Estimates of the Elastic, Dielectric, and Optical Characteristics of a Cubic BAs Single Crystal
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LECTRONIC PROPERTIES OF SEMICONDUCTORS (ATOMIC STRUCTURE, DIFFUSION)
Estimates of the Elastic, Dielectric, and Optical Characteristics of a Cubic BAs Single Crystal S. Yu. Davydov* Ioffe Institute, St. Petersburg, 194021 Russia *e-mail: [email protected] Received March 2, 2020; revised June 22, 2020; accepted June 22, 2020
Abstract—To estimate the physical characteristics of cubic boron arsenide, Keating’s model of force constants and Harrison’s method of bonding orbitals are used. The harmonic and anharmonic characteristics are considered. Comparison of the results with experimental data and other calculations shows the adequate applicability of the approach. Keywords: elastic constants, phonon frequencies, high-frequency and static permittivities, electrooptical coefficient, photoelastic constants DOI: 10.1134/S1063782620110068
1. INTRODUCTION Although cubic boron arsenide (BAs) was synthesized more than six decades ago [1], systematic studies of its basic physical properties began only recently [2]. This material is of interest first of all on account of its high thermal conductivity, first predicted theoretically [3, 4] and then confirmed experimentally [5] (the room-temperature thermal conductivity of BAs is κ = 1300 W m–1 K–1). Therefore, boron arsenide is considered as a promising material capable of competing with costly diamond and boron nitride and revolutionizing high-temperature solid-state electronics [2]. At the same time, it is also noted [2] that many important properties of boron arsenide have not been adequately investigated. Here, we consider a rather large number of characteristics of zinc-blende-structured BAs and compare them with experimental data and the results of calculations performed in other studies. It should be noted that, in most of these calculations, density-functional theory (DFT) is used. Recognizing the unique possibilities of the DFT method of calculations (e.g., in determining the elastic characteristics), we note that the calculated band gap Eg heavily depends on the specific method of calculation and varies from 0.67 to 5.5 eV (see references in [2]), which presents problems in estimating the dielectric and optical characteristics. In this study, in the context of Keating’s and Harrison’s simple models (that previously rather satisfactorily proved themselves in describing tetrahedral crystals), we analytically estimate the elastic and phonon characteristics of boron arsenide, its permittivities, electrooptical coefficient, and photoelastic constants.
2. ELASTIC CONSTANTS AND PHONONS 2.1. Keating’s Model We begin with estimations of the second-order elastic constants cij, using Keating’s model [6] (see also [7]) proposed for application to tetrahedral homopolar crystals and then extended by Martin [8] to ANB8 – N heteropolar compounds. In Keating’s model, the three elastic constants are
α + 3β α−β 4αβ , c12 = , c44 = . (1) a a (α + β)a Here, α and β are the force constants for central and noncentral interactions and a is the lattice constant. For boron arsenide, a is
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