Bound exciton model for an acceptor in a semiconductor

We attempt to clarify an ambiguity in the understanding of the electronic structure of an acceptor in a semiconductor. Instead of using only a single quantity acceptor binding energy EA as in the literature, there is in fact an impurity level EI that plays perhaps a more important role when dealing with the electronic transitions involving the acceptor. Together they determine an excitonic transition energy EA = EI-EA. We discuss the underlying physics and approximations of using three different approaches, all in the framework of a density-functional theory, for calculating the acceptor electronic structure, and point out the different meanings of the results yielded from these approaches and how they should be compared with experimental data to extract EI and EA. Furthermore, the discussions provide a unified view of ``deep'' and ``shallow'' impurities: The characteristics of deep and shallow reflect two different aspects of a complete description of a typical impurity, either known as isoelectronic or acceptor (donor), rather than the spatial extension of the impurity potential.