The effective-mass theory in real semiconductors: Excitons and impurities in diamond and zincblende lattices

Abstract

The relationship between band structure and excitons and impurity states in cubic semiconductors is investigated within the limits of the effective-mass approximation. The close formal analogy between direct excitons and acceptors is discussed. Their similarity is evident from the fact that the two systems are described by essentially the same Hamiltonian. The striking dissimilarity in the observed spectra of these two systems is shown to be due to the different strength of a term («spinorbit» term) in the Hamiltonian. In fact this term is small for excitons, thus allowing a perturbation analysis; for acceptors, in contrast, the «spin-orbit» term is so strong that it has to be included exactly and the energy spectrum has no resemblance at all to that of the hydrogen atom. Comparison with experiment for both excitons and acceptors is good except for Si which is discussed separately. It is finally shown that the application of an external magnetic field can provide very useful information about the electronic states of these materials only when the complexity of the valence bands is included. A recent theory is shown to provide good quantitative interpretation of the fine structure observed in high-resolution measurements of magneto-absorption in Ge and can be used for a better determination of the band parameters for those substances for which they are not currently known.