  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 takes at least
several picoseconds. These time scales are consistent with recent experimental
studies of the exciton formation and relaxation in conjugated polymer-based
materials.
