Monte carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects

TLDR

The study uses a Monte Carlo method to investigate electron transport in Si and GaAs, improving the modeling of high‑energy carrier dynamics. The authors model the semiconductor beyond the effective‑mass approximation with empirical‑pseudopotential band structures, compute scattering rates consistent with the full band, couple the Monte Carlo simulation to a self‑consistent 2‑D Poisson solver to include space‑charge effects, and apply this framework to sub‑micrometer Si field‑effect transistors to study velocity overshoot, nonlocal, off‑equilibrium phenomena, and electron‑electron interactions. Including the full band structure reduces velocity overshoot by transferring carriers to upper conduction valleys, especially at high bias and low temperature, and the simulation results closely match experimental data.

Abstract

The physics of electron transport in Si and GaAs is investigated with use of a Monte Carlo technique which improves the "state-of-the-art" treatment of high-energy carrier dynamics. (1) The semiconductor is modeled beyond the effective-mass approximation by using the band structure obtained from empirical-pseudopotential calculations. (2) The electron-phonon, electron-impurity, and electron-electron scattering rates are computed in a way consistent with the full band structure of the solid, thus accounting for density-of-states and matrix-element effects more accurately than previous transport formulations. (3) The long-range carrier-carrier interaction and space-charge effects are included by coupling the Monte Carlo simulation to a self-consistent two-dimensional Poisson solution updated at a frequency large enough to resolve the plasma oscillations in highly doped regions. The technique is employed to study experimental submicrometer Si field-effect transistors with channel lengths as small as 60 nm operating at 77 and 300 K. Velocity overshoot and highly nonlocal, off-equilibrium phenomena are investigated together with the role of electron-electron interaction in these ultrasmall structures. In the systems considered, the inclusion of the full band structure has the effect of reducing the amount of velocity overshoot via electron transfer to upper conduction valleys, particularly at large biases and low temperatures. The reasonableness of the physical picture is supported by the close agreement of the results of the simulation to available experimental data.