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Journal of Physics and Chemistry of Solids 70 (2009) 433–438

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Journal of Physics and Chemistry of Solids

0022-36

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/jpcs

Study of structural stabilities and optical properties of HgTeunder high pressure

Aimin Hao a,b,c, Xiaocui Yang d, Ruomeng Yu e, Chunxiao Gao b,�, Yonghao Han b,Riping Liu c, Yongjun Tian c

a Department of Mathematics and Physics, Hebei Normal University of Science and Technology, Qinhuangdao 066004, Chinab State Key Laboratory for Superhard Materials, Jilin University, Changchun 130012, Chinac State Key Laboratory for Metastable Materials Science and Technology, College of Materials Science and Engineering, Yanshan University, Qinhuangdao 066004, Chinad Department of Physics, Baicheng Normal College, Baicheng 137000, Chinae College of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

a r t i c l e i n f o

Article history:

Received 2 February 2008

Received in revised form

7 September 2008

Accepted 19 November 2008

Keywords:

A. Chalcogenides

C. Ab initio calculations

C. High pressure

D. Optical properties

D. Phase transitions

97/$ - see front matter & 2008 Elsevier Ltd. A

016/j.jpcs.2008.11.014

esponding author. Tel.: +86 335 2039287.

ail address: cxgao599@yahoo.com.cn (C. Gao)

a b s t r a c t

A theoretical investigation on the structural stabilities and electronic properties of HgTe under high

pressure was conducted using first principles based on density functional theory. Our results

demonstrate that the sequence of the pressure-induced phase transitions of HgTe is from the zinc

blende, to cinnabar, rocksalt, orthorhombic, and CsCl-type structures. The pressure effects on the

optical properties were discussed and compared with previous calculations and experimental data

whenever available.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Among the II–VI semiconductors, the high-pressure behaviorof HgTe has attracted the most attention [1–15]. Bridgman’s initialvolumetric studies suggested that HgTe undergoes a first-orderphase transition at 1.25 GPa with a volume change of �8.4% [1].This transition was subsequently confirmed by resistivity mea-surement [2] and X-ray diffraction study [3], which showed thetransition was from the zinc-blende to the cinnabar structure.

The resistivity measurement as a function of pressure on HgTeshows that it undergoes a sequence of transitions from asemimetal to a semiconductor, and then a metal in a relativelynarrow pressure range [16]. These changes in resistivity are alsoaccompanied by corresponding crystal-structural transitions fromthe zinc blende (ZB; phase I, semimetal) to the cinnabar (phase II,semiconductor), and to the rocksalt (RS) structure (phase III,metal) [17].

Lu et al. [18] reported ab initio total-energy and electronic-structure calculations for various phases of HgTe. They deter-mined that the sequence of the phase transitions was theZB-structure to the cinnabar (Cinn) structure to the RS-structure,

ll rights reserved.

.

and to the b-tin structure. In fact, it was later found that phase IVis not in the b-tin structure.

Full-multiple-scattering calculations [19] indicated that HgTeundergoes several structural phase transitions under pressure, i.e.ZB-Cinn-RS- orthorhombic (Orth) structure. And the spacegroup of the Orth-structure was determined to be Cmcm.

Moon and Wei [20] investigated the band gap of zinc-blendeHg chalcogenides using a corrected local density approximation(LDA) method. They found that HgTe has an inverted bandstructure, with an energy band gap of �0.31 eV.

In the present work, we applied first-principle calculations tostudy the electronic structures, structural stabilities, and opticalproperties of HgTe under pressure. In order to verify thecalculation results, we measured the conductivity in situ underhigh pressure.

2. Computational details

Our first-principle calculations were performed with theCASTEP code in MS modeling based on the plane wave basis set[21], using the ultrasoft pseudopotential for electron–ion interac-tions, and the exchange correlation potential of Perdew and Wang[22] in the local density approximation for electron–electroninteractions. The typical configuration for Hg and Te are 5d106s2

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A. Hao et al. / Journal of Physics and Chemistry of Solids 70 (2009) 433–438434

and 5s25p4, respectively. Integrations in the Brillouin zone (BZ)were performed using special k points generated with 7�7�7,6� 6�2, 6� 6�5, and 8�8�8 mesh parameter grids for theF43m, P3121, Cmcm, and Pm3m phases, respectively. One-electronvalence states were expanded on the basis of plane waves with acutoff energy of 350 eV for all phases.

The total energy as a function of volume was calcu-lated to determine the equilibrium volume and bulk modulusby parabolic fitting to a third Birch–Murnaghan equation ofstate [23].

The space group of phase I is F43m; the Hg atoms are located at(0, 0, 0), and Te at (0.25, 0.25, 0.25), with the lattice constantsa ¼ b ¼ c ¼ 6.453 A (Ref. [8]). The space group of phase II is P3121;the Hg atoms are located at (0.641, 0, 0.333), and Te at(0.562, 0, 0.833), with the lattice constants a ¼ b ¼ 4.383 A,c ¼ 10.022 A (Ref. [10]). The space group of phase III is Fm3m;the Hg atoms are located at (0, 0, 0), and Te at (0.5, 0.5, 0.5; Ref.[19]), with the lattice constants a ¼ b ¼ c ¼ 5.830 A (Ref. [8]). Thespace group of phase IV is Cmcm; the Hg atoms are located at(0, 0.624, 0.250), and Te at (0, 0.152, 0.250), with the latticeconstants a ¼ 5.563 A, b ¼ 6.152 A, and c ¼ 5.105 A (Ref. [14]).The space group of phase V is Pm3m; the Hg atoms are locatedat (0, 0, 0), and the Te at (0.5, 0.5, 0.5), with the latticea ¼ b ¼ c ¼ 3.299 A (Ref. [12]).

Fig. 1. The Gibb’s free energy versus volume for the F43m, P3121, Fm3m, Cmcm, and

Pm3m phases of HgTe.

3. Results and discussion

3.1. Structural stabilities

The theoretical ground-state parameters (lattice parametersand B0) of HgTe are obtained and listed in Table 1, whichalso includes the available experimental and theoretical datafor comparison.

The variations of the Gibb’s free energy (G) with volume (V) forthe five structures are given in Fig. 1, where we can observe thefollowing sequence of phase transitions in HgTe: the ZB-structure-the Cinn-structure-the Orth-structure-the CsCl-structure. Our calculations show that the G–V plots of the Cinn-and RS-structures practically overlap. So we cannot obtain thetransition pressure of the Cinn- to the RS-structure. This is becausethe cinnabar to the RS-structure is a second-order transition,where only the bond length and the bond angle are adjusted when

Table 1Calculated ground state properties of HgTe at ambient and high pressures.

ZB-structure Cinn-structure

Theory Exp. Theory Exp.

a/b/c (A) a ¼ 6.486a a ¼ 4.382 a ¼ 4.48

a ¼ 6.459 a ¼ 6.453e c ¼ 10.028 c ¼ 10.0

B (GPa) 47.6 42.3f 57.7

48.4a 46.7g

47.8h

Eg (eV) 0 0.21

a Ref. [18].b Ref. [10].c Ref. [14].d Ref. [12].e Ref. [8].f Ref. [24].g Ref. [26].h Ref. [25].

it transforms gradually from the sp covalent bonding to a six-coordinated bonding.

The structural phase stability is determined by calculating theGibb’s free energies (G) for the two phases [27]:

G ¼ Etot þ PV þ TS. (1)

In the theoretical calculations, we considered only the zero-temperature limit, so Gibb’s free energy equals the enthalpy (H):

H ¼ Etot þ PV . (2)

At a given pressure a stable structure is one for which enthalpyhas its lowest value and the transition pressures are calculated asthose at which the enthalpy for the two phases are equal [28,29].

The theoretical ground-state parameters of HgTe wereobtained and are listed in Table 2, which also includes the avail-able experimental and theoretical data for comparison. As can beseen, our results are in reasonable agreement with those of theprevious experiments and calculations. Fig. 2 displays the relativevolume V/V0 as a function of pressure for the F43m, P3121, Cmcm,and Pm3m phases, where V0 is the initial equilibrium volume.

Orth-structure CsCl-structure

Theory Exp. Theory Exp.

3b a ¼ 5.612 a ¼ 5.563c a ¼ 3.302 a ¼ 3.299d

22b b ¼ 6.194 b ¼ 6.152c

c ¼ 5.102 c ¼ 5.105c

124.7 277.2

0 0

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Fig. 2. The relative volume dependence as a function of pressure in the F43m,

P3121, Cmcm, Fm3m, and Pm3m phases.

Fig. 3. The partial density of state (DOS) of HgTe under ambient conditions.

Table 2Phase transition pressures of HgTe, together with the available experimental and

theoretical data for comparison.

F43m to P3121 Fm3m to Cmcm Cmcm to Pm3m

Theory Exp. Theory Exp. Theory Exp.

PT (GPa) 1.5 1.4a 13.7 11b 44.7 28c

1.5d 12d 38e

a Ref. [24].b Ref. [8].c Ref. [12].d Ref. [19].e Ref. [9].

A. Hao et al. / Journal of Physics and Chemistry of Solids 70 (2009) 433–438 435

3.2. Band structures and electronic properties

The partial density of states (DOS) of ZB-HgTe at 0 GPa isshown in Fig. 3. The DOS could be mainly divided into seven parts.The first part extending from �12.5 to �11.0 eV is mainly thecontribution of Te-s states; the second from �8.0 to �6.0 eV ofHg-d states; the third from �6.0 to �5.0 eV of Hg-s and Te-p

states; the fourth from �3.0 to 0 eV of Te-p states; the fifth from1.4 to 8.5 eV of Hg-s and Te-p states; the sixth from 9.0 to 10.5 eVof Hg-s states; and the seventh from 11.5 to 12.5 eV of Hg-s statesand Te-p states.

The band structures of the F43m phase at 0 GPa is shown inFig. 4(a). The bottom of conduction band touches the top ofvalence band at G point. This is the typical character of asemimetal. The band structure of the P3121 phase is shown inFig. 4(b). The bottom of the conduction band is located at G point,and the top of the valence band is located at A point, which showsthat P3121-phase HgTe is an indirect band gap semiconductor. Ourresult displays that the lowest conduction drops with increasingpressure. The indirect band gap should become zero when theP3121 phase transform into the Fm3m phase. For the Cmcm andPm3m phases, the conduction band and the valence band overlapat several places, as shown in Figs. 4(c) and (d). This means thatboth the phases of HgTe have metallic properties.

3.3. Optical properties

Dielectric function e(o), which describes the features of linearresponse of the system to an electromagnetic (EM) radiation,governs the propagation behavior of EM waves in a medium. e(o)is connected with the interaction between photons and electrons.Its imaginary part e2(o) can be obtained by calculating themomentum matrix elements between the occupied and unoccu-pied wave functions within the selection rules, and its real parte1(o) can be derived from e2(o) by the Kramer–Kronig relation-ship. All the other optical constants, such as refractive index n(o),absorption coefficient a(o), reflectivity R(o), and electron energy-loss spectrum L(o) can be deduced from e1(o) and e2(o) [30–32].The calculated e1(o) and e2(o) of four phases of HgTe are shownin Fig. 5. We discuss the case of incident radiation with the linearpolarization along the [0 0 1] direction. For ZB-HgTe, the peaks ofthe e2(o) at �1.44, �3.22, �5.70, and 7.18 eV originate from theinterband transitions between valence and conduction bands. Thepeaks at �12.12 and 14.87 eV are very close to what are expectedfor the d-band transitions, and thus the peaks can be associatedwith transitions from the Hg-5d level to a high-density point ofstates in the conduction band. The peak centered at �18.86 eV canbe tentatively associated with the excitation of volume plasmaoscillation. Our result agrees reasonably with the experimentaldata (Ref. [6]). For the high-pressure phases, the optical propertieschange abruptly with increasing pressures. We cannot compareour theoretical results because no experimental data are available.

Furthermore the energy-loss function, that is, the imaginarypart of the reciprocal of the complex dielectric function, was alsoobtained, as shown in Fig. 6. It is an important optical parameter,indicating the energy loss of a fast electron traversing in thematerial. The peaks represent the characteristic behaviors asso-ciated with the plasma oscillations. The corresponding frequen-cies are the so-called plasma frequencies, above which thematerial behaves as a dielectric [e1(o)40] while below this thematerial behaves as a metallic [e1(o)o0]. In the case of [0 0 1]polarization, there is a single strong peak at �17 eV for thecinnabar-HgTe, and at �22 eV for the orthorhombic-HgTe. This isconsistent with the feature of e1(o) shown in Fig. 6, where onemetallic region exists for [0 0 1] polarization.

3.4. In-situ conductivity measurement

In order to validate the results of the calculation, we measuredthe conductivity of HgTe under high pressure. The stoichiometricsample with 99.99% purity was provided by Alfa Aesar Company.The sample was loaded in a diamond anvil cell (DAC). A multilayer

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Fig. 4. The band structures of HgTe at several pressures: (a) the ZB-structure at 0 GPa, (b) the Cinn-structure at 3 GPa, (3) the Orth-structure at 35 GPa, and (4) the CsCl-

structure at 70 GPa.

A. Hao et al. / Journal of Physics and Chemistry of Solids 70 (2009) 433–438436

microcircuit was developed on a DAC for in-situ conductivitymeasurement under high pressure. The method of fabricating amicrocircuit and in-situ conductivity measurement has beendescribed previously [33,34].

Our experimental result indicated that the conductivity is ofthe order of 103O�1 cm�1, and decreases slightly with increasingpressure in the pressure range of 0–1.7 GPa. The conductivitydecreases abruptly at about 1.7 GPa. It was found that theconductivity increases with increasing pressure from 1.7 to12 GPa, indicating the electrical transport feature of a semicon-ductor. At about 12 GPa, the conductivity increases abruptly andthe maximum reaches the order of 104O�1 cm�1. The leveling offof the conductivity above 12 GPa is a strong indication of themetallization of the sample. The experimental result shows thatthe pressure-induced transition sequence is from a semimetal to asemiconductor to a conductor, which is consistent with the

calculated results. The several pressures at which conductivitychanges abruptly are in good agreement with our calculated phasetransition pressures.

4. Conclusions

A theoretical investigation on the structural stabilities andelectronic properties of HgTe under high pressures was performedusing first principles based on density functional theory with theplane wave basis as implemented in the CASTEP code. Our resultsindicate that the sequence of pressure-induced phase transitionsis from the ZB- to the Cinn- to Orth-, and then to the CsCl-structure. Our result indicates that the Cinn- to the RS-structuretransition is a second-order phase transition, where the bondlength and the bond angle change gradually with increasing

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Fig. 5. The calculated e1(o) and e2(o) of HgTe: (a) the ZB-structure at 0 GPa, (b) the Cinn-structure at 3 GPa, (c) the Orth-structure at 35 GPa, and (d) the CsCl-structure

at 70 GPa.

Fig. 6. Energy-loss function of HgTe: (a) the ZB-structure at 0 GPa, (b) the Cinn-structure at 3 GPa, (c) the Orth-structure at 35 GPa, and (d) the CsCl-structure at 70 GPa.

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pressure during the transition. The in-situ conductivity measure-ment confirms that the pressure-induced transition sequence isfrom a semimetal to a semiconductor to a conductor. For theambient-pressure phase, the optical properties agree reasonablywell with experimental data. For the high-pressure phases, theoptical properties change drastically with increasing pressure.

Acknowledgements

This work was supported by the Doctoral Foundation ofHebei Normal University of Science and Technology under Grantno. 2008YB001, the National Natural Science Foundation of Chinaunder Grant nos. 40473034 and 40404007, and the National BasicResearch Program of China under Grant no. 2005CB724404.

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