Femtosecond relaxation of hot electrons by phonon emission in presence of electric field

The femtosecond relaxation of an initial distribution of electrons which interact with phonons in presence of applied electric field is studied numerically. The evolution at such a time scale cannot be described in terms of Boltzmann transport. Here, the Barker–Ferry equation is utilized as a quantum-kinetic model of the process. The numerical treatment of the original formulation of the Barker–Ferry equation becomes difficult since coordinates and time variables are coupled by the field. A transformation which decouples coordinates and time variables in the equation is proposed. A randomized iterative Monte Carlo algorithm is developed to solve the transformed equation. The quantum character of the equation is investigated. An instantaneously created initial condition is favored above the physically more adequate generation term in order to point out the quantum effects. Simulation results are obtained for GaAs material at different evolution times. Effects of collisional broadening and retardation are observed already in the fieldless case. The intracollisional field effect is clearly demonstrated as an effective change of the phonon energy, which depends on the field direction and the evolution time. Moreover, the collisional broadening and retardation are affected by the applied field. The observed phenomena are understood from the structure and the properties of the model equation. r 2002 Elsevier Science B.V. All rights reserved.