Ti, Fe, and Ni in Si and their interactions with the vacancy and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>center: A theoretical study

Transition-metal (TM) impurities from the $3d$ series have been a source of concern in Si technology for nearly 60 years. Surprisingly, numerous issues remain unresolved. In this first-principles theoretical study, we examine the properties of Ti and Ni at a similar level as that used in a recent study of Fe, except that larger supercells are used and that potential-energy surfaces are obtained using the nudged elastic band method (some Fe results have been updated). The equilibrium sites, spin and charge state(s), activation energies for diffusion, and gap levels of the isolated interstitial TMs (${\text{TM}}_{i}$'s) are calculated and match the measured ones when data are available. The interaction of a ${\text{TM}}_{i}$ with a pre-existing vacancy $(V)$ shows that the reaction ${\text{TM}}_{i}+V\ensuremath{\rightarrow}{\text{TM}}_{s}$ (substitutional TM) occurs with a large energy gain, yet smaller than the formation energy of the vacancy. The electrical properties of interstitial and substitutional TM impurities are opposite to each other. In particular, vacancies passivate or partially passivate ${\text{Ti}}_{i}$ and ${\text{Fe}}_{i}$ and thus may play unrecognized but beneficial roles in some processes commonly used by industry. A population analysis of the ${\text{TM}}_{s}$'s shows that the $3d$ shell is not full, even in the case of Ni. The interaction of a TM with the $A$ center (${\text{O},V}$ pair) results in two nearly energetically degenerate configurations, the ${{\text{TM}}_{i},\text{O},V}$ and the ${{\text{TM}}_{s},{\text{O}}_{i}}$ complexes.

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