Thermal transport phenomena beyond the diffusive regime

Heat conduction in semiconductors is mediated by thermally-excited phonons. When dimensions smaller than the mean free path are involved, nondiffusive heat conduction arises. In addition, surface effects related to thermal boundary resistances become significant when the dimensions of the considered media decrease. These two phenomena significantly alter thermal transport in comparison to predictions made with standard heat diffusion and result in larger temperature levels at the heat source, which can be detrimental for electronics devices. We tackle few examples where these effects are observed. By using the Boltzmann Transport Equation (BTE) for phonons or approximated solutions, we show that effective cross-plane thermal conductivity reduction takes place. We then present results of heat conduction from a metallic line of nanometer-scale width towards a flat bulk. We show that 2D ballistic heat conduction takes place and that a ballistic reduction factor associated to the phonon rarefaction effect should be included. The dissipated heat fluxes are reduced in comparison to the Fourier prediction. The consequence is that strong hot spots may arise. We then analyze the effect of surface imperfect transmission in thermal boundary resistance and introduce a method based on acoustics to compute it. We show that confinement and imperfect transmission lead to similar reduction of the effective thermal conductivity.