Electron
Transmission and Time Delay in Semiconductor Superlattices
Donald W.L. Sprung (McMaster University,
Canada)
In a
GaAs/AlGaAs superlattice, well defined minibands
exist for as few as N = 5 periods. The
transmission probability T exhibits
(N-1)
sharp resonances with an average T typically
25%. Pacher et al. showed that by
adding an anti-reflection coating (ARC) on each side of the
superlattice, this
could be significantly increased, thereby making an efficient energy
filter for
electrons. We have exploited the analogy between an electron scattering
from a
potential cell, and the precession of a Dirac spinor, to design an
optimal
filter with transmission over 90%.
The optimal ARC for electrons is quite different from the classical
designs for
optical systems because of the different dispersion law that applies.
The ARC
works by converting the incident plane wave into a Bloch wave of a
periodic
potential. Time dependence of propagation was studied by direct
numerical
solution of the wave equation, using gaussian incident wave packets.
Without an
ARC, transmission is modulated by resonances associated with quasibound
states.
Adding an ARC increases transmission while cutting the time delay by
half.