Electron transmission and phase time in semiconductor superlattices
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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.
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