Interpolation Between the Acoustic Mismatch Model and the Diffuse Mismatch Model for the Interface Thermal Conductance: Application to InN/GaN Superlattice

A model for the thermal conductance of an interface is developed. It interpolates between the widely used acoustic mismatch model and diffuse mismatch model and accounts for the phonon dispersion curves of the materials in contact as calculated from first principles technique. In the present model, the interface morphology is modeled by assuming for the height a Gaussian probability density and a two-dimensional tangential autocorrelation function. The temperature as well as the interface conditions weight the probabilities for the diffuse scattering and the specular behavior of the phonon at the interface. The features of the developed expression for the transmission probability are found to be in excellent agreement with experimental results. The model is applied to predict the phonon events at the interfaces in the InN/GaN superlattice as functions of interface conditions. The results showed that in order to increase the thermal conductance of the InN/GaN superlattice one should decrease the interfaces’ tangential correlation and/or the interfaces’ root mean square roughness. The proposed model can be an efficient tool for engineering high thermal conductivity optoelectronic systems or efficient thermoelectric devices.