Predictor of thermal aberrations via particle filter for online compensation

Abstract. In optical lithography, aberrations induced by lens heating effects of a projection lens lead to degradation of imaging quality. In order to compensate for thermal aberrations, it is crucial to apply an accurate method for thermal aberration prediction. An effective and accurate method for thermal aberration prediction is proposed. A double exponential model is modified in respect of the timing of exposure tools, and a particle filter is used to adjust the double exponential model. Parameters of the model are updated recursively pursuant to the aberration data measured during the exchange of wafers. The updated model is used to predict thermal aberrations during the following exposure of wafers. The performance of the algorithm is evaluated by the simulation of a projection lens for argon fluoride lithography. Simulation results show that predictive errors of primary defocus and astigmatism are significantly reduced, and the mean value of wavefront error in the whole field of view is reduced by about 30% in a vertical line/space pattern. The proposed method is easily adaptable to different types of aberration measurement error.

[1]  I-Chung Chang,et al.  Lens-heating-induced focus drift of I-line step and scan: correction and control in a manufacturing environment , 2001, SPIE Advanced Lithography.

[2]  Siew Ing Yet,et al.  FAST-LH: a manufacturing-environmental friendly method of lens heating monitoring , 2009, Lithography Asia.

[3]  Frank Staals,et al.  Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 NA immersion scanner , 2011, Advanced Lithography.

[4]  Nicholas G. Polson,et al.  A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling , 1992 .

[5]  Sikun Li,et al.  Modeling and optimization of lens heating effect for lithographic projector , 2018 .

[6]  Yuanting Cui.  Fine-tune lens-heating-induced focus drift with different process and illumination settings , 2001, SPIE Advanced Lithography.

[7]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[8]  Joerg Bischoff,et al.  Simulations on step-and-scan optical lithography , 1994, Advanced Lithography.

[9]  Alfred Kwok-Kit Wong,et al.  Resolution enhancement techniques in optical lithography , 2001 .

[10]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[11]  Tomoyuki Matsuyama,et al.  Thermal aberration control in projection lens , 2008, SPIE Advanced Lithography.

[12]  S. Weiland,et al.  Lens Heating Induced Aberration Prediction via Nonlinear Kalman Filters , 2012, IEEE Transactions on Semiconductor Manufacturing.

[13]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[14]  Jan Baselmans,et al.  Full optical column characterization of DUV lithographic projection tools , 2004, SPIE Advanced Lithography.

[15]  Ki-Ho Baik,et al.  Lens heating impact analysis and controls for critical device layers by computational method , 2013, Advanced Lithography.

[16]  Scott Halle,et al.  Lens heating challenges for negative tone develop layers with freeform illumination: a comparative study of experimental vs. simulated results , 2012, Advanced Lithography.

[17]  Takashi Sukegawa,et al.  Advanced aberration control in projection optics for double patterning , 2009, Advanced Lithography.

[18]  Tomoyuki Matsuyama,et al.  An aberration control of projection optics for multi-patterning lithography , 2011, Advanced Lithography.

[19]  Changcheng Yao,et al.  Simulation Research on the Thermal Effects in Dipolar Illuminated Lithography , 2016 .

[20]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .