A Framework for Incorporating Memory Effects of Structural Relaxation in Models for Thermal Oxidation of Silicon

Thermal oxidation of silicon occurs as a result of the transport of oxidizing species through the existing oxide to react with silicon at the Si-SiO₂ interface and form SiO₂. The resulting SiO₂ films are similar to silica glass in their index of refraction, density and other properties, although there are subtle but important differences in their structures. In the present work, we summarize and discuss the physical ingredients necessary for a quantitative understanding of time-dependent structural relaxations of the oxide. For glasses formed by quenching from the melt, the time-dependent recovery of a nonequilibrium structure to its equilibrium state has been widely documented by measurement of quantities such as specific volume, index of refraction, enthalpy, and others1,2 These exhibit nonlinearity with respect to the magnitude of departure from equilibrium, asymmetry with respect to the sign of the departure and memory effects which are sensitive to the thermal and annealing history. Such phenomena are also to be expected in thermally grown silicon dioxide layers. Indeed, measurements have indicated that the density of SiO₂ can be a time-dependent quantity which eventually relaxes toward a final value3. Such structural changes are expected to modify the oxide growth process. For instance, it has been shown in vitreous silica and other glasses that the diffusion of inert gasses is dependent upon the thermal history of the specimen4.