Transport in Nanostructures: A Comparative Analysis Using Monte Carlo Simulation, the Spherical Harmonic Method, and Higher Moments Models

With the modern transistor size shrinking below 45 nm the classical drift-diffusion model to describe transport in the conducting channel is loosing its validity. In short-channel devices carriers get accelerated by the driving field and do not thermalize before they reach the drain contact. Thus, the assumption underlying the classical transport model, that the driving electric field produces a weak perturbation of the local equilibrium distribution function, is violated. Several generalizations of the classical drift-diffusion model are possible. The most common approach in the TCAD community is to introduce higher moments of the distribution function. Another approach is to use a spherical harmonic expansion of the distribution function. We perform a comprehensive analysis of the validity of the highermoments transport models with the model based on spherical harmonic expansion by rigorously comparing their results with results of the Monte Carlo solution of the Boltzmann transport equation.