Charging and Discharging Characteristics of a Quantum Well with an Initially Lorentzian Wave Packet Incident on a DTM Type Potential

Abstract

We study how non-interacting electrons accumulate in the quantum well region of a potential structure (simplified potential structure of Direct Tunneling Memory) after they start moving toward the potential as a quantum mechanical wave packet. The probability $P_{\tiny \mathrm {L}}(t)$ of finding an electron in the well region obtained with an initially Lorentzian wave packet behaves differently in several respects from the probability $P_{\tiny \mathrm {G}}(t)$ obtained with an initially Gaussian wave packet. Surprisingly, $P_{\tiny \mathrm {L}}(t)$ can increase rather than decrease in the decay (discharging) process, implying that the electrons leaking from the well periodically change the direction of motion and move backward to the well. This counterintuitive “backflow effect” is caused by the quantum mechanical interference between the waves with two wave numbers $k_0$ and $k_\mathrm{r}$, where $k_0$ is the most dominant wave number of the initial wave packet, and $k_\mathrm{r}$ is the resonance wave number of the well. We also discuss similarity and difference between $P_{\tiny \mathrm {L}}(t)$ and $P_{\tiny \mathrm {G}}(t)$ in the buildup (charging) process.