Conventional Semiconductor Device Models Based on Partial Differential Equations - II 1 Hot Electron Modeling I : Extended Drift – Diffusion Models

Here μ(E)E = v(E) is the (steady state) drift velocity for the case of homogeneous field E. The field is also space and time dependent, i.e. E = E(x, t). Mobility and diffusion coefficients are steady state quantities, but the carrier velocity may differ considerably from the steady state value v(E), due to abrupt space or time changes of the electric field. v(E) can be considered accurate only if space or time variations of the field are very smooth (adiabatic). Velocity overshoot occurs when the average electron velocity exceeds the steady state (bulk) velocity. A modified version of the drift diffusion equation to include velocity overshoot was proposed by Thornber.