Hot-Electron Emission From Shallowp−nJunctions is Silicon

Abstract

The energy distribution of hot electrons in silicon has been investigated experimentally and theoretically by observation of the energy distribution of electrons emitted into vacuum from a reverse biased $p\ensuremath{-}n$ junction 1000 \AA{} below the surface. This emission has been related by means of the Boltzmann transport equation to the mean free paths for optical phonon emission and impact ionization. Two experiments were performed. In the first, with the junction biased to avalanche breakdown, the product of the mean free paths effectively determines the attenuation length for electrons in the resulting nearly Maxwellian distribution. The dependence of the emitted current on the $n$-layer thickness, which determines the attenuation length, and the field configuration within the junction were determined by removing thin calibrated layers (33 \AA{}) of silicon by boiling water oxidation. The second experiment, in which avalanche breakdown and its complications were avoided by optical generation of carriers, has been analyzed in terms of a plane source of electrons released a known distance below the surface at a given energy. The number of emitted electrons then has a maximum at an energy loss depending on the ratio of the mean free paths. The solution of the transport equation similar to that of Wolff, extended to include the initial transient in a field region, was fitted to the experimental data. A good fit was obtained using mean free paths for optical phonon emission of 60 \AA{} and for impact ionization of 190 \AA{}.