Envelope Equation and Wave Function Matching for Narrow‐Gap Semiconductors

It is shown that Zawadzki's equation for the conduction band envelope in a narrow‐gap semiconductor can be derived from the Ben Daniel‐Duke equation containing a position dependent effective mass if the position dependence of the band edge is taken into account in the Kane type energy dependence of the effective mass. Contrary to the original derivation of Zawadzki generalizations to other types of band structures are easily possible. As examples envelope equations are derived for an anisotropic Kane band structure and for the case of different conduction and valence band masses. In addition, the procedure presented here leads also to the conclusion that the envelope matching condition used till now has to be replaced by a more general and energy dependent one.