Nonlinear surface acoustic waves in crystalline and thin-film systems
R. E. Kumon (National Institute of Standards and Technology, Mail Stop 853, Boulder, CO 80305-3328).
The linear and nonlinear properties of surface acoustic waves (SAWs) in crystalline and laminated media are significantly different from those of SAWs in an isotropic half-space. Selected numerical results are presented for the propagation of initially monofrequency, finite-amplitude SAWs in a variety of surface cuts and directions in several nonpiezoelectric, cubic crystals and thin-film systems. The underlying model equations possess a nonlinearity matrix that characterizes the interactions between harmonics of the SAW. When this matrix is real-valued, simulations show that the particle velocity waveforms can develop compression shocks in some propagation directions and rarefaction shocks in others. When this matrix is complex-valued, simulations indicate that the particle velocity waveforms may exhibit asymmetric distortion as well as oscillations near peaks and shocks. Measurements of pulsed waveforms in the (001) and (111) surface cuts of crystalline silicon obtained by collaborators at the University of Heidelberg are shown to be quantitatively reproduced by the calculated results. In thin-film systems, the combination of nonlinear harmonic generation and frequency dispersion induced by the film can cause complicated harmonic evolution, including spatial growth and decay cycles in some cases. Moreover, simulations indicate that the effects of large residual stresses in thin films may significantly affect nonlinear SAW propagation in these systems.