An Accurate and Simplified Modeling of Energy and Momentum Relaxation Rates for Metal–Oxide–Semiconductor Device Simulation

An accurate and simplified modeling for the energy and momentum relaxation rates has been proposed for simulating a velocity overshoot of electrons in metal–oxide–semiconductor field-effect transistors (MOSFETs). The relaxation rate has been featured by electron energy (w), gate field (E_G), and impurity-doping concentration (N_I). When the rate is defined by f_inv in the inversion layer and by f_bulk in bulk, the relaxation rate (r) in the whole area of MOSFETs can be modeled by an envelope function; r=max ( f_inv, f_bulk). Based on the Boltzmann equation, relation of the relaxation rate to w, E_G, and N_I has been studied and a simple modeling for r(w,E_G,N_I) has been developed. The rate can be expressed by a combination of one-dimensional data arrays. By using the simple modeling, the rate has been readily determined with the help of Monte Carlo simulation, and the validity of the rate modeling has been demonstrated by carrying out device simulation.