t
play

T PB Direct Problem: Diffraction by Grating Structures. 1 W - PowerPoint PPT Presentation

Outline Outline T PB Direct Problem: Diffraction by Grating Structures. 1 W eierstra-InstitutfrAngewandteAnalysisundStochastik Reconstruction of Periodic Surface Structures 2 H. Gro, A. Rathsfeld Sensitivity Analysis


  1. Outline Outline T PB Direct Problem: Diffraction by Grating Structures. 1 W eierstraß-Institut�für�Angewandte�Analysis�und�Stochastik Reconstruction of Periodic Surface Structures 2 H. Groß, A. Rathsfeld Sensitivity Analysis 3 Numerical Aspects of the Scatterometric Tasks of Sensitivity Analysis Measurement of Periodic Surface Structures Uncertainty Estimates for Derived Values Stochastic Geometries 4 Conclusions 5 Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 1 (44) Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 2 (44) . Direct Problem: Diffraction by Grating Structures. Direct Problem: Diffraction by Grating Structures. incoming field reflected modes Lithography y (E ,H ) i i θ photoresist chip production like old-fashioned photography: z photoresist layer illuminated by light scattered from mask, x development: baking and etching procedures − → chip light source wafer chrome photo resist silicon oxide mask transmitted modes standard test configurations: periodic gratings (similarly, biperiodic surface structures) – periodic line-space structure (lines formed by bridges with details of surface geometry in size of wavelength trapezoidal cross section) – biperiodic array of trapezoidal blocks resp. holes Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 4 (44) Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 5 (44)

  2. ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ � ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ ✁ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � . Direct Problem: Diffraction by Grating Structures. Direct Problem: Diffraction by Grating Structures. Scatterometry Spectroscopic reflectrometer operating in the EUV range around 13 nm BESSY II, PTB Lightsource Detector Polarizer θ rot.Analyser Variable Retarder 2 θ Sample M. Wurm, B. Bodermann, and W. Mirandé "Eval. of scatterom. tools for critical dim. metrology" DGaO Proc. 2005, www.dgao-proceedings.de, P 25 Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 6 (44) Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 7 (44) . Direct Problem: Diffraction by Grating Structures. Direct Problem: Diffraction by Grating Structures. Plane wave illumination. 3D time-harmonic Maxwell’s equns. reduce to: x x Domain of Computation: 3 2 x 1 – Curl-Curl equation for three-dimensional amplitude factor of time Rectangular box over one periodic cell Ω harmonic electric field (i.e. E ( x 1 , x 2 , x 3 , t ) = E ( x 1 , x 2 , x 3 ) e − iωt ) Non−local boundary condition: ∇ × ∇ × E ( x 1 , x 2 , x 3 ) − k 2 E ( x 1 , x 2 , x 3 ) = 0 Coupling with boundary elements Including radiation condition (or Absorbing bound. cond. PML or mortaring with Fourier mode sol.) – scalar 2D Helmholtz equation if geometry is constant in x 3 direct- ion and if direction of incoming plane wave is in x 1 − x 2 plane Transmission conditions: Continuous tangential traces ∆ v ( x 1 , x 2 ) + k 2 v ( x 1 , x 2 ) = 0 , v = E 3 , H 3 Continuous tangential traces of curl Quasiperiodic boundary condition: v(x +d ,x ,x )=v(x ,x ,x ) exp(i d ) α period d 1 – two coupled scalar 2D Helmholtz equations if geometry is constant 1 1 1 2 3 1 2 3 v(x ,x +d ,x )=v(x ,x ,x ) exp(i d ) β in x 3 direction but direction of incoming plane wave is not in x 1 − x 2 1 1 2 2 3 2 3 2 plane (conical diffraction) Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 8 (44) Numerical Aspects of the Scatterometric Measurement of Periodic Surface Structures M37, July 21 9 (44)

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend