  A theoretical investigation is made of the dispersion characteristics of
plasmons in a two-dimensional periodic system of semiconductor (dielectric)
cylinders embedded in a dielectric (semiconductor) background. We consider both
square and hexagonal arrangements and calculate extensive band structures for
plasmons using a plane-wave method within the framework of a local theory. It
is found that such a system of semiconductor-dielectric composite can give rise
to huge full band gaps (with a gap to midgap ratio $\approx 2$) within which
plasmon propagation is forbidden. The most interesting aspect of this
investigation is the huge lowest gap occurring below a threshold frequency and
extending up to zero. The maximum magnitude of this gap is defined by the
plasmon frequency of the inclusions or the background as the case may be. In
general we find that greater the dielectric (and plasmon frequency) mismatch,
the larger this lowest band-gap. Whether or not some higher energy gaps appear,
the lowest gap is always seen to exist over the whole range of filling fraction
in both geometries. Just like photonic and phononic band-gap crystals,
semiconducting band-gap crystals should have important consequences for
designing useful semiconductor devices in solid state plasmas.
