Effects of Coulomb interaction on electron dynamics in a double-barrier potential: Decay and trapping

Abstract

The decay of a resonance and electron trapping in the quantum well region of a double barrier potential are studied. We take into account electron-electron interactions at the Hartree level by coupling the time-dependent Poisson and Schr\odinger equations. Since, in this mean-field theory, the effective potential for the electron motion depends on the classical distribution of charge, the Schr\odinger equation becomes nonlinear. We have used the electron sheet density in the well as an adjustable parameter that controls the coupling and thus the degree of the nonlinearity. Without nonlinear coupling, the well generally holds resonance states and, if deep enough, possibly bound states. The nonlinear interaction gives rise to shorter decay times for the resonances, and the existence of a critical electron sheet density above which permanent trapping does not occur.