Shock waves and acoustoelectric domains in piezoelectric semiconductors

摘要

The theory of shock waves is applied to the onehyphen;dimensional version of the general nonlinear electroelastic equations for deformable semiconductors employed in a recent acceleration wave analysis of acoustoelectric domains in piezoelectric semiconductors. Consequently, the mechanical and dielectric nonlinearities are included in the shock wave analysis as well as the semiconduction nonlinearity. Equations are derived for both the propagation velocity and the amplitude of the shock wave as a function of the jumps in certain variables across, and the state of the material immediately ahead of, the wave front. Expressions are obtained for the jumps in other variables across the shock front, such as the electric field, in terms of the amplitude of the shock. Some physical information concerning the evolutionary behavior of certain simplified types of shock is extracted from the rather complicated shock amplitude equation. When the analysis is specialized to the case of infinitesimal shocks, the results reduce to those obtained in the aforementioned analysis of acceleration waves in piezoelectric semiconductors with linear piezoelectric response.