Materials Chemistry and Physics 125 (2011) 66–71
Contents lists available at ScienceDirect
Materials Chemistry and Physics
journal homepage: www.elsevier.com/locate/matchemphys
Pressure induced phase transformation and electronic properties of AlAs
Anurag Srivastava a,∗ , Neha Tyagi a , U.S. Sharma b , R.K. Singh c
a
Advance Materials Research Lab, Indian Institute of Information Technology & Management, Gwalior, M.P. 474010, India
Department of Physics, RJIT, BSF Academy, Tekanpur, Gwalior 475005, India
c
School of Basic Sciences, ITM University, Gurgaon, HRY. 122017, India
b
a r t i c l e
i n f o
Article history:
Received 8 June 2010
Received in revised form 26 July 2010
Accepted 18 August 2010
PACS:
62.50.±p
68.35.Rh
71.20.Nr
71.15.Mb
64.70.Kb
a b s t r a c t
We have performed the first-principle study to analyze the structural and electronic properties of aluminum arsenide under the application of pressure. The computations have been carried out using the
ground state total energy calculation approach of the system. The first-principle approach has been used
to compute the stability of various phases of AlAs, like original zinc blende (B3), intermediate NiAs (B8),
NaCl (B1) and CsCl (B2) type as a function of pressure. The study observes a B3–B8, B3–B1 and B3–B2
transitions at 6.99 GPa, 8.18 GPa and 73.43 GPa. The computed phase transition pressures, lattice parameters, bulk modulus, and energy gaps are in good agreement with their experimental as well as theoretical
counterparts. Band structure and density of states analysis have also been performed and results have
been discussed in detail.
© 2010 Elsevier B.V. All rights reserved.
Keywords:
Phase transition
High pressure
Electronic properties
AlAs
1. Introduction
The operating characteristics of the electronic and optoelectronic devices not only talks about the materials engineering at a
practical level but they are also required for better understanding
of the properties of materials and associated fundamental science
behind them. Theoretical investigations as well as experimental
researches are therefore of vital interest to all those working in
this area of research. The electronic and structural properties of the
complex systems have attracted considerable interest in both fundamental and applied physics. A large amount of work has been
focused on theoretical understanding of a variety of compound
semiconductors and their related properties. These compounds
play an important role in microelectronics, for example, in the
development of light emitting diodes and high frequency low noise
devices for mobile telephones and advanced materials for spintronics [1–13]. The most remarkable aspect of tetrahedrally coordinated
structures is their low density. The openness of these semiconductors is highlighted by the fact that for the homopolar members,
the ratio of the volume of touching atom spheres to that of the
∗ Corresponding author at: Advance Materials Research Lab, Indian Institute of
Information Technology & Management, E-110, First Floor, IIITM Campus Morena
Link Road, Gwalior, M.P. 474010, India. Tel.: +91 751 2449826.
E-mail addresses: [email protected], [email protected] (A. Srivastava).
0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.matchemphys.2010.08.072
unit cell is 0.34 which is less than half for the close-packed element structure (0.74). It is not surprising, because under pressure
tetrahedrally coordinated semiconductors can be transformed to
the structure with higher density [14]. Froyen and Cohen [15] and
Martin [16] reported first on the phase transition in AlAs which was
based on ab initio pseudopotential calculation and suggested that
the high pressure structure could be either rocksalt (B1) or NiAs
(B8). Weinstein et al. [17] reported the pressure induced structural
transition by microscopic examination at 12.3 GPa on loading but
the structure was unknown. Greene et al. [18] have performed an
EDXD study on AlAs up to 46 GPa and found that AlAs transforms
to NiAs structure. This was the first experimental observation of
III–V compound transforming into the NiAs structure. The equilibrium transformation pressure was found to be 7 ± 5 GPa, averaging
the large hysteresis. Onodera et al. [19] have reported B3–B8 phase
transition in AlAs at 14.2 GPa by high pressure X-ray diffraction and
electrical resistivity measurements.
Many methods of calculations have been used to confirm these
results. One of them is to relate the high pressure behavior of
these semiconductors to the type of chemical bonding between
the nearest atoms by examining the electronic charge density
evolution, which has been correlated to the empirical qualitative
concept as ionicity [20,21]. The first-principles electronic structure calculations have allowed detailed studies of the energetics
of the group IVA elements and the groups IIIA–VA and IIB–VIA
compounds under high pressures [22]. Theoretically, III-arsenide
A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71
compounds have been studied by employing different approaches;
from phenomenological methods such as k.p. theory or empirical pseudo-potentials methods [23] to atomistic ab initio methods,
such as the full-potential linear augmented plane wave (FP-LAPW)
method within local density approximation (LDA) or generalized
gradient approximation (GGA) and pseudopotential methods [24].
Recently, Wang et al. [25] have reported the first-principle study of
the phase transition of AlAs in three crystallographic structures,
i.e., B3 (zinc blende), B8 (nickel arsenide) and B1 (rock salt) at
high pressures using the full-potential linearized muffin-tin orbital
(FP-LMTO) scheme within the generalized gradient approximation
(GGA) correction in the framework of the density functional theory
(DFT) and based on the condition of equal enthalpies.
Singh et al. [26–28] have successfully applied three-bodypotential approach to describe the high pressure phase transition
and other properties of Al based compound semiconductors. The
effect of pressure on the structural stability of some III–V and IV–VI
compound semiconductor based alloys has also been investigated
successfully with three-body-potential (TBP) approach [29,30].
Cai and Chen [31] have reported a possible mechanism for B3–B8
transition, characterized by the space group of C2221 , and observed
that there are relatively small values of activation enthalpy and
strain anisotropy for B3–B8 transition of AlAs in comparison to
the B3–B1 case. The calculated transition pressure from B3 to B8
ranges from 6.1 GPa [32] to 9.15 GPa [31], and B3 to B1 phase, from
7.4 GPa [32] to 11.88 GPa [31]. Not much information is available
on B3–B2 transition in this compound. Looking to the technological
importance of this material and success of first-principle methods, we thought it pertinent to analyze the transitions due to the
application of pressure and thereby its material characteristics.
Particularly three transitions B3–B8, B3–B1 and B3–B2 have been
studied. Further the present work also computes lattice constant,
bulk modulus and its pressure derivative, band structure and density of state in different phases of AlAs. These calculations provide a
one stop shop for fundamental understanding of the structural and
electronic properties of the aluminum arsenide.
2. Computational details
The present computations of the structural and electronic properties of aluminum arsenide have been performed using ATK
tool [33]. Atomistix ToolKit (ATK) is a further development of
TranSIESTA-C [34,35] which, in turn, is based on the technology,
models and algorithms developed in the academic code TranSIESTA and, in part, McDCal [36], employing localized basis sets as
developed in SIESTA [37]. The density functional theory (DFT) is, in
principle a very good theory to predict ground state properties (e.g.
total energy, atomic structure, Bulk modulus, etc.). However, DFT
is not a theory to address efficiently the excited state properties
and hence DFT typically underestimates the band gap of semiconductors and insulators by 20–30%. The ATK has been proved to be
a very efficient tool in predicting the transport properties [38–40]
of variety of bulk as well as nanostructured materials, where the
electronic properties have also been discussed in detail. The normconserving pseudopotential is used in density function theory for
total energy calculation of polyatomic systems. The electronic configuration of AlAs is Al: Ne 3s2 3p1 , and As: Ar 3d10 4s2 4p3 . In the
calculation of pseudopotential, the inner-cell configurations for
Al (1s2 2s2 2p6 ), and As (1s2 2s2 2p6 3s2 3p6 3d10 ) have been distinguished from the valence electrons of Al (3s2 3p1 ) and As (4s2 4p3 )
shells, respectively. The Perdew Zunger (PZ) type parameterized
local density approximation (LDA) exchange correlation functional
(LDA-PZ) [41], Perdew, Burke and Ernzerhof (PBE) [42] type parameterized generalized gradient approximation (GGA-PBE) and Zhang
and Yang revised PBE (rev PBE) [43,44] type GGA have been used
67
Fig. 1. Energy vs volume curve for B3, B8, B1 and B2 type phases of AlAs.
for the present computations. In self-consistent manner, the calculation is performed using steepest descent geometric optimization
technique with Pulay algorithm [45] for iteration mixing. The mesh
cut-off is taken as 150Ryd with a k-mesh of 5 × 5 × 5. LDA-PZ type
potential computes total energy much lower than that of GGArevPBE and GGA-PBE approaches. The total energy for original B3
type AlAs using LDA-PZ potential is −469.39 eV and with GGA rev
PBE potential −324.49 eV, which indicates that LDA-PZ potential, is
quite good for the calculation of energies of AlAs in different structural phases like B3, B1, B2 and B8. To get better understanding of
fundamental physics associated with different phases of AlAs, the
Fermi energies, binding energies and band energies have also been
computed using LDA-PZ potential and given in Table 3.
Classical understanding on the phase stability of solids suggests that as the pressure is applied, a particular phase of the solid
becomes unstable and causes a change in the density and the volume, which in turn leads to the overlapping of the electron shells
(charge transfer mechanism) and thus the phase transition takes
place. Under the application of pressure, the B3 type III–V semiconductors are expected to transform into the NaCl (B1) structure
and there is possibility of some intermediate NiAs (B8) type phase
and further increase in pressure may cause stability of CsCl (B2)
type structure. The stability of the phase of the solid can be defined
in terms of its Gibbs free energy (G = U + PV − TS). This free energy
at T = 0 K corresponds to the cohesive energy due to the mutual
interaction of the ions. S is the vibrational entropy at absolute temperature T and V is the volume of the unit cell at pressure P.
3. Results and discussions
3.1. Energy vs volume (E–V) curve, lattice parameter and bulk
modulus
To test the stability of various phases of AlAs, like B3, B8, B1
and B2 under the ambient condition as well as under compression, the calculated total energies have been plotted as a function
of volume in Fig. 1. In ambient condition B3 structure has been
found to be with minimum energy and same under compression
first stabilizes in B8 type, then B1 and finally to the CsCl (B2) type
with the lowest energy. The positive lattice energy difference of the
two competitive structures at zero pressure very well explains the
relative stability criterion given by Sangster et al. [46]. The lattice
parameter corresponding to minima of the E–V curves corresponds
to zero pressure, termed as the equilibrium or theoretical lattice
constant.
68
A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71
Table 1
The lattice constants (a), bulk modulus B0 and its pressure derivative B0 calculated using LDA scheme for AlAs.
Material
B0
B0 (GPa)
Lattice constant a (in Å)
PWa
Exp.
Others
PWa
Exp.
Others
PWa
Exp.
Others
5.66 [18,48]
5.61 [4]
5.63 [7]
5.65 [49]
76.41
82.0 [50]
74.40 [4]
77.09 [49]
64.5 [25]
4.16
5.0 ± 1 [18]
10.7 ± 1.4 [19]
4.18 [4]
4.53 [49]
3.88 [25]
AlAs-B8
5.64 (LDA)
5.72 (GGA-PBE)
5.77 (GGArev
PBE)
3.72(LDA)
3.79 [18]
3.77 [28]
3.72 [32]
56.0
73.0 ± 7 [18]
101 ± 26 [19]
84.9 [25]
93.3 [32]
4.86
4.6 ± 0.7 [18]
4.0 [19]
4.29 [25]
4.58 [32]
AlAs-B1
5.24 (LDA)
–
96.60
–
79.8 [25]
91.5 [32]
5.51
–
4.68 [25]
4.3 [32]
AlAs-B2
3.22(LDA)
–
5.31 [28]
5.22 [32]
5.19 [15]
4.97 [52]
3.56 [51]
78.53
–
–
6.03
–
–
AlAs-B3
a
PW: present work.
In our observations, the equilibrium lattice constant 5.64 Å has
been computed using LDA-PZ scheme and is found to be lower
as compared to those revealed from GGA-PBE (5.72 Å) and GGArevPBE (5.77 Å) approaches for the original B3 type phase of AlAs.
The calculated lattice parameter for B3 type phase is in close agreement with the reported experimental value 5.66 Å [18,48] and other
theoretical values [4,7,49]. Similarly the lattice parameters for B1,
B8 and B2 type phases have also been in close match with the other
theoretical as well as experimental values. The stability analysis of
AlAs in B8 type phase, corresponds to the c/a ratio of 1.59 Å, where
the equilibrium lattice parameters a and c are 3.72 Å and 5.91 Å,
respectively. The c/a ratio, and individual lattice parameters a and
c are in close agreement with their theoretical [25,32] as well as
experimental [18] counterparts as shown in Table 1.
The bulk modulus and its pressure derivative in all the tested
phases B3, B8, B1 and B2 type have been computed using Murnaghan equation of state [47] and their values are compared with
their experimental and theoretical counterparts. The computed
bulk modulus B0 for B3, B8, B1 and B2 type phases has also been
calculated and are in good agreement with the reported values.
However in the case of B8 type phase B0 is comparatively less and
the pressure derivative B0 is slightly higher than the other reported
values in Table 1.
3.2. High pressure phase transition
In order to study the high pressure phase transition in AlAs,
we have obtained converged values in B3, B1, B2 and B8 type
phases. These values have been utilized to determine the total
energy at different lattice parameters and plots of energy vs volume for all the tested phases (B3, B8, B1 and B2) as shown in Fig. 1,
where, total energies correspond to each phase have been plotted
as a function of volume and by drawing tangent of E–V curves of
two competitive structure, the transition pressure has been calculated. Another method of calculation of transition pressure is
by observing the crossover of free energies of two competitive
structures as a function of pressure. It is clear from the E–V curve
that under the ambient condition, AlAs crystallizes in B3 structure. Under the application of pressure original B3 type phase of
AlAs first transforms to NiAs (B8) type phase at around 6.61 GPa
and further compression leads to the B1 phase stable at around
8.18 GPa and finally the most stable hypothetical CsCl (B2) type
phase at around 73.43 GPa. The computed values of transition pressure are in good agreement with their experimental [18,19] as
well as theoretical [25,28,31,32,51,52] counterpart and compared
in Table 2.
3.3. Band structure and density of state (DOS)
In order to have more insight towards understanding the change
in behavior of the material from one particular type of phase to
another under the influence of pressure, the electronic properties
have been studied. In the electronic properties, the band structure
and density of state for AlAs have been analyzed at the theoretical
equilibrium lattice constants in all the stable phases obtained in
the present study. For the B3 type phase, band structure has been
computed with GGA-revPBE, GGA-PBE and LDA-PZ exchange correlation functional approaches. In Fig. 2(a), it is seen that the various
bands have prominent maxima at the central point and minima at the point X of the Brillouin zone. AlAs is an indirect band gap
semiconductor because the top of the valence band and the bottom
of the conduction band are not at the same center point ( ) in the
Brillouin zone. Using LDA-PZ, GGA-PBE and GGA-revPBE exchange
correlation functional, the study computes the indirect band gap
(Eg ) of AlAs as 1.33 eV, 1.53 eV and 1.65 eV respectively. The band
below the 7,8 point constitutes the valence band and those above
the point X6 form the conduction band. The band structure also
shows a direct gap of around 2.28 eV at point 7,8 in valence band
to 6 in conduction band, hence, X6 is the lowest energy point of
the conduction band and 7,8 is the highest point of the valence
band. At room temperature, the gap is sufficiently small so that few
electrons are thermally excited from the valence band to the conduction band and few excited electrons gather in the region of the
conduction band immediately above its minimum at X6, a region
that is termed as “Valley”. In Fig. 2(b), the valence band is crossing
the Fermi level at the point 6,7,8 and conduction band is coming below the Fermi level at the point X6 that clearly indicates B1
type phase of AlAs is metallic in nature. In Fig. 2(c), the valence
band is crossing the Fermi level between the points and X, while
the conduction band is coming below the Fermi level at the point
Table 2
Phase transition pressure in AlAs.
Phase transition pressure (GPa)
Transition type
PW
Exp
Others
B3 → B8
B3 → B1
B3 → B2
6.99
8.18
73.43
7 ± 5 [18], 14.2 [19]
–
–
5.34 [25], 6.1 [32], 7.12 [31], 9.15 [31]
6.24 [25], 7.4 [32], 8.25 [31], 11.88 [31], 7.5 [28]
77.9 [51], 76.8 [52]
A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71
69
Fig. 2. (a) Band structure plot for B3 type phase of AlAs, (b) band structure plot for B1 type phase of AlAs, (c) band structure plot for B2 type phase of AlAs, and (d) band
structure plot for B8 type phase of AlAs.
6 that shows again the metallic nature in case of B2 type phase.
In Fig. 2(d), the valence bands are crossing the Fermi level at the
point 8 and the conduction band is also touching the Fermi level.
This shows that alike B1 and B2 phases, B8 type phase of AlAs is
also metallic. Due to compression, the change of material characteristics from semiconductor to metallic can be seen very well from
their band structure, DOS plots and through the numerical values
of band gap, Fermi energy and band energy as reported in Table 3.
The computed values of indirect band gaps of AlAs are comparatively less than the experimental value and other reported values;
however, it is close to some reported values.
The densities of states for all the four tested phases (B3, B1, B2
and B8) have been shown in Fig. 3(a)–(d). For B3 type phase of AlAs,
the nature of peaks is shown in Fig. 3(a), where one can notice that
there is a band gap at the Fermi level. In this phase, the highest
magnitude peak appears in the conduction band region at around
2.44 eV. The DOS for B1 type phase of AlAs is shown in Fig. 3(b),
there appears one prominent peak near −1.72 eV and two peaks
in the conduction band region among which the highest peak is
around 4.92 eV. The DOS for B2 type phase of AlAs is depicted in
Fig. 3(c), where there is no prominent peak in the valence band
region but there are two peaks in the conduction band region out
Table 3
Band gap (Eg ), Fermi energy and band energy for AlAs.
Material
Bandgap Eg (eV)
a
AlAs-B3
AlAs-B8
AlAs-B1
AlAs-B2
a
PW: present work.
Fermi energy (eV)
PW
Exp.
Others
1.33(I)[LDA]
1.53(I) [GGA]
1.65(I)[GGArev]
1.88[GGArev]
1.72[GGA]
2.28[LDA]
–
–
–
2.16 [48]
2.05 [4], 2.36 [49],
1.84 [9], 1.29 [5],
2.18 [5], 1.56 [10]
–
–
–
–
–
–
Band energy (eV)
3.92 (LDA)
−76.37 (LDA)
−3.94 (LDA)
−4.35 (LDA)
−3.77 (LDA)
−80.42 (LDA)
−77.15 (LDA)
−76.62 (LDA)
70
A. Srivastava et al. / Materials Chemistry and Physics 125 (2011) 66–71
Fig. 3. (a) Density of state plot for B3 type phase of AlAs, (b) density of state plot for B1 type phase of AlAs, (c) density of state plot for B2 type phase of AlAs, and (d) density
of state plot for B8 type phase of AlAs.
of which one is at 2.8 eV and the second one is near 4.24 eV. For
B8 type phase of AlAs, we have shown DOS in Fig. 3(d). There are
three prominent peaks appearing in the valence band region out of
which the highest peak appears around −4.72 eV and also there is
one peak in the conduction band region which is occurring around
4.48 eV.
4. Conclusion
The present first-principle study computes the pressure induced
phase transitions, band structure, density of states, lattice parameter and bulk modulus of AlAs, using the LDA-PZ exchange
correlation scheme. It is clearly noted from the band structure plots
as well as the density of states that the original semiconducting
nature of AlAs in B3 type phase has been transformed to a metallic
one in B1, B8 and B2 type phases due to compression. The calculated bulk modulus for all the tested phases of AlAs compared with
other reported values shows a close match, except in case of B8
type phase, where bulk modulus is less and its pressure derivative is slightly higher to their experimental as well as theoretical
counterparts. As not much information is available about the B3–B2
transition, bulk modulus and pressure derivative in B2 type phase,
the present result will certainly serve as a guide to the investigators
in future.
Acknowledgments
The authors are thankful to ABV-Indian Institute of Information Technology and Management, Gwalior for the financial support
provided to the work as the Faculty initiation grant.
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