Emergence of hydrodynamic heat transport in semiconductors at the nanoscale

Abstract

Several recent experiments have demonstrated the failure of the Fourier heat equation in semiconductors at the nanoscale. We show that a generalized heat transport equation including a hydrodynamic term can explain three of these experiments on a silicon substrate: heater lines experiments both in stationary and nonstationary settings and the nonstationary response in grating experiments. To this end, we solve the hydrodynamic heat equation either numerically or analytically. The non-Fourier response observed in those experimental situations can be easily explained in terms of hydrodynamic concepts, such as friction and vorticity. For instance, the experimentally observed increase of thermal boundary resistance as size decreases can be simply understood as an increase of friction. We conclude that, contrary to common belief, hydrodynamics is a fundamental ingredient of semiconductor heat transport in the nanoscale at room temperature, providing physical insight and a unifying framework on the observed non-Fourier response. The relations between hydrodynamic heat transport with phonon momentum conservation and the Boltzmann transport equation are also provided.