Theoretical investigation of different formulations of the electron-plasmon interaction under transient conditions

We present a comparison of two different methods of including the electron-electron long-range interaction on the dynamics of hot electrons in degenerate GaAs under transient conditions in two different hot electron transistor structures of 60- and 120-nm base widths, respectively. The first approach is quantum mechanically based while the second follows a semiclassical prescription. The calculated energy spectrum, velocity distribution, and percentage of injected carriers collected in the hot electron transistors are determined under three different conditions: the inclusion of the plasmon interaction through the quantum-mechanical formulation, the inclusion of the plasmon interaction through the semiclassical technique, and with no plasmon interaction. The calculated energy spectrums within the two plasmon models are qualitatively similar. They differ only by the extent to which the peaks are broadened and the absolute ratio of collected to injected carriers. Because of the very different energy relaxation within the plasmon models, the ratio of collected to injected electrons is predicted to be far smaller using the quantum-mechanical model than the semiclassical model. Subsequently, knowledge of the absolute ratio of the collected to injected carriers in a hot electron transistor would give some indication of the appropriateness of each model.