Temperature dependence of strains and stresses in undercritical cubic superlattices and heterojunctions.

Abstract

Strained superlattices and heterojunctions subject to variable temperature exhibit changes in their elastic and/or thermal strain and stress components, relative to their values at room temperature. We consider systems grown in arbitrary directions, with thicknesses smaller than the critical value (undercritical systems). In lowest order, the changes are linear with the temperature. The dependence on temperature of the thermal expansion coefficients is taken into account and shown to improve agreement with data. Criteria are established for predicting the form of such changes in any combination of material constituents. Specific applications are treated in detail and comparison is made with existing data from the literature. The effective linear thermal expansion coefficients of the structure, parallel and perpendicular to the direction of growth, are formulated explicitly. The present results are transcribed to the parallel problem of a hydrostatic pressure in the most general case; this extends previously published work, which refers to material constituents with a lattice misfit smaller than the bulk modulus misfit. The latter assumption is valid for most material combinations but not all. \textcopyright{} 1996 The American Physical Society.