Journal of Solid State Physics

Volume 2014 (2014), Article ID 921092, 7 pages

http://dx.doi.org/10.1155/2014/921092

## High Pressure Study of Structural and Electronic Properties of PbSe

^{1}Department of Physics, Banasthali University, Banasthali 304022, India^{2}Department of Pure & Applied Physics, University of Kota, Kota 324010, India^{3}Faculty of Sciences, Manipal University Jaipur, Jaipur 303007, India

Received 30 August 2014; Revised 22 November 2014; Accepted 1 December 2014; Published 30 December 2014

Academic Editor: George Cirlin

Copyright © 2014 P. Bhambhani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

High pressure structural phase transition and electronic properties have been investigated using the linear combination of atomic orbitals (LCAO) method with two exchange-correlation approximations, the generalized gradient approximation (GGA) and local density approximation (LDA). The present study shows phase transitions from B1 to B27 and B27 to B2 at 6.24 GPa and 16.39 GPa, respectively. Lattice constant, bulk modulus, and energy gap of pressure-induced PbSe are found to be in good agreement with previous theoretical and experimental results. Variation of electronic band structure with pressure shows direct band gap along *L* point of the Brillouin zone.

#### 1. Introduction

Systematic studies of IV–VI semiconductor compounds on theoretical as well as experimental background have given overwhelming properties which not only are important for the scientific inquest but have wide scale technological applications [1–9]. These compounds possess intriguing array of narrow energy gap, high carrier mobilities, high dielectric constant, positive temperature coefficient of the band gap and negative pressure dependence of the band gap, and high anisotropy, which are the basic requirements for the application in the branch of the thermoelectronics, optoelectronics, and spintronics [10–15].

Such fascinating properties of the IV–VI semiconductor compounds become a subject of extensive research on the lead chalcogenides PbX (X = S, Se, Te). On account of narrow forbidden gap of PbSe ~0.26 eV (300 K), anomalous order of band gap, and low thermal conductivity, it appeared to be a potential candidate for the technological applications in the field of thermoelectric devices [10, 16–18]. Further, low transition pressure and narrow energy gap of the intermediate phase of this compound make it a suitable candidate for the fabrication of other electronic devices [18, 19]. The anomalous properties of PbSe and IV–VI semiconductor compounds as compared to III–V and II–VI semiconductors are due to interaction of Pb* s*-electron valence bands with the Se* p*-electrons valence band [12].

Excellent properties of this material were aggravated to investigate pressure-induced structural and electronic properties. In the last few decades, a number of investigations on its pressure-induced phase transition and structural properties have been reported; see, for example, [9–12, 18–23]. At ambient conditions, PbSe crystallizes in sixfold-coordinated rock-salt type B1 structure, with space group Fmm. At pressure between 3 and 5 GPa, it transforms from B1 phase to an orthorhombic intermediate phase [11]. The intermediate phase may be GeS (B16, Pbnm), FeB (B27, Pnma), and CrB/TlI (B33, Cmcm) [19, 21, 24, 25]. Further, with increasing pressure between 15 and 16 GPa, structural phase transition takes place from the orthorhombic phase to eightfold coordinated CsCl B2-type phase (space group Pmm) [8–11, 19, 21]. The phase transition from low to high pressure, that is, from intermediate to B2-type phase, is reported as semiconducting to metallic transition [11, 25–27]. Chattopadhyay et al. [8, 9] from X-ray diffraction studies using synchrotron radiation reported TlI, B33-type structure for the intermediate phase of PbSe, while Ovsyannikov et al. reported it to be of GeS-type [22]. This intermediate phase has also been experimentally proposed to be orthorhombic Pnma structure [28]. The theoretical investigations on the intermediate phase of PbSe have less attention in the literature. Thus, the present paper deals with the pressure-induced structural phase transition and electronic properties of PbSe at different pressures using LCAO method.

#### 2. Computational Details

Quantum mechanical periodic LCAO calculations for the ground state total crystal energy are performed using the computer code CRYSTAL06 [29]. There are two fundamental schemes to compute the electronic structure and related properties of solids: one is the Hartee-Fock (HF) approximation and the other is the DFT [30, 31]. In HF, the exchange potential is included exactly and additional terms describe the correlation effects approximately but, in the DFT, both exchange and correlation effects are included. To gain the quantitative validity of results, we have used both the GGA and LDA approximations. The Kohn-Sham Hamiltonian for GGA is constructed by considering the exchange and correlation scheme of Becke [32] and Perdew-Burke-Ernzerhof (PBE) [33], respectively, while LDA approximation is based on Becke [32] and von Barth-Hedin (VBH) [34] schemes, respectively. The basis sets for the S were taken from [35] and due to nonavailability of all electron basis sets of Pb, only its valence part was considered in the present computations [36]. The self-consistent calculations are performed using 29, 35, and 343** k**-points in the irreducible Brillouin zone (BZ) for B1, B2, and B27 phases, respectively, with sufficient tolerances. The level of numerical approximation in evaluating the Coulomb and exchange series appearing in the SCF equations for periodic systems is controlled by five tolerances [29]. In the present calculations, tolerances of the order of 10^{−6}, 10^{−6}, 10^{−6}, 10^{−6}, and 10^{−10} were considered. To achieve self-consistency, 70% mixing of successive cycles is considered and self-consistency is achieved within 10, 12, and 18 cycles for B1, B2, and B27 phases, respectively.

The cohesive energy [37] from the Compton profile data can be derived as follows: where is component of electron momentum along the -axis and and represent Compton profiles of solid and free atoms, respectively. The solid Compton profile () values are calculated from DFT-LCAO method and the free-atom Compton profile () values are taken from Biggs et al. [38–40].

#### 3. Results and Discussion

##### 3.1. Phase Transition and Structural Parameters

The structural parameters were theoretically evaluated first by calculating the total lattice energies over a set of different volumes around the equilibrium values and then were fitted to the third order Birch-Murnaghan equation of state (EOS) using the following relations: where is minimum energy, is corresponding volume, and is the bulk modulus at zero pressure and . The third order Birch-Murnaghan isothermal equation of state [41, 42] relating pressure and volume is given by Calculations were performed in both GGA and LDA frameworks and the respective parameters, that is, lattice constant (), bulk modulus (), and pressure derivative of bulk modulus () for B1, B27, and B2 phases of PbSe, are given in Table 1. As per the device application, high bulk modulus and its pressure derivative are essential parameters for photovoltaic applications in optoelectronic devices [43, 44]. The bulk modulus also defines resistance to change in volume against any mechanical deformation [44]. Therefore, we computed the values of bulk modulus and its derivative using Birch-Murnaghan EOS and summarized them in Table 1. The value of bulk modulus obtained from Birch-Murnaghan EOS agrees well with the value reported by Rached et al. [45]. This variation of is in accordance with the theory of Cohen [46] who obtained an empirical expression for the bulk modulus based on the nearest-neighbor distance. As seen from Table 1, the pressure derivative of bulk modulus () is almost the same for all the three phases with average value of 4.0. On comparing the structural parameters obtained from two different schemes, that is, GGA and LDA, we observed that lattice parameter obtained from LDA approach is larger than GGA while the bulk modulus obtained from GGA is higher as compared to the one obtained from LDA.