The dependence of the radiative transition probability of donor-acceptor pairs on pair separation

Abstract

The probability W( R) for radiative donor-acceptor pair transitions is generally assumed to decrease exponentially with increasing pair separation R, with a characteristic length a. When one centre in the pair is deep and strongly localized and the other one is shallow, a equals half the Bohr radius of the shallower centre. For pairs in GaP involving two shallow centres we have previously reported that a exceeds half this Bohr radius, and have suggested this to be due to the spatial extent of the deeper centre. In the present paper we investigate this point, both experimentally, and by considering Novotny's calculations — for direct transitions — on the R-dependence of W( R), in which the Bohr radii of both donor and acceptor are parameters. According to these calculations, W( R) is not exponential in the case of two shallow centres. In a limited range of R, W( R) is approximately exponential, however, and theoretical “effective values” of a can be obtained. These effective values are compared with experimental data on a for the pair series S P-Si P, S P-Cd Ga, S P-Zn Ga and S P-C P in the indirect semiconductor GaP; a amounts to ∽ 5.4, 7.0, 7.7 and 9.1 Å, respectively. The comparison shows that the difference found between the experimental a and half the Bohr radius of the less localized centre in the pair can indeed be explained by the influence on a of the spatial extent of the more localized centre. This findings implies a non-exponential W( R) for pairs with two shallow centres. This conclusion depends critically on the values used for the Bohr radii of the acceptors, however. These are not accurately known, due to insufficient knowledge of m ∗ h, one of the quantities needed in calculating the radii. We used m ∗ h = 0.36 m 0 to 0.40 m 0, corresponding to the normally used hydrogen-model energy of 40–45 meV. An alternative explanation for the experimental values of a is that in reality m ∗ h is significantly lower than the 0.36 m 0 to 0.40 m 0 used, leading to larger acceptor Bohr radii and, in the extreme case, to no influence on a of the more localized centre and to an exponential W( R). In order to decide between the two possible explanations, additional experiments are presented. These include an accurate comparison of a between S P-C P and O P-C P as well as between S P-Zn Ga and O P-Zn Ga pairs. This is done by analysing the intergral band decay and time-resolved spectra of these pairs. The conclusions for all pairs mentioned are: (i) The Bohr radius of the acceptors involved is significantly larger than calculated from an effective-mass energy of 40–45 meV; they correspond to a hydrogen-model energy of 28 meV ( m ∗ h = 0.25 m 0). (ii) There is in first approximation no influence on the shape of W( R) of the spatial extent of the more localized centre. (iii) The experimental results are well described by an exponential W( R) with a equal to half the Bohr radius of the less localized centre of the pair.