Incorporating photomask shape uncertainty in computational lithography

Abstract

The lithographic performance of a photomask is sensitive to shape uncertainty caused by manufacturing and measurement errors. This work proposes incorporating the photomask shape uncertainty in computational lithography such as inverse lithography. The shape uncertainty of the photomask is quantitatively modeled as a random ?eld in a level-set method framework. With this, the shape uncertainty can be characterized by several parameters, making it computationally tractable to be incorporated in inverse lithography technique (ILT). Simulations are conducted to show the eâ¬ectiveness of using this method to represent various kinds of shape variations. It is also demonstrated that incorporating the shape variation in ILT can reduce the mask error enhancement factor (MEEF) values of the optimized patterns, and improve the robustness of imaging performance against mask shape ?uctuation

Impact of photomask shape uncertainties on computational lithography

“…In this paper, we propose a random field approach to analyze the impact of mask shape uncertainties on inverse lithography solutions [9]. The random field approach is used in topographic optimization with geometrical uncertainty problem, which aims to derive a shape to minimize an objective function, similar to the mask optimization in pixel-based inverse lithography [10].…”