Effects of corrugated boundaries on Rayleigh waves in a piezoelectric semiconductor substrate covered with a metal layer

In the present work, analytical solutions for Rayleigh waves propagating in a metal covered layer over a piezoelectric semiconductor (PSC) substrate with corrugated surface and corrugated interface are obtained. The solutions of the various physical fields can be expressed as a summation of infinite harmonic waves by using the Bloch-Floquet theorem due to the existence of the periodic corrugated surface and corrugated interface. The effects of the height and contour shape of the corrugated surface and corrugated interface, the doping density of the PSC substrate and the thickness of the metal covered layer on the dispersion and attenuation curves and mode shapes of Rayleigh waves are discussed via numerical example. The results show that the existence of the corrugated surface will lead to the decrease of the phase velocity and nonmonotonous change with wavenumber, besides, and significantly increases the attenuation near k0 = & pi; /?(k0 and ? are the wavenumber and period, respectively). In addition, the effects of periodic corrugated surface are much greater than those of periodic corrugated interface and are closely related with the ratio of the wavelength to the structure period. Moreover, the sinusoidal corrugated surface can be used to better control the propagation characteristics of Rayleigh waves by comparison.