Modeling polarization for hyper-NA lithography tools and masks

Lai, Kafai; Rosenbluth, Alan E.; Han, Geng; Tirapu-Azpiroz, Jaione; Meiring, Jason; Goehnermeier, Aksel; Kneer, Bernhard; Totzeck, Michael; Winter, Laurens de; Boeij, Wim de; Kerkhof, Mark van de

doi:10.1117/12.712272

Cited by 16 publications

(11 citation statements)

References 11 publications

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“…[14] that multiplies the planewave amplitude is seen to arise from the decreased density of the angular spectrum at high obliquity. We show in the next subsection that this is essentially a foreshortening effect.…”

Section: Inclination Factor In the Plane Wave Spectrummentioning

confidence: 91%

“…eq. [14]) that this factor can be associated with the single planewave component that propagates in the observation direction.…”

Section: Essential Equivalence Of Kirchoff and Rayleigh-sommerfeld Fomentioning

confidence: 96%

“…More generally, this "field-centric" representation is appropriate for the simulation of most aspects of the lithographic process. For example, rigorous E&M solvers that calculate the mask transmission use field variables, the Jones matrices that characterize the lens 14 use the E field as input, as do the thinfilm matrices that characterize the wafer process stack, and the resist response is likewise proportional to |E| 2 .…”

Section: Generic Imaging Model In Lithographymentioning

confidence: 99%

“…[14] in conventional Fraunhofer-like form by using eq. [8] [16] which is the standard Fraunhofer result, containing the usual obliquity factor γ Object .…”

Section: Inclination Factor In the Plane Wave Spectrummentioning

confidence: 99%

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Radiometric consistency in source specifications for lithography

Rosenbluth¹,

Azpiroz

Lai

et al. 2008

Optical Microlithography XXI

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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.

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Section: Inclination Factor In the Plane Wave Spectrummentioning

confidence: 91%

“…eq. [14]) that this factor can be associated with the single planewave component that propagates in the observation direction.…”

Section: Essential Equivalence Of Kirchoff and Rayleigh-sommerfeld Fomentioning

confidence: 96%

Section: Generic Imaging Model In Lithographymentioning

confidence: 99%

“…[14] in conventional Fraunhofer-like form by using eq. [8] [16] which is the standard Fraunhofer result, containing the usual obliquity factor γ Object .…”

Section: Inclination Factor In the Plane Wave Spectrummentioning

confidence: 99%

See 2 more Smart Citations

Radiometric consistency in source specifications for lithography

Rosenbluth¹,

Azpiroz

Lai

et al. 2008

Optical Microlithography XXI

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show abstract

“…One reason is the increase of NA of the scanners and the use of lower k1 design through scaling, which requires the rigorous treatment of full vectorial effect of the optical train (light source, illuminator, mask pattern shape, mask topography, pellicle, projection lens, and resist stack), as shown in Figure 3 [18] . In EUV lithography, specific effects such as flare mask shadowing and telecentricity error need to be also included.…”

Section: Current Modeling Practicesmentioning

confidence: 99%

Review of computational lithography modeling: focusing on extending optical lithography and design-technology co-optimization

Lai

2012

Advanced Optical Technologies

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Advances in computational lithography over the last 10 years have been instrumental to the continued scaling of semiconductor devices. Competitive scaling requires two types of complementary models: fast predictive empirical models that can be used for pattern correction and verification; rigorous physical models that can be used to identify key physical effects that must be considered to ensure pattern fidelity, but are too resource intensive to use for full chip applications. Today, all computational lithography efforts such as the optical proximity correction (OPC) and the optical rules check (ORC) depend on the ability to predictively model the lithography and metrology processes. We discuss some of the current modeling practices in optics, mask, resist and etching, leading to the " Holy Grail " of predictively modeling entire patterning process which we call " virtual fab " . Extreme ultraviolet (EUV) modeling is discussed due to its potential to extend optical lithography scaling for future nodes. Modeling of novel technologies such as Diblock Copolymer patterning is also discussed to demonstrate new opportunities for continued scaling. Complexity of the " virtual fab " approach is extremely high as there are multiple dimensions in this approach. The need to overcome this complexity, by reducing the number of dimensions of the problem, is evident. Lastly, the ability to leverage lithography modeling in design co-optimization is an important element of semiconductor device scaling.

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