Contribution of drifting carriers to the Casimir-Lifshitz and Casimir-Polder interactions with semiconductor materials

We develop a theory for Casimir-Lifshitz and Casimir-Polder interactions with semiconductor or insulator surfaces that takes into account charge drift in the bulk material through use of the classical Boltzmann equation. We derive frequency-dependent dispersion relations that give the usual Lifshitz results for dielectrics as a limiting case and, in the quasistatic limit, coincide with those recently computed to account for Debye screening in the thermal Lifshitz force with conducting surfaces with small density of carriers.