Aberration-aware robust mask design with level-set-based inverse lithography

Optical proximity correction (OPC) is one of the most widely used Resolution Enhancement Techniques (RET) in mask designs. Conventional OPC is often designed for a set of nominal imaging parameters without giving sufficient attention to the process variations caused by aspherical wavefront leaving the exit pupil of the lithography system. As a result, the mask designed may deliver poor performance with process variations. In this paper, we first describe how a general point spread function (PSF) with wave aberration can degrade the output pattern quality, and then show how the wave aberration function can be incorporated into an inverse imaging framework for robust input mask pattern design against aberrations. A level-set-based time-dependent model can then be applied to solve it with appropriate finite difference schemes. The optimal mask gives more robust performance against either one specific type of aberration or a combination of different types of aberrations.

[1]  Edmund Y. Lam,et al.  The nebulous hotspot and algorithm variability , 2009, Advanced Lithography.

[2]  Ngai Wong,et al.  Level-set-based inverse lithography for photomask synthesis. , 2009, Optics express.

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

[4]  Peter Dirksen,et al.  Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  Christophe Pierrat,et al.  Automated optical proximity correction: a rules-based approach , 1994, Advanced Lithography.

[6]  David K. Smith,et al.  Mathematical Programming: Theory and Algorithms , 1986 .

[7]  Edmund Y. Lam,et al.  Inverse image problem of designing phase shifting masks in optical lithography , 2008, 2008 15th IEEE International Conference on Image Processing.

[8]  Avideh Zakhor,et al.  Optimal binary image design for optical lithography , 1990, Advanced Lithography.

[9]  Hiroyoshi Tanabe,et al.  Fast optical proximity correction: analytical method , 1995, Advanced Lithography.

[10]  Ki-Ho Baik,et al.  Validation of inverse lithography technology (ILT) and its adaptive SRAF at advanced technology nodes , 2008, SPIE Advanced Lithography.

[11]  Bernard Roelof Andries Nijboer.  The diffraction theory of aberrations , 1942 .

[12]  Timothy A. Brunner,et al.  Characterization of linewidth variation , 2000, Advanced Lithography.

[13]  Avideh Zakhor,et al.  Binary and phase-shifting image design for optical lithography , 1991, Other Conferences.

[14]  Edmund Y. Lam,et al.  Regularization of inverse photomask synthesis to enhance manufacturability , 2009, Lithography Asia.

[15]  Peyman Milanfar,et al.  Prewarping techniques in imaging: applications in nanotechnology and biotechnology , 2005, IS&T/SPIE Electronic Imaging.

[16]  Michel Minoux,et al.  Mathematical Programming , 1986 .

[17]  Stanley H. Chan,et al.  Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography. , 2008, Optics express.

[18]  Amyn Poonawala,et al.  Mask Design for Optical Microlithography—An Inverse Imaging Problem , 2007, IEEE Transactions on Image Processing.

[19]  R. Noll.  Zernike polynomials and atmospheric turbulence , 1976 .

[20]  Edmund Y. Lam,et al.  Inverse synthesis of phase-shifting mask for optical lithography , 2007 .

[21]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[22]  Edmund Y. Lam,et al.  Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis , 2010 .

[23]  A. Wong.  Optical Imaging in Projection Microlithography , 2005 .

[24]  Linyong Pang,et al.  Inverse lithography technology (ILT): a natural solution for model-based SRAF at 45-nm and 32-nm , 2007, Photomask Japan.

[25]  Edmund Y. Lam,et al.  Computation lithography: virtual reality and virtual virtuality. , 2009, Optics express.