The effects of diffusion coefficient on the etching process of sacrificial oxide layers

The etching rate in hydrofluoric acid (HF) of a sacrificial oxide layer decreases during the extended etching process, as indicated by experiments with temperature from 298 to 308 K at different HF concentration. Existing models indicate that the etching solution's concentration at the etching front decreases during extended etching since the diffusion distance of HF from the source of the solution increases, resulting in the decrease of the etching rate. However, it is found that the measured etching rates do not decrease as seriously as predicted by the models. The difference of etching rate between the experiments and the model can reach as high as 30% for extended etching process. A modified model is proposed to explain this phenomenon by considering the diffusion coefficient of HF as a function of concentration in the solution. In the modified model, the decrease of the HF concentration causes the increase of the HF diffusion coefficient, which will partly compensate the decrease of the concentration caused by the long diffusion distance. In addition, the diffusion coefficient as a function of temperature is also included in the modified model. It is found that the modified model matches well the experimental data.