Calculated elastic constants for stress problems associated with semiconductor devices

Abstract

Theoretical estimates or experimental determinations of stress fields associated with semiconductor devices are generally simplified with the aid of two elastic constants, Young's modulus E and Poisson's ratio ν. In this paper, a generalized expression for ν has been derived for arbitrary orientations of cubic semiconductor crystals, and the variation of E, ν, and E/(1-ν) for directions within the important {111}, {100}, and {110} planes is examined. The results show that isotropic elasticity theory is exact for all directions within {111} planes and that the composite elastic constant E/(1-ν) which frequently occurs in problems of practical interest is also invariant for all directions within {100} planes. Numerical values for the various elastic constants are tabulated for GaAs, GaP, Si, and Ge.