Vol.3, No.9, 812-815 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.39106
Copyright © 2011 SciRes. OPEN ACCESS
Effect of dislocation scattering on electron mobility in
GaN
R. Karthik, P. Uma Sathyakam, P. S. Mallick*
School of Electrical Engineering, VIT University, Vellore, India; *Corresponding Author: psmallick@ieee.org
Received 21 July 2011; revised 24 August 2011; accepted 21 September 2011.
ABSTRACT
This paper presents the calculation of electron
mobility of GaN at various temperatures using
Relaxation Time Approximation (RTA) method.
The effect of dislocation scattering on electron
mobility in GaN is studied. We have discussed
about the role of important scattering mecha-
nisms in GaN. The electron mobility values thus
obtained are compared with other available ex-
perimental and theoretical results.
Keywords: Dislocation Scattering; Electron Mobility;
Galium Nitride; Scattering
1. INTRODUCTION
Gallium Nitride, a direct bandgap semiconductor, has
emerged as an important material for high-power, opto-
electronic as well as for high temperature devices be-
cause of its large bandgap (3.4 eV), strong bond strength
(2.3 eV/bond) and high breakdown voltage (3 106
V/cm) [1]. Recently the material has become more
popular because of several new applications including
blue light emitting diodes and blue laser diodes [2]. GaN
is normally grown either by metal-organic chemical va-
por deposition (MOCVD), molecular beam epitaxy
(MBE) or hybrid vapor phase epitaxy (HVPE) on sap-
phire (Al2O3) or SiC substrate with large lattice mis-
match. The most commonly used substrate is Al2O3 with
13.8% lattice mismatch and SiC substrate with 4% lattice
mismatch. The large lattice mismatch with the substrate
produces large amount of dislocation at the interfacial
layer resulting very poor interface characteristic. As one
moves away from the interfacial layer, the dislocation
density decreases very fast. This means whole GaN epi-
layer consists of two layers which was suggested by D. C.
Look et al. [3]. In order to calculate the mobility in n-
type GaN, we have considered the two layer model. For
bulk layer away from the interface the dominant scatter-
ing mechanisms are considered to be acoustic phonon
scattering via deformation potential, piezoelectric cou-
pling and non phonon scattering such as ionized impurity
scattering and the neutral impurity scattering. On the
contrary, the dominant scattering mechanism near the
interfacial region is assumed to be dislocation scattering
only. The electrical transport properties of the entire GaN
epilayer would be influenced by dislocation scattering
dominant near the interfacial region. Electron mobility in
GaN and the effect of dislocation scattering on electron
mobility in GaN were studied earlier by many resear-
chers [3-7]. In this paper, we have considered all the im-
portant scattering mechanisms of GaN in more detail
using RTA to obtain electron mobility and we have also
shown the difference between the electron mobility with
and without dislocation scattering.
2. THEORY
Solution of Boltzmann equation using RTA gives elec-
tron mobility as,
*
e
m
(1)
where,
, is average relaxation time over the electron
energies,
is mobility and m* is the effective mass of
electron. The expressions of relaxation time and mobility
caused by different scattering mechanisms are given in
the following sections.
2.1. Ionized Impurity Scattering
The amount of scattering due to electrostatic forces
between the carrier and the ionized impurity depends on
the interaction time and the number of impurities. Larger
impurity concentrations result in a lower mobility [8].
The standard formula for calculating the average relaxa-
tion time is
 
32 0
0
*32 0
0
dd
d
e
dd
d
ii
ii
f
EE E
E
Ef
mEE
E
(2)
Hence the mobility associated with ionized impurity
R. Karthik et al. / Natural Science 3 (2011) 812-815
Copyright © 2011 SciRes. OPEN ACCESS
813
scattering is


32
122
23 *12
128 2π
eln1 1
ii
I
kT
Nm yyy


(3)
where,

2
22
24 *
e
mKT
yn
2.2. Neutral Impurity Scattering
When an electron passes close to neutral atom, its mo-
mentum is transferred through a process in which the free
electrons exchange with a bound electron on the atom.
The relaxation time can be written as [9]

0
20
ni
n
m
ENa
(4)
The mobility associated with neutral impurity scatter-
ing is
3
3
0
ee*
20 80π
ni
nn
m
Na N

(5)
where, a0 and Nn are the effective Bhor radius of donor
and concentration of neutral impurities respectively.
2.3. Acoustic Phonon: Deformation
Potential Scattering
The acoustic mode lattice vibration induces changes in
lattice spacing, which vary the band gap from point to
point. Since the crystal deforms at these points, the po-
tential is called deformation potential. The corresponding
relaxation time can be written as [10]

42
12
2*32
1
π
2
dp
s
EE
Em kT
(6)
where
is crystal density, S is average velocity of
sound and e1 is deformation potential.
The mobility associated with deformation potential
scattering is calculated as

12 42
12
252
1
e22πe
3
dp
dp
s
mEm kT
 (7)
For GaN acoustic deformation potential is 9.2 eV. [8].
2.4. Acoustic Phonon: Piezoelectric
Scattering
The relaxation time is [10]


22
12
2*1 2
22πs
e
pe
pz
EE
hmkT
(8)
where,
2
2E
pz
h
ps
, Piezoelectric coupling co-efficient,
hpz is the piezoelectric constant.
The mobility associated with Piezoelectric scattering
is calculated as

12 222
e
e*12
2*32
e16 2πs
3
p
p
pz
E
meh mkT

 (9)
At 300 K, the piezoelectric potential scattering rate is
about five times smaller than the deformation potential
rate [8].
2.5. Optical Phonon: Polar Scattering
For this scattering,
is a function of the perturbation
strength not a function of energy of the electrons. The
relaxation time is [11]




/
2
32 12
2*1211
1
2πE
e
D
TT
D
po
D
eTT
EkT m


(10)
The corresponding mobility is calculated as
 


12
9212 2
12
*3 211
2π
E
3e
D
po
D
kTT T
kT m


(11)
where

12
3π
8
D
D
T
TT T



The mobility values are limited by the lattice phonon
scatterings such as polar optical phonon scattering,
acoustic-mode deformation potential scattering and pie-
zoelectric potential scattering.
2.6. Dislocation Scattering
The major problem of GaN is unavailability of a lat-
tice-matched substrate. The epitaxial growth of GaN on
Al2O3 has a 13.8% lattice mismatch and a 34% mismatch
in the thermal expansion coefficient. Dislocations are
typically formed due to the large lattice mismatch of
GaN with the substrates on which it is epitaxially grown
(SiC and Sapphire). The relaxation time is [6]

22 *232
22 22
42
84
Ne tD
D
am vm
f

 (12)
where Vt is the component of V perpendicular to disloca-
tion line, “a” is the distance between imperfection cen-
ters along the dislocation line and “f” is their occupation
probability.
The mobility is calculated from the average equilib-
R. Karthik et al. / Natural Science 3 (2011) 812-815
Copyright © 2011 SciRes. OPEN ACCESS
814
rium distribution function as,

32
22
32 *12
30 2π
e
B
dis
D
aKT
fmN
(13)
Since the reciprocal values of relaxation time resulting
from different physical mechanisms are additive, the
scattering caused by the change of dislocation in n-type
semiconductors gives the dominant effect below the
room temperature.
3. RESULTS AND DISCUSSION
Electron mobility considering various types of scat-
tering mechanisms such as ionized impurity, neutral im-
purity, acoustic phonon via potential deformation, piezo-
electric, polar optical phonon and dislocation scattering
is calculated at different temperatures. Table 1 shows the
material parameters of n-type GaN used in our work. The
dislocation density is 1015 m2 and carrier concentrations
in bulk and interfacial layers are taken as 1.3 1017 m3,
7 1024 m3 respectively.
Figure 1 shows the variation of electron mobility with
temperature for various types of scattering mechanisms.
It is found that the acoustic phonon via deformation po-
tential scattering plays a significant role in electron mo-
bility calculation whereas the role of neutral impurity
scattering is negligible. This agrees to the conclusions
made by C. Erginsoy [9]. Ionized impurity scatterings
dominate at low temperature whereas the lattice scatter-
ing dominate at high temperature and the corresponding
mobility values are shown in Figure 1.
We have further investigated the temperature depend-
ence of electron mobility to verify the dislocation scat-
tering model. Figure 2 shows the influence of disloca-
tion scattering on the electron mobility in GaN. It is
found that dislocation scatterings have minimum influ-
ence on electron mobility at low temperature. But how-
ever, the overall effect of dislocation scattering on elec-
tron mobility in GaN is not negligible which agree
qualitatively with other experimental results [6]. The
mobility approaches a T3/2 dependence due to phonon
scattering at high temperature but at low temperature, the
mobility is increasing monotonically with temperature
depending on a T3/2 due to impurity scattering. Our re-
sults agree also with F. Djeffal et al. [19] who have cal-
Figure 1. Variation of electron mobility with temperature for
1) acoustic phonon via deformation potential, 2) ionized im-
purity, 3) polar optical phonon, 4) piezoelectric potential, 5)
neutral impurity and 6) dislocation scatterings. The disloca-
tion density is 1015 m2 and the carrier concentrations in bulk
and interfacial layers are taken as 1.3 1017 m3, 7 1024 m3
respectively.
Figure 2. Variation of electron mobility with temperature in
two-layer model considering 1) without Dislocation Scattering
and 2) with Dislocation Scattering.
culated electron mobility at various temperature upto 800
K.
4. CONCLUSIONS
The electron mobility values in GaN obtained in this
paper will be useful to study the conductivity character-
istics of the devices based on this material. Scientists and
Device engineers are always worried about the lattice
mismatch in GaN crystal which reduces of efficiency of
GaN based devices but sufficient study of this lattice
Table 1. GaN parameters used for mobility calculation.
Symbol
Tpo
S hpz E
1 m*
Value 5.47
0 10.4
0 1044 K6.1 103
Kg·m–3 6.59 103 m·s–1 0.5 (0.375 - 0.6) 9.2 eV 0.22 m0
Ref. [12] [13] [14] [15] [14] [16] [17] [18]
R. Karthik et al. / Natural Science 3 (2011) 812-815
Copyright © 2011 SciRes. OPEN ACCESS
815
mismatch and the consequence of these studies can help
them to obtain an accurate theoretical model.
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