Electron transmission and phase time in semiconductor superlattices

TL;DR

This paper analyzes electron transmission and phase time in semiconductor superlattices, deriving phase-time envelopes at transmission extrema and comparing theoretical predictions with numerical solutions, highlighting the impact of anti-reflection coatings.

Contribution

It introduces a method to describe phase-time extrema in superlattices and compares theoretical results with numerical simulations, emphasizing the effect of anti-reflection coatings on time delay.

Findings

Phase-time peaks and valleys are well described by fitted parameters.

Anti-reflection coatings reduce time delay and increase transmissivity.

Propagation at Bloch velocity aligns with observed time delays.

Abstract

We discuss the time spent by an electron propagating through a finite periodic system such as a semiconductor superlattice. The relation between dwell-time and phase-time is outlined. The envelopes of phase-time at maximum and minimum transmission are derived, and it is shown that the peaks and valleys of phase-time can be well described by parameters fitted at the extrema. For a many-period system this covers most of the allowed band. Comparison is made to direct numerical solutions of the time-dependent Schr\"odinger equation by Veenstra et al. [cond-mat/0411118] who compared systems with and without addition of an anti-reflection coating (ARC). With an ARC, the time delay is consistent with propagation at the Bloch velocity of the periodic system, which significantly reduces the time delay, in addition to increasing the transmissivity.