Excitonic effects in optically excited semiconductors with LO-phonon coupling

We study the relaxation behavior of a one-dimensional two band semiconductor under the influence of longitudinal optical phonons at finite temperatures. The attention is focused on the time behavior for excitonic excitations. By truncating the Heisenberg equations of motion we obtain a system of quantum kinetic equations which describe the dynamics on a femtosecond time scale. Apart from the Coulomb terms that appear within the framework of the Hartree-Fock approximation they include additional Coulomb corrections that can be identified as vertex corrections to the electron-phonon interaction. The numerical calculations show that these additional terms are essential for the description of the excitonic dynamics for both nonlinear and linear response. [S0163-1829(99)10911-1].