Monte Carlo Simulation of High-Energy Electron Transport in Silicon: Is There a Short-Cut to Happiness?

We discuss the present understanding of the physics of electron transport at high energies in Si and show that recent progress has been made on the experimental and theoretical determination of electron-phonon and pair-production rates. The resulting transport model allows us to simulate hot-electron effects in Si devices with better confidence than in the past. We then present results of a Monte Carlo study of carrier multiplication in silicon bipolar and field-effect transistors and of electron injection into silicon dioxide. Qualitative and, in most cases, quantitative agreement is obtained only by accounting for the correct band structure, all relevant scattering processes (phonons, Coulomb, impact ionization) and the highly nonlocal properties of electron transport in small silicon devices. In addition, we show that quantization effects in inversion layers cause a shift of the threshold-energy for impact ionization which is very significant for the calculation of the substrate current in field-effect transistors. Conservation of parallel momentum, image-force corrections, dynamic screening of the interparticle Coulomb interaction, and improvements to the WKB approximation are necessary to treat correctly the injection of electrons from silicon into silicon dioxide. We argue against the validity of models - analytic or Monte Carlo - which treat hot-electron transport with oversimplified physical approximations. In a few words, there is no short-cut.