THE CARRIER CONTRIBUTION TO THE ELASTIC-CONSTANTS IN SMALL-GAP MATERIALS

We present a simple theoretical analysis of the carrier contribution t o the second and third order elastic constants in nonparabolic materia ls on the basis of an electron dispersion law by taking into account v arious 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, InSb, InAs, GaAs, Hg1-xCdxTe, and latti ce matched In1-xGaxAsyP1-y increase with the increase of carrier degen eracy in different manners which, depend on the material parameters an d band structure. A relationship between the said contributions and th e thermoelectric power has been derived for materials obeying arbitrar y dispersion laws in the presence of a classically large magnetic fiel d. Our analysis is based on the derivation of a more generalized band structure of the materials which agrees well with the relationship sug gested. It is also observed that the second and third order elastic co nstants increase with the decrease of alloy composition for ternary an d quaternary compounds, respectively. The corresponding well-known res ults for degenerate wide-gap materials can be derived as special cases of our generalized analysis. (C) 1998 American Institute of Physics. [S0021-8979(98)08101-8].