Continuum Modeling of High-Field Transport in Semiconductors

Continuum approaches are renowned in mathematical physics for their parsimony, robustness, and numerical efficiency, and for these reasons are especially valuable for physics-based modeling. For this paper the relevant field is semiconductor device engineering where the original continuum description of diffusion-drift theory remains in wide use. However, this theory is known to be inadequate for describing high-field transport, and efforts to improve on it, while having a long history, are generally regarded as phenomenological and useful only when buttressed by extensive experimental characterization. With this as motivation, we develop a new physics-based approach that we call drag history theory using classical field theoretic methods rather than via the traditional route based on the Boltzmann equation. Critical to our theory are various material response functions that we characterize specifically for silicon using Monte Carlo simulations of a high-voltage diode. Most important is the response function for the drag force felt by the electron gas as it flows through the lattice wherein one needs to properly account for its non-instantaneous nature. By weighing the contributions of mechanical and thermal inertia and thermal diffusion, we also discuss the conditions under which the full description can be simplified with significant computational benefits.