Study of the influence of the nonequilibrium point defect concentration gradient on the dopant flux during ion implantation in silicon at high temperatures

Abstract

A relationship in a closed form for a dopant flux in silicon in the presence of the nonequilibrium point-defect concentration and its gradient is derived from the first principles on the basis of solving a simplified boundary value problem. The experimental dopant atom distributions (profiles) obtained after ion implantation of B and P into Si at high temperatures are treated with the help of this relationship. The calculation results show that the exponential dependence of a dopant diffusivity at a distance from the surface can be attributed to the superposition of two effects: the presence of an exponentially decreasing excess of the point-defect concentration versus depth and the influence of the point-defect concentration gradient on the total dopant flux. Omission of the flux component attributed to the nonequilibrium point-defect concentration gradient can result in an overestimation of the point-defect density by more than one order. The conceptual model of the radiation-induced dopant redistribution formulated in terms of a generalised (complete) boundary value problem is reduced to a simplified one by using the assumptions: (i) the dominant interaction of dopant atoms with only one kind of the point defects; (ii) the quasi-equilibrium between the subsystems of the dominant point defects and the complex defects (dopant atom + point defect); (iii) the adiabaticapproximation for the nonequilibrium dilute solutions of dopant atoms and point defects in solids.