Analytical prediction of out-of-plane deflection of photomask protective membrane

[Display omitted] •Pellicle membranes improve wafer yield and protect photomask from accidental damage.•Deflection of pellicle membrane subjected to a distributed load is predicted.•Fringe reflectometry is adopted to measure the 3D topographies of membranes.•A simple and accurate approach is used to predict the rigidity of pellicle membranes. In semiconductor manufacturing, photomask protective membranes (also known as pellicles) play a critical role in minimizing chip defects and improving the wafer yield. The pellicle quality is generally quantified by its rigidity. Accordingly, the present study proposes an analytical model based on thin plate theory for predicting the out-of-plane deflection of photomask protective membranes with known dimensions and material parameters as a function of the external distributed load. Experiments are then performed using a fringe reflectometry system to measure the three-dimensional topographies of protective membranes with different thicknesses and materials under the effects of an external load applied at the mid-point position. Based on the experimental results, linear regression equations are derived to predict the out-of-plane deflection of the membrane as a function of the magnitude of the external load. Finally, the proposed analytical model is used to predict the rigidity of three different kinds of membranes.