A closed-form relationship was derived for the dopant flux in the presence of a non-equilibrium point defect concentration. Its gradient was deduced from first principles by solving a simplified boundary value problem. The dopant distributions which were found after high-temperature B and P implantation were analyzed by using the above relationship. The theoretical results showed that the exponential dependence of the dopant diffusivity at a distance from the surface could be attributed to the superposition of 2 effects. These were an exponential decrease in the excess point defect concentration, and the effect of the point-defect concentration upon the total dopant flux. It was suggested that the omission of the flux component that was attributed to the non-equilibrium point defect concentration gradient could result in an over-estimation, of the point defect density, by more than an order of magnitude.

V.I.Koldyaev: Nuclear Instruments and Methods in Physics Research B, 1995, 106[1-4], 446-53