The carrier contribution to the elastic constants in small-gap materials

Abstract

We present a simple theoretical analysis of the carrier contribution to the second and third order elastic constants in nonparabolic materials on the basis of an electron dispersion law by taking into account various anisotropies of the energy band structure within the framework of k.p formalism. It is found that the carrier contributions to the elastic constants in n-Cd₃As₂, lnSb, InAs, GaAs, Hg_1-xCd_xTe, and lattice matched ln_1-xGa_xAs_yP_1-y increase with the increase of carrier degeneracy in different manners which, depend on the material parameters and band structure. A relationship between the said contributions and the thermoelectric power has been derived for materials obeying arbitrary dispersion laws in the presence of a classically large magnetic field. Our analysis is based on the derivation of a more generalized band structure of the materials which agrees well with the relationship suggested. It is also observed that the second and third order elastic constants increase with the decrease of alloy composition for ternary and quaternary compounds, respectively. The corresponding well-known results for degenerate wide-gap materials can be derived as special cases of our generalized analysis.