Analysis of Dopant Diffusion in Si with Stacking Faults

Abstract

The mathematically self-consistent solutions of the equations for the dopant diffusions and the oxidation stacking faults, considered self-interstitial and vacancy concentrations in silicon as unknowns, were not previously obtained. In order to solve the problem, a new equation is derived from the dopant diffusion equations. Simultaneously solving this equation and the oxidation stacking fault equation, a set of mathematically self-consistent solutions is analytically obtained. Using the experimental results of dopant diffusions and oxidation stacking faults at 1373 K, the mechanisms of the dopant diffusions and silicon self-diffusion are investigated. It was found that self-, P and B diffusions depend on the interstitialcy mechanism by about 60, 45 and 35%, respectively, while Sb diffusion is almost governed only by the vacancy mechanism. Furthermore, fitting the approximate solutions previously obtained to the present solutions yielded the self-interstitial and vacancy diffusivity values as D I =3.1 × 10 -14 m 2 s -1 and D V =1.6 × 10 -15 m 2 s -1 at 1373 K.