Analysis of the dispersion relation for Lithium niobate inversion layer

A new design using an Lithium niobate inversion layer has been gaining interest in the development of broadband and higher frequency transducers. In a ferroelectric inversion layer, the piezoelectric constants are opposite in sign to those of a regular layer. In this paper, the wave propagates is investigated along y-coordinate direction in the inversion layer. Based on the fundamental piezoelastic equations of piezoelectric material, the equations of motion can be divided into two groups. One group is for the antiplane in x-direction, and another one is for the plane problem in y-z plane. Then the dispersion relation is established by using of the boundary and continuous condition. Numerical solutions of the dispersion relation show frequency against wave number.