Transient heat transport by carriers and phonons in semiconductors

Abstract

The electron and phonon temperature distribution in semiconductors initially heated on the surface with a short laser pulse is calculated as a function of position and time. We solved the coupled one-dimensional heat diffusion equations for electron and phonon systems in the linear approximation in which the physical parameters of the sample are temperature independent. We also consider the heat pulse at the surface of the semiconductor as a boundary condition for each electron and phonon system. We believe that the transient heat transport experiments are a very suitable way of measuring the electron and phonon temperatures ${T}_{e,p}(x,t)$ in the sample, and they also yield the relaxation time associated with the different relaxation processes, e.g., electron-electron, phonon-phonon, and electron-phonon relaxation times, respectively. We provide a detailed quantitative theory for heat transient transport and find that the mechanism for electron energy relaxation time is strongly dependent on the size of the sample. For thin-film semiconductors the main relaxation process is due to heat diffusion by carriers, however the energy relaxation in larger samples is due to electron-phonon energy interaction. On the other hand, for nondegenerate semiconductors the typical ratio of the heat conductivities of electrons and phonons satisfies ${\ensuremath{\kappa}}_{e}/{\ensuremath{\kappa}}_{p}\ensuremath{\sim}{10}^{\ensuremath{-}3};$ under these circumstances the phonon energy relaxation time is due to heat diffusion by phonons and it is sample size independent. It is exciting that the electron temperature distribution function can be measured experimentally by means of the thermoelectric effect in semiconductors as a function of time.