Elastic and inelastic scattering at low temperature in low-dimensional phononic structures

A technique is described for modeling the low-temperature thermal behavior of phononic components patterned into amorphous dielectric membranes, such as SixNy. Ballistic, elastic diffusive, localized, and inelastic diffusive transport are included. The model is well suited to studying components where heat is carried by a discrete set of large-scale acoustic modes. The scheme gives not only the average fluxes of components having statistically characterized microstructure, but also the spread in behavior of notionally identical devices. It is applicable to a wide range of geometries. The method is illustrated by simulating the behavior of a number of simple structures and studying the interactions between the different transport mechanisms. A single-stage Fabry-Perot resonator is used to identify likely operating characteristics of phononic filters.