Combined master and Fokker-Planck equations for the modeling of the kinetics of extended defects in Si

A method is proposed to reduce the number of equations and the calculation time of a one-step modeling of the kinetics of extended defects formed after ion implantation of dopants in silicon. The oscillations of the formation energy curves versus the number of atoms of small interstitial defects and its smooth evolution for large defects are accounted for combining a master equation with a Fokker-Planck one. The reduction neither affects the prediction of the self-interstitial supersaturation maintained by the extended defects nor the more “reduction sensitive” parameters such as the defect densities and total number of atoms frozen in the defects. The proposed method is a key step on the way from the modeling of physical effects responsible for boron transient enhanced diffusion to the predictive simulation of p+/n junction depths in development environments.