Calculation of velocity overshoot in submicron devices using an augmented drift-diffusion model

A one-dimensional steady-state augmented drift-diffusion model, which includes an extra field-gradient term for the velocity overshoot effect, has been implemented with the standard drift-diffusion formalism to simulate submicron semiconductor devices. Numerical schemes and transport coefficients for this augmented model are discussed. We find that one cannot directly include the field gradient term in the equivalent mobility model and leave the modified Einstein relation intact, since the diffusivity has to be positive to preserve the ellipticity of the continuity equation and hence the stability of the entire numerical system. The accuracy and validity of the augmented drift-diffusion model can be assessed by the velocity profiles for typical submicron n⁺-n-n⁺ structures of both Si and GaAs in comparison with those from Monte Carlo and hydrodynamic simulations.