Fast calculation of images for high numerical aperture lithography

Rosenbluth, Alan E.; Gallatin, Gregg M.; Gordon, Ronald L.; Hinsberg, William D.; Hoffnagle, John A.; Houle, Frances A.; Lai, Kafai; Львов, А. А.; Sanchez, Martha I.; Seong, Nakgeuon

doi:10.1117/12.537716

Cited by 19 publications

(17 citation statements)

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“…Eq. [12] states the intuitively plausible result that when the planewave components are uniformly distributed in solid angle Ω, the field that propagates outward in some direction r will become equal to the amplitude of the particular planewave component ( ) A r which is propagating in that same direction, phase-shifted across the propagation distance (with additional π/2 quadrature phase shift), and attenuated with a 1/R 2 intensity scaling.…”

Section: Inclination Factor In the Plane Wave Spectrummentioning

confidence: 99%

See 1 more Smart Citation

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: 99%

“…refs. [8][9][10][11][12][13], the source integration is carried out in the direction cosine units α S , β S of the eq. [1] grid (or in pupil coordinates where the direction cosines are simply scaled by a factor of NA), with the source intensities being treated as the square of the illuminating E-field.…”

Section: Generic Imaging Model In Lithographymentioning

confidence: 99%

Radiometric consistency in source specifications for lithography

Rosenbluth¹,

Azpiroz

Lai

et al. 2008

Optical Microlithography XXI

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“…Another issue is the runtime issue itself, including model build time and OPC run time. It has been shown that no overhead is needed in the OPC run time for the inclusion of Jones matrix pupils [18]. All the Jones matrix pupil information is absorbed in the TCC and thereby in the SOCS kernels.…”

Section: Nm M1 Wet Jones Pupilmentioning

confidence: 99%

Modeling polarization for hyper-NA lithography tools and masks

Lai¹,

Rosenbluth²,

Han³

et al. 2007

SPIE Proceedings

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We present a comprehensive modeling study of polarization effects for the whole optical chain including exposure tool and mask, with strong emphasis on the impact of the Jones Matrix of the projection lens. First we start with the basic of polarization and then the polarization effect of each components of the optical chain will be discussed. Components investigated are source polarization, rigorous EMF effect, mask blank birefringence, pellicle effect and projection lens. We also focus on comparing the relative merits of different types of representation of Jones matrix of the projection lens and outlined ways to decompose the Jones Matrix. Methodologies such as Pauli matrix, PQM, Jones-Zernike expansion and IPS-Zernike expansion are among the ones investigated. The polarization impact on lithography and OPC on realistic 45nm and 32nm node process levels is discussed. Issues in OPC modeling with Jones Matrix is highlighted. Concerns regarding the standardization of the implementation of Jones Matrix in the lithography community are considered and a standard has been proposed and received wide acceptance. Last we discuss the challenge of using polarization and some novel ideas to deal with polarization in hyper NA era. Throughout the paper the resist component is not included so as to isolate the effect of resist from that of the other components. INTRODUCTIONThe advent of optical immersion lithography has dissolved the NA=1 barrier and is carving novel pathways for advanced semiconductor manufacturing. Nowadays hyper-NA (NA >1) immersion lithography is considered to be a strong contender for device manufacturing at the 45nm and 32nm nodes. The use of water immersion enables a further increase in resolution and is strongly competing with the option of an early wavelength transition to EUV.

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“…( Figure 2) As we have shown in a previous paper 2 , the sum of the path variations along split rays is zero. This allows us to treat split rays as a single recombined ray after every element 2,7 . The polarization of a ray in the entrance pupil can be propagated to the exit pupil using the matrix The image produced by a lens with birefringence can be computed using conventional vector image calculation methods as developed by Flagello et al 4,5 in the early '90s.…”

Section: Birefringence Ray Spliting and Image Calculationmentioning

confidence: 99%

“…Therefore image calculations for 157nm optics need to include birefringence effects to generate valid results. Birefringence can be accounted for using a matrix representation of the lens pupil 2,7 . This is different from conventional single pupil scalar aberration calculations.…”

Section: Introductionmentioning

confidence: 99%

Assessing the impact of intrinsic birefringence on 157-nm lithography

Seong¹,

Lai²,

Rosenbluth

et al. 2004

SPIE Proceedings

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Birefringence can be represented using the matrix generated by multiplying together Jones matrices for the separate lens elements. Conventional vector imaging methods, which use orthogonal electric field components in resist combined to yield the intensity, can be extended to handle this matrix representation of the optical pupil. The mean amplitude ratio of the off-diagonal elements in the matrix pupil is shown to correspond quite well to the birefringence-induced CD error.

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Fast calculation of images for high numerical aperture lithography

Cited by 19 publications

References 0 publications

Radiometric consistency in source specifications for lithography

Radiometric consistency in source specifications for lithography

Modeling polarization for hyper-NA lithography tools and masks

Assessing the impact of intrinsic birefringence on 157-nm lithography

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