Understanding hot-electron transport in silicon devices: Is there a shortcut?

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Abstract
Results of a Monte Carlo study of carrier multiplication in silicon bipolar and field‐effect transistors and of electron injection into silicon dioxide are presented. 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, it is shown 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. The validity of models—analytic or Monte Carlo—which treat hot‐electron transport with oversimplified physical approximations is argued against. In a few words, there is no shortcut.