The oxygen dimer

  The first stage of O precipitation is considered to be the formation of a dimer, O_2i. It was originally proposed that rapidly diffusing O₂ molecules could lead to enhanced oxygen diffusion [137]. However theoretical calculations [138] showed that an O₂ molecule in Si dissociates into two O_i with a large associated gain in energy. Later calculations showed oxygen molecules to be unstable compared to nearest neighbour pairs of bonded interstitial oxygen defects [135,114,121,115].

The evidence for the dimer started with results in 1981 showing thermal donor formation rates decreased towards the sample surface. Interpreting this as oxygen out-diffusion gave oxygen diffusivities enhanced by more than four orders of magnitude [139].

There are 17 thermal donors which are likely to involve increasing numbers of oxygen atoms. The growth rates of these donors have been monitored and it is found that they grow with an activation energy around 1.8 eV - much lower than the energy for a single O_i hop [140]. There have been suggestions that VO₂ complexes could diffuse rapidly [141] but the evidence is not conclusive. The early suggestion [137] that oxygen pairs could diffuse rapidly has been supported by SIMS measurements of the out-diffusion of oxygen [142] between 500 and 700$^\circ$C, and recent experiments [143,144] studying carefully the loss of O_i from solution at temperature as low as 350$^\circ$C. These show that the process is second order below 400$^\circ$C but of higher orders, up to 8, as T increases to 500$^\circ$C. The low temperature process must be controlled by the formation of oxygen dimers. The change in order of the process is then explained by an instability of the dimer above about 450$^\circ$C and thus larger numbers of oxygen atoms are required to diffuse together to form a stable precipitate.

A plane wave supercell calculation [115] gave a binding energy for the oxygen dimer of 1.0 eV. However other calculations suggest that dimers will not bind [135]. Semi-empirical CNDO/S techniques showed that the dimer has a binding energy of 0.1 eV and the saddle point for its migration is 1.36 eV [121]. The saddle point for dimer diffusion was found to lie close to an over-coordinated oxygen square defect - rather similar to the known structure of the nitrogen pair [145] (see Chapter 7). However this was obtained from total energy calculations of manually selected intermediate structures, and re-examination of this problem using ab initio methods with constrained optimisation would be desirable.