Accuracy of diffraction-based overlay metrology using a single array target

Ku, Yi-Sha; Pang, Hanbin; Hsu, Wei-Feng; Shyu, Deh-Ming

doi:10.1117/1.3275449

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…In electrical engineering Maxwell solvers for electromagnetic scattering problems have wide and important applications, which range from semiconductor metrology in integrated circuits (ICs) production [1][2][3], to designing elements on nanophotonic chips [4,5], and to analysing metamaterials [6,7]. In these cases, it is required to have fast and accurate Maxwell solvers, especially for the cases where the number of unknowns is large.…”

Section: Introductionmentioning

confidence: 99%

A Normal-vector-field-based Preconditioner for a Spatial Spectral Domain-integral Equation Method for Multi-Layered Electromagnetic Scattering Problems

Sun¹,

Dilz²,

Beurden³

2022

PIER C

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A normal-vector-field-based block diagonal-preconditioner for the spatial spectral integral method is proposed for an electromagnetic scattering problem with multi-layered medium. This preconditioner has a block-diagonal matrix structure for both 2D TM polarization and 3D cases. Spectral analysis shows that the preconditioned system has a more clustered eigenvalue distribution, compared to the unpreconditioned system. For the cases with high contrast or negative permittivity, numerical experiments illustrate that the preconditioned system requires fewer iterations than the unpreconditioned system. The total computation time is reduced accordingly while the accuracy based on the normal-vector field formulation of the solution is preserved.

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Section: Introductionmentioning

confidence: 99%

A Normal-vector-field-based Preconditioner for a Spatial Spectral Domain-integral Equation Method for Multi-Layered Electromagnetic Scattering Problems

Sun¹,

Dilz²,

Beurden³

2022

PIER C

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“…[20][21][22][23] The trend of device down scaling and complicated stack structure motivates the enhanced metrology tool needed for foundry manufacturing. [24][25][26][27][28][29][30] Optical scatterometry technique is attracting attention to characterize critical dimensions (CDs) and overlays in the next generation semiconductor technology, due to its rapid measurement speed, nondestructive measurement, and complete pattern profile information, such as the width, side wall angle (SWA), and height. The experimental scatterometry spectra are collected and compared with the theoretical spectra calculated by the rigorous coupled wave Copyright: American Scientific Publishers analysis (RCWA) algorithm to extract the geometric shape information.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Beam Incident on the One-Dimensional Diffraction Gratings with the High-K Metal Gate Stack Structures

Kuo¹,

Frederick²

2014

j nanosci nanotechnol

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Optical scatterometry has attracted extensive interest in extracting the geometric shape information of nanolithography patterns because of the trend of shrinking device size and complicated stack structure. RCWA is the numerical algorithm implemented in the current scatterometry tool to calculate the diffraction efficiency. However, the known weakness for the RCWA method is the analysis of metallic gratings illuminated by the TM wave. This research applies the FDTD method using the Gaussian beam excitation source to analyze the diffraction efficiency of HKMG gratings for the use in the optical scatterometry and verifies the numerical diffraction efficiency discrepancy between the Gaussian beam and plane wave excitation methods. The numerical study is carried out with the line/space nanolithography patterns on the HKMG process stacks at 45 nm node technology. The nanolithography patterns are modeled as 1-D surface relief gratings. The 0th order diffraction efficiency is analyzed as a function of CDs, SWAs, incident angles and pitches of the gratings. The study presents the impact of the polarizations of the incident waves on the diffraction efficiency. In addition, this research investigates the phase of the 0th diffraction order as a function of the SWAs and illustrates the corresponding SWA parameter effect on the phase distribution. This research suggests the minimum beam radius to converge the numerical diffraction efficiency using Gaussian beam excitation to it using the plan wave.

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“…The simulation of electromagnetic scattering from finitely sized dielectric objects in a multilayered dielectric medium has several important applications. Among these applications are metrology for integrated-circuit production [1], metamaterials [2], and elements on nanophotonic chips [3]. Fast and accurate numerical methods are very important in these fields of research.…”

Section: Introductionmentioning

confidence: 99%

2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation

2017

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We present a method to simulate two-dimensional scattering by dielectric objects embedded in a dielectric layered medium with transverse magnetic polarization through a domain integral equation formulation. A mixed spatial-spectral discretization is employed with both a spatial and a spectral representation along the direction of the layer interfaces. In the spectral domain, a discretization on a path through the complex plane is used on which the Green function is well behaved. To calculate the field-material interaction in the spatial domain, an auxiliary field is employed similar to the Li factorization rules. Numerical results show that this auxiliary-field formulation significantly improves accuracy, compared to a formulation that directly employs the electric field.

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Accuracy of diffraction-based overlay metrology using a single array target

Cited by 6 publications

References 18 publications

A Normal-vector-field-based Preconditioner for a Spatial Spectral Domain-integral Equation Method for Multi-Layered Electromagnetic Scattering Problems

A Normal-vector-field-based Preconditioner for a Spatial Spectral Domain-integral Equation Method for Multi-Layered Electromagnetic Scattering Problems

Gaussian Beam Incident on the One-Dimensional Diffraction Gratings with the High-K Metal Gate Stack Structures

2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation

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