Upload
nguyenkhanh
View
232
Download
3
Embed Size (px)
Citation preview
Lecture 6: Electron-Beam Lithography, Part 2
Technology for Micro- and NanostructuresMicro- and Nanotechnology
Peter Unger
mailto: peter.unger @ uni-ulm.de
Institute of Optoelectronics
University of Ulm
http://www.uni-ulm.de/opto
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 5Basic Principle of Electron-Beam LithographyThe Electron-Optical ColumnLens Errors and Beam SizeMark RegistrationField Overlay and Stitching
Part 2, Lecture 6Physics of Lenses for ElectronsScatter Effects of Electron BeamsThe Proximity Correction
Peter Unger, Technology for Micro- and Nanostructures — Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 – p. 2/29
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
Forces in Electromagnetic Fields
Electric Fields~F = m~a = qe ~E
Magnetic Fields~F = m~a = qe (~v × ~B)
Lorentz Force
No Focusing of Electron Beams in Homogeneous Electrostaticand Magnetic Fields
Any Axially Symmetric Electrostatic or Magnetic Field has theProperty 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
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
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
δmin
αopt
Beam Divergence Angle α
Res
olut
ion
δ
Diffractionδ ~ 1/α
SphericAberationδ ~ α3
Sum of Diffractionand Spheric Aberation
Peter Unger, Technology for Micro- and Nanostructures — Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 – p. 10/29
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. 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
Electron-Beam Lithography at 100 keV
Resist:PMMA/MAA
Dose:1 mC/cm2
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
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
β2f
)+ ηE · β
2f
β2b
· exp(− r2
β2b
)]
Peter Unger, Technology for Micro- and Nanostructures — Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 – p. 16/29
The Proximity Function
Double Gausssian Model for the Proximity Function f(r)
f(r) = k
[exp
(− r2
β2f
)+ ηE · β
2f
β2b
· exp(− r2
β2b
)]
βf – Forward Scattering WidthBroadening of the Electron Beam
βb – Backward Scattering WidthSecondary Electron Emission from the Substrate
ηE – Backscatter CoefficientRatio 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. 120–123, 1987)
Peter Unger, Technology for Micro- and Nanostructures — Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 – p. 18/29
Electron Scattering at Different Electron Energies
(after Michael Hatzakis, IBM J. Res. Develop., vol. 32, no. 4, pp. 441–453, 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
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
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 Beamβf Decreases with Increasing Electron Energy E
Backward Scattering:Secondary Electron Emission from the Substrateβb Increases with Increasing EnergyBackscatter Coefficient ηE ∝ Z
Proximity Effect CorrectionDose VariationPattern Partitioning
Peter Unger, Technology for Micro- and Nanostructures — Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 – p. 24/29
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
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 CorrectionPattern Partitioning and Dose Variation
Digital Pattern GeneratorMark Registration (Using Electron Detectors)Stage ControlDeflection Correction(Shift, Scale, Rotation, Non-Orthogonality)Deflection UnitBeam Blanker
Peter Unger, Technology for Micro- and Nanostructures — Lecture 6: Electron-Beam Lithography, Part 2, Version of November 28, 2012 – p. 28/29
Further Reading
Henry I. SmithSubmicron- and nanometer-structures technology, 2nd editionLecture 4, Electron Optics and the TEMLecture 5, Scanning Electron Beam SystemsLecture 14, Electron-Beam LithographyLecture 15, Electron Scattering and Proximity EffectsNanoStructures 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