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In the pioneering work by Esaki and Tsu the occurrence of negative differential conductivity (NDC)
in semiconductor superlattices was predicted. This initiated
an important field of research in semiconductor physics,
which is still of highest interest. While the original
treatment of transport is based on a simplified solution
of the semiclassical Boltzmann equation for electrons in the miniband,
several alternate treatments have been suggested in the subsequent
time. These can be essentially grouped into three
categories: (i) miniband transport, (ii) Wannier-Stark hopping, and
(iii) sequential tunneling. Using a quantum transport formulation
based on nonequilibrium Green functions these approaches
can be identified as limiting cases, which hold in a certain
parameter range each. In particular it is found that
the original Esaki-Tsu approach gives qualitatively
and sometimes also quantitatively good agreement with more
sophisticated treatments.
The occurrence of NDC has two major implications: The formation of electric field domains and the possibility ofgain, which has been observed only lately. It is shown, that all three standard approaches provide gain in the NDC region up to a maximum frequency, where the photon energy roughly equals the potential drop per period. Again a full quantum transport treatment verifies the simpler results. The occurrence of dispersive gain is a general phenomena, which is not only restricted to superlattice transport as recently demonstrated by experiments in quantum cascade lasers. |
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