Time-dependent investigation of the resonant tunneling in a double-barrier quantum well

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Abstract
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.