Mechanisms of charge-state determination in hydrogen-based impurity complexes in crystalline germanium

Recent experiments suggest that hydrogen may become bound to, and then tunnel around, substitutional carbon, silicon, or oxygen impurities in crystalline germanium. All these complexes are electrically active; [H,C] and [H,Si] are shallow acceptors, while [H,O] is a shallow donor. This paper attempts to elucidate the basic physical mechanisms controlling the charge state of such complexes as a function of the choice of the substitutional atom. A minimal-basis Bethe-cluster approach is used with the cluster comprising the ten-atom tetrahedral cage (including the substitutional atom) and enclosed H site, the latter coupled to all ten atoms of the cage. The important local correlation effect which tends to favor single occupation of the H site is modeled with a Hubbard-type term at that site. The charge state of the [H,C], [H,Si], and [H,O] complexes is associated with double occupation of the H site. Four aspects of the model are involved in favoring double occupation: (1) a low value of the H-site energy, (2) a reduced local correlation effect at the H site, (3) small hybridization between the H site and cage, and (4) a low value of the substitutional-site energy relative to that of the host. Results for the charge state for H at the cage center and for H near the substitutional atom are discussed in detail. Several useful formal results for local self-energies and local Green's functions are presented