Dr. Kehan Tian Profile

Dr. Kehan Tian

at IBM Corp

SPIE Involvement:

Author

Publications (14)

Proceedings Article | 13 March 2012 Paper

Fast source independent estimation of lithographic difficulty supporting large scale source optimization

David DeMaris, Maria Gabrani, Sankha Sarkar, Nathalie Casati, Ronald Luijten, Kafai Lai, Kehan Tian

Proceedings Volume 8326, 832614 (2012) https://doi.org/10.1117/12.916433

KEYWORDS: Optical proximity correction, Lithography, Metals, Source mask optimization, Diffraction, Image quality, Modulation transfer functions, SRAF, Resolution enhancement technologies, Spatial frequencies

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Proceedings Article | 5 April 2011 Paper

Design specific joint optimization of masks and sources on a very large scale

K. Lai, M. Gabrani, D. Demaris, N. Casati, A. Torres, S. Sarkar, P. Strenski, S. Bagheri, D. Scarpazza, A. Rosenbluth, D. Melville, A. Wächter, J. Lee, V. Austel, M. Szeto-Millstone, K. Tian, F. Barahona, T. Inoue, M. Sakamoto

Proceedings Volume 7973, 797308 (2011) https://doi.org/10.1117/12.879787

KEYWORDS: Source mask optimization, Photomasks, Lithography, Standards development, Algorithm development, Resolution enhancement technologies, Diffraction, Visualization, Photovoltaics

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Proceedings Article | 23 March 2011 Paper

Applicability of global source mask optimization to 22/20nm node and beyond

Kehan Tian, Moutaz Fakhry, Aasutosh Dave, Alexander Tritchkov, Jaione Tirapu-Azpiroz, Alan Rosenbluth, David Melville, Masaharu Sakamoto, Tadanobu Inoue, Scott Mansfield, Alexander Wei, Young Kim, Bruce Durgan, Kostas Adam, Gabriel Berger, Gandharv Bhatara, Jason Meiring, Henning Haffner, Byung-Sung Kim

Proceedings Volume 7973, 79730C (2011) https://doi.org/10.1117/12.879703

KEYWORDS: Source mask optimization, Photomasks, Resolution enhancement technologies, Optical proximity correction, Tolerancing, Optical lithography, SRAF, Image processing, Lithography, Semiconducting wafers

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Proceedings Article | 14 March 2011 Paper

Qualification, monitoring, and integration into a production environment of the world's first fully programmable illuminator

Gregory McIntyre, Daniel Corliss, Remco Groenendijk, Rene Carpaij, Ton van Niftrik, Guillaume Landie, Takao Tamura, Thomas Pepin, James Waddell, Jerry Woods, Chris Robinson, Kehan Tian, Richard Johnson, Scott Halle, Ryoung-Han Kim, Erin Mclellan, Hirokazu Kato, Anthony Scaduto, Carl Maier, Matt Colburn

Proceedings Volume 7973, 797306 (2011) https://doi.org/10.1117/12.879483

KEYWORDS: Mirrors, Diffractive optical elements, Fiber optic illuminators, Scanners, Optical proximity correction, Lithography, Nanotechnology, Manufacturing, Glasses, Environmental monitoring

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Proceedings Article | 16 March 2010 Paper

Demonstrating the benefits of source-mask optimization and enabling technologies through experiment and simulations

David Melville, Alan Rosenbluth, Kehan Tian, Kafai Lai, Saeed Bagheri, Jaione Tirapu-Azpiroz, Jason Meiring, Scott Halle, Greg McIntyre, Tom Faure, Daniel Corliss, Azalia Krasnoperova, Lei Zhuang, Phil Strenski, Andreas Waechter, Laszlo Ladanyi, Francisco Barahona, Daniele Scarpazza, Jon Lee, Tadanobu Inoue, Masaharu Sakamoto, Hidemasa Muta, Alfred Wagner, Geoffrey Burr, Young Kim, Emily Gallagher, Mike Hibbs, Alexander Tritchkov, Yuri Granik, Moutaz Fakhry, Kostas Adam, Gabriel Berger, Michael Lam, Aasutosh Dave, Nick Cobb

Proceedings Volume 7640, 764006 (2010) https://doi.org/10.1117/12.846716

KEYWORDS: Source mask optimization, Photomasks, Metals, Lithography, Optical proximity correction, Line edge roughness, Resolution enhancement technologies, Diffractive optical elements, Semiconducting wafers, Scanning electron microscopy

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Proceedings Article | 16 March 2009 Paper

Benefits and trade-offs of global source optimization in optical lithography

Kehan Tian, Azalia Krasnoperova, David Melville, Alan Rosenbluth, Dario Gil, Jaione Tirapu-Azpiroz, Kafai Lai, Saeed Bagheri, Chia-chen Chen, Bradley Morgenfeld

Proceedings Volume 7274, 72740C (2009) https://doi.org/10.1117/12.814305

KEYWORDS: Diffraction, Printing, Source mask optimization, Optical lithography, Resolution enhancement technologies, Photomasks, Semiconducting wafers, Lithographic illumination, Lithography, Manufacturing

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Proceedings Article | 16 March 2009 Paper

Intensive optimization of masks and sources for 22nm lithography

Alan Rosenbluth, David Melville, Kehan Tian, Saeed Bagheri, Jaione Tirapu-Azpiroz, Kafai Lai, Andreas Waechter, Tadanobu Inoue, Laszlo Ladanyi, Francisco Barahona, Katya Scheinberg, Masaharu Sakamoto, Hidemasa Muta, Emily Gallagher, Tom Faure, Michael Hibbs, Alexander Tritchkov, Yuri Granik

Proceedings Volume 7274, 727409 (2009) https://doi.org/10.1117/12.814844

KEYWORDS: Photomasks, Source mask optimization, Lithography, Optimization (mathematics), Wavefronts, Manufacturing, Chemical elements, Fiber optic illuminators, Image processing, Optics manufacturing

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Proceedings Article | 16 March 2009 Paper

Experimental result and simulation analysis for the use of pixelated illumination from source mask optimization for 22nm logic lithography process

Kafai Lai, Alan Rosenbluth, Saeed Bagheri, John Hoffnagle, Kehan Tian, David Melville, Jaione Tirapu-Azpiroz, Moutaz Fakhry, Young Kim, Scott Halle, Greg McIntyre, Alfred Wagner, Geoffrey Burr, Martin Burkhardt, Daniel Corliss, Emily Gallagher, Tom Faure, Michael Hibbs, Donis Flagello, Joerg Zimmermann, Bernhard Kneer, Frank Rohmund, Frank Hartung, Christoph Hennerkes, Manfred Maul, Robert Kazinczi, Andre Engelen, Rene Carpaij, Remco Groenendijk, Joost Hageman, Carsten Russ

Proceedings Volume 7274, 72740A (2009) https://doi.org/10.1117/12.814680

KEYWORDS: Photomasks, Source mask optimization, Diffractive optical elements, Manufacturing, Lithographic illumination, Lithography, Semiconducting wafers, Photovoltaics, Polarization, Printing

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Proceedings Article | 16 March 2009 Paper

A computational technique to optimally design in-situ diffractive elements: applications to projection lithography at the resist resolution limit

Gonzalo Feijóo, Jaione Tirapu-Azpiroz, Alan Rosenbluth, Assad Oberai, Jayanth Jagalur Mohan, Kehan Tian, David Melville, Dario Gil, Kafai Lai

Proceedings Volume 7274, 72741E (2009) https://doi.org/10.1117/12.814251

KEYWORDS: Wavefronts, Holograms, Electromagnetism, Near field, Lithography, Optical design, Photomasks, Diffraction gratings, Optical lithography, Spatial frequencies

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Near-field interference lithography is a promising variant of multiple patterning in semiconductor device fabrication that can potentially extend lithographic resolution beyond the current materials-based restrictions on the Rayleigh resolution of projection systems. With H₂O as the immersion medium, non-evanescent propagation and optical design margins limit achievable pitch to approximately 0.53λ/nH₂O = 0.37λ. Non-evanescent images are constrained only by the comparatively large resist indices (typically1.7) to a pitch resolution of 0.5/nresist (typically 0.29). Near-field patterning can potentially exploit evanescent waves and thus achieve higher spatial resolutions. Customized near-field images can be achieved through the modulation of an incoming wavefront by what is essentially an in-situ hologram that has been formed in an upper layer during an initial patterned exposure. Contrast Enhancement Layer (CEL) techniques and Talbot near-field interferometry can be considered special cases of this approach. Since the technique relies on near-field interference effects to produce the required pattern on the resist, the shape of the grating and the design of the film stack play a significant role on the outcome. As a result, it is necessary to resort to full diffraction computations to properly simulate and optimize this process. The next logical advance for this technology is to systematically design the hologram and the incident wavefront which is generated from a reduction mask. This task is naturally posed as an optimization problem, where the goal is to find the set of geometric and incident wavefront parameters that yields the closest fit to a desired pattern in the resist. As the pattern becomes more complex, the number of design parameters grows, and the computational problem becomes intractable (particularly in three-dimensions) without the use of advanced numerical techniques. To treat this problem effectively, specialized numerical methods have been developed. First, gradient-based optimization techniques are used to accelerate convergence to an optimal design. To compute derivatives of the parameters, an adjoint-based method was developed. Using the adjoint technique, only two electromagnetic problems need to be solved per iteration to evaluate the cost function and all the components of the gradient vector, independent of the number of parameters in the design.

Proceedings Article | 16 March 2009 Paper

Source optimization for three-dimensional image designs through film stacks

David Melville, Alan Rosenbluth, Kehan Tian, Dario Goldfarb, Stefan Harrer, Matthew Colburn

Proceedings Volume 7274, 72743D (2009) https://doi.org/10.1117/12.814700

KEYWORDS: Photomasks, 3D image processing, Binary data, Radon, Lithography, Tolerancing, Manufacturing, 3D printing, Photoresist processing, Printing

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Proceedings Article | 11 April 2008 Paper

Radiometric consistency in source specifications for lithography

Alan Rosenbluth, Jaione Tirapu Azpiroz, Kafai Lai, Kehan Tian, David O.S. Melville, Michael Totzeck, Vladan Blahnik, Armand Koolen, Donis Flagello

Proceedings Volume 6924, 69240V (2008) https://doi.org/10.1117/12.775121

KEYWORDS: Diffraction, Photomasks, Solids, Lithography, Semiconducting wafers, Wave propagation, Apodization, Computer simulations, Fourier transforms, Thin films

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There is a surprising lack of clarity about the exact quantity that a lithographic source map should specify. Under the plausible interpretation that input source maps should tabulate radiance, one will find with standard imaging codes that simulated wafer plane source intensities appear to violate the brightness theorem. The apparent deviation (a cosine factor in the illumination pupil) represents one of many obliquity/inclination factors involved in propagation through the imaging system whose interpretation in the literature is often somewhat obscure, but which have become numerically significant in today's hyper-NA OPC applications. We show that the seeming brightness distortion in the illumination pupil arises because the customary direction-cosine gridding of this aperture yields non-uniform solid-angle subtense in the source pixels. Once the appropriate solid angle factor is included, each entry in the source map becomes proportional to the total |E|^2 that the associated pixel produces on the mask. This quantitative definition of lithographic source distributions is consistent with the plane-wave spectrum approach adopted by litho simulators, in that these simulators essentially propagate |E|^2 along the interfering diffraction orders from the mask input to the resist film. It can be shown using either the rigorous Franz formulation of vector diffraction theory, or an angular spectrum approach, that such an |E|^2 plane-wave weighting will provide the standard inclination factor if the source elements are incoherent and the mask model is accurate. This inclination factor is usually derived from a classical Rayleigh-Sommerfeld diffraction integral, and we show that the nominally discrepant inclination factors used by the various diffraction integrals of this class can all be made to yield the same result as the Franz formula when rigorous mask simulation is employed, and further that these cosine factors have a simple geometrical interpretation. On this basis one can then obtain for the lens as a whole the standard mask-to-wafer obliquity factor used by litho simulators. This obliquity factor is shown to express the brightness invariance theorem, making the simulator's output consistent with the brightness theorem if the source map tabulates the product of radiance and pixel solid angle, as our source definition specifies. We show by experiment that dose-to-clear data can be modeled more accurately when the correct obliquity factor is used.

Proceedings Article | 27 March 2007 Paper

Global optimization of masks, including film stack design to restore TM contrast in high NA TCC's

Alan Rosenbluth, David Melville, Kehan Tian, Kafai Lai, Nakgeuon Seong, Dirk Pfeiffer, Matthew Colburn

Proceedings Volume 6520, 65200P (2007) https://doi.org/10.1117/12.713050

KEYWORDS: Photomasks, Lithography, Source mask optimization, Optimization (mathematics), Diffraction, Reflectivity, Wavefronts, Binary data, Tolerancing, Optical proximity correction

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We provide an expanded description of the global algorithm for mask optimization introduced in our earlier papers, and discuss auxiliary optimizations that can be carried out in the problem constraints and film stack. Mask optimization tends inherently to be a problem with non-convex quadratic constraints, but for small problems we can mitigate this difficulty by exploiting specialized knowledge that applies in the lithography context. If exposure latitude is approximated as maximization of edge slope between image regions whose intensities must print with opposite polarity, we show that the solution space can be approximately divided into regions that contain at most one local minimum. Though the survey of parameter space to identify these regions requires an exhaustive grid search, this search can be accelerated using heuristics, and is not the rate-limiting step at SRAM scale or below. We recover a degree of generality by using a less simplified objective function when we actually assess the local minima. The quasi-binary specialization of lithographic targets is further exploited by searching only in the subspace formed by the dominant joint eigenvectors for dark region intensity and bright region intensity, typically reducing problem dimensionality to less than half that of the full set of frequency-domain variables (i.e. collected diffraction orders). Contrast in this subspace across the bright/dark edge will approximately reflect exposure latitude when we apply the standard fixed edge-placement constraints of lithography. However, during an exploratory stage of optimization we can define preliminary tolerances which more explicitly reflect constraints on devices, e.g. as is done with compactor codes for design migration. Our algorithm can handle vector imaging in a general way, but for the special case of unpolarized illumination and a lens having radial symmetry (but arbitrary source shape) we show that the bilinear function which describes vector interference within the film stack can be expressed in terms of three generic radial functions, enabling rapid numerical evaluation of the Hopkins kernel. By inspection these functions show that one can in principle recover classical scalar-like imaging even at high NA by exposing a very thin layer spaced above a reflective substack. The reflected image largely restores destructive interference in TM polarized fringes, if proper phasing is achieved. With an ideal reflector, the first-order azimuthal contrast loss term vanishes in all TCC components, and complete equivalence to scalar imaging is obtained in classical two-beam imaging.

Proceedings Article | 28 April 2006 Paper

Three dimensional optics for three dimensional imaging: physics, fabrication, and computation

W. Arora, W. Sun, K. Tian, P. Stellman, L. Waller, G. Barbastathis

Proceedings Volume 6188, 618810 (2006) https://doi.org/10.1117/12.665753

KEYWORDS: 3D image processing, Optical components, Nanolithography, Holograms, Photonic crystals, Dispersion, Geometrical optics, Holography, Diffraction, Optics manufacturing

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Proceedings Article | 18 October 2004 Paper

The Nanostructured Origami 3D fabrication and assembly process

George Barbastathis, Hyun Jin In, Will Arora, Tilman Buchner, Kehan Tian, Henry Smith

Proceedings Volume 5554, (2004) https://doi.org/10.1117/12.562581

KEYWORDS: Nanolithography, Nanostructuring, Silicon, Zone plates, Kinematics, Diffraction, Manufacturing, 3D modeling, Electron beam lithography, Gold

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Showing 5 of 14 publications

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