Characteristics of velocity overshoot in GaAs under uniform-field conditions

The origins of velocity overshoot in homogeneous bulk GaAs under stepped forcing conditions on the electric field are analyzed by phase-portrait methods. The balance equations for particle energy and momentum taken from the uniform-field version of the semiempirical transport equation model are used to define the direction field for charge flow in an energy-velocity phase space. Certain general characteristics of the flow patterns in the nonstationary regime are examined, with emphasis on the classification of possible intrinsic behavior exhibited by the steady states for different applied fields, on the approach to the steady state, and on the role of initial conditions. It is shown that flows describable by such a model have two types of stable generalized dynamical behavior: damped oscillatory behavior under applied fields for which the steady-state energy lies near the intervalley separation energy, and damped aperiodic behavior outside this range of fields. The analysis is illustrated with results deduced from realistic input data on energy and momentum relaxation rates taken from published steady-state Monte Carlo calculations for GaAs at three representative impurity densities.