Quasi-analytical simulation of ultrafast thermalization of photoexcited electrons in a semiconductor quantum well.

We propose an analytic function approach to study the system of electron and phonon relaxation during an ultrafast processes in a single quantum well. A Gauss-type energy function is used to simulate the relaxation of nonthermal photoexcited electrons. The time variation of parameters describing the amplitude, width of Gauss-type function and the temperature of background electrons are determined by solving the Boltzmann equation with electron-electron and electron-phonon interactions. We found that the excited electrons thermalize with the background electrons within 200fs which is in agreement with experiment. After 300fs, our formulas are automatically reduced to an electron temperature model.