Analysis of the Williams-Hayfield Model for Oxidation Kinetics

A theoretical analysis is presented for the physical model of thermal oxidation proposed by Williams and Hayfield. A rate is deduced herein for oxide film thickness as a function of time . The growth rate exponential falloff parameter is , where is a uniform density of trapped electrons in the oxide, is the Kelvin temperature, and the parameters ε, , and are the static dielectric constant of the oxide, Boltzmann's constant, and electronic charge magnitude, respectively. Numerical computations compare this rate law with the logarithmic growth law proposed in the original analysis.