Vacancies and dopant diffusivity

The change in vacancy concentration as a function of dopant density has a direct effect on the diffusivity of that dopant. [2] For low dopant concentrations the diffusivity of the dopant increases as the vacancy concentration increases if the dopant diffuses via a vacancy mechanism, as most do. This effect may be detectable even if the vacancy concentration is too small to have a measurable impact on doping. The charge on a vacancy can also have a significant effect. If the vacancy concentration gets too high, then defect clusters form and the diffusivity drops abruptly. To see how this can work in detail, we will consider the cases of As and P diffusivities in Si. 

The diffusivity of the dopant can be different through vacancies of various charge states. The total diffusivity of a dopant might be, for example [2] 

The first term is diffusion through neutral vacancies. The second term is for charged vacancies. The ratio of n/ui is due to the connection between dopant and vacancy concentrations. For n=10 ° As cm (all As ionized) and ni=1.5xl0 cm at 1400 K, 

In this situation, typical of As movement, diffusion through charged defects dominates the result. It is clear that a constant (concentration independent) diffusivity cannot be expected for As in Si. As the As concentration falls within the sample, the diffusivity also falls because of the change in n. Consequently, the concentration gradient for As diffusing into a Si wafer is greater than one might expect for a constant diffusivity. 

When the vacancy concentration rises sufficiently, the diffusivity of an impurity may drop dramatically if the impurity and the vacancy form clusters. This is the case for both As and P. For As, when the dopant concentration exceeds 10 ° cm. As atoms 

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