Space Charge in Growing Oxide Films. IV. Rate Effects Deduced by an Averaging Technique

An analysis of nondiffusing and diffusing space‐charge effects in growing oxide films using simple models provides justification for the equation ${\mathrm{L(t)}}^2{\mathrm{=L}}_{\infty }^2\text{[1−}\exp \mathrm{(-t/\tau )]}$ as a first approximation for describing film growth, where L(t) is the film thickness and t is the time of oxidation. The limiting film thickness squared L_∞² and the pseudo rise‐time τ are functions of the space‐charge concentration and are temperature‐dependent, increasing linearly with temperature for most cases. Space‐charge effects for a given defect concentration are predicted to be more important at low temperatures; growth tends to become parabolic at higher temperatures.