2.3 Linear Parabolic Description of Thermal Oxidation Growth

Even though experimental results have been able to show, with reproducibility, the ability to control oxide thickness and quality using various parameters such as temperature, pressure, crystal orientation, and oxidation environment, a complete understanding for how the oxide grows is not yet given. The initial first-order model for oxide growth kinetics was suggested by Bruce Deal and Andrew Grove at Fairchild Semiconductor in 1965 [42]. This linear parabolic model, more commonly referred to as the Deal-Grove model, is used as a starting point for many more recent works attempting to model oxidation kinetics [175]. Although the Deal-Grove model can, within an acceptable accuracy, predict oxide growth beyond 30nm, its main drawbacks are the inability to explain oxide features, when two- and three-dimensional geometries are required and its inability to accurately describe the initial oxidation for very thin layers ($<30$nm). This lead to the introduction of a model by Massoud et al. [143], [144], which is meant to deal with thinner oxides. Many other models have been proposed after Massoud in order to deal with the thin oxide regime, which is suggested to have a growth rate limited by the chemical reaction and not by the diffusion of oxidants, as Deal-Grove and Massoud suggest.