On the interface connection rules for effective-mass wave functions at an abrupt heterojunction between two semiconductors with different effective mass

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Abstract
The problem of the connection rules for effective-mass wave functions across an abrupt heterojunction is investigated by expressing the results of a one-dimensional, tight-binding approximation in terms of effective-mass wave functions. It is shown that the widely used conventional connection rules of continuous wave function and slope break down if the effective masses on the two sides are different, except if a certain interface matrix element happens to equal the geometric mean of two analogous bulk matrix elements, a case referred to as χ normal. In this case the conventional connection rules yield correct energy eigenvalues, but the effective-mass wave functions themselves differ from true probability amplitudes by a factor depending on the local effective mass, different on the two sides. Heterojunctions that deviate from χ normality may, to the first order, be described as if a δ-function potential had been added at the interface.

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