  Free standing InP quantum dots have previously been theoretically and
experimentally shown to have a direct band gap across a large range of
experimentally accessible sizes. We demonstrate that when these dots are
embedded coherently within a GaP barrier material, the effects of quantum
confinement in conjunction with coherent strain suggest there will be a
critical diameter of dot (60A), above which the dot is direct, type I, and
below which it is indirect, type II. However, the strain in the system acts to
produce another conduction state with an even lower energy, in which electrons
are localized in small pockets at the interface between the InP dot and the GaP
barrier. Since this conduction state is GaP X_1c-derived and the highest
occupied valence state is InP, Gamma-derived, the fundamental transition is
predicted to be indirect in both real and reciprocal space (``type II'') for
all dot sizes. This effect is peculiar to the strained dot, and is absent in
the free-standing dot.
