Modeling of subcontinuum thermal transport across semiconductor-gas interfaces

A physically rigorous computational algorithm is developed and applied to calculate subcontinuum 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 classic problem of temperature drop across a solid-gas interface is investigated with a simultaneous treatment of solid and gas phase properties for the first time. 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. A reduced-order model is developed that captures the thermal resistance of the gas-solid interface. The formulation is then applied to the problem of combined gas-solid heat transfer in a two-dimensional nanoporous bed and the overall thermal resistance of the bed is characterized in terms of the governing parameters. These two examples exemplify the broad utility of the model in practical nanoscale heat transfer applications.