Study of elastic properties and their pressure dependence of zincblende structure semiconductors

Abstract

A three-body force potential is used to derive the correct expressions for third-order elastic constants and pressure derivatives of second-order elastic constants for the zincblende structure semiconductors following the lines of Sharma and Verma. These corrected expressions are used for the first time to study the elastic properties and their pressure dependence of ZnS, ZnSe, and ZnTe. It is found that the inclusion of the corrections and the van der Waals interactions yield more reasonable values of the third-order elastic constants and the pressure derivatives of secondorder elastic constants than those obtained by earlier workers from their somewhat erroneous expressions.Ein Dreikorperkraftpotential wird benutzt, um die korrekten Ausdriicke fur die elastischen Konstanten dritter Ordnung und die Druckableitungen der elastischen Konstanten zweiter Ordnung fur Halbleiter mit Zinkblendestruktur entsprechend dem Herangehen von Sharma und Verma abzuleiten. Diese korrigierten Ausdriicke werden benutzt, um erstmals die elastischen Eigenschaften und ihre Druckabhgngigkeit fur ZnS, ZnSe und ZnTe zu untersuchen. Es wird gefunden, daB die Einbeziehung der Korrekturen und die van der Waals-Wechselwirkungen vernunftigere Werte der elastischen Konstanten dritter Ordnung und der Druckableitungen der elastischen Konstanten zweiter Ordnung liefern als die von anderen Autoren friiher aus ihren etwas fehlerhaften Ausdriicken erhaltenen.

High pressure phase transitions and variation of elastic constants of some II-VI semiconductors

“…The latter are considered to consist of the long-range Coulomb and three-body interactions (Singh, 1982) and the short-range van der Waals and overlap repulsion (Singh and Singh, 1987a) effective upto the second neighbour ions. Their expressions for ZB and RS structures are given by…”

“…In this approach, the three-body interactions (TBI) are considered to arise from the charge-transfer mechanism (Singh, 1982) caused by the deformation of the electron charge density (or electron-shells) of the overlapping ions. In order to predict the structural phase transitions in 11-VI semiconductors, we have expressed the Gibbs free energy, G, as a function of the pressure and the three-body-potential (TBP) energy in equilibrium at 0 K. For this purpose we have represented the lattice energy (V) by a three-body potential, which consists of the long-range Coulomb and three-body interactions (Singh, 1982), and the short-range van der Waals attraction (Singh and Singh, 1987a) and overlap repulsion effective upto the. next nearest neighbour ions.…”

Crystal dynamics of zinc chalcogenides I: an application to ZnS

“…Proceeding with the use of the three body crystal potential given by Eq. (1), Sharma and Verma [21] derived the expressions for the second order elastic constants and used by Singh and Singh [20] for ZBS crystals. We report them here as their corrected expressions.…”

“…The model parameters (b, ρ , and f(r 0 )) were determined by using the expressions (19)(20)(21) Court et al [31], Jai Shankar et al [32] and Kunc et al [33] and the model parameters are shown in Table 1. These values of the VDW coefficients are shown in Table 2.…”

“…Furthermore, the effects of long-range (LR) three body interactions (TBI), short-range (SR) interactions, and van der Waals (VDW) attraction are significant in partially ionic and covalent crystals [19]. Although VDW interactions (VDWI) have much effective force, Singh and Singh [20] used only three body force shell model (TSM) formulations for ZnS, ZnSe, and ZnTe without inclusion of VDWI. As far as the calculations on third order elastic constants (TOEC) and pressure derivatives of second order elastic constants (SOEC) are concerned, Sharma and Verma [21] have reformulated the expressions derived by Garg et al [22].…”