Gallium $($Ga$)$ focused ion beams $($FIBs$)$ are generally used for micro$-$ and nanoscale

machining of silicon surfaces. Suppose after such a treatment some Ga residue is left on the

surface of a silicon wafer. This wafer was next annealed at $900$ o C for $5$ minutes. We know that

the primary mechanism of diffusion in silicon is via vacancies. Ga impurities will diffuse in

undoped silicon via neutral and positively charged vacancies. The contribution from each of the

vacancies is as follows: