  We develop a new theory for Casimir-Lifshitz and Casimir-Polder interactions
with semiconductor surfaces that takes into account charge drift in the bulk
material. The corresponding frequency-dependent dispersion relations describe a
crossover between Lifshitz results for dielectrics and for good conductors. In
the quasi-static limit, our calculated reflection amplitudes coincide with
those recently computed to account for Debye screening in the thermal Lifshitz
force with conducting surfaces with small density of carriers.
