Ab initio spin-polarised local density functional cluster
theory (AIMPRO) was used to explore the properties of Au-H
defects. Full details of the technique have been given before and will
not be repeated here [12]. Large tetrahedral H-terminated
clusters, containing 131 and 297 atoms with the configurations
Si 
H 
and Si 
H 
respectively, were used in
this investigation. The basis consisted of N Cartesian s, p
Gaussian orbitals sited on each atom. N independent d-orbitals
were sited on the Au atom. The charge density is fitted to M
Gaussian functions. In this study, (N,M) are: Au(6,12), Si(4,5) and
H(2,3). The pseudo-wave functions were expanded in independent
combinations of the N Gaussian orbitals on atoms at the centre of
the cluster but a fixed linear combination of the N orbitals was
used on those outside the defect core. The pseudopotentials were
those of Bachelet et al. These were placed on all atoms except
H. The self-consistent energy was found together with the analytic
forces on each atom. The structure was then relaxed using a conjugate
gradient algorithm.
This method has been successfully applied to the study of Ni and Ni-H complexes in silicon [13] as well as the ferrocene molecule [14] and Ni defects in diamond [15].
Of particular interest here are the donor and acceptor energy levels associated with the defects. But there are several problems relating to the formalism in extracting these levels. The acceptor or (-/0) level, relative to the conduction band, is simply the energy difference between a negatively charged and neutral defect with an additional electron in the lowest conduction band state. Suppose d is the Kohn-Sham energy level of the highest occupied level associated with the ionised defect and let c be the Kohn-Sham level associated with the conduction band minimum. Now, provided the relaxation of the defect when the electron is promoted between these levels can be ignored, the difference in the energies of these configurations is, according to Slater's transition state argument and Janak's theorem, simply the difference in the d and c levels found for an electronic configuration corresponding to half-occupancy, i.e, one-half a electron is removed from the level d and placed in level c. If this were the only approximation, the errors would be very slight. Unfortunately, density functional theory is not strictly applicable to the excited state configuration and as such band gaps are substantially underestimated. However, the use of a H-terminated cluster often leads to a band gap which exceeds the experimental one and is a consequence of the large confining potential exerted on the cluster by the terminating H atoms. In diamond, these two effects tend to cancel with the result that the gap is fortuitously in agreement with the experimental gap. The use of the Slater scheme to calculate excitation energies then leads to values in reasonable agreement with known optical transitions [16]. Unfortunately, in silicon the cluster band gaps are between a factor three and four too large. To deal with this problem, we have chosen to scale the Slater's transition state energies by the ratio of the correct Si band gap and the cluster gap. This has the effect of severely reducing all the donor-acceptor levels. In an analogous way, donor levels can be found by promoting half a electron from the valence band to the lowest unoccupied defect level corresponding to the positively charged defect. The technique is easily extended to second acceptor or donor levels. While the approach is not completely satisfactory, it does lead to levels in known cases which are within 0.2-0.3 eV of experiment, although it appears that the levels found are deeper than the experimental ones.