If a realspace calculation is performed without using either periodic boundary conditions or an embedding technique then the only other alternative is to use clusters. A realspace cluster of atoms has a surface array of dangling bonds that need to be saturated in some way in order to remove them from the gap and correctly simulate bulk material. This is achieved by terminating the dangling bonds with H atoms, concentrating surface charge in correctly orientated chemical bonds.
Justification for the use of a H terminated cluster approach comes from the apparent scalability in chemical bonding from molecular species into semiconductor bulk. For example, disiloxane, (SiH3)2O has a Si-O-Si vibrational stretch mode of 1107 cm-1, only 2.5% less than that of Oi in Si. It has a Si-O bond length of 1.634 Å, less than 1.5% longer than the bondlengths we calculate here for Oi in Si (see Chapter 6).
If the surface H atoms are allowed to move, the number of iterations required to reach a minimum energy structure is vastly increased. Surface H sits in a shallow potential and as the defect core relaxes there is a `relaxation ripple' which runs out to the edge of the cluster. Often over half of the conjugate gradient iterations are spent moving the surface hydrogens with little overall change in the cluster energy or defect core structure. If the surface H atoms are not allowed to move then it is questionable to what extent the resultant cluster is in a fully relaxed ground state structure. Ideally there should be no motion of the cluster surface indicating minimal interaction with the defect at the cluster core, but in practise such clusters are prohibitively large. Fixing surface H atoms can lead to incorrect structures where there is a large volume change, e.g. substitutional carbon and VOn centres.
A compromise between these two solutions that has been used for much of this work is to confine the hydrogen atoms in an additional quadratic `spring' potential. This is a crude first approximation to the additional rigidity that would be provided if the cluster was embedded in bulk. Using a standard Si-Si bond spring constant gave a potential that was too restricting, so where used in these calculations, the spring strength is 5.0 eV/Å. Various other simple methods have been tried with less success.