Application of compound matrices to the study of SAW and PSAW propagation in layered structures

It was demonstrated in, that the use of compound matrices in the matrix formalism makes it possible to calculate acoustic mode velocities in a layered structure with thick film layers and is an useful tool to derive the analytic expressions for the acoustic mode propagation. The advantages, as well as the weak points related to the use of compound matrices in matrix methods of solutions of acoustic equations in comparison to their initial matrices are discussed, when applied to calculations of SAW and PSAW propagation in layered structures, exploiting thick films. Using an ldquoimaginablerdquo layered structure consisting of a thick isotropic diamond film on the isotropic diamond substrate, we illustrate and compare an ldquoexponentialrdquo unstable algorithm resulting by the use of initial matrices and the stable one calculated using their compound matrices. We report a number of compound matrix properties that are required for their implementation for acoustic wave analysis. Results of the calculations performed exploiting the initial matrices and their compound ones are discussed and compared for the of SAW and PSAW propagation along a layered structure: an AlN piezoelectric film deposited on a thick isotropic diamond layer, grown, in turn, on an isotropic polycrystal Si. Calculated results obtained for this structure and the layered structure with crystal Si substrate are discussed.