Pulse thermodiffusive processes in semiconductors

A one-dimensional problem for the determination of transient electron and phonon temperatures in bounded semiconductors is solved analytically and an exact expression is obtained. The model includes the heating of one of the surfaces of the sample by a rectangular thermal pulse of an arbitrary duration, separate electron and phonon heat boundary conditions, and electron-phonon energy interaction. The characteristic times of the transient processes are introduced through the electron and phonon thermal diffusion time, τ e,p , and electron-phonon energy relaxation time, τ e . For nondegenerate semiconductors, the electron subsystem is described by the essentially nonequilibrium temperature whereas the phonon temperature is equal to the ambient equilibrium temperature. The heat diffusion process is characterised by parameter τ e in the case of a thin sample as compared with the electron cooling length, while time τ e becomes the characteristic relaxation parameter for long samples. The thermoelectric response is obtained and the analysis is made for the long and short heat pulses.