Profile estimation of high-concentration arsenic or boron diffusion in silicon

A unified analytic approximation for high-concentration arsenic and boron diffusion profiles is presented. The unified profile is represented by a quadratic expression with coefficients determined by the impurity concentration near the surface and the total number of diffused impurities. The junction depth, the total number of impurities, and the sheet resistance calculated by this unified approximate profile are very close to recent results. Application of this approximate expression to the profile estimation of high-concentration phosphorus diffusion in silicon is also presented.