Dynamics of exciton formation and relaxation in photoexcited semiconductors

We investigate the dynamics of the exciton formation and relaxation on a picosecond time scale following a pulsed photoexcitation of a semiconductor. The study is conducted in the framework of the density matrix theory complemented with the dynamics controlled truncation scheme. We truncate the phonon branch of the resulting hierarchy of equations and propose the form of coupling among single-phonon-assisted and higher-order phonon-assisted density matrices so as to ensure the energy and particle-number conservation in a closed system. Time scales relevant for the exciton formation and relaxation processes are determined from numerical investigations performed on a one-dimensional model for the values of model parameters representative of a typical organic and inorganic semiconductor. The exciton dynamics is examined for different values of central frequency of the exciting field, temperature, and microscopic model parameters, such as the strengths of carrier-carrier and carrier-phonon couplings. We find that for typical organic semiconductor parameters, formation of bound excitons occurs on a several-hundred-femtosecond time scale, while their subsequent relaxation and equilibration take at least several picoseconds. These time scales are consistent with recent experimental studies of the exciton formation and relaxation in conjugated polymer-based materials.