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 approximately 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.