Global source optimization for MEEF and OPE

Matsui, Ryota; Noda, Tomoya; Aoyama, Hajime; Kita, Naonori; Matsuyama, Tomoyuki; Flagello, Donis G.

doi:10.1117/12.2008267

Cited by 8 publications

(8 citation statements)

References 10 publications

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“…The use of the controllable illumination pupil consisting of numerous point sources may become popular in conventional imaging systems such as microscopes; this approach has already been realized in advanced lithography systems [24][25][26][27][28]. We believe that our basic theory can be utilized to determine the basic specifications for the controllable illumination pupil from the viewpoint of spatial coherence.…”

Section: B Possible Application Of Our Approach For Determining Basimentioning

confidence: 96%

“…Let us assume that the illumination pupil consists of N point sources. In this regard, we remark that, to enhance the imaging properties in advanced micro-photolithography, the complex free-form illumination shape has been utilized recently [24][25][26][27][28]. The illumination pupil can comprise more than 10,000 deg of point sources.…”

Section: Intensity Matrix: Case Of N Point Sourcesmentioning

confidence: 96%

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Analytical solution for Gamo entropy under spatially partial coherent illumination

Yashiki¹

2015

J. Opt. Soc. Am. A

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We present a methodology for obtaining the analytical solution of the Gamo entropy, defined by the intensity matrix proposed by Gamo [J. Opt. Soc. Am.47, 976 (1957)JOSAAH0030-394110.1364/JOSA.47.000976]. The matrix, which consists of numerous image amplitudes at all the sampling points of the entire imaging plane, is generally infinite-dimensional. The essence of our theory is that the computational difficulties arising because of the infinite-dimensionality are avoided by introducing the inner products of two image amplitudes. The integral in continuous space plays the role of a buffer against the infinite-dimensionality. The validity of the approach is confirmed by comparing our analytical solution and Yamazoe's numerical simulations [J. Opt. Soc. Am. A28, 448 (2011)JOAOD60740-323210.1364/JOSAA.28.000448].

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Section: B Possible Application Of Our Approach For Determining Basimentioning

confidence: 96%

Section: Intensity Matrix: Case Of N Point Sourcesmentioning

confidence: 96%

Analytical solution for Gamo entropy under spatially partial coherent illumination

Yashiki¹

2015

J. Opt. Soc. Am. A

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“…The typical controllable parameters for this measurement include the illumination pupils, one-dimensional measurement patterns, and orientations of measurement patterns. To enhance the imaging quality of the latest ArF exposure apparatus, the illumination pupil consists of more than 10,000 deg of freedom, which are known as intelligent illuminator units by the Nikon Corporation [19][20][21][22][23]. Thus, the free-form shape of nonsymmetric illumination is available for this design.…”

Section: Measurement Of Full Wavefront Aberration a Simultaneous Linmentioning

confidence: 98%

Parity decomposition theory of full wavefront aberration measurement using the intensity differences of aerial images in microlithography

Yashiki¹

2015

Appl. Opt.

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The theory of full wavefront aberration measurements is developed using the intensity differences of aerial images, which are the projected images of one-dimensional measurement patterns consisting of single- or multibars. The key concept is the parity decomposition about the optical axis for two optical components: illumination pupil and wavefront aberration. An additional mathematical treatment, which is a perturbative approach with regard to aberration, is applied to the partially coherent imaging formula. The intensity difference of the two peaks has terms that are linear to the odd and even aberration with rigorously canceled squared aberration terms. The full wavefront aberration measurement is realized from simultaneous linear equations about the intensity difference. The validity of this approach is numerically confirmed under practical lithography conditions.

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“…In these methods, the pattern errors, as a generally utilized merit function in the iteration procedure, can be defined by calculating the cumulative sum of the difference between the resist pattern (RP) and the desired image with point-by-point. Moreover, multifarious merit functions have been employed to evaluate the simulation results and convergence effect in SO methods, such as the edge-placement errors, normalizedimage log slope, and mask-error enhancement factor [19], [21], [22]. Thus, the threshold and the sigmoid functions can be employed to approximately represent the layout pattern after the resist effect is exerted on the wafer surface [23], [24].…”

Section: Introductionmentioning

confidence: 99%

Inverse Lithography Source Optimization via Particle Swarm Optimization and Genetic Combined Algorithm

et al. 2023

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Inverse lithography technologies (ILTs) are critical for improving the imaging performance of lithography in advanced technology nodes. Pixel-based source optimization (SO), as an efficient part of ILTs, can be implemented via heuristic approaches to achieve high-performance lithographic imaging. In this paper, a SO approach based on a combination of the particle-swarm optimization and genetic algorithms (PSO-GA) is proposed to determine the optimal intensity distribution of the source via iterations. The pixelated source can be decoded into the optimized variables of the merit functions in the SO model. The proposed PSO-GA algorithm, as a highefficiency hybrid algorithm, can transform the discrete SO problem into the optimal search solution for the merit function, thereby inversely enhancing the lithographic-imaging performance. In the forward-imaging model in the lithography, the extraction of the mask's effective diffraction spectrum is implemented to calculate the layout of resist patterns. The simulation results highlight the superior performance of the proposed approach in achieving pixelated SO over the traditional GA and PSO algorithm in terms of convergence capacity.

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Global source optimization for MEEF and OPE

Cited by 8 publications

References 10 publications

Analytical solution for Gamo entropy under spatially partial coherent illumination

Analytical solution for Gamo entropy under spatially partial coherent illumination

Parity decomposition theory of full wavefront aberration measurement using the intensity differences of aerial images in microlithography

Inverse Lithography Source Optimization via Particle Swarm Optimization and Genetic Combined Algorithm

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