Normal modes of carrier waves in semiconductor plates

A dispersion relation for waves in an extrinsic semiconductor plate or film with an applied electric field is derived. It is shown that there exists an infinite number of modes. An arbitrary perturbation can be expressed as a superposition of modes. Expressions for the expansion coefficients are derived. Finally, it is shown that a perturbation which is initially a plane wave in a thick plate, remains an approximate plane wave in a time interval corresponding to the decay time, except near the boundaries. Thus, an apparent discrepancy between the theories of infinite- and finite-dimension semiconductors is resolved.