The role of single oxygen or metal induced defect and correlated multiple defects in the formation of conducting filaments

We study the dependence of the formation energies of oxygen and metal induced defects in Ta2O5, TaO2, TaO, TiO2 and Ti4O7 on the chemical potential of electron and atomic constitutes. In the study of single defect, metal induced defects are found to be preferable to oxygen induced defects. This is against the experimental fact of the dominant role of oxygen induced defects in the RS process. A simple multiple defects picture without correlated atomic rearrangement does not cure this problem. The problem is resolved under the correlated multiple defect picture where the multiple defects result in correlated atomic rearrangement and the final products show certain atomic ordering.