High Pressure Band Structure and Metallization in Zinc Sulphide

The theoretical investigation of the electronic band structure, density of states and metallization of technologically important semiconductor zinc sulphide (ZnS) under high pressure is obtained using the full potential linear muffin-tin orbital (FP-LMTO) method. The ground state properties and band gap values are compared with the experimental results. Zinc sulphide becomes metal and superconductor under high pressure, but before this they undergo structural phase transition from zinc blende phase to rocksalt phase. The density of states at the Fermi level (N(EF)) is enhanced as the pressure is further increased, which leads to the superconductivity in zinc sulphide. The non-occurrence of metallization and structural phase transition simultaneously in zinc sulphide is also confirmed.


Introduction
The electronic band structure study of crystalline materials play a basic role in condensed matter physics, because the better understanding of the various physical properties of solids mainly depend upon their and structure [1]. Currently there is lot of interest in the study of materials under high pressure. The physical properties of materials undergo a variety of changes when they are subjected to high pressure. This paper contains the details of the theoretical investigation of the electronic band structure, density of states and metallization of a semiconductor, ZnS under high pressure. Group II-VI compounds are widely investigated under normal and high pressures; since they act as photographic materials, solid electrolytes and liquid semiconductors [1].The increase of pressure means the significant decrease in volume, which results in the change of electronic states and crystal structure [3]. Subjecting zinc sulphide to high pressure induces structural phase transition, semiconductor -metal transition and superconducting transition at giga pascal (10 9 pascal = 1GPa) pressures [4]. It is felt that many important parameters are involved in these calculations and further theoretical studies are needed to improve the agreement with the experiment. In all the above studies, only very little information is provided about the high pressure band structure and density of states of ZnS [5]. In particular no work has been reported regarding the metallization of ZnS. The band structures of ZnS corresponding to various pressures are obtained using the full potential linear muffin-tin orbital (FP-LMTO) method [2]. We have used FP-LMTO method with in generalized gradient approximation (GGA) [6] and exchange-correlation potential of Ceperley and Alder as parametrized by Perdew and Zunger [7]. The electronic configuration of Zn and S are [Ar] 3d 10 4s 2 (Z = 30) and [Ne] 3s 2 3p 4 (Z = 16) respectively. The valence electronic configurations chosen in our calculation are 3d 10 4s 2 for Zn and3s 2 3p 4 for S. There are 18 valence electrons contributing to the valence bands [2]. The final energy convergence is within 10 -5 Ry. The calculated total energies are fitted to Murnaghan's equation of state (EOS), to determine the pressure derivative of bulk modulus B o ' [8]. The calculated values of pressure and lattice constant are given in Table.1.

Band Structure and Density of States
The relation connecting reduced volume and pressure of ZnS is given in Fig.1. Pressure increases with decreasing of reduced volume. The relation connecting reduced volume and lattice constant is given in Fig.2 Lattice constant decreases with decreasing reduced volume. The relation connecting energy band gap and pressure is given in Fig.3. When pressure increases band gap decreases and reaches zero at metallization pressure [1].  (Fig. 4). The three bands appearing below the Fermi level are due to the 4s 2 3d 4 electrons of Zn (Fig.4).The empty conduction bands above the Fermi level are due to 3p, 3d states of Zn and S.   The characteristic features of ZnS band structure are similar to the previous calculations [1]. The fundamental energy gap is between the half-filled p like valence band due to sulphur and empty p like conduction band due to zinc. At normal pressure, the band gap of ZnS is direct (3.6856 eV) with top of the valence band in Γpoint and the bottom of the conduction band in a Γ point (Fig. 4).The calculated band gap is in agreement with the experimental value than previous theoretical value ( Table 2).As the pressure increases the width of the valence band and the empty conduction band get widened. These changes lead to the closing of the band gap under pressure (Fig.5). The density of states (DOS) (states/Ry.) calculations for all the reduced volumes has been carried out but here we have given the DOS histograms of ZnS corresponding to normal pressure (Fig.6) and metallization pressure (Fig.7).At normal pressure (Fig. 6)the levels arising from 3s 2 electrons of S give the short spike near the origin. The long spike near the Fermi energy is due to4p 6 4s 2 3d 4 electrons of Zn and3p 4 electrons of S. The short peaks above the Fermi energy E F are due to the 3p, 3d states of Zn and S. The above normal pressure trend is changed under high pressure. The increase of pressure leads to the broadening of bands which results in the decrease of density of states value in most of the energy regions and increase in the width of the valence band and empty conduction band. When pressure increases the value of E F increases whereas no density of states is available at the Fermi level up to metallization pressure. In Fig. 7, there are appreciable values of N(E F ) for ZnS (V/V o =0.6254) in ZnS structure, which indicate the occurrence of metallization in ZnS. Further increase in pressure leads to enhanced density of states at the Fermi level which induces super conductivity. In ZnS, metallization takes place by the indirect closure (Fig.5) of band gap between valence band (at Γ-point) and conduction band (at X-point) [1]. The metallization volume of ZnS is V/V o =0.6254, which corresponds to the pressure P M =115.75 GPa. The general features of high pressure band structure is similar to previous calculations [3,5]. From our calculation, in ZnS an indirect closure of band gap occurs.
The density of states histograms of ZnS at high pressure is given in Fig.7.At this pressure ZnS is in cubic structure. From the histogram, it is seen that the heights of the spikes are considerably reduced when compared to Fig.6. Reason is when pressure increased E F increases whereas no density of states is available at the Fermi level up to metallization pressure. There are appreciable values for DOS at V/V o = 0.6254 (Fig. 7) indicating metallization in ZnS [1].When pressure increases (reduced volume decreases) the value of the DOS at Fermi energy, E F (N(E F )) increases [5].

Structural Phase Transition
The ground state properties of ZnS is studied from the total energies obtained from the FP-LMTO method [2]. The calculated total energies were fitted to Murnaghan's equation of state [1] To obtain the equilibrium lattice constant and other ground state properties. In Table.2, experimental and theoretical values of lattice constant and bulk modulus are compared, there is a close similarity between experiment [4] and theory [3] is obtained. The bulk modulus at normal pressure B o is a parameter of great physical significance in high pressure physics and few other thermo-physical properties. The value of B o is related to the electron density. The structure with highest B o will have low electron density and vice versa. Zinc sulphide becomes metal and superconductor under high pressure, but before this they undergo structural phase transition from zinc blende phase to rocksalt phase. Total energy versus reduced volume curve for ZnS is given in Fig.8. In this figure ZnS is stable up to (V/Vo) T =0.9356, further reduction of volume NaCl is the stable structure. In our calculation zinc blende phase to rocksalt phase transition occurs at 14.2 GPa corresponding phase transition volume (V/Vo) T =0.9356 (Table.3). Enthalpy versus Pressure curve for ZnS is given in Fig.9. In this figure ZnS is stable upto (P) T =14.2.GPa, further increase of pressure Nacl is the stable structure. This value is good agreement with the experimental value of 15 Gpa [4].

Metallization
Most of the metallization is associated with a structural transition from a low coordination non-metallic to a high coordination metallic phase [1]. At normal pressure, ZnS is a direct gap semiconductor. With increase of the pressure, the band gap decreases and at a particular pressure, there is a closing of the band gap. Similar to alkali halides, the electronic band structure calculations on ZnS suggest that metallization is due to the reordering of the energy bands with the empty p -like band (of Zn) dropping in energy and touching the top of the filled p -like band of S [1].The band structure and density of states corresponding to metallization of ZnS is shown in Figs. 5 and 7 respectively. In ZnS, metallization takes place by the indirect closure (Fig.5) of band gap between valence band (at Γ-point) and conduction band (at X-point). The metallization volume is V/V o =0.6254 (NaCl structure), and the corresponding pressure P M is 115.75 GPa (Table.3). From Fig.7, it is seen that at high pressure the levels arising from different electrons produces the heights of the spikes considerably reduced when compared to Fig.5. Reason is when pressure increased E F increases whereas no density of states is available at the Fermi level up to metallization pressure.

Conclusions
The high pressure band structure and density of states of ZnS is investigated. The metallization reduced volume is V/V o =0.6254 (NaCl structure), and the corresponding pressure P M is 115.75 GPa. In our calculation zinc blende phase to rocksalt phase transition occurs at 14.2 Gpa. This value is good agreement with the experimental value of 15 Gpa [4].