Electron-electron interaction in semiconductors with application to hot-electron transistors in silicon and gallium arsenide

The authors use a temperature-dependent Green function approach within the random-phase approximation to evaluate the imaginary self-energy and hence to derive a path length due to electron-electron interaction. This total path length includes plasmon and single-particle absorption processes (energy gain) as well as plasmon emission, and single-particle excitation processes (energy loss). They can separate this total path length into one due to effective energy loss (energy loss-energy gain), which is relevant to the working of hot-electron transistors, and one due to the individual processes, which can be compared with the commonly used expression for plasmons due to Ferrell (1956, 1957) and the Born approximation for single-particle behaviour. They find that the Bohm and Pines and Ferrell approach of introducing a wave-vector cut-off to separate collective and single-particle behaviour breaks down as the density is lowered and therefore these commonly used expressions break down. They derive shorter path lengths for plasmon emission and longer path lengths for single-particle excitation for low energies of the incident electrons and low doping. They also find that for low doping and low energies of the incident electrons the majority of the contribution for the single particle as well as the plasmon comes from q