Electronic structure of amorphous GeS

Solid State Communications, Vol. 73, No. 2, pp. 163-166, 1990. Printed in Great Britain.

0038-1098/90 $3.00 + .00 Pergamon Press plc

ELECTRONIC STRUCTURE OF A M O R P H O U S GeS V. Drchal and J. Mfilek* Institute of Physics, Czechoslovak Academy of Sciences, Na Slovance 2, 180 40 Praha 8, Czechoslovakia (Received 24 July 1989 by P.H. Dederichs) The recursion method applied to the tight-binding Hamiltonian in Harrison's parametrization is used to calculate the electronic structure of a-GeS. The atomic structure is represented by a three-dimensional continuous random network model containing 430 atoms characterized by the 4:2 coordination and random statistics of the Ge(Ge, S~_,) tetrahedra. Our results are in a good agreement with other calculations and with accessible experimental data. We also investigate the local environment effects, charge transfer and the interactions among lone pairs at non-bonded S atoms forming close pairs.

AMORPHOUS germanium sulphide is an interesting material that may be regarded as an intermediate case between tetrahedrally bonded a-Ge, and a-GeS2, whose structure is, to a first approximation, isomorphous with vitreous silica. An old controversy surrounds the short-range order in a-GeX (X = S, Se or Te), particularly the atomic coordination, because some experimental data point to 3 : 3 coordination as in crystal, while others point to 4:2 coordination corresponding to a natural valence of Ge and X. It has been suggested [!] that two structural modifications of a-GeX, 4:2 and 3:3, may exist, depending on the method of preparation and the history of the sample. However, the accurate X-ray diffraction studies [2], and thorough EXAFS and X-ray emission and absorption measurments [3] confirmed the 4:2 coordination in a-GeS. On the other hand, there is strong evidence in favour of the 3 : 3 coordination in a-GeSe and a-GeTe [4]. Further details may be found in [l], [4] and [5]. Two structural modifications of a-GeS with 4:2 coordination are conceivable, namely a three-dimensional network with random statistics of tetrahedra Ge(Ge, S4_,), and a layered structure, composed mainly of the Ge(Ge:S_,) units. Recently we have studied the structural continuous random network (CRN) models of these two modifications [5]. We have found by comparison with experimental data that the three-dimensional CRN represents well the structure of a-GeS, while the layered structure composed solely of Ge(GezS_,) units seems unlikely. * Present address: Joint Institute of Nuclear Research, Dubna, Head Post Office, Box 79, Moscow, USSR.

The electronic structure of a-GeS was first studied by White, who estimated the bounds of the spectrum [6]. The electronic density of states (DOS) was calculated by Magek and Velick~ in [7] and by Ma~ek [8] using the cluster-Bethe-lattice (CBL) method and the recursion method applied to a periodic CRN model. This model contained 64 atoms and it was built from Ge(Ge2S2) units only. It was found that the CBL method yields a good approximation for the DOS of a-GeS. The aim of the present work is to calculate the electronic structure of a-GeS represented by a realistic large-scale C R N structural model with random statistics of Ge(Ge, S4_,) building units, and. particularly. to investigate the local environment effects, charge transfer and also the interactions between electrons on the non-bonded sulphur atoms that form close pairs. The model contains 215 Ge and 215 S atoms, 188 Ge-Ge and 399 Ge-S bonds. Owing to the preferential heteropolar bonding the stoichiometric a-GeS contains no S-S bonds. The numbers of Ge-Ge and Ge-S bonds are close to their theoretical values (ratio I : 2) and the statistics of tetrahedra Ge(Ge,.S4_,) roughly corresponds to the random model [9]. The model was computer relaxed with respect to the sum of the Keating deformation energy and the potential of the repulsion forces acting between non-bonded S atoms forming close pairs [5]. We use the tight-binding sp 3 Hamiltonian parametrized according to Harrison's prescription [10] (see Table 1). It has been verified [7] that this parametrization gives correct bandgaps and valence band widths in the series GeS, GeSe and GeTe. Of course. it gives the conduction bands with lower accuracy. We have employed the recursion method [I I] to

163

E L E C T R O N I C S T R U C T U R E OF A M O R P H O U S GeS

164

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Vol. 73, No. 2

,

,

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,

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,

,

,

,

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s (3D)

to w ,

b._

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Ge (3D)

Ge-(GezS2)

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Fig. 1. The local densities of states for sulphur atoms and for germanium atoms that represent centres of various tetrahedra Ge(Ge4_, S, ), n = 0, I, . . . 4, calculated for three-dimensional random model of a-GeS. The statistical fluctuations are visualized by hatching. study the electronic structure of a-GeS represented by our model. Thirty levels of the continued fraction were used to calculate the local density of states (LDOS) for each s, Px, Py, and p. orbital at properly selected atoms. In order to minimize the effect of unsaturated bonds on the surface, we have chosen 18 Ge and 11 S atoms that belong to the most central part of the model. The Ge atoms were selected so as to represent all types oftetrahedra Ge(Ge,,S4_,), n = 0, 1. . . . . 4.

Table 1. Parameters in e V of the tight-binding Hamiltonian for a-GeS. The row S . . . S contains the interaction parameters for non-bonded sulphur atoms at the distance 3.33 Atom

Es

Ep

Ge S

- 14.38 - 20.80

- 6.38 - 10.27

Bond

V (ss~r)

V (spa)

V (ppa)

V (ppn)

Ge-Ge Ge-S S... S

- 1.792 - 2.089 - 0.962

2.355 2.745 1.264

4.147 4.834 2.226

- 1.037 - 1.208 - 0.557

-20

-I0

ENERGY

(eV)

0

-30

-20

-I0

O

ENERGY (eV)

Fig. 2. Comparison of the component DOS for Ge and S atoms calculated for the three-dimensional random model (top), for the layered uniform model (middle) and for the Bethe lattice (bottom). The contribution of s-states is indicated by dotted line. The LDOSs for S atoms (which are always bonded to two Ge atoms) and for Ge atoms that represent centres to different building units Ge(Ge, s4_,) were averaged over ensembles of several atoms that have identical environment. These LDOSs together with their r.m.s, deviations are shown in Fig. 1. It was impossible to calculate the fluctuations for the cluster Ge(S4) because our model contains only one unit of this type. The LDOSs for Ge atoms with varying neighbourhoods were averaged with proper weights corresponding to the random model [9] to calculate the average DOS at the Ge atom. This quantity together with the average DOS at the S atom are shown in Fig. 2 (top panel). For a comparison, we have calculated the electronic structure also for our other model representing the layered structure of aGeS which was built solely from Ge(Ge2S2) units [5]. The results are shown in Fig. 2 (middle panel). In all cases, the spectrum consists of three main parts: (i) a narrow split-off valence band centred at 23 eV, which is built mainly of sulphur s-states, (ii) a broad valence band ranging approximately from 20 to - 10 eV, composed of bonding combinations of the germanium s- and p-states and of the sulphur p-states, and, (iii) the conduction band formed from -

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E L E C T R O N I C S T R U C T U R E OF A M O R P H O U S GeS

Vol. 73, No. 2

03 0

-30

-I0

-20

ENERGY

(eV)

0

-30

-20

-I0

ENERGY

0

(eV)

Fig. 3. The local densities of states for two sulphur atoms forming a close pair. The interaction between electrons is included (full line). The results in the case without interaction are shown for comparison (dotted line). the antibonding combinations of the germanium sand p-states with the sulphur p-states. The large peak at the top of the sulphur valence band belongs to the non-bonding lone-pair p-orbitals at S atoms. The lowest part of the germanium conduction band is formed mainly of the Ge s-states. The sulphur s-states are concentrated mainly in the lowest narrow valence band at - 2 3 eV and they almost do not participate in higher bands. They contribute not only to the sulphur LDOS, but also to the germanium LDOS, as they take part in Ge-S bonds. When we go through the series G e ( G e J . . . . Ge(S~), we can observe that their weight gradually increases. The main valence band and the conduction band have a complex structure that reflects the complex bonding relations in a-GeS, where both the homopolar Ge-Ge, and heteropolar Ge-S bonds are present. This was discussed by Magek [8] and a similar situation was found also by O'Reilly et al. [12] in a-GeSe and a-GeTe when they assumed 4 : 2 coordination. Comparison of LDOSs at Ge atoms that belong to different Ge(GenS~_n) tetrahedra (Fig. 1) shows strong local environment effects. It is interesting to make a comparison of the LDOS for Ge(Ge_,Se,) unit (Fig. 1) with the averaged DOS at Ge atom (top of Fig. 2) and with the DOS calculated for a layered model of a-GeS that contains only the tetrahedra Ge(Ge2S_,) (middle panel of Fig. 2). All these DOSs are very similar. It is the reason why it is impossible using the spectroscopic data to decide which structural model, layered or three-dimensional, correctly represents the structure of a-GeS [7], [13]. This also shows that the structural disorder represented by the

165

distribution of the Ge(Ge, S4_n) tetrahedra is important only on the local scale, but not on average. Within the BL calculations the randomness of bond angles, of dihedral angles and of the building units Ge(Ge~_,,S,) is neglected. The closed rings of atoms are neglected, too. One would therefore expect that our results and those obtained by BL method using the same parametrization [8] will substantially differ. However, the differences are smaller than expected (see bottom panel of Fig. 2). This was explained [8] by the fact that S atoms with strong tendency to dehybridization effectively decouple the covalent network into relatively independent molecular units [14] and this tendency is further enhanced by complex bonding relations, The calculated DOS could be compared with optical. X-ray and photoemission spectra. The optical spectra of a-GeS were experimentally studied by Zfiv~tovfi and Abrahfim [15] who have found optical gap 1.5 eV. Our esitmate 1.37 eV for the band gap is in a good agreement with this value in view of inherent inaccuracies of the recursion method. The X-ray emission and absorption spectra were measured by Drahokoupil et al. [3]. Unfortunately, the resolution of these Ge K spectra is low, so that a detailed comparison of band shapes is not possible. Nevertheless, the main features, like the band widths and positions, of these spectra and of the calculated density of the Ge p-states are in agreement. Note also a small deep lying satellite in the emission spectrum of a-GeS~ (Figs. 1 and 4 of [3]) which corresponds to the non-negligible admixture of p-states in the lowest valence band of G e ( S J and Ge(GeS3) units at - 2 3 eV. The agreement with experimental data confirms the validity of our structural model and assumed bonding relations. The heteropolar character of the Ge-S bonds leads to the charge transfer between Ge and S atoms. To estimate its value we have calculated the net charges on the S atoms and on the Ge atoms with all types of their surrounding by integrating the averaged LDOSs (shown in Fig. 1) up to the Fermi level EF that lies at - 8.7 eV in the middle of the gap. The results are summarized in Table 2. Notice a roughly linear dependence of the charge transferred from the Ge atoms on the number of the nearest neighbour S atoms. To investigate the interactions between electrons on the non-bonded sulphur atoms that form close

Table 2. Net charges q in units le[ on the S atoms and on the Ge atoms ht different environments

Atom

S

Ge(Ge4)

Ge(Ge3 S)

Ge(Ge_,S,)

Ge(GeS3)

Ge(S~)

q

- 0.42

0.12

0.27

0.40

0.60

0.76

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ELECTRONIC STRUCTURE OF AMORPHOUS GeS

pairs [5], we have calculated the LDOSs for these S atoms taking into account the interactions between their atomic orbitals. We have used the values prescribed by Harrison's parametrization for a pair of sulphur atoms at a distance 3.33,~. These values represent the upper estimate because the distance 3.33 A corresponds to the closest pair of S atoms in our model (it is smaller than the van der Waals distance 3.7A in elemental sulphur) and the interaction parameters scale as (distance)--' within the parametrization used. The interactions between sulphur atoms forming close pairs have two important effects (see Fig. 3): (i) they split the sulphur s-band at - 2 3 eV, and (ii) they split the peak of non-bonding lone-pair p-orbitais at approximately - 10 eV, producing a localized state in the gap (cf. [16]). The main results of the present work may be summarized as follows: (i) the calculated electronic structure agrees with calculations done by other authors and with accessible experimental data, (ii) the local environment effects are important, but the total DOS is insensitive to variations of local environment, (iii) there is a significant charge transfer among Ge and S atoms, (iv) the interactions among electrons on the S atoms that form close pairs produce localized states in the gap.

14.

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