Kinetics of oxide film growth on metal crystals—III. Perturbation treatment of space charge fields

Abstract

A perturbation analysis of the effects of diffusing space charge on rate of oxide film growth is developed by considering small deviations C″ 1( x) from homogeneous field distributions C′ 1( x). The ratio C″ 1 (extremum)/ C 1(max) is found to be proportional to C k(max) L(t) 2 T in zero surface charge field E 0, where L( t) is the oxide film thickness, T is the temperature, and C k(max) is the maximum boundary concentration of the diffusing species k producing the space charge. The ratio of particle perturbation current J″ 1 to unperturbed current J′ 1 is also proportional to C k(max) L(t) 2 T for zero E 0; J″ 1 is positive for k = 1 but negative for k = 2, assuming species 2 to be oppositely charged from species 1. This result for J″ 1 J′ 1 also holds when E 0 is large and inversely proportional to L( t), which is the case whenever the surface charge density is determined by the interplay of two diffusion currents. These results show that space charge causes deviations from the parabolic growth law which increase in importance with decreasing temperature. Space charge also modifies the logarithmic-type growth law obtained for E 0 independent of L( t). For this case, J″ 1 J′ 1 varies exponentially with E 0L(t) T .