A new model for the plasma anodization of silicon at constant current

A new physical model is described for the plasma anodization of Si. The model is constructed from the continuity equation for the charged oxidizing agent O−, with transport by field-imposed drift and by diffusion. It is argued that at constant total current, the field in the oxide layer is constant in space and in time. A loss term for O− ions is also incorporated in the model; the resulting gradual drop of the O− contribution to the total (constant) current at increasing depth into the oxide explains the observed decrease of the oxidation rate with time. The O− loss can occur, i.a., by detachment O−→O+e− or by two-step mechanisms resulting overall in 2O−→O2+2e−. The model predicts an exponential decay of O− in the oxide. At constant current the oxide width as a function of time is given by w=A ln(1+Bt), where A is the characteristic penetration distance of O− in the oxide and AB is the initial oxide growth rate, determined by the subsurface O− current density. The two-parameter model provides excellent fits to available experimental data; standard deviations are ∼1% of the final oxide width. From the parameters, numerical values are derived of underlying physical constants. A lower limit is also deduced for the O− loss rate constant.