Experimental evidence and interpretation of dopant–point defect pair diffusion

Abstract

Experimental verification along with detailed simulation of up-hill dopant diffusion in the vicinity of a damage layer consisting of dislocation loops is presented. The effect of dopant up-hill diffusion, predicted on the basis of the so-called dopant–point defect pair diffusion model, is explained by the additional dopant current driven by the gradient of point defect concentration. The gradient of point defects (self-interstitials, in the present case) is caused by the strong absorption of self-interstitials by dislocation loops in the damage layer. The present simulation of phosphorus diffusion in preamorphized silicon crystal shows that the pertinent phosphorus profiles, displaying the up-hill diffusion, allow reliable extraction of parameters governing the coupled phosphorus and self-interstitial diffusion dynamics. Three different derivations of the pair diffusion model are investigated. It is shown that the pair diffusion model is consistent with a derivation of transport equations from the master equation assuming that the elementary jump frequency Γ0 is enhanced locally by the presence of self-interstitials according to Γ0(CI/C*I). It is also shown that the same assumption made on the level of the final diffusion equation leads to incomplete formulation of the relevant dynamics.