Modeling of Subcontinuum Thermal Transport Across Semiconductor-Gas Interfaces

A physically rigorous computational algorithm is developed and applied to calculate sub-continuum thermal transport in structures containing semiconductor-gas interfaces. The solution is based on a finite volume discretization of the Boltzmann equation for gas molecules (in the gas phase) and phonons (in the semiconductor). A partial equilibrium is assumed between gas molecules and phonons at the interface of the two media, and the degree of this equilibrium is determined by the accommodation coefficients of gas molecules and phonons on either side of the interface. Energy balance is imposed to obtain a value of the interface temperature. The problem of heat transfer between two parallel plates is investigated. A range of transport regimes is studied, varying from ballistic phonon transport and free molecular flow to continuum heat transfer in both gas and solid. In particular, the thermal interface resistance (or temperature slip) at a gas-solid interface is extracted in the mesoscopic regime where a solution of the Boltzmann equation is necessary. This modeling approach is expected to find applications in the study of heat conduction through microparticle beds, gas flows in microchannel heat sinks and in determining gas gap conductance in thermal interface materials.