Numerical Solution of Optimal Design Problems for Binary Gratings

Elschner, Johannes; Schmidt, G.

doi:10.1006/jcph.1998.6071

Cited by 44 publications

(25 citation statements)

References 28 publications

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“…There is still the necessity to cross-check the resulting designs with a more exact, that is an electromagnetic-theory-based computational method, as the risk of falsely predicting an important specification can be significantly reduced in this way. In order to combine the benefits of scalar and electromagnetic diffraction theories, one can think of direct electromagnetic-theory based post-optimization of gratings as for example in [20] with starting values obtained from (fast) scalar methods, or of using an electromagnetic-theory-based propagation operator within the algorithms discussed in this paper (B.H. Kleemann 2004, private communication).…”

Section: Discussionmentioning

confidence: 99%

Theoretical and experimental properties of a binary linear beam-splitting element with a large fan angle

Ferstl¹,

Hermerschmidt²,

Dias³

et al. 2004

Journal of Modern Optics

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Diffractive beam-splitting elements with a large fan angle of about 45° were realized as binary phase elements for application in a commercial laser device operating at the wavelength of 635 nm. The fan-out elements designated to split a laser beam into a line of 43 equal power spots were fabricated in silica by means of microstructuring techniques and replicated in acrylate by ultraviolet curing. Two different gratings have been designed using scalar unidirectional iterative methods, based on the iterative discrete on-axis and on the direct binary search algorithms. The optical properties of both gratings obtained by these scalar methods were compared with simulations based on rigorous electromagnetic calculations in order to verify and control the application-relevant specifications. The experimentally measured optical performance of the replicated fan-out elements is in good agreement with the theoretical predictions. The complete procedure for realizing the linear beam splitters, that is the design method, the fabrication of the master, and the replication process, will be presented. The optical properties and characteristic data of the replicas will be compared with scalar simulations as well as rigorous calculations; the results will be discussed

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Section: Discussionmentioning

confidence: 99%

Theoretical and experimental properties of a binary linear beam-splitting element with a large fan angle

Ferstl¹,

Hermerschmidt²,

Dias³

et al. 2004

Journal of Modern Optics

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“…However, the FE method described there converges in context with TM polarization only for certain special materials. This problem is solved by Elschner and Schmidt at the WIAS by an improved formulation FEM procedure [9,10,11]. Thus, stability and convergence for both cases of polarization and almost arbitrary materials are obtained.…”

Section: The Finite Element Methodsmentioning

confidence: 99%

Improved optical linewidth measurement by means of alternating dark field illumination and model-based evaluation

2005

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The dark field microscopy method with alternating grazing incidence illumination (AGID), developed at the PTB, offers the possibility to measure structures with lateral dimensions below the classical resolution limit. Moreover, this method offers the advantage of better dimensional measurements of phase objects, since higher contrasts compared to conventional bright field microscopy are obtained. As an example, the AGID-method can be used for the determination of linewidths on photomasks or wafers. A newly developed prototype measuring system based on the alternating dark field illumination is be presented. This system uses two diode lasers with the wavelength 374 nm as lightsources. This new method is be compared with conventional bright field microscopy. The distribution of intensity of an image of a given structure depends on the illumination and the geometrical parameters as well on the optical parameters. In particular the dependence on the polarization and the angle of incidence of the illumination is discussed. For modeling of the intensity distribution in the image we are using two different rigorous diffraction theories. On the one hand we use the rigorous coupled wave analysis (RCWA) method for the calculation of the diffracted electric and magnetic fields and on the other hand the finite elements (FEM) method. These two models are used for determining the linewidth from measurement data of the new prototype system. It will be shown that the newly developed system is a suitable tool for optical linewidth measurements which represents a meaningful addition to existing optical linewidth measurement systems.

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“…Here the Helmholtz equations are solved for finite homogenous elements with continuous boundary conditions. The program package DiPoG from the Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany is based on this method, which originally has been formulated by of Bao et al [9] and been improved by the authors of DiPoG, Elschner, Schmidt, Hinder, and Rathsfeld [10,11,12]. DiPoG uses a different approximation to the real geometrical structures than Microsim.…”

Section: The Finite Element Methodsmentioning

confidence: 99%

Investigation and evaluation of scatterometric CD metrology methods

Wurm

Bodermann

Mirandé

2005

Nano- And Micro-Metrology

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With decreasing critical dimensions (CD) on lithography masks, increasing demands on CD metrology techniques come along. Already today the results of the three standard methods for CD measurements currently used, atomic force microscopy (AFM), scanning electron microscopy (SEM), and optical microscopy, typically do not yield the same results. This is because of, e.g. incomplete knowledge of the material parameters, insufficient modelling accuracy orespecially in the case of optical microscopy -insufficient resolution. With decreasing CDs these systematic differences increase. The need on new cross-calibration strategies arises.Non-imaging metrology methods like scatterometry as non destructive, non diffraction limited, fast optical methods offer access to the geometrical parameters of periodic structures like e.g. top and bottom CD, pitch, side-wall angle, line height, or roughness. Therefore, these methods provide independently achieved additional information that can be used for cross-calibration.At the PTB two scatterometers are in use (VIS @ λ=633 nm and EUV @ λ=13.55 nm). A third device (DUV @ λ=193 nm) is under construction. It will offer a wide spectrum of measuring principles like scatterometry, ellipsometric scatterometry, reflectometry, polarisation reflectometry, and using a broadband light source spectroscopic ellipsometry and spectroscopic reflectometry.For simulation and modelling of the intensity distribution of the diffraction pattern two programs based on the rigorous coupled-wave analysis (RCWA) method and a finite element method (FEM), respectively are used. The program features will be illustrated. A comparison of the simulations with the results achieved with the scatterometers on different types of lithography masks (chrome on glass, EUV-masks) will be presented as well.

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Numerical Solution of Optimal Design Problems for Binary Gratings

Cited by 44 publications

References 28 publications

Theoretical and experimental properties of a binary linear beam-splitting element with a large fan angle

Theoretical and experimental properties of a binary linear beam-splitting element with a large fan angle

Improved optical linewidth measurement by means of alternating dark field illumination and model-based evaluation

Investigation and evaluation of scatterometric CD metrology methods

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