Femtosecond Evolution of Spatially Inhomogeneous Carrier Excitations Part I: Kinetic Approach

The ultrafast evolution of optically excited carriers which propagate in a quantum wire and interact with three dimensional phonons is investigated. The equation, relevant to this physical problem, is derived by a first principle approach. The electron-phonon interaction is described on a quantum-kinetic level by the Levinson equation, but the evolution problem becomes inhomogeneous due to the spatial dependence of the initial condition. The initial carrier distribution is assumed Gaussian both in energy and space coordinates, an electric field can be applied along the wire. A stochastic method, described in Part II of the work, is used for solving the equation. The obtained simulation results characterize the space and energy dependence of the evolution in the zero field case. Quantum effects introduced by the early time electron-phonon interaction are analyzed. 1 The Coupled Electron-Phonon System We consider a system of electrons which interact with the lattice vibrations. The electric forces which accelerate the electrons are due to the structure potential and the applied bias, Coulomb interaction between the electrons is neglected. The description of the system is provided by both the electron and the phonon degrees of freedom. We derive the Wigner equation for the coupled electronphonon system. The corresponding Hamiltonian is given by the free electron part H0, the structure potential V (r), the free-phonon Hamiltonian Hp, and the electron-phonon interaction He−p: H = H0 + V +Hp +He−p = − 2 2m ∇r + V (r) + ∑