Generalized Rayleigh surface waves in a piezoelectric semiconductor half space

In this paper, plane strain surface waves, also named generalized Rayleigh surface waves, in a transversely isotropic piezoelectric semiconductor half space are investigated. The governing equations of generalized Rayleigh surface waves include the equations of motion, Gauss' law of electrostatics and the conservation of charge. Based on the basic theory of elastic-dynamic equations, the governing equations are deduced as equations related to the displacement, the electric potential and the perturbation of the carrier density and are solved analytically. We discuss dispersion curves and the attenuation tendency of generalized Rayleigh waves for real wave number cases. The results reveal that the semiconductor should lead to phase velocity decreasing, and the anomalous dispersion and damping of generalized Rayleigh waves. However, enough in-plane biasing electric field along the wave propagation should lead to the amplification of the waves. The influence of the out-plane biasing electric field is so slight that it can be omitted. These properties should be reproduced in the case of real frequencies. The results obtained may provide theoretical guidance for the design of high-performance surface acoustic wave devices made of piezoelectric semiconductors.