An Analytical Formulation of the Length Coefficient for the Augmented Drift-Diffusion Model Including Velocity Overshoot

We analyze the one-dimensional augmented driftdiffusion current equation [1] including velocity overshoot in inhomogeneous fields and derive an analytical formulation for the length coefficient L [2] suitable for practical device simulation applications. This is accomplished by starting from the energy balance equation and examining in detail the physical meaning and the functional dependence of the length coefficient through the effect of the carrier temperature and of the distribution relaxation. To simplify the analytical formulation, we first assume small concentration gradients and the perturbation treatment of the field gradients on the homogeneous-field steady state. A general and unified form of L is derived in a form which includes the functional relations of the mobility versus the carrier temperature and of the carrier temperature versus the electric field. In Si, our model is corroborated by the results from the Monte Carlo method and appears to be suitable for modeling of velocity overshoot in Si submicrometer devices.