The growth of wave discontinuities in piezoelectric semiconductors

Abstract

The reference coordinate description of the general nonlinear differential equations describing the interaction of finitely deformable, polarizable, n-type semiconductors with the quasistatic electric field is applied in the study of acceleration waves in piezoelectric semiconductors. As a consequence, the mechanical and dielectric nonlinearities are included in the treatment as well as the semiconduction nonlinearity. The general equation for the propagation velocity of the disturbance is obtained as a function of the state of the material immediately ahead of the wavefront. In the special case of plane waves entering a homogeneous steady state, the growth equation for the amplitude of the acceleration wave is determined and, of course, the propagation velocity and coefficients in the growth equation depend on the propagation direction, but otherwise are constant. The relation between acceleration waves and the formation and propagation of acoustoelectric domains is indicated. The solutions of the growth equation indicate the formation of a shock in a finite time for conditions conducive to domain formation except in certain unusual cases possibly occurring with purely transverse acceleration waves. In the course of the treatment the condition for the threshold field for domain formation is determined under quite general circumstances. When the electrical conduction equation, which can be quite general in this treatment, is specialized to the simple form usually employed for anisotropic semiconductors, the aforementioned more general condition reduces to the anisotropic generalization of the well-known elementary result. In addition, the behavior of weak waves is discussed.