Free-electron density and transit time in a finite superlattice

In this paper we have calculated the free-electron density in a finite superlattice. Resonant tunneling causes a buildup of particle density in the well regions, giving rise to an accumulation of electrons in those regions. Using our results, we have estimated the change in barrier heights and well depths caused by the electrostatic force. A negligible change is found for a double-well structure having well widths of 40 Å and barrier widths of 20 Å. Our approach could be extended to calculate the tunneling current self-consistently. Additionally we have used a time-dependent solution of Schrödinger's equation to estimate the trapping time of the electrons due to the resonant effect. The results show that the probability density oscillates several times between the two wells, leaking out gradually at each step. After about 2.4×10^-13 s, most of the waves centered about the resonant energies have been transmitted.