Effect of dislocation scattering on electron mobility in GaN

doi:10.4236/ns.2011.39106

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Vol.3, No.9, 812-815 (2011) Natural Science

http://dx.doi.org/10.4236/ns.2011.39106

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: [email protected]

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,





 (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

*32 0

EE E

mEE









(2)

Hence the mobility associated with ionized impurity

R. Karthik et al. / Natural Science 3 (2011) 812-815

813

scattering is





122

23 *12

128 2π

eln1 1

Nm yyy









(3)

where,



24 *

mKT





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]



ENa





 (4)

The mobility associated with neutral impurity scatter-

ing is

ee*

20 80π

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]



2*32

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

252

e22πe

mEm kT







  (7)

For GaN acoustic deformation potential is 9.2 eV. [8].

2.4. Acoustic Phonon: Piezoelectric

Scattering

The relaxation time is [10]



2*1 2

22πs

hmkT





 (8)

where,





















, Piezoelectric coupling co-efficient,

hpz is the piezoelectric constant.

The mobility associated with Piezoelectric scattering

is calculated as







12 222

e*12

2*32

e16 2πs

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]









32 12

2*1211

2πE

eTT

EkT m















(10)

The corresponding mobility is calculated as

 



9212 2

*3 211

2π

kTT T

kT m













(11)

where



3π

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

Ne tD

am vm









 (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

814

rium distribution function as,



32 *12

30 2π

dis

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 m–2 and carrier concentrations

in bulk and interfacial layers are taken as 1.3  1017 m–3,

7  1024 m–3 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 T–3/2 dependence due to phonon

scattering at high temperature but at low temperature, the

mobility is increasing monotonically with temperature

depending on a T–3/2 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 m–2 and the carrier concentrations in bulk

and interfacial layers are taken as 1.3  1017 m–3, 7  1024 m–3

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

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

815

mismatch and the consequence of these studies can help

them to obtain an accurate theoretical model.

REFERENCES

[1] Jain, S.C., Willander, M., Narayan, J. and Van Over-

straeten, R. (2000) III-nitride: Growth, characterization

and properties. Journal of Applied Physics, 87, 965.

doi:10.1063/1.371971

[2] Nakamura, S., Pearton, S.J. and Fasal, G. (2000) The blue

LASER diodes. Springer, Berlin.

[3] Look, D.C. and Sizelove, J.R. (1999) Dislocation Scat-

tering in GaN. Physical Review Letter, 82, 1237.

doi:10.1103/PhysRevLett.82.1237

[4] Dutikrushna, P., Sarkar, C.K., Mukhopadhyay, D. and

Mallick, P.S. (2005) Hot electron microwave incremental

conductivity of GaN. Journal of Optics, 34, 172-175.

[5] Hosein, E. (2009) The effect of hydrostati pressure on

material parameters and electrical transport properties in

bulk GaN. Physics Letters A, 373, 1773-1776.

doi:10.1016/j.physleta.2009.03.013

[6] Ng, H.M., Doppalapudi, D., Moustakas, T.D., Weimann,

N.G. and Eastman, L.F. (1998) The role of dislocation

scattering in n type GaN films. Applied Physical Letters,

73, 821. doi:10.1063/1.122012

[7] Weimann, N.G., Eastman, L.F., Doppalapudi, D., Ng,

H.M. and Moustakas, T.D. (1998) Scattering of electrons

at threading dislocations in GaN. Journal of Applied Physics,

83, 3656. doi:10.1063/1.366585

[8] Dhar, S. and Ghosh, S. (1999) Low field electron mobil-

ity in GaN. Journal of Applied Physics, 86, 2668.

doi:10.1063/1.371108

[9] Erginsoy, C. (1950) Neutral impurity scattering in semi-

conductors. Physical Review, 79, 1013.

doi:10.1103/PhysRev.79.1013

[10] Nag, B.R. (1980), Electron transport in compound semi-

conductors. Springer-Verlag, Berlin.

[11] Look, D.C. (1989) Electrical characterization of GaAs

materials and devices. Willey, New York.

[12] Lin, M.E., Sverdiov, B.N., Strite, S., Morkoe, H. and

Drakin, A.E. (1993) Refractive indices of Wurtzite and

Zincblende GaN. Electronics Letters, 29, 1759.

doi:10.1049/el:19931172

[13] Wang, Y.J., Kaplan, R., Ng, H.K., Doverspike, K., Gaskil,

D.K., Ikedo, T., Amano, H. and Akasaki, I. (1996) Mag-

neto-optical studies of GaN and GaN/AlxGa1-xN: Donor

zeeman spectroscopy and two dimensional electron gas

cyclotron resonance. Journal of Applied Physics, 79,

8007. doi:10.1063/1.362351

[14] Morkoc, H. (1999) Nitride Semiconductors and devices,

Springer-Verlag, Heidelberg/Berlin/New York.

doi:10.1007/978-3-642-58562-3

[15] Schroeder, D.K. (1990), Semiconductor material and

device characterization. Wiley, New York.

[16] Bykhovski, A.D., Kaminski, V.V., Shur, M.S., Chen, Q.C.

and Khan, M.A. (1996) Piezoelectric effect in wurtzite n

type GaN. Applied Physical Letters, 68, 818.

doi:10.1063/1.116543

[17] Shan, W., Schmidt, S., Yang, X.H., Song, J.J. and Golden-

berg, B. (1996) Optical properties of wurtzite GaN grown

by low-pressure metalorganic chemical-vapor deposition.

Journal of Applied Physics, 79, 3691.

doi:10.1063/1.361200

[18] Perlin, P., Staszewska, E.L. and Suchanek, B. (1996)

Determination of the effective mass of GaN from infrared

reflectivity and Hall effect. Applied Physical Letters, 68,

1114. doi:10.1063/1.115730

[19] Djeffal, F., Arar, D., Lakhdar, N., Bendib, T., Dibi, Z. and

Chahdi, M. (2009) An approach based on particles warm

computation to study the electron mobility in wurtzite

GaN. Microelectronics Journal, 40, 357-359.

doi:10.1016/j.mejo.2008.07.041