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

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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

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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

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Electrostatic Electron Einzel Lens

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Cross Section of a Magnetic Electron Lens

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Functioning of a Magnetic Electron Lens

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Lens Errors in Electron-Beam Optics

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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

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Electron-Beam Lithography at 100 keV

Resist:PMMA/MAA

Substrate:Silicon

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Electron-Beam Lithography at 100 keV

Resist:PMMA/MAA

Dose:1 mC/cm2

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Basic Electron Scattering Mechanisms

(after Hersener and Ricker)

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Double Gaussian Model for the Dose Distribution

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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

)]

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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

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Monte-Carlo Simulations of the Scattering

(after Jones, Blythe, and Ahmed, J. Vac. Sci. Technol. B, vol. 5, pp. 120–123, 1987)

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Electron Scattering at Different Electron Energies

(after Michael Hatzakis, IBM J. Res. Develop., vol. 32, no. 4, pp. 441–453, 1988)

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Scattering at Different Electron Energies

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Forward Scattering

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Proximity Distributions at Different Electron Energies

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The Backscatter Coefficient

(after Hunger and Küchler, 1979)

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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

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Pattern Partitioning

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Pattern Partitioning and Dose Variation

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Example of Proximity Correction

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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

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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

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