Special Section on Computational Lithography

Optimal approximation of transfer cross coefficient for system transmission based on tensorial signal methods

[+] Author Affiliations
Romuald Sabatier

Institut Fresnel, École Centrale Marseille-CNRS 6133, Marseille 13397, France and STMicroelectronics, Rousset, France

Caroline Fossati

Institut Fresnel, École Centrale Marseille-CNRS 6133, Marseille 13397, France

Salah Bourennane

Institut Fresnel, École Centrale Marseille-CNRS 6133, Marseille 13397, France

Antonio Di Giacomo

STMicroelectronics, Rousset, France

J. Micro/Nanolith. MEMS MOEMS. 8(3), 031407 (August 28, 2009). doi:10.1117/1.3213237
History: Received December 09, 2008; Revised July 10, 2009; Accepted July 16, 2009; Published August 28, 2009
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In photolithography, aerial image simulation of the mask has become mandatory. To compute aerial images, transmission cross coefficients (TCCs), drawn from Hopkins optical system transmission function, are arranged as a four-way array (four-entry table) called a fourth-order tensor. To estimate the kernels using the linear algebra–based methods, the existing algorithms unfold this tensor into a matrix. To reduce the computational load, this matrix is approximated by lower rank order matrix owing to the singular value decomposition (SVD). We propose to adopt the multilinear algebra tools to the tensor of TCC values in order to keep this data tensor as a whole entity. For runtime improvement, we use a fixed point algorithm to estimate only the needed eigenvectors. To estimate the optimal number of needed eigenvectors, two well-known criteria of signal processing and information theory are adopted. This tensorial approach leads to a fast and accurate algorithm to compute aerial images.

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© 2009 Society of Photo-Optical Instrumentation Engineers

Topics

Matrices ; Algorithms

Citation

Romuald Sabatier ; Caroline Fossati ; Salah Bourennane and Antonio Di Giacomo
"Optimal approximation of transfer cross coefficient for system transmission based on tensorial signal methods", J. Micro/Nanolith. MEMS MOEMS. 8(3), 031407 (August 28, 2009). ; http://dx.doi.org/10.1117/1.3213237


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