltzmann transport equation and our ensemble semi-classical three-valley Monte
Carlo simulation approach that we employ in order to
solve this equation for the III–V nitride semiconductors, GaN, AlN, and InN. The material parameters,
corresponding to bulk wurtzite GaN, AlN, and InN,
are also presented in Sect. 33.1. Then, in Sect. 33.2, using results obtained from our ensemble semi-classical
three-valley Monte Carlo simulations of the electron
transport within these III–V nitride semiconductors, we
study the nature of the steady-state electron transport
that occurs within these materials. Transient electron
transport within the III–V nitride semiconductors is
also discussed in Sect. 33.2. A review of the III–
V nitride semiconductor electron transport literature,
in which the evolution of the field is discussed and
a survey of the current literature is presented, is then
featured in Sect. 33.3. Finally, conclusions are provided
in Sect. 33.4.
33.1 Electron Transport Within Semiconductors
and the Monte Carlo Simulation Approach
The electrons within a semiconductor are in a perpetual state of motion. In the absence of an applied electric
field, this motion arises as a result of the thermal energy
that is present, and is referred to as thermal motion. From
the perspective of an individual electron, thermal motion
may be viewed as a series of trajectories, interrupted by
a series of random scattering events. Scattering may arise
as a result of interactions with the lattice atoms, impurities, other electrons, and defects. As these interactions
lead to electron trajectories in all possible directions,
i. e., there is no preferred direction, while individual
electrons will move from one location to another, when
taken as an ensemble, and assuming that the electrons
are in thermal equilibrium, the overall electron distribu-
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
33.1.1 The Boltzmann Transport Equation
An electron ensemble may be characterized by its
distribution function, f (r, p, t), where r denotes the
position, p represents the momentum, and t indicates
time. The response of this distribution function to an
applied electric field, E, is the issue at stake when
one investigates the electron transport within a semiconductor. When the dimensions of the semiconductor
are large, and quantum effects are negligible, the ensemble of electrons may be treated as a continuum, so
the corpuscular nature of the individual electrons within
the ensemble, and the attendant complications which
arise, may be neglected. In such a circumstance, the
evolution of the distribution function, f (r, p, t), may
be determined using the Boltzmann transport equation.
In contrast, when the dimensions of the semiconductor are small, and quantum effects are significant, then
the Boltzmann transport equation, and its continuum description of the electron ensemble, is no longer valid. In
such a case, it is necessary to adopt quantum transport
methods in order to study the electron transport within
the semiconductor [33.35].
For the purposes of this analysis, we will focus
on the electron transport within bulk semiconductors,
i. e., semiconductors of sufficient dimensions so that
the Boltzmann transport equation is valid. Ashcroft and
Mermin [33.36] demonstrated that this equation may be
expressed as
∂f
∂ f = − ṗ · ∇p f − ṙ · ∇r f +
.
(33.1)
∂t
∂t scat
The first term on the right-hand side of (33.1) represents
the change in the distribution function due to external
forces applied to the system. The second term on the
right-hand side of (33.1) accounts for the electron diffusion which occurs. The final term on the right-hand side
of (33.1) describes the effects of scattering.
Owing to its fundamental importance in the analysis of the electron transport within semiconductors,
a number of techniques have been developed over the
years in order to solve the Boltzmann transport equation. Approximate solutions to the Boltzmann transport
equation, such as the displaced Maxwellian distribution function approach of Ferry [33.14] and Das and
Ferry [33.15] and the nonstationary charge transport
analysis of Sandborn et al. [33.37], have proven useful. Low-field approximate solutions have also proven
elementary and insightful [33.17, 20, 38]. A number of
these techniques have been applied to the analysis of
the electron transport within the III–V nitride semiconductors, GaN, AlN, and InN [33.14, 15, 17, 20, 38, 39].
Alternatively, more sophisticated techniques have been
developed which solve the Boltzmann transport equation
directly. These techniques, while allowing for a rigorous
solution of the Boltzmann transport equation, are rather
involved, and require intense numerical analysis. They
are further discussed by Nag [33.40].
For studies of the electron transport within the III–V
nitride semiconductors, GaN, AlN, and InN, by far
the most common approach to solving the Boltzmann
transport equation has been the ensemble semi-classical
Monte Carlo simulation approach. Of the III–V nitride semiconductors, the electron transport within GaN
807
Part D 33.1
tion will remain static. Accordingly, no net current flow
occurs.
With the application of an applied electric field, E,
each electron in the ensemble will experience a force,
−q E. While this force may have a negligible impact
upon the motion of any given individual electron, taken
as an ensemble, the application of such a force will
lead to a net aggregate motion of the electron distribution. Accordingly, a net current flow will occur, and the
overall electron ensemble will no longer be in thermal
equilibrium. This movement of the electron ensemble in
response to an applied electric field, in essence, represents the fundamental issue at stake when we study the
electron transport within a semiconductor.
In this section, we provide a brief tutorial on the issues at stake in our analysis of the electron transport
within the III–V nitride semiconductors, GaN, AlN, and
InN. We begin our analysis with an introduction to the
Boltzmann transport equation. This equation describes
how the electron distribution function evolves under the
action of an applied electric field, and underlies the
electron transport within bulk semiconductors. We then
introduce the Monte Carlo simulation approach to solving this Boltzmann transport equation, focusing on the
ensemble semi-classical three-valley Monte Carlo simulation approach used in our simulations of the electron
transport within the III–V nitride semiconductors. Finally, we present the material parameters corresponding
to bulk wurtzite GaN, AlN, and InN.
This section is organized in the following manner. In Sect. 33.1.1, the Boltzmann transport equation
is introduced. Then, in Sect. 33.1.2, our ensemble semiclassical three-valley Monte Carlo simulation approach
to solving this Boltzmann transport equation is presented. Finally, in Sect. 33.1.3, our material parameter
selections, corresponding to bulk wurtzite GaN, AlN,
and InN, are presented.
33.1 Electron Transport and Monte Carlo Simulation
808
Part D
Materials for Optoelectronics and Photonics
Part D 33.1
has been studied the most extensively using this ensemble Monte Carlo simulation approach [33.13, 16,
18, 19, 21, 22, 27, 29, 32], with AlN [33.24, 25, 29] and
InN [33.23, 28, 29, 31] less so. The Monte Carlo simulation approach has also been used to study the electron
transport within the two-dimensional electron gas of the
AlGaN/GaN interface which occurs in high electron
mobility AlGaN/GaN field-effect transistors [33.41,42].
At this point, it should be noted that the complete solution of the Boltzmann transport equation requires the
resolution of both steady-state and transient responses.
Steady-state electron transport refers to the electron
transport that occurs long after the application of an applied electric field, i. e., once the electron ensemble has
settled to a new equilibrium state (we are not necessarily referring to thermal equilibrium here, since thermal
equilibrium is only achieved in the absence of an applied
electric field). As the distribution function is difficult to
visualize quantitatively, researchers typically study the
dependence of the electron drift velocity (the average
electron velocity determined by statistically averaging
over the entire electron ensemble) on the applied electric field in the analysis of steady-state electron transport;
in other words, they determine the velocity–field characteristic. Transient electron transport, by way of contrast,
refers to the transport that occurs while the electron
ensemble is evolving into its new equilibrium state. Typically, it is characterized by studying the dependence of
the electron drift velocity on the time elapsed, or the
distance displaced, since the electric field was initially
applied. Both steady-state and transient electron transport within the III–V nitride semiconductors, GaN, AlN,
and InN, are reviewed within this paper.
33.1.2 Our Ensemble Semi-Classical Monte
Carlo Simulation Approach
For the purposes of our analysis of the electron transport within the III–V nitride semiconductors, GaN, AlN,
and InN, we employ ensemble semi-classical Monte
Carlo simulations. A three-valley model for the conduction band is employed. Nonparabolicity is considered
in the lowest conduction band valley, this nonparabolicity being treated through the application of the Kane
model [33.43].
In the Kane model, the energy band of the Γ valley
is assumed to be nonparabolic, spherical, and of the
form
~2 k2
= E (1 + αE) ,
2m ∗
(33.2)
where ~k denotes the crystal momentum, E represents
the energy above the minimum, m ∗ is the effective
mass, and the nonparabolicity coefficient, α, is given
by
1
m∗ 2
α=
1−
,
(33.3)
Eg
me
where m e and E g denote the free electron mass and the
energy gap, respectively [33.43].
The scattering mechanisms considered in our analysis are (1) ionized impurity, (2) polar optical phonon,
(3) piezoelectric [33.44, 45], and (4) acoustic deformation potential. Intervalley scattering is also considered.
Piezoelectric scattering is treated using the well established zinc blende scattering rates, and so a suitably
transformed piezoelectric constant, e14 , must be selected. This may be achieved through the transformation
suggested by Bykhovski et al. [33.44, 45]. We also assume that all donors are ionized and that the free
electron concentration is equal to the dopant concentration. The motion of three thousand electrons is examined
in our steady-state electron transport simulations, while
the motion of ten thousand electrons is considered in
our transient electron transport simulations. The crystal
temperature is set to 300 K and the doping concentration is set to 1017 cm−3 in all cases, unless otherwise
specified. Electron degeneracy effects are accounted
for by means of the rejection technique of Lugli and
Ferry [33.46]. Electron screening is also accounted for
following the Brooks–Herring method [33.47]. Further
details of our approach are discussed in the literature [33.16, 21–24, 29, 32, 48].
33.1.3 Parameter Selections
for Bulk Wurtzite GaN, AlN, and InN
The material parameter selections, used for our simulations of the electron transport within the III–V nitride
semiconductors, GaN, AlN, and InN, are tabulated in
Table 33.1. These parameter selections are the same as
those employed by Foutz et al. [33.29]. While the band
structures corresponding to bulk wurtzite GaN, AlN,
and InN are still not agreed upon, the band structures of
Lambrecht and Segall [33.49] are adopted for the purposes of this analysis. For the case of bulk wurtzite GaN,
the analysis of Lambrecht and Segall [33.49] suggests
that the lowest point in the conduction band is located
at the center of the Brillouin zone, at the Γ point, the
first upper conduction band valley minimum also occurring at the Γ point, 1.9 eV above the lowest point
in the conduction band, the second upper conduction
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
33.1 Electron Transport and Monte Carlo Simulation
selections are from Foutz et al. [33.29]
Parameter
Mass density g/cm3
Longitudinal sound velocity (cm/s)
Transverse sound velocity (cm/s)
Acoustic deformation potential (eV)
Static dielectric constant
High-frequency dielectric constant
Effective mass (Γ1 valley)
Piezoelectric constant, e14 C/cm2
Direct energy gap (eV)
Optical phonon energy (meV)
Intervalley deformation potentials (eV/cm)
Intervalley phonon energies (meV)
GaN
AlN
InN
6.15
6.56 × 105
2.68 × 105
8.3
8.9
5.35
0.20 m e
3.75 × 10−5
3.39
91.2
109
91.2
3.23
9.06 × 105
3.70 × 105
9.5
8.5
4.77
0.48 m e
9.2 × 10−5
6.2
99.2
109
99.2
6.81
6.24 × 105
2.55 × 105
7.1
15.3
8.4
0.11 m e
3.75 × 10−5
1.89
89.0
109
89.0
Table 33.2 The valley parameter selections corresponding to bulk wurtzite GaN, AlN, and InN. These parameter selections
are from Foutz et al. [33.29]. These parameters were originally determined from the band structural calculations of
Lambrecht and Segall [33.49]
GaN
AlN
InN
Valley number
1
2
3
Valley location
Valley degeneracy
Effective mass
Intervalley energy separation (eV)
Energy gap (eV)
Nonparabolicity eV−1
Valley location
Valley degeneracy
Effective mass
Intervalley energy separation (eV)
Energy gap (eV)
Nonparabolicity eV−1
Valley location
Valley degeneracy
Effective mass
Intervalley energy separation (eV)
Energy gap (eV)
Nonparabolicity eV−1
Γ1
1
0.2 m e
−
3.39
0.189
Γ1
1
0.48 m e
−
6.2
0.044
Γ1
1
0.11 m e
−
1.89
0.419
Γ2
1
me
1.9
5.29
0.0
L-M
6
me
0.7
6.9
0.0
A
1
me
2.2
4.09
0.0
L–M
6
me
2.1
5.49
0.0
K
2
me
1.0
7.2
0.0
Γ2
1
me
2.6
4.49
0.0
band valley minima occurring along the symmetry lines
between the L and M points, 2.1 eV above the lowest
point in the conduction band; see Table 33.2. For the
case of bulk wurtzite AlN, the analysis of Lambrecht
and Segall [33.49] suggests that the lowest point in the
conduction band is located at the center of the Brillouin zone, at the Γ point, the first upper conduction
band valley minima occurring along the symmetry lines
between the L and M points, 0.7 eV above the lowest
point in the conduction band, the second upper conduction band valley minima occurring at the K points, 1 eV
above the lowest point in the conduction band; see Table 33.2. For the case of bulk wurtzite InN, the analysis
of Lambrecht and Segall [33.49] suggests that the lowest point in the conduction band is located at the center
of the Brillouin zone, at the Γ point, the first upper conduction band valley minimum occurring at the A point,
2.2 eV above the lowest point in the conduction band,
Part D 33.1
Table 33.1 The material parameter selections corresponding to bulk wurtzite GaN, AlN, and InN. These parameter
809
810
Part D
Materials for Optoelectronics and Photonics
Part D 33.2
the second upper conduction band valley minimum occurring at the Γ point, 2.6 eV above the lowest point in
the conduction band; see Table 33.2. We ascribe an effective mass equal to the free electron mass, m e , to all of
the upper conduction band valleys. The nonparabolicity
coefficient, α, corresponding to each upper conduction
band valley is set to zero, so the upper conduction band
valleys are assumed to be completely parabolic. For our
simulations of the electron transport within gallium arsenide (GaAs), the material parameters employed are
mostly from Littlejohn et al. [33.50], although it should
be noted that the mass density, the energy gap, and the
sound velocities are from Blakemore [33.51].
It should be noted that the energy gap associated
with InN has been the subject of some controversy
since 2002. The pioneering experimental results of Tansley and Foley [33.52], reported in 1986, suggested that
InN has an energy gap of 1.89 eV. This value has
been used extensively in Monte Carlo simulations of
the electron transport within this material since that
time [33.23, 28, 29, 31]; typically, the influence of the
energy gap on the electron transport occurs through its
impact on the nonparabolicity coefficient, α. In 2002,
Davydov et al. [33.53], Wu et al. [33.54], and Matsuoka
et al. [33.55], presented experimental evidence which
instead suggests a considerably smaller energy gap for
InN, around 0.7 eV. As this new result is still the subject
of some controversy, we adopt the traditional Tansley
and Foley [33.52] energy gap value for the purposes of
our present analysis, noting that even if the newer value
for the energy gap was adopted, it would only change
our electron transport results marginally; the sensitivity of the velocity–field characteristic associated with
bulk wurtzite GaN to variations in the nonparabolicity
coefficient, α, has been explored, in detail, by O’Leary
et al. [33.32].
The band structure associated with bulk wurtzite
GaN has also been the focus of some controversy. In particular, Brazel et al. [33.56] employed ballistic electron
emission microscopy measurements in order to demonstrate that the first upper conduction band valley occurs
only 340 meV above the lowest point in the conduction
band for this material. This contrasts rather dramatically
with more traditional results, such as the calculation of
Lambrecht and Segall [33.49], which instead suggest
that the first upper conduction band valley minimum
within wurtzite GaN occurs about 2 eV above the lowest point in the conduction band. Clearly, this will have
a significant impact upon the results. While the results
of Brazel et al. [33.56] were reported in 1997, electron
transport simulations adopted the more traditional intervalley energy separation of about 2 eV until relatively
recently. Accordingly, we have adopted the more traditional intervalley energy separation for the purposes
of our present analysis. The sensitivity of the velocity–
field characteristic associated with bulk wurtzite GaN to
variations in the intervalley energy separation has been
explored, in detail, by O’Leary et al. [33.32].
33.2 Steady-State and Transient Electron Transport
Within Bulk Wurtzite GaN, AlN, and InN
The current interest in the III–V nitride semiconductors, GaN, AlN, and InN, is primarily being fueled by
the tremendous potential of these materials for novel
electronic and optoelectronic device applications. With
the recognition that informed electronic and optoelectronic device design requires a firm understanding of the
nature of the electron transport within these materials,
electron transport within the III–V nitride semiconductors has been the focus of intensive investigation
over the years. The literature abounds with studies on
steady-state and transient electron transport within these
materials [33.13–34, 38, 39, 41, 42, 48]. As a result of
this intense flurry of research activity, novel III–V nitride semiconductor-based devices are starting to be
deployed in today’s commercial products. Future developments in the III–V nitride semiconductor field
will undoubtedly require an even deeper understand-
ing of the electron transport mechanisms within these
materials.
In the previous section, we presented details of the
Monte Carlo simulation approach that we employ for the
analysis of the electron transport within the III–V nitride
semiconductors, GaN, AlN, and InN. In this section,
an overview of the steady-state and transient electron
transport results we obtained from these Monte Carlo
simulations is provided. In the first part of this section,
we focus upon bulk wurtzite GaN. In particular, the
velocity–field characteristic associated with this material will be examined in detail. Then, an overview of our
steady-state electron transport results, corresponding to
the three III–V nitride semiconductors under consideration in this analysis, will be given, and a comparison with
the more conventional III–V compound semiconductor,
GaAs, will be presented. A comparison between the tem-
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
33.2.1 Steady-State Electron Transport
Within Bulk Wurtzite GaN
Our examination of results begins with GaN, the most
commonly studied III–V nitride semiconductor. The
velocity–field characteristic associated with this material is presented in Fig. 33.1. This result was obtained
through our Monte Carlo simulations of the electron
transport within this material for the bulk wurtzite
GaN parameter selections specified in Table 33.1 and
Table 33.2; the crystal temperature was set to 300 K
and the doping concentration to 1017 cm−3 . We see that
for applied electric fields in excess of 140 kV/cm, the
electron drift velocity decreases, eventually saturating at
1.4 × 107 cm/s for high applied electric fields. By examining the results of our Monte Carlo simulation further,
an understanding of this result becomes clear.
First, we discuss the results at low applied electric
fields, i. e., applied electric fields of less than 30 kV/cm.
This is referred to as the linear regime of electron trans-
Electron velocity (107 cm/s)
3.0
2.0
1.0
0.0
0
200
811
Part D 33.2
perature dependence of the velocity–field characteristics
associated with GaN and GaAs will then be presented,
and our Monte Carlo results will be used to account
for the differences in behavior. A similar analysis will
be presented for the doping dependence. Next, detailed
simulation results for AlN and InN will be presented. Finally, the transient electron transport that occurs within
the III–V nitride semiconductors, GaN, AlN, and InN,
is determined and compared with that in GaAs.
This section is organized in the following manner.
In Sect. 33.2.1, the velocity–field characteristic associated with bulk wurtzite GaN is presented and analyzed.
Then, in Sect. 33.2.2, the velocity-field characteristics associated with the III–V nitride semiconductors
under consideration in this analysis will be compared
and contrasted with that of GaAs. The sensitivity of
the velocity–field characteristic associated with bulk
wurtzite GaN to variations in the crystal temperature will
then be examined in Sect. 33.2.3, and a comparison with
that corresponding to GaAs presented. In Sect. 33.2.4,
the sensitivity of the velocity–field characteristic associated with bulk wurtzite GaN to variations in the
doping concentration level will be explored, and a comparison with that corresponding to GaAs presented.
The velocity–field characteristics associated with AlN
and InN will then be examined in Sect. 33.2.5 and
Sect. 33.2.6, respectively. Our transient electron transport analysis results are then presented in Sect. 33.2.7.
Finally, the conclusions of this electron transport analysis are summarized in Sect. 33.2.8.
33.2 Steady-State and Transient Electron Transport
400
600
Electric field (kV/cm)
Fig. 33.1 The velocity–field characteristic associated with
bulk wurtzite GaN. Like many other compound semiconductors, the electron drift velocity reaches a peak, and at
higher applied electric fields it decreases until it saturates
port as the electron drift velocity is well characterized
by the low-field electron drift mobility, µ, in this regime,
i. e., a linear low-field electron drift velocity dependence on the applied electric field vd = µE, applies in
this regime. Examining the distribution function for this
regime, we find that it is very similar to the zero-field
distribution function with a slight shift in the direction
opposite to the applied electric field. In this regime,
the average electron energy remains relatively low, with
most of the energy gained from the applied electric field
being transferred into the lattice through polar optical
phonon scattering.
If we examine the average electron energy as a function of the applied electric field, shown in Fig. 33.2, we
see that there is a sudden increase at around 100 kV/cm.
In order to understand why this increase occurs, we note
that the dominant energy loss mechanism for many of
the III–V compound semiconductors, including GaN,
is polar optical phonon scattering. When the applied
electric field is less than 100 kV/cm, all of the energy
that the electrons gain from the applied electric field is
lost through polar optical phonon scattering. The other
scattering mechanisms, i. e., ionized impurity scattering, piezoelectric scattering and acoustic deformation
potential scattering, do not remove energy from the electron ensemble: they are elastic scattering mechanisms.
However, beyond a certain critical applied electric field
strength, the polar optical phonon scattering mechanism
can no longer remove all of the energy gained from the
applied electric field. Other scattering mechanisms must
start to play a role if the electron ensemble is to remain
in equilibrium. The average electron energy increases
812
Part D
Materials for Optoelectronics and Photonics
Part D 33.2
until intervalley scattering begins and an energy balance
is re-established.
Electron energy (eV)
GaN
2.0
1.0
0.0
0
200
400
600
Electric field (kV/cm)
Fig. 33.2 The average electron energy as a function of the
applied electric field for bulk wurtzite GaN. Initially, the
average electron energy remains low, only slightly higher
than the thermal energy, 32 kB T . At 100 kV/cm, however,
the average electron energy increases dramatically. This
increase is due to the fact that the polar optical phonon
scattering mechanism can no longer absorb all of the energy
gained from the applied electric field
Number of particles
3000
1
2000
As the applied electric field is increased beyond
100 kV/cm, the average electron energy increases until
a substantial fraction of the electrons have acquired
enough energy in order to transfer into the upper
valleys. As the effective mass of the electrons in
the upper valleys is greater than that in the lowest valley, the electrons in the upper valleys will be
slower. As more electrons transfer to the upper valleys (Fig. 33.3), the electron drift velocity decreases.
This accounts for the negative differential mobility observed in the velocity–field characteristic depicted in
Fig. 33.1.
Finally, at high applied electric fields, the number of
electrons in each valley saturates. It can be shown that in
the high-field limit the number of electrons in each valley
is proportional to the product of the density of states
of that particular valley and the corresponding valley
degeneracy. At this point, the electron drift velocity stops
decreasing and achieves saturation.
Thus far, electron transport results corresponding to
bulk wurtzite GaN have been presented and discussed
qualitatively. It should be noted, however, that the same
phenomenon that occurs in the velocity–field characteristic associated with GaN also occurs for the other III–V
nitride semiconductors, AlN and InN. The importance
of polar optical phonon scattering when determining the
nature of the electron transport within the III–V nitride
semiconductors, GaN, AlN, and InN, will become even
more apparent later, as it will be used to account for
much of the electron transport behavior within these
materials.
33.2.2 Steady-State Electron Transport:
A Comparison of the III–V Nitride
Semiconductors with GaAs
2
3
1000
0
0
200
400
600
Electric field (kV/cm)
Fig. 33.3 The valley occupancy as a function of the applied
electric field for the case of bulk wurtzite GaN. Soon after
the average electron energy increases, electrons begin to
transfer to the upper valleys of the conduction band. Three
thousand electrons were employed for this simulation. The
valleys are labeled 1, 2, and 3, in accordance with their
energy minima; the lowest energy valley is valley 1, the
next higher energy valley is valley 2, and the highest energy
valley is valley 3
Setting the crystal temperature to 300 K and the level of
doping to 1017 cm−3 , the velocity–field characteristics
associated with the III–V nitride semiconductors under
consideration in this analysis – GaN, AlN, and InN – are
contrasted with that of GaAs in Fig. 33.4. We see that
each of these III–V compound semiconductors achieves
a peak in its velocity–field characteristic. InN achieves
the highest steady-state peak electron drift velocity,
4.1 × 107 cm/s at an applied electric field of 65 kV/cm.
This contrasts with the case of GaN, 2.9 × 107 cm/s
at 140 kV/cm, and that of AlN, 1.7 × 107 cm/s at
450 kV/cm. For GaAs, the peak electron drift velocity
of 1.6 × 107 cm/s occurs at a much lower applied electric field than that for the III–V nitride semiconductors
(only 4 kV/cm).
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
140 kV/cm
InN
4 kV/cm
GaAs
450
kV/cm
GaN
107
AlN
106
10
0
100
1000
Electric field (kV/cm)
Fig. 33.4 A comparison of the velocity–field characteristics associated with the III–V nitride semiconductors, GaN,
AlN, and InN, with that associated with GaAs. After [33.29]
with permission, copyright AIP
33.2.3 Influence of Temperature
on the Electron Drift Velocities
Within GaN and GaAs
The temperature dependence of the velocity–field characteristic associated with bulk wurtzite GaN is now
examined. Figure 33.5a shows how the velocity–field
characteristic associated with bulk wurtzite GaN varies
as the crystal temperature is increased from 100 to
700 K, in increments of 200 K. The upper limit, 700 K,
is chosen as it is the highest operating temperature that
7
a) Drift velocity (10 cm/s)
b)
3.0
Drift velocity (107 cm/s)
2.5
GaAs
GaN
2.0
2.5
2.0
100 K
1.5
100 K
300 K
1.5
300 K
1.0
1.0
500 K 700 K
0.5
0
500 K
0.5
700 K
0
100
200
300
400
500
600
Electric field (kV/cm)
0
0
5
10
15
20
Electric field (kV/cm)
Fig. 33.5a,b A comparison of the temperature dependence of the velocity–field characteristics associated with (a) GaN
and (b) GaAs. GaN maintains a higher electron drift velocity with increased temperatures than GaAs does
813
Part D 33.2
may be expected for AlGaN/GaN power devices. To
highlight the difference between the III–V nitride semiconductors with more conventional III–V compound
semiconductors, such as GaAs, Monte Carlo simulations of the electron transport within GaAs have also
been performed under the same conditions as GaN. Figure 33.5b shows the results of these simulations. Note
that the electron drift velocity for the case of GaN is
much less sensitive to changes in temperature than that
associated with GaAs.
To quantify this dependence further, the low-field
electron drift mobility, the peak electron drift velocity,
and the saturation electron drift velocity are plotted as
a function of the crystal temperature in Fig. 33.6, these
results being determined from our Monte Carlo simulations of the electron transport within these materials. For
both GaN and GaAs, it is found that all of these electron
transport metrics diminish as the crystal temperature
is increased. As may be seen through an inspection of
Fig. 33.5, the peak and saturation electron drift velocities
do not drop as much in GaN as they do in GaAs in
response to increases in the crystal temperature. The
low-field electron drift mobility in GaN, however, is seen
to fall quite rapidly with temperature, this drop being
particularly severe for temperatures at and below room
temperature. This property will likely have an impact on
high-power device performance.
Delving deeper into our Monte Carlo results yields
clues to the reason for this variation in temperature dependence. First, we examine the polar optical phonon
scattering rate as a function of the applied electric field
strength. Figure 33.7 shows that the scattering rate only
Drift velocity (cm/s)
108
65 kV/cm
33.2 Steady-State and Transient Electron Transport
814
Part D
Materials for Optoelectronics and Photonics
Part D 33.2
a) Drift velocity (107 cm/s)
Mobility (cm2/Vs)
b) Drift velocity (107 cm/s)
2500
2.5
GaN
3.5
3.0
2000
2.0
1500
1.5
1000
1.0
Mobility (cm2/Vs)
12 000
GaAs
10 000
2.5
8000
2.0
6000
1.5
4000
1.0
500
0.5
0.0
100
200
300
400
500
600
700
Temperature (K)
0
0.5
2000
0.0
100
200
300
400
500
600
700
Temperature (K)
0
Fig. 33.6a,b A comparison of the temperature dependence of the low-field electron drift mobility (solid lines), the peak
electron drift velocity (diamonds), and the saturation electron drift velocity (solid points) for (a) GaN and (b) GaAs. The
low-field electron drift mobility of GaN drops quickly with increasing temperature, but its peak and saturation electron
drift velocities are less sensitive to increases in temperature than GaAs
a) Scattering rate (1013 s–1)
b) Scattering rate (1012 s–1)
10
10
GaN
500 K
8
700 K
GaAs
700 K
8
500 K
300 K
100 K
6
6
300 K
100 K
4
4
2
2
0
0
0
200
400
600
Electric field (kV/cm)
0
5
10
15
20
Electric field (kV/cm)
Fig. 33.7a,b A comparison of the polar optical phonon scattering rates as a function of the applied electric field strength
for various crystal temperatures for (a) GaN and (b) GaAs. Polar optical phonon scattering is seen to increase much more
quickly with temperature in GaAs
increases slightly with temperature for the case of GaN,
from 6.7 × 1013 s−1 at 100 K to 8.6 × 1013 s−1 at 700 K,
for high applied electric field strengths. Contrast this
with the case of GaAs, where the rate increases from
4.0 × 1012 s−1 at 100 K to more than twice that amount
at 700 K, 9.2 × 1012 s−1 , at high applied electric field
strengths. This large increase in the polar optical phonon
scattering rate for the case of GaAs is one reason for the
large drop in the electron drift velocity with increasing
temperature for the case of GaAs.
A second reason for the variation in temperature dependence of the two materials is the occupancy of the
upper valleys, shown in Fig. 33.8. In the case of GaN, the
upper valleys begin to become occupied at roughly the
same applied electric field strength, 100 kV/cm, independent of temperature. For the case of GaAs, however,
the upper valleys are at a much lower energy than those
in GaN. In particular, while the first upper conduction
band valley minimum is 1.9 eV above the lowest point
in the conduction band in GaN, the first upper conduc-
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
b) Number of particles
3000
3000
GaN
2500
2000
2000
1500
1500
700 K
1000
700 K
1000
100 K
500
GaAs
100 K
2500
500
0
0
0
100
200
300
400
500
600
Electric field (kV/cm)
0
5
10
15
20
Electric field (kV/cm)
Fig. 33.8a,b A comparison of the number of particles in the lowest energy valley of the conduction band, the Γ valley,
as a function of the applied electric field for various crystal temperatures, for the cases of (a) GaN and (b) GaAs. In
GaAs, the electrons begin to occupy the upper valleys much more quickly, causing the electron drift velocity to drop as
the crystal temperature is increased. Three thousand electrons were employed for these steady-state electron transport
simulations
tion band valley is only 290 meV above the bottom of
the conduction band in GaAs [33.51]. As the upper conduction band valleys are so close to the bottom of the
conduction band for the case of GaAs, the thermal energy (at 700 K, kB T 60 meV) is enough in order to
allow for a small fraction of the electrons to transfer
into the upper valleys even before an electric field is
applied. When electrons occupy the upper valleys, intervalley scattering and the upper valleys’ larger effective
masses reduce the overall electron drift velocity. This
a) Drift velocity (107 cm/s)
is another reason why the velocity–field characteristic
associated with GaAs is more sensitive to variations in
crystal temperature than that associated with GaN.
33.2.4 Influence of Doping on the Electron
Drift Velocities Within GaN and GaAs
One parameter that can be readily controlled during
the fabrication of semiconductor devices is the doping concentration. Understanding the effect of doping
b) Drift velocity (107 cm/s)
2.0
3.0
1017 cm–3
1016 cm–3
GaN
1.5
GaAs
1017 cm–3
2.0
1.0
1018
1018 cm–3
cm–3
1.0
0.0
1019
cm–3
0.5
1019 cm–3
0
0
100
200
300
500
400
600
Electric field (kV/cm)
0
5
10
15
20
Electric field (kV/cm)
Fig. 33.9a,b A comparison of the dependence of the velocity–field characteristics associated with (a) GaN and (b) GaAs
on the doping concentration. GaN maintains a higher electron drift velocity with increased doping levels than GaAs does
815
Part D 33.2
a) Number of particles
33.2 Steady-State and Transient Electron Transport
816
Part D
Materials for Optoelectronics and Photonics
Part D 33.2
a) Drift velocity (107 cm/s)
3
Mobility (cm2/Vs)
b) Drift velocity (107 cm/s)
1600
2.0
GaN
1200
Mobility (cm2/Vs)
GaAs
8000
1.5
2
6000
800
1.0
4000
1
400
0
1016
1017
1018
1019
Doping concentration (cm–3)
0
0.5
0.0
1016
2000
1017
1018
1019
Doping concentration (cm–3)
0
Fig. 33.10a,b A comparison of the low-field electron drift mobility (solid lines), the peak electron drift velocity (diamonds), and the saturation electron drift velocity (solid points) for (a) GaN and (b) GaAs as a function of the doping
concentration. These parameters are more insensitive to increases in doping in GaN than in GaAs
on the resultant electron transport is also important.
In Fig. 33.9, the velocity–field characteristic associated
with GaN is presented for a number of different doping concentration levels. Once again, three important
electron transport metrics are influenced by the doping
concentration level: the low-field electron drift mobility, the peak electron drift velocity, and the saturation
electron drift velocity; see Fig. 33.10. Our simulation results suggest that for doping concentrations of less than
1017 cm−3 , there is very little effect on the velocity–field
characteristic for the case of GaN. However, for doping
concentrations above 1017 cm−3 , the peak electron drift
velocity diminishes considerably, from 2.9 × 107 cm/s
for the case of 1017 cm−3 doping to 2.0 × 107 cm/s for
the case of 1019 cm−3 doping. The saturation electron
drift velocity within GaN is found to only decrease
slightly in response to increases in the doping concentration. The effect of doping on the low-field electron
drift mobility is also shown. It is seen that this mobility
drops significantly in response to increases in the doping concentration level, from 1200 cm2 /Vs at 1016 cm−3
doping to 400 cm2 /Vs at 1019 cm−3 doping.
As we did for temperature, we compare the sensitivity of the velocity-field characteristic associated with
GaN to doping with that associated with GaAs. Figure 33.9 shows this comparison. For the case of GaAs,
it is seen that the electron drift velocities decrease much
more with increased doping than those associated with
GaN. In particular, for the case of GaAs, the peak
electron drift velocity decreases from 1.8 × 107 cm/s at
1016 cm−3 doping to 0.6 × 107 cm/s at 1019 cm−3 dop-
ing. For GaAs, at the higher doping levels, the peak in the
velocity-field characteristic disappears completely for
sufficiently high doping concentrations. The saturation
electron drift velocity decreases from 1.0 × 107 cm/s
at 1016 cm−3 doping to 0.6 × 107 cm/s at 1019 cm−3
doping. The low-field electron drift mobility also diminishes dramatically with increased doping, dropping
from 7800 cm2 /Vs at 1016 cm−3 doping to 2200 cm2 /Vs
at 1019 cm−3 doping.
Once again, it is interesting to determine why the
doping dependence in GaAs is so much more pronounced than it is in GaN. Again, we examine the polar
optical phonon scattering rate and the occupancy of
the upper valleys. Figure 33.11 shows the polar optical phonon scattering rates as a function of the applied
electric field, for both GaN and GaAs. In this case, however, due to screening effects, the rate drops when the
doping concentration is increased. The decrease, however, is much more pronounced for the case of GaAs
than for GaN. It is believed that this drop in the polar
optical phonon scattering rate allows for upper valley occupancy to occur more quickly in GaAs rather
than in GaN (Fig. 33.12). For GaN, electrons begin
to occupy the upper valleys at roughly the same applied electric field strength, independent of the doping
level. However, for the case of GaAs, the upper valleys are occupied more quickly with greater doping.
When the upper valleys are occupied, the electron drift
velocity decreases due to intervalley scattering and the
larger effective mass of the electrons within the upper
valleys.
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
b) Scattering rate (1012 s–1)
10
10
GaN
8
1017
6
cm–3
GaAs
8
1016 cm–3
6
1018 cm–3
1017 cm–3
4
1019
cm–3
2
0
4
1018 cm–3
2
1019 cm–3
0
0
200
400
600
Electric field (kV/cm)
0
5
10
15
20
Electric field (kV/cm)
Fig. 33.11a,b A comparison of the polar optical phonon scattering rates as a function of the applied electric field, for both
(a) GaN and (b) GaAs, for various doping concentrations
a) Number of particles
b) Number of particles
3000
3000
1017 cm–3
1018 cm–3
GaN
GaAs
2500
1019 cm–3
2000
2000
1017 cm–3
1500
1019 cm–3
1000
1000
500
0
0
200
400
600
Electric field (kV/cm)
0
0
5
10
15
20
Electric field (kV/cm)
Fig. 33.12a,b A comparison of the number of particles in the lowest valley of the conduction band, the Γ valley, as
a function of the applied electric field, for both (a) GaN and (b) GaAs, for various doping concentration levels. Three
thousand electrons were employed for these steady-state electron transport simulations
33.2.5 Electron Transport in AlN
AlN has the largest effective mass of the III–V nitride
semiconductors considered in this analysis. Accordingly, it is not surprising that this material exhibits
the lowest electron drift velocity and the lowest lowfield electron drift mobility. The sensitivity of the
velocity–field characteristic associated with AlN to variations in the crystal temperature may be examined
by considering Fig. 33.13. As with the case of GaN,
the velocity–field characteristic associated with AlN
is extremely robust to variations in the crystal tem-
perature. In particular, its peak electron drift velocity,
which is 1.8 × 107 cm/s at 100 K, only decreases to
1.2 × 107 cm/s at 700 K. Similarly, its saturation electron drift velocity, which is 1.5 × 107 cm/s at 100 K,
only decreases to 1.0 × 107 cm/s at 700 K. The lowfield electron drift mobility associated with AlN also
diminishes in response to increases in the crystal temperature, from 375 cm2 /Vs at 100 K to 40 cm2 /Vs
at 700 K.
The sensitivity of the velocity–field characteristic
associated with AlN to variations in the doping concentration may be examined by considering Fig. 33.14. It
817
Part D 33.2
a) Scattering rate (1013 s–1)
33.2 Steady-State and Transient Electron Transport
818
Part D
Materials for Optoelectronics and Photonics
Part D 33.2
a) Drift velocity (107 cm/s)
b) Drift velocity (107 cm/s)
2.0
Mobility (cm2/Vs)
400
2.0
AlN
AlN
100 K
1.5
1.0
1.5
300
1.0
200
0.5
10
700 K
500 K
0.5
300 K
0
0
200
800
1000
600
Electric field (kV/cm)
400
0.0
100
200
300
400
500
600
700
Temperature (K)
0
Fig. 33.13a,b The velocity–field characteristic associated with AlN (a) for various crystal temperatures. The trends in
the low-field mobility (solid line), the peak electron drift velocity (diamonds), and the saturation electron drift velocity
(solid points), are also shown. AlN exhibits its peak electron drift velocity at very high applied electric fields. AlN has
the lowest peak electron drift velocity and the lowest low-field electron drift mobility of the III–V nitride semiconductors
considered in this analysis (b)
a) Drift velocity (107 cm/s)
b) Drift velocity (107 cm/s)
2.0
2.0
1018 cm–3
1017cm–3
AlN
1.5
Mobility (cm2/Vs)
250
AlN
200
1.5
150
1019 cm–3
1.0
1.0
100
0.5
0.5
0
0
200
400
800
1000
600
Electric field (kV/cm)
0.0
1016
50
1017
1018
1019
Doping concentration (cm–3)
0
Fig. 33.14a,b The velocity–field characteristic associated with AlN for various doping concentrations (a). The trends in
the low-field electron drift mobility (solid line), the peak electron drift velocity (diamonds), and the saturation electron
drift velocity (solid points), are also shown (b)
is noted that the variations in the velocity–field characteristic associated with AlN in response to variations
in the doping concentration are not as pronounced as
those which occur in response to variations in the
crystal temperature. Quantitatively, the peak electron
drift velocity drops from 1.7 × 107 cm/s at 1017 cm−3
doping to 1.3 × 107 cm/s at 1019 cm−3 doping. Similarly, its saturation electron drift velocity drops from
1.4 × 107 cm/s at 1017 cm−3 doping to 1.2 × 107 cm/s at
1019 cm−3 doping. The influence of doping on the lowfield electron drift mobility associated with AlN is also
observed to be not as pronounced as for the case of crystal temperature. Figure 33.14b shows that the low-field
electron drift mobility associated with AlN decreases
from 140 cm2 /Vs at 1016 cm−3 doping to 100 cm2 /Vs
at 1019 cm−3 doping.
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
b) Drift velocity (107 cm/s)
Mobility (cm2/Vs)
10000
5.0
100 K
InN
4.0
InN
4.0
8000
3.0
6000
2.0
4000
1.0
2000
3.0
300 K
500 K
2.0
700 K
1.0
0
0
50
100
150
0
100
250
200
300
Electric field (kV/cm)
0
200
300
400
500
600
700
Temperature (K)
Fig. 33.15a,b The velocity–field characteristic associated with InN for various crystal temperatures (a). The trends in
the low-field electron drift mobility (solid line), the peak electron drift velocity (diamonds), and the saturation electron
drift velocity (solid points), are also shown. (b) InN has the highest peak electron drift velocity and the highest low-field
electron drift mobility of the III–V nitride semiconductors considered in this analysis
33.2.6 Electron Transport in InN
ing Fig. 33.15. As with the cases of GaN and AlN,
the velocity–field characteristic associated with InN
is extremely robust to increases in the crystal temperature. In particular, its peak electron drift velocity,
which is 4.4 × 107 cm/s at 100 K, only decreases to
3.2 × 107 cm/s at 700 K. Similarly, its saturation electron drift velocity, which is 2.0 × 107 cm/s at 100 K,
only decreases to 1.5 × 107 cm/s at 700 K. The lowfield electron drift mobility associated with InN also
InN has the smallest effective mass of the three III–V
nitride semiconductors considered in this analysis. Accordingly, it is not surprising that it exhibits the highest
electron drift velocity and the highest low-field electron drift mobility. The sensitivity of the velocity-field
characteristic associated with InN to variations in the
crystal temperature may be examined by considera) Drift velocity (107 cm/s)
b) Drift velocity (107 cm/s)
Mobility (cm2 Vs)
4
1017cm–3
4.0
InN
InN
3
5000
4000
3.0
3000
2
2.0
1018 cm–3
2000
1019 cm–3
1.0
0.0
1
1000
0
50
100
150
200
250
300
Electric field (kV/cm)
0
1016
1017
1018
1019
Doping concentration (cm–3)
0
Fig. 33.16a,b The velocity–field characteristic associated with InN for various doping concentrations (a). The trends in
the low-field electron drift mobility (solid line), the peak electron drift velocity (diamonds), and the saturation electron
drift velocity (solid points), are also shown (b)
819
Part D 33.2
a) Drift velocity (107 cm/s)
33.2 Steady-State and Transient Electron Transport
820
Part D
Materials for Optoelectronics and Photonics
Part D 33.2
a) Drift velocity (107 cm/s)
b) Drift velocity (107 cm/s)
5.0
10.0
GaN
560 kV/cm
4.0
8.0
900 kV/cm
280 kV/cm
6.0
3.0
210 kV/cm
4.0
675 kV/cm
450 kV/cm
2.0
140 kV/cm
1.0
2.0
225 kV/cm
70 kV/cm
0.0
AlN
1800 kV/cm
0.0
0.1
0.2
0.3
0.4
Distance (µm)
c) Drift velocity (107 cm/s)
0.0
0.00
0.01
0.02
0.03
0.04
0.05
Distance (µm)
d) Drift velocity (107 cm/s)
6.0
10.0
InN
260 kV/cm
8.0
130 kV/cm
6.0
4.0
97.5 kV/cm
65 kV/cm
4.0
GaAs
16 kV/cm
5.0
8 kV/cm
3.0
6 kV/cm
4 kV/cm
2.0
2.0
1.0
32.5 kV/cm
2 kV/cm
0.0
0.0
0.2
0.4
0.6
0.8
Distance (µm)
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Distance (µm)
Fig. 33.17a–d The electron drift velocity as a function of the distance displaced since the application of the electric field
for various applied electric field strengths, for the cases of (a) GaN, (b) AlN, (c) InN, and (d) GaAs. In all cases, we
have assumed an initial zero field electron distribution, a crystal temperature of 300 K, and a doping concentration of
1017 cm−3 . After [33.29] with permission, copyright AIP
diminishes in response to increases in the crystal temperature, from about 9000 cm2 /Vs at 100 K to below
1000 cm2 /Vs at 700 K.
The sensitivity of the velocity–field characteristic
associated with InN to variations in the doping concentration may be examined by considering Fig. 33.16.
These results suggest a similar robustness to the doping concentration for the case of InN. In particular, it is
noted that for doping concentrations below 1017 cm−3 ,
the velocity–field characteristic associated with InN
exhibits very little dependence on the doping concentration. When the doping concentration is increased above
1017 cm−3 , however, the peak electron drift velocity diminishes. Quantitatively, the peak electron drift velocity
decreases from 4.1 × 107 cm/s at 1017 cm−3 doping to
3.2 × 107 cm/s at 1019 cm−3 doping. The saturation electron drift velocity only drops slightly, however, from
1.8 × 107 cm/s at 1017 cm−3 doping to 1.5 × 107 cm/s
at 1019 cm−3 doping. The low-field electron drift mobility, however, drops significantly with doping, from
4700 cm2 /Vs at 1016 cm−3 doping to 1500 cm2 /Vs at
1019 cm−3 doping.
33.2.7 Transient Electron Transport
Steady-state electron transport is the dominant electron
transport mechanism in devices with larger dimensions.
For devices with smaller dimensions, however, transient
electron transport must also be considered when evaluating device performance. Ruch [33.57] demonstrated,
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
140 kV/cm is a critical field for the onset of velocity overshoot effects. As mentioned in Sect. 33.2.2,
140 kV/cm also corresponds to the peak in the velocityfield characteristic associated with GaN; recall Fig. 33.4.
Steady-state Monte Carlo simulations suggest that this
is the point at which significant upper valley occupation
begins to occur; recall Fig. 33.3. This suggests that velocity overshoot is related to the transfer of electrons to
the upper valleys. Similar results are found for the other
III–V nitride semiconductors, AlN and InN, and GaAs;
see Figs. 33.17b–d.
We now compare the transient electron transport
characteristics for the materials. From Fig. 33.17, it is
clear that certain materials exhibit higher peak overshoot velocities and longer overshoot relaxation times.
It is not possible to fairly compare these different semiconductors by applying the same applied electric field
strength to each of the materials, as the transient effects
occur over such a disparate range of applied electric
field strengths in each material. In order to facilitate
such a comparison, we choose a field strength equal
to twice the critical applied electric field strength for
each material. Figure 33.18 shows a comparison of the
velocity overshoot effects amongst the four materials
considered in this analysis, i. e., GaN, AlN, InN, and
Drift velocity (107 cm/s)
8.0
InN
InN
6.0
GaAs
4.0
2.0
AlN
0.0
0.0
0.1
0.2
0.3
0.4
Distance (µm)
Fig. 33.18 A comparison of the velocity overshoot amongst
the III–V nitride semiconductors and GaAs. The applied
electric field strength chosen corresponds to twice the critical applied electric field strength at which the peak in the
steady-state velocity–field characteristic occurs (Fig. 33.4),
i. e., 280 kV/cm for the case of GaN, 900 kV/cm for the
case of AlN, 130 kV/cm for the case of InN, and 8 kV/cm
for the case of GaAs. After [33.29] with permission,
copyright AIP
821
Part D 33.2
for both silicon and GaAs, that the transient electron
drift velocity may exceed the corresponding steadystate electron drift velocity by a considerable margin
for appropriate selections of the applied electric field.
Shur and Eastman [33.58] explored the device implications of transient electron transport, and demonstrated
that substantial improvements in the device performance can be achieved as a consequence. Heiblum
et al. [33.59] made the first direct experimental observation of transient electron transport within GaAs.
Since then there have been a number of experimental investigations into the transient electron transport
within the III–V compound semiconductors; see, for
example, [33.60–62].
Thus far, very little research has been invested
into the study of transient electron transport within
the III–V nitride semiconductors, GaN, AlN, and InN.
Foutz et al. [33.21] examined transient electron transport within both the wurtzite and zinc blende phases
of GaN. In particular, they examined how electrons,
initially in thermal equilibrium, respond to the sudden
application of a constant electric field. In devices with
dimensions greater than 0.2 µm, they found that steadystate electron transport is expected to dominate device
performance. For devices with smaller dimensions, however, upon the application of a sufficiently high electric
field, they found that the transient electron drift velocity
can considerably overshoot the corresponding steadystate electron drift velocity. This velocity overshoot was
found to be comparable with that which occurs within
GaAs.
Foutz et al. [33.29] performed a subsequent analysis
in which the transient electron transport within all of the
III–V nitride semiconductors under consideration in this
analysis were compared with that which occurs within
GaAs. In particular, following the approach of Foutz
et al. [33.21], they examined how electrons, initially in
thermal equilibrium, respond to the sudden application
of a constant electric field. A key result of this study,
presented in Fig. 33.17, plots the transient electron drift
velocity as a function of the distance displaced since the
electric field was initially applied for a number of applied electric field strengths and for each of the materials
considered in this analysis.
Focusing initially on the case of GaN (Fig. 33.17a),
we note that the electron drift velocity for the applied electric field strengths 70 kV/cm and 140 kV/cm
reaches steady-state very quickly, with little or no
velocity overshoot. In contrast, for applied electric
field strengths above 140 kV/cm, significant velocity
overshoot occurs. This result suggests that in GaN,
33.2 Steady-State and Transient Electron Transport
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Materials for Optoelectronics and Photonics
Part D 33.3
GaAs. It is clear that among the three III–V nitride
semiconductors considered, InN exhibits superior transient electron transport characteristics. In particular, InN
has the largest overshoot velocity and the distance over
which this overshoot occurs, 0.3 µm, is longer than in
either GaN and AlN. GaAs exhibits a longer overshoot
relaxation distance, approximately 0.7 µm, but the electron drift velocity exhibited by InN is greater than that
of GaAs for all distances.
33.2.8 Electron Transport: Conclusions
In this section, steady-state and transient electron
transport results, corresponding to the III–V nitride
semiconductors, GaN, AlN, and InN, were presented,
these results being obtained from our Monte Carlo simulations of the electron transport within these materials.
Steady-state electron transport was the dominant theme
of our analysis. In order to aid in the understanding
of these electron transport characteristics, a comparison was made between GaN and GaAs. Our simulations
showed that GaN is more robust to variations in crystal temperature and doping concentration than GaAs,
and an analysis of our Monte Carlo simulation results
showed that polar optical phonon scattering plays the
dominant role in accounting for these differences in behavior. This analysis was also performed for the other
III–V nitride semiconductors considered in this analysis
– AlN and InN – and similar results were obtained. Finally, we presented some key transient electron transport
results. These results indicated that the transient electron
transport that occurs within InN is the most pronounced
of all of the materials under consideration in this review
(GaN, AlN, InN, and GaAs).
33.3 Electron Transport Within III–V Nitride Semiconductors: A Review
Pioneering investigations into the material properties of
the III–V nitride semiconductors, GaN, AlN, and InN,
were performed during the earlier half of the twentieth
century [33.63–65]. The III–V nitride semiconductor
materials available at the time, small crystals and powders, were of poor quality, and completely unsuitable for
device applications. Thus, it was not until the late 1960s,
when Maruska and Tietjen [33.66] employed chemical
vapor deposition to fabricate GaN, that interest in the
III–V nitride semiconductors experienced a renaissance.
Since that time, interest in the III–V nitride semiconductors has been growing, the material properties of these
semiconductors improving considerably over the years.
As a result of this research effort, there are currently
a number of commercial devices available that employ
the III–V nitride semiconductors. More III–V nitride
semiconductor-based device applications are currently
under development, and these should become available
in the near future.
In this section, we present a brief overview of the
III–V nitride semiconductor electron transport field. We
start with a survey describing the evolution of the field.
In particular, the sequence of critical developments that
have occurred that contribute to our current understanding of the electron transport mechanisms within the
III–V nitride semiconductors, GaN, AlN, and InN, is
chronicled. Then, some of the current literature is presented, with particular emphasis being placed on the
most recent developments in the field and how such
developments are modifying our understanding of the
electron transport mechanisms within the III–V nitride
semiconductors, GaN, AlN, and InN. Finally, frontiers
for further research and investigation are presented.
This section is organized in the following manner.
In Sect. 33.3.1, we present a brief survey describing the
evolution of the field. Then, in Sect. 33.3.2, the current literature is discussed. Finally, frontiers for further
research and investigation are presented in Sect. 33.3.3.
33.3.1 Evolution of the Field
The favorable electron transport characteristics of the
III–V nitride semiconductors, GaN, AlN, and InN, have
long been recognized. As early as the 1970s, Littlejohn
et al. [33.13] pointed out that the large polar optical
phonon energy characteristic of GaN, in conjunction
with its large intervalley energy separation, suggests
a high saturation electron drift velocity for this material. As the high-frequency electron device performance
is, to a large degree, determined by this saturation electron drift velocity [33.14], the recognition of this fact
ignited enhanced interest in this material and its III–V
nitride semiconductor compatriots, AlN and InN. This
enhanced interest, and the developments which have
transpired as a result of it, are responsible for the III–V
nitride semiconductor industry of today.
In 1975, Littlejohn et al. [33.13] were the first to report results obtained from semi-classical Monte Carlo
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
temperature influences the velocity-field characteristic
associated with bulk wurtzite GaN. Later that year,
Kolník et al. [33.19] reported on employing full-band
Monte Carlo simulations of the electron transport within
bulk wurtzite GaN and bulk zinc blende GaN, finding
that bulk zinc blende GaN exhibits a much higher lowfield electron drift mobility than bulk wurtzite GaN.
The peak electron drift velocity corresponding to bulk
zinc blende GaN was found to be only marginally
greater than that exhibited by bulk wurtzite GaN. In
1997, Bhapkar and Shur [33.22] reported on employing ensemble semi-classical three-valley Monte Carlo
simulations of the electron transport within bulk and
confined wurtzite GaN. Their simulations demonstrated
that the two-dimensional electron gas within a confined
wurtzite GaN structure will exhibit a higher low-field
electron drift mobility than bulk wurtzite GaN, by almost an order of magnitude, this being in agreement with
experiment. In 1998, Albrecht et al. [33.27] reported on
employing ensemble semi-classical five-valley Monte
Carlo simulations of the electron transport within bulk
wurtzite GaN, with the aim of determining elementary
analytical expressions for a number of electron transport metrics corresponding to bulk wurtzite GaN, for
the purposes of device modeling.
Electron transport within the other III–V nitride
semiconductors, AlN and InN, has also been studied
using ensemble semi-classical Monte Carlo simulations
of the electron transport. In particular, by employing
ensemble semi-classical three-valley Monte Carlo simulations, the velocity–field characteristic associated with
bulk wurtzite AlN was studied and reported by O’Leary
et al. [33.24] in 1998. They found that AlN exhibits
the lowest peak and saturation electron drift velocities
of the III–V nitride semiconductors considered in this
analysis. Similar simulations of the electron transport
within bulk wurtzite AlN were also reported by Albrecht et al. [33.25] in 1998. The results of O’Leary
et al. [33.24] and Albrecht et al. [33.25] were found
to be quite similar. The first known simulation of the
electron transport within bulk wurtzite InN was the
semi-classical three-valley Monte Carlo simulation of
O’Leary et al. [33.23], reported in 1998. InN was demonstrated to have the highest peak and saturation electron
drift velocities of the III–V nitride semiconductors. The
subsequent ensemble full-band Monte Carlo simulations
of Bellotti et al. [33.28], reported in 1999, produced
results similar to those of O’Leary et al. [33.23].
The first known study of transient electron transport within the III–V nitride semiconductors was that
performed by Foutz et al. [33.21], reported in 1997. In
823
Part D 33.3
simulations of the steady-state electron transport within
bulk wurtzite GaN. A one-valley model for the conduction band was adopted in their analysis. Steady-state
electron transport, for both parabolic and nonparabolic
band structures, was considered in their analysis, nonparabolicity being treated through the application of the
Kane model [33.43]. The primary focus of their investigation was the determination of the velocity-field
characteristic associated with GaN. All donors were assumed to be ionized, and the free electron concentration
was taken to be equal to the dopant concentration. The
scattering mechanisms considered were (1) ionized impurity, (2) polar optical phonon, (3) piezoelectric, and
(4) acoustic deformation potential. For the case of the
parabolic band, in the absence of ionized impurities,
they found that the electron drift velocity monotonically
increases with the applied electric field strength, saturating at a value of about 2.5 × 107 cm/s for the case
of high applied electric fields. In contrast, for the case
of the nonparabolic band, and in the absence of ionized impurities, a region of negative differential mobility
was found, the electron drift velocity achieving a maximum of about 2 × 107 cm/s at an applied electric field
strength of about 100 kV/cm, with further increases in
the applied electric field strength resulting in a slight decrease in the corresponding electron drift velocity. The
role of ionized impurity scattering was also investigated
by Littlejohn et al. [33.13].
In 1993, Gelmont et al. [33.16] reported on ensemble semi-classical two-valley Monte Carlo simulations
of the electron transport within bulk wurtzite GaN,
this analysis improving upon the analysis of Littlejohn
et al. [33.13] by incorporating intervalley scattering into
the simulations. They found that the negative differential mobility found in bulk wurtzite GaN is much more
pronounced than that found by Littlejohn et al. [33.13],
and that intervalley transitions are responsible for this.
For a doping concentration of 1017 cm−1 , Gelmont
et al. [33.16] demonstrated that the electron drift velocity achieves a peak value of about 2.8 × 107 cm/s at an
applied electric field of about 140 kV/cm. The impact of
intervalley transitions on the electron distribution function was also determined and shown to be significant.
The impact of doping and compensation on the velocity-field characteristic associated with bulk wurtzite
GaN was also examined.
Since these pioneering investigations, ensemble
Monte Carlo simulations of the electron transport within
GaN have been performed numerous times. In particular, in 1995 Mansour et al. [33.18] reported the use of
such an approach in order to determine how the crystal
33.3 Electron Transport Within III–V Nitride Semiconductors
824
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Materials for Optoelectronics and Photonics
Part D 33.3
this study, ensemble semi-classical three-valley Monte
Carlo simulations were employed in order to determine
how the electrons within wurtzite and zinc blende GaN,
initially in thermal equilibrium, respond to the sudden
application of a constant electric field. The velocity overshoot that occurs within these materials was examined.
It was found that the electron drift velocities that occur
within the zinc blende phase of GaN are slightly greater
than those exhibited by the wurtzite phase owing to the
slightly higher steady-state electron drift velocity exhibited by the zinc blende phase of GaN. A comparison with
the transient electron transport that occurs within GaAs
was made. Using the results from this analysis, a determination of the minimum transit time as a function of the
distance displaced since the application of the applied
electric field was performed for all three materials considered in this study: wurtzite GaN, zinc blende GaN,
and GaAs. For distances in excess of 0.1 µm, both phases
of GaN were shown to exhibit superior performance (reduced transit time) when contrasted with that associated
with GaAs.
A more general analysis, in which transient electron
transport within GaN, AlN, and InN was studied, was
performed by Foutz et al. [33.29], and reported in 1999.
As with their previous study, Foutz et al. [33.29] determined how electrons, initially in thermal equilibrium,
respond to the sudden application of a constant electric field. For GaN, AlN, InN, and GaAs, it was found
that the electron drift velocity overshoot only occurs
when the applied electric field exceeds a certain critical
applied electric field strength unique to each material.
The critical applied electric field strengths, 140 kV/cm
for the case of wurtzite GaN, 450 kV/cm for the case
of AlN, 65 kV/cm for the case of InN, and 4 kV/cm
for the case of GaAs, were shown to correspond to the
peak electron drift velocity in the velocity-field characteristic associated with each of these materials; recall
Fig. 33.4. It was found that InN exhibits the highest
peak overshoot velocity, and that this overshoot lasts
over prolonged distances compared with AlN, InN, and
GaAs. A comparison with the results of experiment was
performed.
In addition to Monte Carlo simulations of the electron transport within these materials, a number of other
types of electron transport studies have been performed.
In 1975, for example, Ferry [33.14] reported on the
determination of the velocity-field characteristic associated with wurtzite GaN using a displaced Maxwellian
distribution function approach. For high applied electric fields, Ferry [33.14] found that the electron drift
velocity associated with GaN monotonically increases
with the applied electric field strength (it does not saturate), reaching a value of about 2.5 × 107 cm/s at an
applied electric field strength of 300 kV/cm. The device
implications of this result were further explored by Das
and Ferry [33.15]. In 1994, Chin et al. [33.17] reported
on a detailed study of the dependence of the low-field
electron drift mobilities associated with the III–V nitride
semiconductors, GaN, AlN, and InN, on crystal temperature and doping concentration. An analytical expression
for the low-field electron drift mobility, µ, determined
using a variational principle, was used for the purposes
of this analysis. The results obtained were contrasted
with those from experiment. A subsequent mobility
study was reported in 1997 by Look et al. [33.38].
Then, in 1998, Weimann et al. [33.26] reported on
a model for determining how the scattering of electrons by the threading dislocations within bulk wurtzite
GaN influence the low-field electron drift mobility. They
demonstrated why the experimentally measured lowfield electron drift mobility associated with this material
is much lower than that predicted from Monte Carlo
analyses: threading dislocations were not taken into account in the Monte Carlo simulations of the electron
transport within the III–V nitride semiconductors, GaN,
AlN, and InN.
While the negative differential mobility exhibited
by the velocity-field characteristics associated with the
III–V nitride semiconductors, GaN, AlN, and InN, is
widely attributed to intervalley transitions, and while
direct experimental evidence confirming this has been
presented [33.67], Krishnamurthy et al. [33.34] suggest that the inflection points in the bands located in
the vicinity of the Γ valley are primarily responsible for the negative differential mobility exhibited by
wurtzite GaN instead. The relative importance of these
two mechanisms (intervalley transitions and inflection
point considerations) were evaluated by Krishnamurthy
et al. [33.34], for both bulk wurtzite GaN and an AlGaN
alloy.
33.3.2 Recent Developments
There have been a number of interesting recent developments in the study of the electron transport within the
III–V nitride semiconductors which have influenced the
direction of thought in this field. On the experimental
front, in 2000 Wraback et al. [33.33] reported on the
use of a femtosecond optically detected time-of-flight
experimental technique in order to experimentally determine the velocity–field characteristic associated with
bulk wurtzite GaN. They found that the peak electron
Electron Transport Within GaN, AlN and InN: Monte Carlo Analysis
et al. [33.71] and reported in 2002. Bulutay et al. [33.72]
studied the electron momentum and energy relaxation
times within the III–V nitride semiconductors and reported the results of this study in 2003. It is particularly
interesting to note that their arguments add considerable credence to the earlier inflection point argument
of Krishnamurthy et al. [33.34]. In 2004, Brazis and
Raguotis [33.73] reported on the results of a Monte Carlo
study involving additional phonon modes and a smaller
intervalley energy separation for bulk wurtzite GaN.
Their results were found to be much closer to the experimental results of Wraback et al. [33.33] than those
found previously.
The influence of hot-phonons on the electron
transport mechanisms within the III–V nitride semiconductors, GaN, AlN, and InN, has been the focus
of considerable recent investigation. In particular, in
2004 Silva and Nascimento [33.74], Gökden [33.75], and
Ridley et al. [33.76], to name just three, presented results
related to this research focus. These results suggest that
hot-phonon effects play a significant role in influencing
the nature of the electron transport within the III–V nitride semiconductors, GaN, AlN, and InN. In particular,
Ridley et al. [33.76] point out that the saturation electron drift velocity and the applied electric field strength
at which the peak in the velocity–field characteristic occurs are both influenced by hot-phonon effects. The role
that hot-phonons play in influencing device performance
was studied by Matulionis and Liberis [33.77]. Research
into the role that hot-phonons play in influencing the
electron transport mechanisms within the III–V nitride
semiconductors, GaN, AlN, and InN, seems likely to
continue into the foreseeable future.
33.3.3 Future Perspectives
It is clear that our understanding of the electron transport within the III–V nitride semiconductors, GaN,
AlN, and InN, is, at present at least, in a state of
flux. A complete understanding of the electron transport mechanisms within these materials has yet to be
achieved, and is the subject of intense current research.
Most troubling is the discrepancy between the results
of experiment and those of simulation. There are a two
principal sources of uncertainty in our analysis of the
electron transport mechanisms within these materials:
(1) uncertainty in the material properties, and (2) uncertainty in the underlying physics. We discuss each of
these subsequently.
Uncertainty in the material parameters associated
with the III–V nitride semiconductors, GaN, AlN, and
825
Part D 33.3
drift velocity, 1.9 × 107 cm/s, is achieved at an applied
electric field strength of 225 kV/cm. No discernible
negative differential mobility was observed. Wraback
et al. [33.33] suggested that the large defect density
characteristic of the GaN samples they employed, which
were not taken into account in Monte Carlo simulations
of the electron transport within this material, accounts
for the difference between this experimental result and
that obtained using simulation. They also suggested that
decreasing the intervalley energy separation from about
2 eV to 340 meV, as suggested by the experimental results of Brazel et al. [33.56], may also account for these
observations.
The determination of the electron drift velocity from
experimental measurements of the unity gain cut-off frequency, f t , has been pursued by a number of researchers.
The key challenge in these analyses is the de-embedding
of the parasitics from the experimental measurements
so that the true intrinsic saturation electron drift velocity
may be obtained. Eastman et al. [33.68] present experimental evidence which suggests that the saturation
electron drift velocity within bulk wurtzite GaN is about
1.2 × 107 –1.3 × 107 cm/s. A more recent report, by
Oxley and Uren [33.69], suggests a value of
1.1 × 107 cm/s. The role of self-heating was also probed
by Oxley and Uren [33.69] and shown to be relatively
insignificant. A completely satisfactory explanation for
the discrepancy between these results and those from
the Monte Carlo simulations has yet to be provided.
Wraback et al. [33.70] performed a subsequent study
on the transient electron transport within wurtzite GaN.
In particular, using their femtosecond optically detected
time-of-flight experimental technique in order to experimentally determine the velocity overshoot that occurs
within bulk wurtzite GaN, they observed substantial velocity overshoot within this material. In particular, a peak
transient electron drift velocity of 7.25 × 107 cm/s was
observed within the first 200 fs after photoexcitation for
an applied electric field strength of 320 kV/cm. These
experimental results were shown to be consistent with
the theoretical predictions of Foutz et al. [33.29].
On the theoretical front, there have been a number of
recent developments. In 2001, O’Leary et al. [33.30] presented an elementary, one-dimensional analytical model
for the electron transport within the III–V compound
semiconductors, and applied it to the cases of wurtzite
GaN and GaAs. The predictions of this analytical model
were compared with those of Monte Carlo simulations
and were found to be in satisfactory agreement. Hotelectron energy relaxation times within the III–V nitride
semiconductors were recently studied by Matulionis
33.3 Electron Transport Within III–V Nitride Semiconductors
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Materials for Optoelectronics and Photonics
Part D 33
InN, remains a key source of ambiguity in the analysis of
the electron transport with these materials [33.32]. Even
for bulk wurtzite GaN, the most studied of the III–V
nitride semiconductors considered in this analysis, uncertainty in the band structure remains an issue [33.56].
The energy gap associated with InN and the effective mass associated with this material continue to fuel
debate; see, for example, Davydov et al. [33.53], Wu
et al. [33.54], and Matsuoka et al. [33.55]. Variations
in the experimentally determined energy gap associated with InN, observed from sample to sample, further
confound matters. Most recently, Shubina et al. [33.78]
suggested that nonstoichiometry within InN may be responsible for these variations in the energy gap. Further
research will have to be performed in order to confirm
this. Given this uncertainty in the band structures associated with the III–V nitride semiconductors, it is
clear that new simulations of the electron transport
will have to be performed once researchers have settled on the appropriate band structures. We thus view
our present results as a baseline, the sensitivity analysis
of O’Leary et al. [33.32] providing some insights into
how variations in the band structures will impact upon
the results.
Uncertainty in the underlying physics is considerable. The source of the negative differential mobility
remains a matter to be resolved. The presence of hotphonons within these materials, and how such phonons
impact upon the electron transport mechanisms within
these materials, remains another point of contention. It is
clear that a deeper understanding of these electron transport mechanisms will have to be achieved in order for the
next generation of III–V nitride semiconductor-based
devices to be properly designed.
33.4 Conclusions
In this paper, we reviewed analyses of the electron transport within the III–V nitride semiconductors GaN, AlN,
and InN. In particular, we have discussed the evolution of the field, surveyed the current literature, and
presented frontiers for further investigation and analysis. In order to narrow the scope of this review, we
focused on the electron transport within bulk wurtzite
GaN, AlN, and InN for the purposes of this paper. Most
of our discussion focused upon results obtained from
our ensemble semi-classical three-valley Monte Carlo
simulations of the electron transport within these materials, our results conforming with state-of-the-art III–V
nitride semiconductor orthodoxy.
We began our review with the Boltzmann transport
equation, since this equation underlies most analy-
ses of the electron transport within semiconductors.
A brief description of our ensemble semi-classical
three-valley Monte Carlo simulation approach to
solving the Boltzmann transport equation was then
provided. The material parameters, corresponding
to bulk wurtzite GaN, AlN, and InN, were then
presented. We then used these material parameter
selections, and our ensemble semi-classical threevalley Monte Carlo simulation approach, to determine
the nature of the steady-state and transient electron
transport within the III–V nitride semiconductors. Finally, we presented some recent developments on
the electron transport within these materials, and
pointed to fertile frontiers for further research and
investigation.
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