It is short range properties that govern the nature of disordered silicon and germanium. These depend on the local bonding configurations of atoms in these systems. It is there therefore important to look at the changes that small volumes of local disorder effect an otherwise perfect crystal. Such an environment occurs in point defects in a crystal which effects the bonding topologies and therefore the electronic structure by introducing new energy levels to the electronic density of states.
The two types of defects considered here are silicon self interstitials and vacancies. Self-interstitials are among the basic intrinsic defects that are important in many solid state processes such as diffusion. A silicon interstitial is an atom within the structure which is located at a non-crystallographic position. This causes the structure to relax around this additional atom and also changes the local bonding configuration. An interstitial atom can assume one of many different bonding topologies in tetrahedral semiconductors. The more common sites considered in previous calculations are those where the interstitial atom has a position with hexagonal or tetrahedral symmetry[95, 96, 97], (and references therein) although these are not necessarily the most stable interstitial configuration. The bonding of these atoms within the crystalline structure depends on whether the defect carries a charge which also changes the defect states found in the band gap. Only neutral defects will be considered here.
A lattice site where no atom is found is known as a vacancy. Again, there is substantial relaxation of the crystal around the defect site. For a neutral vacancy the bonding topology is simpler than for that of the interstitial. This has been examined previously by several methods such as empirical potentials and Green's functions methods[95, 98, 99, 100]. The surrounding atoms relax into the site of the vacancy and the dangling bond on each atom surrounding the defect pair up to form two new covalent bonds.
It is possible to apply the empirical and ab initio molecular dynamics methods used previously to systems which are non-periodic by the use of supercells. This is similar to the technique used for the surface calculation presented in Chapter 5. In that case, the system was periodic in two directions, requiring the supercell geometry only in the direction perpendicular to the plane of the surface. In this chapter point defects of silicon, where the structure is non-periodic in all three dimensions, are examined by this method, using both empirical and ab initio techniques.
Interstitial configurations and the vacancy defects will be examined by both ab initio and empirical molecular dynamics techniques. Firstly, total energy pseudopotential calculations will be used to determine the bonding topologies of the defects which are useful input for the empirical potential described in Chapter 4. There have been previous first principles calculations on such defects, but due to the high computer time necessary only very small supercells have been used. The use of small supercells is investigated by the empirical method and it is shown that large supercells are required in order to eliminate finite size effects that are evident in the smaller calculations. The calculations preformed here are at zero temperature so that the interstitial configuration found in each case is the `nearest' metastable state to the initial atomic positions. It is still impractical to carry out finite temperature ab initio molecular dynamics in order to perform annealing to find lower energy defect configurations. In order to investigate point defects further, an empirical potential is then used. The phonon spectra of the large supercells containing the defects are calculated directly by diagonalisation of the dynamical matrix. Since this contains all the vibrational information, localised vibrational modes around the defect are found. Also, a similar statistical analysis of the vibrational spectra as that in Chapter 4 gives the free energy of the defects. Knowledge of the vibrational free energy for two interstitial configurations then allows the transition temperature from one defect site to another to be found. This analysis of free energies of the defects from the phonon states is important for the study of defect migration through a crystal.
The dynamical matrix of a system contains all the information about elasticity of the crystal. Therefore, in principle, it is possible to calculate the elastic constants of the crystal just from the dynamical matrix. This is done at several defect concentrations and characteristic defect stiffening is observed.