Theory of binding energies of acceptors in semiconductors

Acceptor binding energies are calculated using the full 6 × 6 effective-mass acceptor Hamiltonian for both shallow and deep levels. It is found that for homopolar semiconductors (Si and Ge) the method is valid for both shallow and deep acceptors, in agreement with a similar result obtained previously by Pantelides and Sah for donors in Si. Screening the impurity potential by the dielectric function $\epsilon \mathrm{}\left(q\right)\mathrm{}$ is again found to be very important. The point-charge model is found to be adequate for shallow single acceptors and the relatively shallow double acceptors in Ge, but completely inadequate for the deep double acceptors in Si and triple acceptors in Ge. Use of model potentials, however, which reflect the chemical nature of individual impurities, is shown to be capable of reproducing the observed values. When model potentials from the literature are used, agreement with experiment is only modest, due to a sensitivity of the calculation on the core part of the impurity potential. Similar calculations in heteropolar semiconductors (GaP, GaAs, etc.) show that good agreement is obtained only for very shallow levels. For deeper levels, effects due to differences in the anion and cation sites are dominant. It is argued that these effects lie outside the effective-mass theory.