Analysis of P and Sb diffusion during thermal oxidation in silicon

Using experimental results of oxidation-enhanced/retarded diffusions (OED/ORD) for P/Sb in silicon, OED and ORD equations are rewritten into differential equations for self-interstitials and vacancies ( I and V ). An extended relation of the local equilibrium between I and V , V I m = n , is derived from asymptotic forms of formal solutions of OED and ORD equations. The differential equations are solved using V I m = n , i.e., OED and ORD equations are simultaneously solved without any assumptions. Consequently, OED/ORD were governed by only the interstitialcy/vacancy mechanism. The local equilibrium between I and V did not occur in the present diffusion time range. From the obtained results, diffusivities of I and V , i.e., D I =2.4×10 -9 cm 2 s -1 and D V =2.1×10 -10 cm 2 s -1 , and also their thermal equilibrium concentrations, C I 0 =3.3×10 16 cm -3 and C V 0 =2.2×10 17 cm -3 , were determined at 1100°C.