Nonlinear elasticity in III-N compounds: Ab initio calculations
S. P. Lepkowski
Unipress—Institute of High Pressure Physics, Polish Academy of Sciences, ulica Sokolowska 29, 01-142 Warszawa, Poland
J. A. Majewski
Institute of Theoretical Physics, Faculty of Physics, Warsaw University, ulica Hoża 69, 00-681 Warszawa, Poland
G. Jurczak
Institute of Fundamental Technological Research, Polish Academy of Sciences, ulica ŚwiJtokrzyska 21, 00-049 Warszawa, Poland
Received 26 August 2005; published 1 December 2005
We have studied the nonlinear elasticity effects in zinc-blende and wurtzite crystallographic phases of III-N
compounds. Particularly, we have determined the pressure dependences of elastic constants in InN, GaN, and
AlN by performing ab initio calculations in the framework of plane-wave pseudopotential implementation of
the density-functional theory. The calculations have been performed employing two exchange-correlation
functionals, one within the local density approximation and the other within the generalized gradient approxi-
mation. We have found that C
11
,C
12
in zinc-blende nitrides and C
11
,C
12
,C
13
,C
33
in wurtzite nitrides depend
significantly on hydrostatic pressure. Much weaker dependence on pressure has been observed for C
44
elastic
constant in both zinc-blende and wurtzite phases. Further, we have examined the influence of pressure depen-
dence of elastic constants on the pressure coefficient of light emission, dE
E
/ dP, in wurtzite InGaN / GaN and
GaN/AlGaN quantum wells. We have shown that the pressure dependence of elastic constants leads to a
significant reduction of dE
E
/ dP in nitride quantum wells. Finally, we have considered the influence of non-
linear elasticity of III-N compounds on the properties of hexagonal nitride quantum dots QDs. For typical
wurtzite GaN / AlN QDs, we have shown that taking into account pressure dependence of elastic constants
results in the decrease of volumetric strain in the QD region by about 7%. Simultaneously, the average z
component of the piezoelectric polarization in the QDs increases by 0.1 MV/ cm compared to the case when
linear elastic theory is used. Both effects, i.e., decrease of volumetric strain as well as increase of piezoelectric
field, decrease the band-to-band transition energies in the QDs.
DOI: 10.1103/PhysRevB.72.245201 PACS numbers: 78.67.De, 62.20.Dc, 62.50.+p, 78.67.Hc
I. INTRODUCTION
The electronic and optical properties of semiconductor
heterostructures depend crucially on the strain arising from
the lattice mismatch. Commonly, the strain effects in quan-
tum structures, i.e., quantum wells QWs, wires, or dots
QDs, are described within the standard elasticity theory, in
which the deformation energy is described by terms qua-
dratic in the strain tensor components and elastic constants
are independent of the strain so-called linear theory. Nev-
ertheless, there are circumstances where this simple approach
is not sufficient.
Nonlinear elastic properties of GaAs and InAs have re-
cently attracted significant attention. First, Frogley et al. pro-
posed that pressure dependences of elastic constants in GaAs
and InAs are required to explain anomalously the small pres-
sure coefficient of band gap dE
G
/ dP in strained InGaAs
layers.
1
They showed that the main contribution, responsible
for drastic reduction of dE
G
/ dP in biaxial strained layers of
InGaAs, came from the pressure dependence of a two-
dimensional Poisson’s ratio,
2D
P, defined for zinc-blende
structure as 2C
12
/ C
11
. Second, Ellaway et al. calculated
pressure dependences of elastic constants for InAs and dis-
cussed their influence on the properties of InAs/ GaAs QDs.
2
They noticed that the hydrostatic strain component in the
InAs/ GaAs QDs is significantly overestimated by calcula-
tions based on the linear theory of elasticity. Taking into
account the pressure dependence of elastic constants reduces
the hydrostatic strain by about 16%.
2
Recently, it has also
been shown that pressure dependences of elastic constants in
GaAs and InAs are decisive to determine the pressure coef-
ficients of the light emission dE
E
/ dP in InAs/GaAs
QDs.
3,4
For the case of wurtzite III-N compounds, the nonlinear
elasticity effects have not been systematically studied yet. A
pioneering paper in this field was published by Kato and
Hama who calculated the pressure dependence of the elastic
stiffness tensor for wurtzite AlN.
5
Later on, Vaschenko et al.
used these results to estimate the influence of the nonlinear
elasticity on dE
E
/ dP in hexagonal AlGaN / GaN QWs.
6
Re-
cently, we have investigated the pressure dependences of
elastic constants, in zinc-blende InN and GaN.
7
We have
shown that one has to take the effects of nonlinear elasticity
into account in order to determine dE
E
/ dP in cubic
InGaN / GaN QWs.
7
In this work, we focus on the nonlinear elasticity effects
in group III nitrides crystallizing in wurtzite structure. Par-
ticularly, we have determined the pressure dependences of
elastic constants in wurtzite InN, GaN, and AlN by perform-
ing ab initio calculations in the framework of plane-wave
pseudo-potential implementation of the density-functional
theory.
8,9
We have used two approximations to the exchange-
correlation functionals, the standard local density approxima-
PHYSICAL REVIEW B 72, 245201 2005
1098-0121/2005/7224/24520112/$23.00 ©2005 The American Physical Society 245201-1