Profile estimation of an implanted-diffused arsenic layer in silicon

The nonlinear diffusion coefficient of a solid-state diffusion equation is approximated by a linear function of concentration, and then the resulting diffusion equation is solved exactly by the method of self-similar solution to obtain a simple expression for the profile estimation of an implanted-diffused arsenic layer in silicon. This expression is dependent only upon the total implant dose and the initial junction depth, but not the specific form of the initial profile. However, as the diffusion time is long enough, only the total implant dose is of significance. The approximate profile, junction depth, surface concentration, and sheet resistance agree quite well with those obtained by solving the nonlinear diffusion equation numerically or by carrying out the diffusion experimentally.