2.3.4 Other One-Dimensional Oxide Growth Models

Massoud's model attempted to correct what was lacking from the Deal-Grove model, mainly the inability of the model to accurately represent thin oxide growth. Since Massoud, many other attempts to model the thin oxide have been suggested in literature. Some have a very similar approach to that presented by Massoud, where additional terms are added to the linear parabolic model in order to introduce additional fitting parameters [37], [218], [220], [221]. However, in most of the presented models, extracting an explicit expression for the oxide thickness as a function of oxidation time is not possible. The model described in [218] suggests the addition of a term with a logarithmic dependence on the oxide thickness, while the model from [220], [221] inserts an error function in the parabolic rate constant $B\slash A$.

Another direction in which researchers have attempted to improve on the initial idea is by neglecting the effect of diffusion altogether and only concentrating on modeling the extra thin film oxide growth [132]. This lead to the idea that there might be silicon atoms penetrating into the oxide and even being pushed to the oxide surface, where they can react to grow more oxide.

More recently researchers have looked at a reaction rate approach to oxide growth, which is gaining some traction [41], [110]. The idea behind this model is that the main assumption made by the Deal-Grove model of a steady state regime is incorrect. It is also suggested that it is wrong to assume a sharp Si-SiO$_2$ interface where all reactions take place. It is quite well known today that the interface between silicon and silicon dioxide is not a smooth one and many researchers are studying the interface at a molecular level, which is the most promising way to understand ultra-thin oxides needed for modern IC devices. Section 2.1.1 gives a further discussion regarding the atomistic view of the Si-SiO$_2$ interface.

It should also be noted that, even with the introduction of the Massoud model, and other linear-parabolic models some limitations discussed regarding the Deal-Grove model are still present. Mainly, two- and three-dimensional effects are not described by these models, nor is the growth of a thin native oxide even at room temperature.