Phase stability, chemical bonds, and gap bowing of In
x
Ga
1-x
N alloys: Comparison between cubic
and wurtzite structures
C. Caetano,
1
L. K. Teles,
1,
* M. Marques,
2
A. Dal Pino, Jr.,
1
and L. G. Ferreira
3
1
Departamento de Física, Instituto Tecnológico de Aeronáutica, Comando-Geral de Tecnologia Aeroespacial,
12228-900 São José dos Campos, SP, Brazil
2
Departamento de Microondas e Optoeletrônica, Divisão de Engenharia Eletrônica, Instituto Tecnológico de Aeronáutica,
Comando-Geral de Tecnologia Aeroespacial, 12228-900 São José dos Campos, SP, Brazil
3
Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970 Campinas, SP, Brazil
Received 22 February 2006; revised manuscript received 26 May 2006; published 27 July 2006
Thermodynamic, structural, and electronic properties of wurtzite In
x
Ga
1-x
N alloys are studied by combining
first-principles total energy calculations with the generalized quasichemical approach, and compared to previ-
ous results for the zinc-blende structure. Results for bond-lengths, second-nearest-neighbors distances, and
bowing parameter are presented. We observed that the wurtzite results are not significantly different from the
ones obtained previously for the zinc-blende structure. The calculated phase diagram of the alloy shows a
broad and asymmetric miscibility gap as in the zinc-blende case, with a similar range for the growth tempera-
tures, although with a higher critical temperature. We found a value of 1.44 eV for the gap bowing parameter
giving support to the recent smaller band gap bowing findings. We emphasize that other theoretical results may
suffer from incomplete sets of atomic configurations to properly describe the alloy properties, and experimental
findings. Moreover one must take into account a broad composition range in order to obtain reliable results.
DOI: 10.1103/PhysRevB.74.045215 PACS numbers: 61.66.Dk, 64.75.+g, 71.20.Nr
I. INTRODUCTION
In the past decade remarkable progress has been made in
the development of optical and electronic devices based on
group-III nitrides AlN, GaN, InN, and their alloys. Light
emitting diodes and laser diodes operating in the green-
blue-UV spectral region and high-frequency, high-power,
and high-temperature electronic devices have been success-
fully fabricated.
1–7
A common feature of these device struc-
tures is the use of ternary In
x
Ga
1-x
N or Al
x
Ga
1-x
N alloys.
Alloying among the group-III nitrides allows a change in the
band gap from 1.89 eV in InN to 6.28 eV in AlN with an
intermediate value of 3.44 eV for GaN at 300 K.
8
How-
ever, recent reports state the value of 0.70– 0.90 eV for the
energy gap of InN, which allows an even wider range of
variation for the band gap,
9–14
that can now be tuned from
the near infrared to the deep ultraviolet. This wide spectral
range offers possibilities for the use of group-III nitrides in a
variety of device applications. For instance, the energy gaps
available in the InGaN alloy system provide an almost per-
fect match with the complete solar spectrum, which makes
InGaN a potential material for high efficiency multijunction
solar cells.
15,16
With this narrowed gap of InN, it becomes
necessary to reevaluate many of the material parameters of
InN and their composition dependence in group-III-nitride
alloys, e.g., the bowing parameter.
15–17
Under ambient conditions AlN, GaN, and InN crystallize
in the hexagonal wurtzite W structure. Although, epitaxial
AlN, GaN, and InGaN layers have also been successfully
grown on in the metastable zinc-blende ZB phase,
18–20
up
to now, quaternary nitride-based alloys were grown only in
the W structure. In the wurtzite structure the four nearest
neighbors of an atom are located at the corners of a slightly
deformed tetrahedron that surrounds the central atom sym-
metrically, which in the case of the nitrides is compressed
in the direction of the c axis. The degree of deformation
depends on the ratio c / a. If the c / a ratio has the ideal value
of
8 / 3 = 1.633 and if the single internal coordinate of the
structure is equal to 3 / 8 of the corresponding wurtzite struc-
ture, the nearest-neighbor atoms are positioned at exactly the
same sites as in a crystal having zinc-blende structure. De-
spite the close structural similarities between these two
phases, their electronic structures are different.
21
The study
of the ZB-W polytypism stability in the III-V and II-VI semi-
conductors and the differences in their electronic structure
has attracted considerable attention up to now.
21–26
There are theoretical studies of the properties of the
W-InGaN alloy and all of them use very simplified
models.
17,27–32
To the best of our knowledge, there is no the-
oretical work reported so far which contemplates, in an equal
footing, both, a reasonably sized model supercell and the
statistics of the alloy. All of them use only one or very few
alloy configurations. While for the wurtzite structure the cal-
culations were more simplified, for the zinc blende one there
are a set of rigorous works which comply with alloy
statistics.
33–38
The absence of rigorous calculations per-
formed for the W structure maybe justified for the following
reasons: a structural similarities between W and ZB struc-
tures; b there is a common expectation that the ZB and W
alloys should have approximately the same properties, in-
cluding, for example, the bowing parameter for the energy
gap and critical temperature under which there is alloy phase
separation;
6,39
and c the calculation procedure is simpler
for ZB than for W structure, since for the ZB calculations
only one lattice constant must be optimized, while for the W,
it is necessary to optimize the three lattice parameters: the
lattice constants c, a, and the internal parameter u, which
extremely increases the number of necessary calculations. In
the literature one sees arguments in favor and against a ZB
calculation as a equivalent to W, but proper proofs are not
PHYSICAL REVIEW B 74, 045215 2006
1098-0121/2006/744/0452158 ©2006 The American Physical Society 045215-1
brought to you by CORE View metadata, citation and similar papers at core.ac.uk
provided by Repositorio da Producao Cientifica e Intelectual da Unicamp