Simulation of Si and GaAs Devices Including Velocity Overshoot: An extended Drift-Diffusion Formalism

Velocity overshoot, which is a consequence of high electric field gradients existing in devices with submicron feature size must be accounted for in accurate numerical semiconductor models. Thornber has suggested augmenting the standard drift-diffusion current equations with an overshoot correction term which is proportional to the gradient of the local electric field [1]. The proportionality constant is a phenomenological length constant. In this paper we describe numerical simulations of Si diodes, n-MOSFET's and GaAs MESFET's based on this extended drift diffusion formalism. The phenomenological length coefficient has been calculated as a function of electric field by Monte Carlo methods. The extended drift-diffusion current equation has been incorporated in a simulator which solves the current continuity and Poisson's equations over a two-dimensional grid. The simulations are then compared with physically rigorous ensemble Monte Carlo calculations. It is concluded that this extended drift- diffusion formalism, which represents a simple, efficient and easy to implement approach to modeling velocity overshoot effects in small size field-effect transistors, predicts drain currents and average velocities which are in good agreement with Monte Carlo simulation results over a wide range of the device parameter space for both GaAs and Si devices.