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 ﬁeld 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 eﬀectiveness 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 ﬂuctuation.
With ever decreasing of feature sizes, the measurement of lens aberration has become increasingly important for the
imaging quality control of projection lithographic tools. In this paper, we propose a method for in-situ aberration
measurement based on a quadratic aberration model, which represents the bilinear relationship between the aerial image
intensity and the Zernike coefficients. The concept of cross triple correlation (CTC) is introduced, so that the quadratic
model can be calculated in a fast speed with the help of fast Fourier transform (FFT). We then develop a method for the
Zernike coefficients characterization using the genetic optimization algorithm from the through focus aerial images of a
nine contacts mask pattern. Simulation results demonstrate that this method is simple to implement and will have
potential applications for in-situ metrology of lens aberration in lithographic tools.