Role of point defects in the growth of the oxidation-induced stacking faults in silicon

Abstract

A new mechanism, describing the growth of the oxidation-induced stacking faults (OISF) in silicon has been formulated. This mechanism predicts the temperature, time, and oxygen-pressure dependences of the length of the faults in agreement with experimental measurements. The formulation of the mechanism and the derivation of an equation for the length is based on the following assumptions. (a) The growth of the stacking faults at the heterogeneous nucleation sites is analogous to the crystalline growth at the surface kinks. (b) There is an excess of silicon atoms at the Si${\mathrm{O}}_{2}$-Si interface. The concentration of the excess silicon atoms depends on the partial pressure of oxygen during oxidation and on the concentration of the charged vacancies in the adjacent bulk of the silicon. (c) The self-diffusion in silicon occurs by the formation and migration of the charged vacancies. The resultant derivation and comparison with experiment strongly support the new mechanism. (i) The equation describing the length of OISF has been derived to be $L={K}^{\ensuremath{'}}{P}_{{\mathrm{O}}_{2}}^{m}{t}^{n}\mathrm{exp}(\ensuremath{-}\frac{Q}{\mathrm{kT}})$, which is exactly the same as borne out of experimental findings reported earlier. (ii) Values of $m$ and $n$ have been derived and were found to be in good agreement with previously measured values. (iii) Expressions for ${K}^{\ensuremath{'}}$ and $Q$ have been obtained. Using these expressions and available data from literature, ${K}^{\ensuremath{'}}$ and $Q$ were calculated and were found to be in excellent agreement with experiment. (iv) Two different sets of values of $m$, ${K}^{\ensuremath{'}}$ and $Q$ for lower and higher temperature ranges have been obtained. This is in agreement with experimental observation which clearly indicated existence of two temperature ranges (one \ensuremath{\le} 1150\ifmmode^\circ\else\textdegree\fi{}C and the other \ensuremath{\ge} 1200\ifmmode^\circ\else\textdegree\fi{}C).