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Method and apparatus for computing electromagnetic scattering properties of structures and reconstruction of approximate structures

A technology of electromagnetic scattering and computational structure, applied in opto-mechanical equipment, microlithography exposure equipment, circuits, etc., can solve the problems that cannot be solved iteratively and reliably, the integral equation is highly unstable, and the condition number is high.

Active Publication Date: 2017-10-27
ASML NETHERLANDS BV
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Problems solved by technology

However, stability turns out to be a big problem, especially for evanescent modes, for example the scheme presented in [2] has been found to be highly unstable for the integral equation mentioned above, as in this paper middle Figure 16 shown in the picture
Without further measures for stability, the resulting linear system of integral equations has a very high condition number and thus cannot be reliably solved iteratively

Method used

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  • Method and apparatus for computing electromagnetic scattering properties of structures and reconstruction of approximate structures
  • Method and apparatus for computing electromagnetic scattering properties of structures and reconstruction of approximate structures
  • Method and apparatus for computing electromagnetic scattering properties of structures and reconstruction of approximate structures

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Embodiment Construction

[0066] This specification discloses one or more embodiments that incorporate the features of this invention. The disclosed embodiment(s) are merely illustrative of the invention. The scope of the invention is not limited to the disclosed embodiment(s). The invention is defined by the appended claims.

[0067] References to "one embodiment," "an embodiment," "example embodiment," etc. in the described embodiments and the specification indicate that the described embodiment(s) may include a particular feature, structure, or characteristic, but each An embodiment may not necessarily include a specific feature, structure or characteristic. Furthermore, such phrases are not necessarily referring to the same embodiment. Furthermore, when a particular feature, structure or characteristic is described in relation to an embodiment, it is to be understood that implementing such feature, structure or characteristic in relation to other embodiments whether or not explicitly described i...

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Abstract

A method of computing the electromagnetic scattering properties of a structure comprising materials of different properties and the structure is periodic in at least one transverse direction and extends in a perpendicular direction, comprising: by analyzing a plurality of modes in at least one transverse direction Each corresponding mode in , performs a pseudospectral polynomial (Chebyshev) expansion in the vertical direction multiplied by the integral of the 1D Green's function using the same sample points in the orthogonal direction for all of the modes (1350 ), numerically solve the volume integral equation for electromagnetic scattering for each mode. The integration is performed by solving a regularized linear system of equations between the first (1116) and second (1120) discrete transformation steps to compute (1118) the values ​​of the regularized Chebyshev polynomial coefficient vector (γ). The results of the numerical solution are used to calculate the electromagnetic scattering properties of the structure.

Description

[0001] Cross References to Related Applications [0002] This application claims priority to US Provisional Application 61 / 875,340, filed September 9, 2013, which is hereby incorporated by reference in its entirety. technical field [0003] This application relates to the calculation of electromagnetic scattering properties of structures. [0004] The invention can be applied, for example, in the metrology of microstructures, for example to evaluate the critical dimension (CD) performance of a lithographic apparatus. Background technique [0005] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. Photolithographic equipment may be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device, alternatively called a mask or reticle, may be used to generate the circuit pattern to be formed on the individual layers of the IC. The pattern may be transfe...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G03F7/20G01N21/95G01N21/956
CPCG03F7/705G03F7/70625G01B2210/56G01N21/956G03F7/70483G03F7/70633H01L22/12G03F7/706847H01L21/0274
Inventor M·C·范伯登
Owner ASML NETHERLANDS BV
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