Plane-wave approximation of carrier waves in semiconductor plates with nonisotropic mobility

Starting from the two-dimensional carrier-wave theory of Kino and Robson the minimum thickness of a semiconductor plate that is able to support an approximate plane wave with the dispersion relation being practically equal to that of the one-dimensional theory is estimated. In the limit of small external permittivity such a plane wave is approximated by the fundamental lateral mode, whereas in the limit of large external permittivity a superposition of a few orders of the lateral modes is necessary. At small plate thickness the fundamental mode stays an approximate plane wave. It does the same for larger external permittivity, however, with a changed dispersion relation.