Determination of mask opening size in creating a fluid hole on brittle material by double-side sand blasting

In creating a hole on brittle materials by double-side sand blasting, the rebounding sand particle flux during the process may result in underetching at the edge of the mask opening, and leads to a larger sized fluid hole than the desired one. Determination of the correct mask opening size was made mainly by trial and error in the past. In this paper, relationships between the mask opening size and desired size of a hole on both the front and the back sides of the substrate are derived. For the front side, by taking into account the underetching effect, an equation is derived based on the kinetic energy theory. For the back side, there is negligible rebounding sand particles, and the mask opening size is set to be equal to the desired size of the hole. Experiments were conducted to verify the derived relationships. It is found that the measured sizes of the eroded holes on both the front and the back sides of the wafer substrate are distributed normally. The desired hole sizes deviate slightly from the median of a normal distribution curve, and the maximum predicted errors are 2.4% and 3.0% for front side and the back side sand blasting, respectively. The very satisfactory result together with ANOVA and test of homogeneity of variance of the predicted errors for various hole size shows that the derived relationships is applicable for determination of the mask opening size in the sand blasting process.