Calculation of electron mobility and effect of dislocation scattering in GaN
The electron mobility of GaN has been obtained at various temperatures by the relaxation time approximation method. The effect of dislocation scattering has also been discussed and calculated alongwith other important scattering mechanisms in this material. The results agree with other available...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2007
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| Zitieren: | Calculation of electron mobility and effect of dislocation scattering in GaN / J. Kundu, C.K. Sarkar, P.S. Mallick // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 1-3. — Бібліогр.: 8 назв. — англ. |
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Kundu, J. Sarkar, C.K. Mallick, P.S. 2017-05-26T05:49:02Z 2017-05-26T05:49:02Z 2007 Calculation of electron mobility and effect of dislocation scattering in GaN / J. Kundu, C.K. Sarkar, P.S. Mallick // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 1-3. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 72.20.Dp, 78.35.+c https://nasplib.isofts.kiev.ua/handle/123456789/117661 The electron mobility of GaN has been obtained at various temperatures by the relaxation time approximation method. The effect of dislocation scattering has also been discussed and calculated alongwith other important scattering mechanisms in this material. The results agree with other available experimental and theoretical data. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Calculation of electron mobility and effect of dislocation scattering in GaN Article published earlier |
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Calculation of electron mobility and effect of dislocation scattering in GaN |
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Calculation of electron mobility and effect of dislocation scattering in GaN Kundu, J. Sarkar, C.K. Mallick, P.S. |
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Calculation of electron mobility and effect of dislocation scattering in GaN |
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Calculation of electron mobility and effect of dislocation scattering in GaN |
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Calculation of electron mobility and effect of dislocation scattering in GaN |
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Calculation of electron mobility and effect of dislocation scattering in GaN |
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calculation of electron mobility and effect of dislocation scattering in gan |
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Kundu, J. Sarkar, C.K. Mallick, P.S. |
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Kundu, J. Sarkar, C.K. Mallick, P.S. |
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2007 |
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English |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The electron mobility of GaN has been obtained at various temperatures by the
relaxation time approximation method. The effect of dislocation scattering has also been
discussed and calculated alongwith other important scattering mechanisms in this
material. The results agree with other available experimental and theoretical data.
|
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1560-8034 |
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https://nasplib.isofts.kiev.ua/handle/123456789/117661 |
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Calculation of electron mobility and effect of dislocation scattering in GaN / J. Kundu, C.K. Sarkar, P.S. Mallick // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 1. — С. 1-3. — Бібліогр.: 8 назв. — англ. |
| work_keys_str_mv |
AT kunduj calculationofelectronmobilityandeffectofdislocationscatteringingan AT sarkarck calculationofelectronmobilityandeffectofdislocationscatteringingan AT mallickps calculationofelectronmobilityandeffectofdislocationscatteringingan |
| first_indexed |
2025-11-26T00:10:45Z |
| last_indexed |
2025-11-26T00:10:45Z |
| _version_ |
1850595721482338304 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 1-3.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
1
PACS 72.20.Dp, 78.35.+c
Calculation of electron mobility and effect
of dislocation scattering in GaN
Janardan Kundu1, C.K. Sarkar2 and P.S. Mallick1
1Department of Electronics and Communication Engineering, National Institute of Science and Technology,
Palur Hills, Berhampur 761 008, India
E-mail: psmallick@yahoo.com
2Department of Electronics and Telecommunication Engineering, Jadavpur University,
Kolkata 700 032, India
Abstract. The electron mobility of GaN has been obtained at various temperatures by the
relaxation time approximation method. The effect of dislocation scattering has also been
discussed and calculated alongwith other important scattering mechanisms in this
material. The results agree with other available experimental and theoretical data.
Keywords: electron mobility, dislocation scattering, gallium nitride.
Manuscript received 31.12.06; accepted for publication 26.03.07; published online 01.06.07.
1. Introduction
Gallium nitride, a direct bandgap semiconductor, has
emerged as an important material for high-power,
optoelectronic as well as for high temperature devices
because 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 vapor deposition (MOCVD),
molecular beam epitaxy (MBE) or hybrid vapor phase
epitaxy (HVPE) on sapphire (Al2O3) or SiC substrate
with large lattice mismatch. 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 we move away from the
interfacial layer, the dislocation density decreases very
fast. This suggests that whole GaN epilayer consists of
two layers which was also 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 scattering
mechanism is considered to be acoustic phonon
scattering via deformation potential, piezoelectric
coupling and the 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 the
dislocation scattering dominant near the interfacial
region. In this paper, the two-layer model of GaN has
been considered for theoretical calculation of electron
mobility. Effect of dislocation scattering in the
interfacial layer has been calculated and clarified.
2. Theory
The electron mobility considering various scattering
mechanisms can be given by solving the Boltzmann
equation in the relaxation time approximation as
*m
e τ
=µ , (1.1)
where τ is the average relaxation time over the
electron energies and µ is the mobility, and m is the
effective mass of electron. In the following sections, the
expressions of relaxation time and mobility caused by
different scattering mechanisms have been given.
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
relaxation time is given by
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 1-3.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
2
ε
ε
ε
ε
ε
εετ
=ετ
∫
∫
∞
∞
d
d
df
d
d
df
m
e
ii
ii
0
0
2/3
0
0
3/2
*
)(
)( . (1.2)
The mobility associated with ionized impurity scattering
has been calculated as
[ ])1/()1ln(
)(2128
2/1*32
2/322/1
yyymeN
kT
I
ii
+−+Ζ
∈π
=µ , (1.3)
where
ne
KTm
y
22
2)(*24
h
∈
= .
Neutral impurity scattering
When an electron passes close to neutral atom,
momentum can be transferred through a process in
which the free electron exchanges with a bound electron
on the atom. The relaxation time can be written as [5]
.
20
)(
0
*
aN
m
n
ni
h
=ετ (1.4)
The mobility associated with the neutral impurity
scattering has been calculated as
∈π
==µ
3
3
0 80
*
20 hh nn
ni
N
me
aN
e
, (1.5)
where a0 is the effective Bohr radius of donor, and Nn is
the concentration of neutral impurities.
Acoustic phonon: deformation potential scattering
The acoustic mode lattice vibration induced changes in
lattice spacing, which change the bandgap from point to
point. Since the crystal is ’deformed’ at these points, the
potential is called the deformation potential. The
corresponding relaxation time can be written as [6]
2/1
2/3*2
1
24
)(2
)( −ε
ρπ
=ετ
kTmE
s
dp
h
, (1.6)
where ρ is the crystal density, S is the average velocity
of sound, and e1 is the deformation potential. Here, ρ s2
= c1 is the longitudinal elastic constants.
The mobility associated with the deformation potential
scattering has been calculated as
.
)(3
22
* 2/32/52
1
242/1
kTmE
es
m
e dp
dp ∗
ρπ
=
τ
=µ
h
(1.7)
For GaN the acoustic deformation potential is equal
to 9.2 eV [4].
Acoustic phonon: piezoelectric potential scattering
A relaxation time can be defined for the piezoelectric
potential mechanism because the energy change during
the collision is small. The relaxation time is [6]
2/1
2/1*22
2
)(
22
)( ε
∈π
=ετ
kTmpe
pe
h
, (1.8)
where
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∈ρ
=
2
2
s
h
p pz is the piezoelectric coupling
coefficient, pzh is the piezoelectric constant. The
mobility associated with the piezoelectric potential
scattering has been calculated as
2/12/3*2
22/1
*
)(3
216)(
kTmeP
h
m
e pe
pe
∈π
=
ετ
=µ . (1.9)
At 300 K, the piezoelectric potential scattering rate is
about five times smaller than the deformation potential
rate [4].
Optical phonon: polar scattering
For this scattering, a relaxation time solution to the
Boltzmann equation is not possible. Since τ becomes a
function of the perturbation strength itself instead of just
the energy ε of electrons. The relaxation time
( ) ( )
.
)()(
/1
2)( 2/1
112/1*2
/2
2/3 ε
∈−∈
χ−
π=ετ
−−
∞mkTe
TTe
D
D
TT
po
Dh
(1.10)
The corresponding mobility calculated as
( )
( ) .
)(3
/)1()(π2 2/1
112/3*
/2/122/12/9
ε
∈−∈
χ−
=µ
−−
∞mkTe
TTekT
D
D
TT
po
Dh
(1.11)
The mobilities limited by the lattice phonons
(including polar optical phonon, acoustic-mode
deformation potential and piezoelectric potential)
scattering are independent of impurity levels, so their
temperature dependence is universal for GaN [4].
Dislocation scattering
One of the biggest problems of GaN is the lack of a
lattice-matched substrate, since bulk GaN is very
difficult to grow in large sizes. Thus, epitaxial growth of
GaN on Al2O3, which has a 14 % lattice mismatch and
34 % mismatch in the thermal expansion coefficient.
Due to the large lattice mismatch of GaN with the
substrates, on which it is epitaxially grown (SiC and
sapphire), dislocations are typically formed. The
relaxation time is
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 1. P. 1-3.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
3
( ) 2/322*22
24
2*22
0 4/
)8(
Dt
D
Lmv
LfNe
ma
h+
∈∈
=τ , (1.12)
where Vt is the component of V perpendicular to
dislocation line, a is the distance between imperfection
centers along the dislocation line, and f is their
occupation probability.
Averaging with the equilibrium distribution
function, the mobility calculated as
m
NmLe
TKa
D
f 2/1*3
2/3
B
22
0
2
)()(230 εεπ
=µ . (1.13)
Since the reciprocal values of the relaxation time
resulting from different physical mechanism are
additive, the scattering caused by the charge of
dislocation in n-type semiconductors gives the dominant
effect below the room temperature [7].
3. Results and discussion
The theoretical results for mobilities including different
types of scattering mechanisms such as ionized impurity,
neutral impurity, acoustic phonon via potential
deformation, piezoelectric, polar optical phonon and
dislocation scattering at different temperatures have been
calculated using the parameters of n-type GaN. The
dislocation density is 1015 m−2 and the carrier
concentrations in bulk and interfacial layers are taken as
1.3×1017 and 7×1024 m−3, respectively.
Fig. 1 represents the variation of electron mobility
with temperature for various types of scattering
mechanisms such as ionized impurity, neutral impurity,
acoustic phonon via deformation potential, piezoelectric
scattering, polar optical phonon scattering and
dislocation scattering individually.
Fig. 1. Variation of electron mobility with temperature for
acoustic phonons via deformation potential (1), ionized
impurity (2), polar optical phonon (3), piezoelectric poten-
tial (4), neutral impurity (5) and dislocation scatterings (6).
Fig. 2. Variation of electron mobility with temperature in two-
layer model considering without (1) and with (2) the
dislocation scattering.
From Fig. 2, we can conclude that the influence of
the dislocation scattering on the mobility of GaN,
compared to different lattice scatterings becomes
significant at a high density of dislocations at the
interfacial layer of GaN above 109 cm−2.
4. Conclusion
We have calculated the combined electron mobility of
GaN with two-layer model by considering the various
scattering mechanism such as ionized impurity, neutral
impurity, potential deformation, piezoelectric potential,
polar optical phonon and dislocation scattering. In
Fig. 2, we have shown the effect of dislocation scattering
in the mobility analysis of GaN with two-layer model,
and we found that the dislocation scattering plays a
dominant role in mobility analysis when the dislocation
density is high and can indeed directly affect mobility.
From the above results, we can conclude that the
agreement between measured and calculated mobility is
better at the room temperature than at lower
temperatures. This can be explained by decreasing
proportion of ionized electrons in GaN at lower
temperature. Overall the calculated mobility at the room
temperature and at 150 K agrees quite satisfactorily with
the published theoretical and experimental results [6-8].
References
1. S.C. Jain, M. Willander, J. Narayan and R. Van Over-
straeten, III-nitrides: growth, characterization and pro-
perties // J. Appl. Phys. 87, No. 3, p. 965-1006 (2000).
2. S. Nakamura, S.J. Pearton and G. Fasal, The blue
LASER diodes. Springer, Berlin, 2000.
3. D.C. Look, J.R. Sizelove, Dislocation scattering in
GaN // Phys. Rev. Lett. 82, No. 6, 1999.
4. D.C. Look, Electrical characterization of GaAs
materials and devices. Wiley, New York, 1989.
5. C. Erginsoy // Phys. Rev. 79, p. 1013 (1950).
6. D.A. Anderson and N. Apsley // Semiconductor
Science and Technology 1, June 9 (1986).
7. B. Podor // Phys. status solidi 16, p. k167 (1966).
8. Subhabrata Dhar and Subhasis Ghosh // J. Appl.
Phys. 86 (5), 1st Sept. (1999).
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