Exact Solutions to Acoustoelectric Interactions in Arbitrary Geometries

Abstract

Acoustoelectric interactions occur when free carriers in a semiconductor interact with the fields of an acoustic wave in a piezoelectric medium. These interactions can amplify acoustic waves, as well as give rise to extremely large phononic nonlinearities and strong non-reciprocal effects. The field of acoustoelectric devices is currently dependent on analytical and perturbative solutions for the two simplest arrangements of piezoelectric-semiconductor materials. While these canonical models have allowed the field to advance substantially, new geometries are arising that do not satisfy assumptions integral to these models. These assumptions include the treatment of the interactions between the acoustic fields and free carriers as weak, the neglect of the tensorial nature of the material properties, the omission of the spatial variations in the phonons' electric field profiles, and the disregard of elastic coupling across material boundaries, among others. We develop, for the first time, a finite element method (FEM) model to solve for acoustoelectric interactions in arbitrary geometries that avoids making the assumptions of the canonical models. We verify the FEM model using results for amplification, dispersion, and non-reciprocity obtained from the canonical models in their regime of validity. We then examine the acoustoelectric effect in two geometries not covered by the canonical models: a thin piezoelectric film placed on a semiconductor substrate and a fully 2D waveguide under a thin semiconductor layer. This work lays the foundation for accurate modeling of arbitrary acoustoelectric geometries such as those currently being developed for all-acoustic radio frequency (RF) signal processing, acoustoelectrically enhanced photonic devices, and quantum acoustoelectric devices.