Temporally and Spatially Resolved Electron-Phonon Quantum Kinetics

A quantum kinetic theory that is able to resolve interaction processes between carriers and phonons in time and in space is presented. The dynamics of spatially localized wave-packets is analyzed accounting for coherent as well as incoherent phonons. It is found that, as a consequence of the energy–time uncertainty, a fast initial carrier transport takes place leading to occupations of space regions which are out of reach at early times within a semiclassical description on the level of the Boltzmann equation. The charge separation that accompanies the transport of electrons is a source of coherent phonons. The corresponding polarizations of the ion-lattice show oscillations that form a spatially expanding wavefront. Adding incoherent phonons leads to a damping of these waves due to phonon-assisted carrier redistributions.