Internal structure of acceptor-bound excitons in wide-band-gap wurtzite semiconductors

Abstract

We describe the internal structure of acceptor-bound excitons in wurtzite semiconductors. Our approach consists in first constructing, in the context of angular momentum algebra, the wave functions of the two-hole system that fulfill Pauli's exclusion's principle. Second, we construct the acceptor-bound exciton states by adding the electron states in a similar manner that two-hole states are constructed. We discuss the optical selection rules for the acceptor-bound exciton recombination. Finally, we compare our theory with experimental data for CdS and GaN. In the specific case of CdS for which much experimental information is available, we demonstrate that, compared with cubic semiconductors, the sign of the short-range hole-exchange interaction is reversed and more than one order of magnitude larger. The whole set of data is interpreted in the context of a large value of the short-range hole-exchange interaction ${\ensuremath{\Xi}}_{0}=3.4\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{meV}$. This value dictates the splitting between the ground-state line ${\text{I}}_{1}$ and the other transitions. The values we find for the electron-hole spin-exchange interaction and of the crystal-field splitting of the two-hole state are, respectively, $\ensuremath{-}0.4\ifmmode\pm\else\textpm\fi{}0.1$ and $0.2\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{meV}$. In the case of GaN, the experimental data for the acceptor-bound excitons in the case of Mg and Zn acceptors, show more than one bound-exciton line. We discuss a possible assignment of these states.