Theoretical study of the cinnabar phases in GaAs and GaP
A. Mujica and A. Mun
˜
oz
Departamento de Fı ´sica Fundamental y Experimental, Universidad de La Laguna, La Laguna E-38205, Tenerife, Spain
R. J. Needs
Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
Received 18 August 1997
We present an ab initio pseudopotential study of the cinnabar phases of GaAs and GaP, which are covalently
bonded fourfold-coordinated structures formed from twisted tetrahedra. We find that these phases are not
thermodynamically stable. We suggest, however, that cinnabar-GaP could be formed as a metastable phase by
releasing pressure from the Cmcm phase, as recently observed in GaAs. S0163-18299805703-8
The latest experimental and theoretical research on the
high-pressure phases of III-V and II-VI compounds has re-
sulted in the emergence of a picture largely at variance with
what seemed established a few years ago.
1,2
A surprising
point to emerge has been the strong similarity between the
observed high-pressure phases of II-VI and III-V com-
pounds. The orthorhombic Cmcm phase is common to both
families of compounds.
1–3
There is also evidence for the
stability of an Immm phase, which is the binary analog of the
monatomic simple hexagonal structure observed in Si and
Ge.
2
A further similarity is that a phase with a structure very
similar to the cinnabarlike structure of ZnTe-II Ref. 1 has
recently been observed in a high-pressure study of GaAs.
4
The cinnabar structure was once thought to be exclusive
to the mercury chalcogenides, although it was recently dis-
covered at high pressures in CdTe and ZnTe.
1
The recent
observation of a cinnabar phase in GaAs Ref. 4 was the
first, to our knowledge, of a cinnabar phase outside of the
II-VI compounds. Cinnabar-GaAs was obtained on decom-
pression from the high-pressure Cmcm phase GaAs-II, and,
as the pressure was further decreased, it transformed into the
zinc-blende structure GaAs-I. As the direct transition from
the zinc-blende to cinnabar structures was not observed, the
phase may well be metastable. However, the fact that the
cinnabar phase is indeed stable in several II-VI compounds,
together with the similarities between the high-pressure
phases of III-V and II-VI compounds, casts doubt on this. It
also raises the question of whether one can obtain a cinnabar
phase in other III-V compounds.
In this Brief Report we show results of a theoretical study
of the energetics and structural properties of the cinnabar
structure in GaAs and GaP. We used the plane-wave PW
pseudopotential PP implementation of the density-
functional theory within the local-density approximation
LDA. The details of the calculation are similar to those
reported in previous work.
5
The accuracy and success of the
method have also been amply tested before.
2
To our knowl-
edge, this is the first theoretical study of the cinnabar struc-
ture in any III-V compound.
The cinnabar structure
6
space group P 3
1
21; see Fig. 1
belongs to the trigonal system, and at fixed volume is com-
pletely specified by two internal parameters ( u
1
, u
2
) , and one
axial ratio, c / a . In the basis of the lattice generators of the
trigonal system which in units of the lattice constant, a , we
take to be a
1
=(1,0,0), a
2
=( -
1
2
, 3/2,0), and a
3
=(0,0,c / a )] the atomic positions of the six atoms of the
basis are ( -u
1
, -u
1
,0), ( u
1
,0,
1
3
), and (0,u
1
,
2
3
) for atoms of
species 1, and ( -u
2
, -u
2
,
1
2
), ( u
2
,0,
5
6
), and (0,u
2
,
1
6
) for
atoms of species 2 hereafter, 1 will stand for the cation and
2 for the anion. The symmetry is increased for certain val-
ues of the structural parameters. Thus, when u
1
=u
2
=
2
3
and
c / a = 6 2.449, it becomes the rocksalt structure space
group Fm 3
¯
m , which we have studied previously in these
materials,
2
and which will not concern us here. Of more
relevance to the present study is that the configurations cor-
responding to ( u
1
, u
2
) =(0.5+
1
,0.5 +
2
) and ( u
1
' , u
2
' )
=(0.5-
1
,0.5 -
2
) are equivalent up to a c -axis rotation of
FIG. 1. a Perspective view of the cinnabar structure for the
case u
1
=u
2
=0.5, c / a =2.203. b Top view of the cinnabar struc-
ture for u
1
=0.539, u
2
=0.505. c Same as b, for u
1
=u
2
=0.5.
Circles of the same size correspond to atoms in the same layer.
Elevations are given in units of
1
6
c / a . d Comparison between the
positions of the nearest neighbors in zinc blende grey circles and
the cinnabar structure of c.
PHYSICAL REVIEW B 15 JANUARY 1998-I VOLUME 57, NUMBER 3
57 0163-1829/98/573/13444/$15.00 1344 © 1998 The American Physical Society