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phys. stat. sol. (b) 244, No. 1, 244–255 (2007) / DOI 10.1002/pssb.200672551

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Effect of pressure on the structural properties

and electronic band structure of GaSe

U. Schwarz**, 1, D. Olguin***, 1, A. Cantarero2, M. Hanfland3, and K. Syassen*, 1

1 Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany 2 Department of Materials Sciences, University of Valencia, 46000 Burjasot, Spain 3 European Synchrotron Radiation Facility, BP 220, 38043 Grenoble, France

Received 7 August 2006, accepted 14 August 2006

Published online 5 December 2006

PACS 61.50.Ah, 61.50.Ks, 62.50.+p, 64.30.+t, 71.20.Nr

The structural properties of GaSe have been investigated up to 38 GPa by monochromatic X-ray diffrac-

tion. The onset of the phase transition from the ε -GaSe to a disordered NaCl-type structural motif is ob-

served near 21 GPa. Using the experimentally determined lattice parameters of the layered ε -phase as in-

put, constrained ab-initio total energy calculations were performed in order to optimize the internal struc-

tural parameters at different pressures. The results obtained for the nearest-neighbor Ga–Se distance agree

with those derived from recent EXAFS measurements. In addition, information is obtained on the changes

of Ga–Ga and Se–Se bond lengths which were not accessible to a direct experimental determination yet.

Based on the optimized structural parameters, we report calculations of band gap changes of ε -GaSe un-

der pressure. The optical response and electronic band structure of the metallic high-pressure phase of

GaSe are discussed briefly.

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

The application of hydrostatic pressure is a means to tune the structural anisotropy and related changes in the electronic properties of layered materials. In this context, the layered polytypes of the III–VI semi-conductors [1] have been the subject of extensive high-pressure (HP) experimental investigations. One of the early HP studies of layered GaSe was motivated by the strong tendency of exciton formation in lay-ered semiconductors [2]. Recent HP experiments performed on the most common ε -polytype of GaSe have addressed the structural properties [3, 4], the dielectric response [5], band gap changes including a band crossing from direct to indirect [6–8], the photoluminescence [9], the Raman scattering [10], and the electric transport behavior [11]. Furthermore, the transition of GaSe at around 20 GPa to a metallic HP phase [12] has been characterized by X-ray diffraction [13, 14], X-ray absorption [3], and Raman scattering [10]. We report here the results of powder X-ray diffraction studies of GaSe at pressures up to 38 GPa (Sec-tion 3). Our starting material was the hexagonal ε -polytype (Fig. 1). Furthermore, we present results of total energy calculations of ε -GaSe as a function of pressure (Section 4); these are aimed at the optimiza-tion of the internal structural parameters (atom positions) of layered GaSe for the given experimental unit

* Corresponding author: e-mail: [email protected], Fax: ++49 711 689 1444

** Present address: Max-Planck-Institut für Chemische Physik fester Stoffe, Nötnitzer Staße 40, 01187 Dresden, Germany

*** Present address: Dept. de Física, CINVESTAV–IPN, 07300 México D.F., Mexico

phys. stat. sol. (b) 244, No. 1 (2007) 245

www.pss-b.com © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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Paper

cell dimensions. The reason for optimizing the structure via an ab initio calculation is that a direct deter-mination of internal structural parameters under pressure by diffraction methods is difficult due to the inherent tendency to form stacking faults. Our results fully reproduce the experimental data for the near-est neighbor Ga–Se distances determined by EXAFS [3, 4]. Hence, we may assume that the pressure change of the other interatomic distances are also well described by our approach. Based on the diffrac-tion data and structure optimization, we consider the evolution of the band structure of layered GaSe under pressure (Section 5), in particular with respect to a change of the fundamental band gap from direct at ambient pressure to indirect at high pressure. Finally, the optical reflectivity and calculated band struc-ture of the metallic HP phase of GaSe are discussed briefly (Section 6).

2 Structural details

The layers in the various polytypes of GaSe [1] consist of a four-sheet sequence of hexagonal planes of Se, Ga, Ga, and Se, respectively (cf. Fig. 1). Within the layers, the Ga atoms are four-coordinated by one Ga and three Se atoms forming a distorted tetrahedron. The Se atoms are bonded to three Ga atoms. The layers interact weakly through what is usually termed ‘van der Waals-like’ forces. The β , γ , δ , and ε polytypes correspond to different stacking sequences of the layers. In all layered polytypes, the Se atoms of a second layer are centered over triangles of Se atoms in the first layer. The crystal structure of ε-GaSe is hexagonal, space group P6m2 ( 1

3hD , No. 187 [15, 16]). In the Ref. [15], the hexagonal cell

parameters at ambient pressure are given as a = 3.743 Å and c = 15.919 Å ( 4 253c a/ = . ). In this paper, we label the inequivalent Se and Ga atoms as indicated in Fig. 1. In principle, there are four internal positional parameters as defined in the caption of Fig. 1. From the zero-pressure structural data of GaSe [15] we can realize that within experimental error

Ga Ga1 2r s+ = / and

Se Se1 2r s+ = / . This

implies that the bond lengths Ga2–Se1 and Ga1–Se2 are equal. In other words, the internal structure of the layers is identical and the local environment of the Se1 and Se2 atoms (or Ga1 and Ga2 atoms) is the same till the third neighbor. In order to save computation time during the structure optimization de-scribed below, we keep the constraint 1 2r s+ = / which reduces the number of internal parameters from 4 to 2. This assumption appears justified because the atomic environment is different only at the fourth neighbors. Furthermore, in an unconstrained structure optimization for the structurally related γ -InSe we indeed found identical nearest neighbor In–Se distances [17].

Fig. 1 (online colour at: www.pss-b.com) Schematic view of the crystal structure of ε-

GaSe. The space group is P6m2 (No. 187). The hexagonal unit cell contains 4Z = formula

units. There are two inequivalent Se atoms in the unit cell (Wyckoff positions 2i and 2g) at

[15]

2 1

Se Se3 3( ) 0 15r r, , ± , = .

and

Se Se(0 0 ) 0 35s s, , ± , = . .

The two inequivalent Ga atoms (Wyckoff positions 2h and 2g) are at [15]

1 2

Ga Ga3 3( ) 0 425r r, , ± , = .

and

Ga Ga(0 0 ) 0 075s s, , ± , = . .

246 U. Schwarz et al.: Effect of pressure on properties and band structure of GaSe

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

3 Diffraction studies

Crystals of ε -GaSe were synthesized from the elements using the Bridgman method [15, 18]. After gen-tle grinding, a powder sample was loaded into a diamond anvil cell using methanol-ethanol as a pressure medium. Pressure was measured by the ruby luminescence method [19]. Monochromatic diffraction experiments were carried out at the beamline ID9 of the European Synchrotron Radiation Facility, Gre-noble, using image plate detection. The X-ray beam (wavelength 0.45798 Å or 0.44618 Å) was colli-mated to a nominal diameter of 30 µm. In order to improve powder averaging, the DAC was rocked by ±3 degrees. The scanned two-dimensional diffraction patterns were corrected for tilt and scanner distor-tions and converted to intensity-vs.-2Θ data using the FIT2D software [20]. Determination of peak posi-tions, indexing, structure solution, and refinements of lattice parameters were performed using the CSD [21] and GSAS [22] program packages. Figure 2 shows diffraction diagrams of GaSe at selected pressures. The pattern at ambient pressure is consistent with the ε -phase assignment. The ambient pressure lattice parameters are obtained as

3 759a = . Å and 15 97c = . Å. Both these values are larger by ∼0.3% compared to Ref. [15]. The unusu-ally large width of the (103) reflection is attributed to stacking disorder introduced by the grinding of the sample. The ε -phase is observed up to 22.8 GPa. However, at this pressure an admixture or a HP phase is present already. That phase is almost fully developed at 27.8 GPa. The pressure-induced phase transi-tion is not reversible on releasing the pressure, in accordance with results of, e.g., HP Raman studies [10]. The Bragg reflections of the HP modification indicate a face-centered cubic arrangement, consistent with a NaCl-type structural motif. However, diffraction peaks of the HP phase are extremely broad, as

5 10 15 20 25Diffraction angle (degree)

Inte

nsity

(ar

b. u

nits

)

004

100,

101

200

220

222

38.8

27.8

22.8

16.8

7.4

0

P (GPa)

400

420

GaSe

103

110

104

201

203

207

0 5 10 15 20Pressure (GPa)

3.6

3.8

4.0

Latti

ceP

aram

eter

(Å)

0 10 20 30 40Pressure (GPa)

30

35

40

45

50

Vol

ume

per

form

ula

unit

(Å3 )

εεεε-phase

a

c/4

εεεε-Phase

GaSe

NaCl-type

Fig. 2 (online colour at: www.pss-b.com) Left: X-ray diffraction diagrams of GaSe at different pres-

sures. Indexing of the ambient-pressure pattern refers to the ε -phase. The sluggish phase transition to the

cubic high-pressure phase proceeds in the range 21 to 27 GPa. The diagram at 38.8 GPa is indexed as face

centered cubic. Open triangles attached to diagrams of the ε -phase mark a disorder-induced feature. Right:

Volume per formula unit of GaSe as a function of pressure. The inset shows the measured lattice param-

eters a and c of the ε -phase versus pressure. The solid lines correspond to fitted expressions (see text).

phys. stat. sol. (b) 244, No. 1 (2007) 247


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was also observed by Takumi et al. [14]. At this point, we attribute the large width of the Bragg peaks to a large degree of site disorder and related internal strain. By annealing at moderate temperatures (150 °C), the quality of our diffraction patterns could not be improved. A more systematic thermal an-nealing study is needed in order to prove that the structure of the HP phase is indeed of the undistorted rocksalt type. On the theoretical side, one could think of testing the dynamical stability of rocksalt GaSe. The diffraction diagrams have been analyzed to extract information on lattice parameters and specific volume. For this purpose we assume that the HP phase of GaSe is indeed of the NaCl type. We do not rule out a more complicated ordering pattern of the constituent ions (or a description as simple cubic in case of a fully disordered site occupancy), but this does not affect the determination of the specific vol-ume from the observed diffraction patterns. The volume per formula unit as a function of pressure in shown in Fig. 2. Near 20 GPa, the relative volume change at the phase transition is about –8%. The unit cell parameters of the ε-phase are also displayed in Fig. 2. While the c-axis is highly compressible initially, the rate of its relative change with pressure approaches that of the a-axis at higher pressures. In other words, the unit cell of ε-GaSe de-forms nearly isotropically at pressures above 10 GPa. The c/a ratio drops from 4.253 at ambient to 4.053 at 20 GPa. Table 1 lists experimental values for lattice parameters and the volume per formula unit at different pressures. The lattice parameter versus pressure data of the ε phase were fitted by the expression

01

0

0

0

( ) 1l P l P

ββ

β

- / ¢

¢Ê ˆ= + .Á ˜Ë ¯ (1)

This analytical form is similar to an inverted Murnaghan-type relation [23]. In Eq. 1, 0l stands for a unit

cell parameter, 0

β for the inverse linear compressibility, and 0

β ¢ for the pressure derivative of the mo-dulus β , all taken at ambient pressure. The obtained parameter values are collected in Table 2. At zero pressure the c-axis is about five times more compressible compared to the a-axis. The pressure deriva-tives

0β ¢ differ by a factor of two. We note that the linear compressibility values obtained here are in

good agreement with values derived from the experimental [24] and calculated [25] elastic constants. Also, the overall change of the c-axis at a pressure of 20 GPa obtained by Gauthier et al. [26] using mi-cro-photographic measurements on GaSe crystals agrees surprisingly well with the X-ray diffraction data.

Table 1 Volume per formula unit and lattice parameters of GaSe as a function of pressure.

phase P (GPa) V (Å3) a (Å) c (Å)

ε-phase 0.001 48.85 3.7591 15.968 1.26 47.09 3.735 15.59 2.4 46.02 3.717 15.38 3.0 45.33 3.700 15.29 4.75 44.04 3.675 15.06 5.0 43.98 3.677 15.03 7.35 42.52 3.639 14.83 10.2 41.15 3.613 14.56 12.3 40.09 3.576 14.48 16.7 38.57 3.532 14.28 20.3 37.43 3.494 14.16

HP 22.8 31.06 4.990 26.3 30.69 4.969 27.8 30.69 4.969 38.8 29.72 4.920 19.4 (d) 31.25 5.000



Table 2 Parameters of Eq. (1) that characterize the change in the unit cell dimensions of ε -GaSe under

pressure. See text for explanations.

axis 0l (Å)

0β (GPa)

0β ¢

( )a P 3.759 198(10) 9(2) ( )c P 15.97 44(2) 18.7(7)

We resort to a third-order Birch relation [27] to fit the experimental ( )P V data. The obtained param-eters for the bulk modulus and its first pressure derivative at ambient pressure are

034(2)B = GPa and

06 4(5)B = .¢ . The bulk modulus of the HP phase, averaged over the range 20 to 38 GPa, is 380(30) GPa,

i.e. about ten times larger than the bulk modulus value of the ε-phase at ambient. Different pressures have been reported in the literature for the ε-phase to cubic transition of GaSe, ranging from 16 to 29 GPa [3, 4, 10, 12]. It is believed that the large pressure span in part arise from the stress conditions in a particular experimental run, i.e. the hydrostaticity of the pressure medium. In none of the experimental investigations an attempt was made to determine the thermodynamic equilibrium pressure for the layered and HP phases. In view of the non-reversibility of the phase transition, the equi-librium pressure could be significantly lower than the onset pressure of the transition observed on up-stroke at room temperature.

4 Constrained structure optimization

As for layered GaSe at ambient pressure, ab initio methods have been employed in lattice dynamics calculations [25] and in the interpretation of photoemission experiments [28, 29]. It appears that fully relaxed ab initio calculations of the pressure-dependent structural or dynamical properties of layered GaSe have not been reported so far. In this work, we have performed constrained total energy calcula-tions of ε -GaSe in order to obtain optimized internal structural parameters. For the calculation of the total energy we employed the relativistic full potential linearized augmented plane wave method (FP-LAPW) within the density functional theory (DFT) approximation [30]. For the exchange and correlation potential we used the generalized gradient approximation (GGA) [31]. Relativ-istic corrections have been taken into account via the spin–orbit Hamiltonian. We have checked the convergence of the calculations in terms of the size of the plane-wave basis set and the k-points sampling within the irreducible part of the Brillouin zone. We used

MT max10R K = , where

maxK is the plane wave

cutoff and MT

R is the atomic sphere radius. The latter was chosen equal to 2 a.u. The Ga 3d states were treated as valence band states using the local orbital extension of the LAPW method [30]. A set of 12 k-points, equivalent to a 7 × 7 × 1 Monkhorst–Pack grid [32] in the unit cell, was used in the structure optimization at the different pressures. The constrained structure optimization procedure has been the following. The lattice parameters a and c of ε -GaSe at different pressures were taken from the experimental study, i.e., the calculations were forced to agree with the lattice constants at 300 K. At a given pressure, we started with a fixed positional (internal) parameter for the Ga atoms (i.e.

Gar was fixed) and allowed the atomic position

Ser of Se atoms

to relax towards the minimum in total energy. In a second step, we allowed for the relaxation of the Ga–Ga bond distance (

Gar is changed, while

Ser is kept constant). This process was iterated until conver-

gence was achieved, usually after two iterations at a given pressure. As a final check we relaxed the unit cell parameters for fixed atomic positions. In all cases the unit cell parameters converged towards the original input data, within numerical uncertainties. Figure 3 shows, as an example, the calculated total energy as a function of Se–Se and Ga–Ga bond distances for the experimental unit cell parameters at zero pressure. The optimized distance is taken as the minimum of a fitted parabola. The converged value of the Ga–Ga bond length is 2.44 Å, correspond-ing to

Ga0 4235r = . (cf. Fig. 1). The optimized values of the positional parameters of Se (

Se0 1504r = . ) is

essentially identical to that of Ref. [15].

phys. stat. sol. (b) 244, No. 1 (2007) 249


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ε -GaSe

Se -SeGa -Ga

0 GPa

To

tal e

ne

rgy

(Ry)

Interatomic distance (Å)

Fig. 3 Variation of the total energy of ε-GaSe with Ga–Ga bond length and with interatomic Se2–Se2

distance, as calculated for experimental values of the lattice parameters at zero pressure and 300 K. Here,

Gar was varied while

Ser was held constant (cf. Fig. 1) and vice versa. The plot refers to converged condi-

tions, i.e. the locations of the minima of the parabolas fitted to the calculated points correspond to the op-

timized distances. An offset of 34995 Ryd is applied to the energy scale. Figure 4 summarizes the results as deduced from the optimization procedure for the pressure range up to 20 GPa. The top left panel shows the Ga–Se and Ga–Ga interatomic distances. The change in the Ga–Se bond length with pressure has been determined experimentally from EXAFS measurements [3, 4]. A subset of the experimental data taken from Ref. [4] is also plotted in Fig. 4. Our results are in very good agreement with the experimental data. Hence, our approach to the structure optimization is mean-ingful and we can expect that the optimization yields realistic values for the other interatomic distances. The information on the Ga–Ga bond distance is of particular interest because the localization of Ga-derived s electrons in this bond is responsible for the semiconducting behavior of GaSe. We find that the Ga–Ga bond length decreases under pressure. At 20 GPa, the total change (–5.7%) is slightly larger compared to that of the Ga–Se bond distance (–4.5%). In the top right panel of Fig. 4 we compare the intra- and interlayer Se–Se distances. The intralayer Se–Se distance (the Se1–Se1 and Se2–Se2 distances are equal) changes by only –1.4% in the pressure range up to 20 GPa. So, the layer thickness is hardly affected by the application of pressure. On the other hand and as expected, the interlayer Se–Se distance changes strongly with pressure; this effect domi-nates the compressibility behaviour along the c-axis as is evident from the projection of the interlayer Se–Se distance onto the c-axis also shown in the top right panel of Fig. 4. The pressure dependence of the Ga–Ga–Se bond angle is shown in the bottom left panel of Fig. 4. The angle increases continuously with increasing pressure, the overall change amounts to about 2 de-grees in the pressure range up to 20 GPa. Based on EXAFS measurements of the Ga–Se bond distance under pressure, Pellicer-Porres et al. [3] proposed a scenario for the internal structural changes of ε-GaSe under pressure. They postulated chan-ges of the Ga–Ga and Se–Se bond lengths which are largely consistent with the results presented in Fig. 4. So, our structure optimization supports the assumptions which entered into the structure model proposed in Ref. [3].

5 Electronic structure of e-GaSe under pressure

The electronic structure of GaSe at ambient pressure was first calculated in a two-dimensional approxi-mation by Bassani et al. using a tight–binding method [33]. Calculated band structures of the β and γ polytypes of GaSe were reported in, e.g., Refs. [34–40]. Some of these calculations were of empirical



0 5 10 15 20 25

2.30

2.35

2.40

2.45

2.50

ε-GaSe

Ga-Se

Ga-GaInte

rato

mic

Dis

tanc

e (Å

)

Pressure (GPa)

ε -GaSe

Å

0 4 8 12 16 20

118.5

119.0

119.5

120.0

120.5

121.0

121.5

ε-GaSe

Ga-

Ga-

Se

bond

ang

le

Pressure (GPa)

nature, aiming at an interpretation of observed optical transitions (see also Ref. [41]). The ε polytype of GaSe was considered in recent DFT calculations of Refs. [28, 29]. To our knowledge, the effect of pres-

sure on the band structure of the ε polytype has not been calculated before, except for the band structure at 7 GPa given in Ref. [11]. Figure 5 shows the band structures of ε -GaSe at zero pressure and 16 GPa, as obtained from our con-strained FPLAPW calculations, i.e. for the experimental lattice parameters at room temperature and for the corresponding optimized internal structural parameters. The corresponding density of states (DOS) curves are also shown in Figure 5. At ambient pressure, ε -GaSe comes out as a direct gap semiconductor with the fundamental gap at the Brillouin zone center (Γ-point), in accordance with experiments. The calculated gap at zero pressure is 0.89 eV, while the experimental gap is 2.12 eV at 10 K [1, 42]. This difference can be attributed to the well-known ‘local density error’ [43]. Here, we are mainly interested in the pressure variation of band gaps which is expected to be predicted in close agreement with experi-ment [43, 44].

Fig. 4 Structural properties of ε -GaSe as a function

of pressure: Nearest neighbor Ga–Ga and Ga–Se

distances (top left), Se1–Se1 intralayer and Se1–Se2

interlayer distances (top right), and the Ga–Ga–Se

bond angle. The solid symbols and lines refer to the

results of the constrained structure optimization proce-

dure (see text). Open symbols in the top left panel

represent the experimental data from EXAFS meas-

urements of Ref. [4].

phys. stat. sol. (b) 244, No. 1 (2007) 251


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Γ Σ ∆ Γ

0 GPa

ε -GaSe

16 GPa

Γ Σ ∆ Γ

ε -GaSe

Fig. 5 Calculated electronic structure of ε-GaSe: energy bands and total density of states at ambient pressure and at

16 GPa. Also shown are band gap energies as a function of pressure. EΓ1

and EΓ2

refer to the two lowest-energy gaps

at the Γ-point, EH, E

K, and E

M to indirect gaps between the top of the valence band at Γ and conduction band states at

the zone boundary.

Comparing the electronic structures at 0 and 16 GPa, the top of the valence band at the Γ-point flattens along Γ-M, i.e. the effective mass component of the holes increases in that direction; it is practically infinity at 16 GPa. The bottom of the conduction band at the Γ-point as well as the higher lying states at Γ move up in energy (we take the origin at the top of the valence band). At the edge of the Brillouin

-4 -3 -2 -1 0 1 2 3 40

5

10

15

20

16 GPa

0 GPa

ε-GaSe

EF

DO

S (

stat

es/e

V c

ell)

Energy (eV)

M

b1

b3

b2

L

A∆Γ

ΣT

H

K



zone, i.e. at the M-, K-, and H-points, the energy separation between the Fermi level and the valence band states increases. The lowest conduction bands at M, K, and H are initially located between 0.3 and 0.8 eV above the Γ-point minimum of the conduction band. These bands shift down with pressure, so that at 16 GPa GaSe is an indirect gap semiconductor, the smallest gap being between the top of the valence band at Γ- and the H-point. The differences between the band structures of GaSe at 0 and 16 GPa can be understood by referring to the dominant orbital characters of the various bands; these are discussed in detail in several of the early reports on band structure calculations cited above. For instance, the top of the valence band at Γ is mainly of antibonding Se-p

z character, while the lower-lying valence bands have predomi-

nantly Se-p px y

character. Under pressure, the Se atoms facing the interlayer region get much closer initially. The resulting stronger interlayer interaction tends to drive up in energy the Se-p

z band edge

state relative to Se-p px y

states. The repulsion of the pz orbitals also causes, in part, the flatness of

the valence band at high pressure. The very bottom of the conduction band is formed by anti-bonding Ga-s orbitals but with small admixtures of Se-p p

x y and Se-p

z. Since the Ga–Ga distance decreases un-

der pressure, the anti-bonding Ga–s move up in energy, leading to an increase of the gaps at the Γ-point. At ambient pressure, the density of states (DOS) (Fig. 5) has a contribution of Se-p

z orbitals just be-

low the Fermi energy and at around –1.2 eV there is a peak due to a contribution from Se-p px y

states (in the ∆-direction); these states also contribute to the large DOS at lower energy. The Ga-s contribution to the DOS at the bottom of the conduction band also produces the peak at around 2 eV. At high pressure (16 GPa) there are no sharp features in the DOS any more. The dominant contribution to the DOS in the valence band regime shifts down in energy relative to the Fermi level. As for the conduction band region, the fundamental gap narrows and the bands mix and spread out, giving rise to lower DOS maxima and the disappearance of the small gap at around 3 eV. Figure 5 includes a more detailed look at the evolution of the low-lying band gaps with increasing pressure. The three main observations are: (1) At low pressures, the band structure calculations reproduce, at least qualitatively, the well-known change in sign [45] from negative to positive of the pressure coefficient of the lowest direct gap of ε -GaSe (labeled E

Γ1 in Fig. 5); the sign change is related to a competition between interlayer and in-

tralayer interactions, see Ref. [8] for a recent discussion. Above 4 GPa the pressure shift of EΓ1

is almost linear, the average value being 51 meV/GPa between 4 and 20 GPa. The behavior of E

Γ1 and the linear

pressure shift of the next direct gap Γ2

E (related to EΓ by spin–orbit interaction) is qualitatively similar

to that of γ -InSe [17]. The gap Γ2

E is predicted to shift by 45 meV/GPa (average value for 0 to 20 GPa). For comparison, a value of 40 meV/GPa follows from the low-pressure data in Fig. 2 of Ref. [45]. (2) The indirect gaps E

M (1.22 eV), E

H (1.54 eV), and E

K (1.66 eV) between the valence band maxi-

mum at Γ and low-lying conduction band states at the M-, H-, and K-points shift to lower energy with increasing pressure, but at different initial rates (fitted values are approximately –270, –250, and –170 meV/GPa) and with different degrees of nonlinearity. As a result, the ordering of the indirect gaps at high pressure becomes different from that at low pressure. In absolute values, the indirect gap E

H

exhibits the largest overall shift of all the low-lying band gaps. (3) The direct gap E

Γ1 and the two indirect gaps E

M and E

H cross near 4 GPa. At this pressure, GaSe is

predicted to become an indirect-gap semiconductor, with the indirect EH gap being lowest in the range up

to 20 GPa. An extrapolation of results on gap crossings for InSe-GaSe alloys reported by Manjón et al. [7] indicates that a gap crossing in ε-GaSe should occur at a pressure significantly lower than 4 GPa. In the case of InSe the crossing was predicted at 8 GPa [17] while the experimental value is given as 4.2 GPa [7]. There is no reason to assume that the experimental results, derived from optical absorption, are affected by stacking fault formation. Also, the broadening of the excitonic absorption peak of ε-GaSe at rather low pressure [2, 46] may indicate that at ambient pressure the indirect gaps are closer in energy to the direct gap than calculated here. Therefore, the possible discrepancies mentioned above could, for instance, mean that wavevector-dependent corrections of the calculated energy gaps [43] are necessary in order to better simulate the gap crossing in layered III–VI semiconductors.

phys. stat. sol. (b) 244, No. 1 (2007) 253


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6 Electronic properties of the high-pressure phase

A NaCl-type phase of GaSe is expected to be metallic. This follows from simple valence electron count-ing, giving an odd number of valence electrons in the primitive cell. Indeed, Dunn and Bundy [12] ob-served a transition of GaSe to a metallic state at about 22 GPa, where GaSe becomes superconducting with a

cT of about 5 K.

The metallic behavior of the HP phase of GaSe is also evident from optical reflectance spectra (Fig. 6). The spectra were measured in a diamond anvil cell and the sample was brought in direct contact with one of the diamonds. The absolute reflectance

dR was measured at the diamond-sample interface,

taking into account corrections for the spectral characteristics of the microscope spectrometer. One should keep in mind that

dR is lower compared to the reflectivity at a hypothetical sample-vacuum inter-

face because of the different refractive index matching. The near-infrared reflectivity of GaSe is ob-served to increase significantly at the phase transition (cf. Fig. 6). The HP phase shows a plasma-edge-like feature located at roughly 1 eV. The spectral position of the edge is not only determined by the free carrier density, but also by screening due to direct interband absorption at higher energy. We have performed a band structure calculation for the high pressure phase, assuming it has an or-dered NaCl-type structure. Figure 6 shows the band structure and DOS for a lattice parameter of a = 4.95 Å which corresponds to an experimental pressure value of 30 GPa. The three lowest bands shown in the band structure plot of Fig. 6 are derived from Se p-states. The minimum of the lowest con-duction band is found at the X-point, about 5 eV below the Fermi level. A small electron pocket occurs at the Γ-point. An interesting feature is the pronounced local maximum of the DOS at the Fermi level. If

0 1 2 3 4Energy (eV)

0.0

0.1

0.2

0.3

Ref

lect

ance

Rd

GaSe

10 GPa

16 GPa

29 GPa

GaSe (B1)

GaSe

Λ Γ ∆

Fig. 6 Top left: Optical reflectance spectra of polycrystalline GaSe at different pressures. The quantity R

d refers to the reflectance at the inter-

face between diamond window and sample. Top right and bottom left: Energy band structure and DOS of NaCl(B1)-type GaSe at 30 GPa (lattice parameter a = 4.95 Å).



it were at ambient pressure, the situation might be favorable for lowering the electronic energy through a structural distortion and a related opening of a (pseudo-)gap at the Fermi level. At high pressures, the gain in band structure energy may not be sufficient to overcome the stronger repulsion. It may, however, still lead to enhanced electron–phonon coupling.

7 Summary

The main results of the present study can be summarized as follows: (1) We report equation of state data, obtained by X-ray diffraction, for the ε-phase of GaSe up to 20 GPa and for the high pressure modification up to 38 GPa. The micro-photographic measurements of the c-axis compressibility of ε-GaSe by Gauthier et al. [26] are consistent with the diffraction results. (2) Using the experimental lattice parameters of ε-GaSe as a function of pressure, we have performed constrained structure optimizations by an ab initio total energy method in order to calculate the internal structural parameters at different pressures. The obtained value for the Ga–Se bond distance and its change with pressure are in very good agreement with results derived from EXAFS data [3]. This is a clear indication that we can have confidence in the other interatomic distances provided by the optimiza-tions. Of particular interest are the rate of change of the weak interlayer bond with pressure and the fact, that the homonuclear Ga–Ga bond is predicted to shorten under pressure. (3) Using the optimized structural parameters, we have calculated the effect of pressure on the elec-tronic states of ε-GaSe near the Fermi level. The calculations predict a transition from a direct- to an indirect-gap semiconductor at 4 GPa. This pressure value is larger than the crossover pressure indicated by optical high-pressure studies of layered III–VI selenides [7]. (4) Our optical reflectance spectra of GaSe under pressure are consistent with a metallic nature of the ‘cubic’ high pressure modification. We report band structure calculations for that phase assuming that it adopts an undistorted NaCl-type structure. The calculated DOS shows a pronounced local maximum of the density of states at the Fermi level.

Acknowledgements We thank K. Kunc for a critical reading of the manuscript and S. Lacher for the growth of the GaSe crystals. D. O. acknowledges support from CONACYT (Mexico). Part of this work was supported under the Spanish-German Acciones Integradas Program.

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