Technology for Micro- and Nanostructures Micro- and Nanotechnology

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1 Lecture 6: Electron-Beam Lithography, Part 2 Technology for Micro- and Nanostructures Micro- and Nanotechnology Peter Unger mailto: uni-ulm.de Institute of Optoelectronics University of Ulm Copyright 2012 by Peter Unger Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 1/29 Outline of Lectures 5 and 6: E-Beam Lithography Part 1, Lecture 5 Basic Principle of Electron-Beam Lithography The Electron-Optical Column Lens Errors and Beam Size Mark Registration Field Overlay and Stitching Part 2, Lecture 6 Physics of Lenses for Electrons Scatter Effects of Electron Beams The Proximity Correction Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 2/29

2 Basic Principle of Electron-Beam Lithography Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 3/29 Cross Section of an Electron-Optical Column Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 4/29

3 Forces in Electromagnetic Fields Electric Fields Magnetic Fields F = m a = q e E F = m a = q e ( v B) Lorentz Force No Focusing of Electron Beams in Homogeneous Electrostatic and Magnetic Fields Any Axially Symmetric Electrostatic or Magnetic Field has the Property of a Focusing Lens Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 5/29 Electrostatic Electron Einzel Lens Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 6/29

4 Cross Section of a Magnetic Electron Lens Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 7/29 Functioning of a Magnetic Electron Lens Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 8/29

5 Lens Errors in Electron-Beam Optics Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 9/29 Aberation and Diffraction of an Objective Lens Resolution δ δ min Diffraction δ ~ 1/α Sum of Diffraction and Spheric Aberation Spheric Aberation δ ~ α 3 α opt Beam Divergence Angle α Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 10/29

6 Electron-Beam Lithography at 100 kev Resist: PMMA/MAA Substrate: Silicon Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 11/29 Electron-Beam Lithography at 100 kev Resist: PMMA/MAA Substrate: Silicon Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 12/29

7 Electron-Beam Lithography at 100 kev Resist: PMMA/MAA Dose: 1 mc/cm 2 Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 13/29 Basic Electron Scattering Mechanisms (after Hersener and Ricker) Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 14/29

8 Double Gaussian Model for the Dose Distribution Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 15/29 The Proximity Function Double Gausssian Model for the Proximity Function f(r) f(r) = k [ exp ( ) r2 βf 2 + η E β2 f β 2 b exp ( )] r2 βb 2 Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 16/29

9 The Proximity Function Double Gausssian Model for the Proximity Function f(r) f(r) = k [ exp ( ) r2 βf 2 β f Forward Scattering Width Broadening of the Electron Beam + η E β2 f β 2 b exp β b Backward Scattering Width Secondary Electron Emission from the Substrate ( )] r2 βb 2 η E Backscatter Coefficient Ratio of Backscattered to Forward Scattered Dose Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 17/29 Monte-Carlo Simulations of the Scattering (after Jones, Blythe, and Ahmed, J. Vac. Sci. Technol. B, vol. 5, pp , 1987) Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 18/29

10 Electron Scattering at Different Electron Energies (after Michael Hatzakis, IBM J. Res. Develop., vol. 32, no. 4, pp , 1988) Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 19/29 Scattering at Different Electron Energies Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 20/29

11 Forward Scattering Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 21/29 Proximity Distributions at Different Electron Energies Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 22/29

12 The Backscatter Coefficient (after Hunger and Küchler, 1979) Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 23/29 Interaction of the Electron Beam with the Substrate Forward Scattering: Broadening of the Electron Beam β f Decreases with Increasing Electron Energy E Backward Scattering: Secondary Electron Emission from the Substrate β b Increases with Increasing Energy Backscatter Coefficient η E Z Proximity Effect Correction Dose Variation Pattern Partitioning Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 24/29

13 Pattern Partitioning Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 25/29 Pattern Partitioning and Dose Variation Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 26/29

14 Example of Proximity Correction Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 27/29 Data Flow for Electron-Beam Lithography Physical Design (CAD System) = Pattern Data File Proximity Correction Pattern Partitioning and Dose Variation Digital Pattern Generator Mark Registration (Using Electron Detectors) Stage Control Deflection Correction (Shift, Scale, Rotation, Non-Orthogonality) Deflection Unit Beam Blanker Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 28/29

15 Further Reading Henry I. Smith Submicron- and nanometer-structures technology, 2nd edition Lecture 4, Electron Optics and the TEM Lecture 5, Scanning Electron Beam Systems Lecture 14, Electron-Beam Lithography Lecture 15, Electron Scattering and Proximity Effects NanoStructures Press, 437 Peakham Road, Sudbury, MA 01776, USA 1994 Peter Unger, Technology for Micro- and Nanostructures Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 p. 29/29