A tight-binding study of acceptor levels in semiconductors

Abstract

Acceptor binding energies in zinc-blende semiconductors are determined within the tight-binding formalism. The importance of tting the valence-band masses in the 100 as well as 111 directions is discussed, and parametrizations that speci cally t the valence-band anisotropy are used to calculate Ge acceptor levels in AlxGa1,xAs alloys. The sensitivity of the calculated energies to the parameters that determine bulk masses is investigated, as well as the e ect of varying the on-site energy of the impurity. A comparison is made between rst-neighbor and second-neighbor hopping models. For shallow levels, both approaches give the same results. For deeper levels, however, important di erences arise. Experimental evidence suggests that rst-neighbor models are better suited for describing intermediate to deep levels. I IntroductionThe e ective mass theory EMT has long been a principal tool for investigating shallow impurity states in semiconductors 1, 2 . In EMT, it is assumed that the impurity w ave function is highly delocalized in real space, which in turn implies a strong localization in k space. As a result, the electronic properties of the host material may be described by only a few parameters related to the dispersion near the k point in consideration. For instance, in the Luttinger-Kohn version of k p theory, the electronic structure of the host is completely de ned in terms of the spin-orbit energy and the three Luttinger parameters LP's , which also determine the impurity energy level. Because each host material has a di erent set of LP's, and acceptor binding energies are known to vary widely from host to host, it is clear that the impurity level within EMT must depend sensitively on these bulk parameters.Another result of EMT is that, for a given material, any singly ionized acceptor should have the same binding energy, regardless of the species. H o wever, experimentally it is known that such energies can vary widely from impurity to impurity. F or example, an In acceptor in Si has a binding energy of 157 meV, compared to 45 meV for a B acceptor in the same host 3 . Such deviations from EMT are attributed to centralcell e ects, and demonstrate that the binding energies can also be very sensitive to the details of the potential in the immediate neighborhood of the impurity.Recently, an approach w as presented 4 for calculating impurity states in semiconductors based on the tight-binding TB formalism. The localized basis set of TB provides a natural description for deep levels, while the highly delocalized shallow levels are treated by means of very large unit cells together with a scaling law that allows extrapolation to the bulk limit 4 . In other words, the TB approach is not intrinsically restricted to either the shallow or deep limits. For the TB approach to be useful, however, a clear understanding of how the calculated energies depend on the TB parameters is required. In particular, the sensitivity of EMT on the LP's and the the role of central-cell e ects must be understood in the context of the curr...