Comment on "Optical-transition cross sections involving impurities in semiconductors"

Abstract

It is shown how, in contrast with matrix elements of the momentum operator, matrix elements of the position operator between shallow impurity levels in semiconductors associated with one band and states in a band of opposite parity are very sensitive to slight variations of assumptions made about impurity wave functions. Since recent results of Chaudhuri for absorption due to transitions between acceptor levels and conduction bands based on a formulation involving matrix elements of the position operator are in disagreement with those published by other authors using a formulation in terms of momentum matrix elements, it is inferred that Chaudhuri's results are in error due to a small departure of the wave functions used from true energy eigenfunctions. When small improvements, deducible from published work of Bowlden, are made to impurity wave functions, it is shown that consistency between matrix elements of position and momentum operators is obtained, and it is the matrix elements of the position operator which are altered by the small changes in wave functions.