Thermal Contact Resistance of a Silicon Nanowire on a Substrate

Increased interest in determining the thermal contact resistance encountered in various nanoscale devices derives from its role as a critical bottleneck to thermal transport at submicron scales. In the present work, the contact resistance of one such configuration — a silicon nanowire on a Si substrate — has been studied. A model based on the phonon Boltzmann transport equation (BTE) in the solid and Fourier conduction in the surrounding gas is used, in conjunction with a previously published finite volume method. This approach enables the accurate computation and examination of the relative magnitudes of constriction resistance, air thermal resistances, and the bulk resistance of the wire on transverse heat transport. The results confirm that the effective resistance is dominated by constriction resistance even for low and moderate wire acoustic thicknesses and that the constriction resistance is well represented by ballistic-limit models. In the mesoscale regime when the constriction is partially diffusive, a simple addition of diffusive and ballistic resistances is shown to work reasonably well, in agreement with previously published estimates. For higher wire acoustic thicknesses, the effects of bulk scattering in the wire cannot be ignored and a simple additive formula is inadequate. The fluid surrounding the wire can act as a complementary parallel pathway for thermal transport; however, in the high gas-phase Knudsen regime, the constriction resistance remains the controlling factor for overall thermal conductance.