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.

在半导体制造中，光掩模保护膜（也称为防护膜）在最小化芯片缺陷和提高晶圆产量方面起着至关重要的作用。防护膜质量通常通过其刚性来量化。因此，本研究提出了一种基于薄板理论的分析模型，用于预测具有已知尺寸和材料参数的光掩模保护膜的面外偏转，该偏转是外部分布载荷的函数。然后，使用条纹反射测量系统进行实验，以在中点位置施加的外部载荷的作用下，测量具有不同厚度和材料的保护膜的三维形貌。根据实验结果，推导出线性回归方程，以预测膜的平面外挠度作为外部载荷大小的函数。最后，所提出的分析模型用于预测三种不同类型膜的刚度。