The temporal development of the wave function within a double-barrier quantum well is studied by numerically solving the time-dependent Schrödinger equation. One-dimensional AlGaAs-GaAs-AlGaAs and AlAs-GaAs-AlAs structures are considered in this study. The build-up time and the decay constant of the resonant probability amplitude have been computed as functions of the system parameters. In general, these times are considerably different in magnitude. The amplitude of the wave function trapped inside the well is found to depend crucially on the initial energy spread. The results are in good agreement with those of a recent photoluminescence experiment.

A quantum mechanical simulation method of charge transport in very small semiconductor devices, based on the numerical solution of the time-dependent Schrodinger equation (coupled self-consistently to the Poisson equation to determine the electrostatic potential in the device), is presented. Carrier transport is considered within the effective mass approximation, while the effects of the electron-phonon interaction are included in an approximation that is consistent with the results of the perturbation theory and gives the correct two-point time correlation function. Numerical results for the transient behavior of a planar ultrasubmicrometer three-dimensional GaAs MESFET (gate length of 26 nm) are also presented. They indicate that extremely fast gate-step response times (switching times) characterize such shortchannel GaAs devices.

Effect of inclusion of selfconsistently determined electron temperature on the electron-plasmon interaction

We compared two different formulations, the electron-field and electron-electron models, for electron-plasmon scattering in bulk semiconducting materials. The calculations employ three different expressions for the plasmon dispersion relation and are made at two different temperatures. It is found that the functional form of the dispersion relation greatly affects the electron-plasmon-scattering rate. The electron-field model is found to predict a higher scattering rate than the electron-electron model, independent of the form of the dispersion relation. Either model predicts the same order-of-magnitude scattering rate, which is found, in the case of bulk degenerate GaAs, to be comparable to the polar optical-phonon-scattering rate. Based on these calculations, plasmon scattering appears to be an important mechanism limiting electron transport in degenerate semiconductors and related semiconductor devices.

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