A bound exciton model of acceptors in semiconductors

We point out that the electronic structure of an acceptor bears a close similarity to that of an isoelectronic impurity bound exciton with a larger electronegativity (known as ``acceptor-like bound exciton'') [Hopfield et al., PRL 17, 312(1966)], and to some extent to that of a free exciton in a semiconductor. Instead of using only one quantity \textbf{\textit{acceptor binding energy}} E$_{\mathrm{A}}$ (based on Coulomb interaction) when dealing with the electronic transitions involving an acceptor, another quantity \textbf{\textit{impurity binding energy}} E$_{\mathrm{I}}$, depending on the atomic orbital difference, is usually more important in the transition processes. E$_{\mathrm{I}}$ resembles the role of the electron bound state or conduction band edge, whereas E$_{\mathrm{A}}$ resembles the hole or exciton binding energy, respectively, in the isoelectronic impurity or free exciton case. Furthermore, instead of viewing the acceptor impurity as a ``shallow impurity'' and isoelectronic impurity as a ``deep impurity'', it would be more appropriate to view for both impurity types that the bare electron bound state involves a localized potential, and the ionized impurity has a long-range Coulomb potential. A first-principles calculation of the total energy difference yields approximately E$_{\mathrm{I}}$ -- E$_{\mathrm{A}}$, but the energy needed to generate free holes is in fact E$_{\mathrm{I}}$.