We have developed a model  for thermal oxidation of AlGaAs using the continuity equation based on the principle of oxidant mass conservation (Figure 1). Oxidant transport is found to be related to the structure-dependent oxidation process (Figure 2). The model takes into account several processing control parameters all in one single equation and therefore can be easily applied to the process control of device fabrication. The relevant control parameters in the device processing include layer thickness, oxidation temperature, oxidation time, spacing between two devices, Al composition, and mesa geometry. Theoretical calculations agree well with reported experimental values. We also apply this model to study the batch process control of VCSEL fabrication. It is found that, in the order of importance, the following parameters will contribute to the fluctuation in the final aperture size: (1) Al composition (can be completely eliminated if AlAs is used); (2) oxidation temperature; (3) initial mesa size; (4) oxidation time; (5) AlGaAs layer thickness; and (6) spacing between two devices.
Figure 1: Master equation used to model the thermal oxidation of AlGaAs. Rho is the oxidant concentration, D is the diffusion coefficient, and v results from the oxidant transport blockade via several possible mechanisms including the following: the pressure difference built up by oxidation reaction by-product out-diffusion or external forces such as surface tension at the oxide/AlGaAs interface, the internal stress in the oxide, and the oxidant diffusion path termination due to formation of porous AlOxHy and the stuffing of pores in the oxide with As containing reaction by-products.
Figure 2: Schematics of thermal oxidation of AlGaAs. (a) Cross-sectional view. (b) Top view for lateral oxidation in a straight mesa configuration. (c) Top view lateral oxidation in a circular mesa configuration.