Biomedical Engineering Reference
In-Depth Information
TABLe 12.1
Decision.Matrix.for.Selection.of.Resist.Tone.and.Exposure.Strategy
Desire
d Outcome
Action
Protect Pattern
Protect Background
Pattern Density
Resist Tone
Expose
Sparse
<50%.coverage
Negative
Positive
Pattern
Dense
>50%.coverage
Positive
Negative
Background
12.3.3.2 Resolution
The.resolving.power.of.an.optical.system.is.frequently.expressed.in.terms.of.the.Rayleigh.
limit:
λ
δ
=
0 61
.
d
NA
.
where.λ.is.the.radiation.wavelength..In.the.case.of.electrons.it.is.the.de.Broglie.wavelength.
that. is. used..
NA
. is. the. numerical. aperture,. approximately. 0.005. for. most. Gaussian. EBL.
systems.
Table.12.2.shows.the.diffraction.limited.resolving.power.as.a.function.of.beam.voltage..
Diffraction.limited.resolution.is.rarely.achieved.in.practice..A.variety.of.other.contributing.
factors.such.as.aberrations,.noise,.scattering.in.the.resist,.mutual.repulsive.effects.between.
electrons,.and.diffusive.effects.in.the.resist.have.limited.nanoscale.lithographic.patterning.
to.low.single.digits.under.the.best.circumstances.(Broers,.1996;.Broers.et.al.,.1989;.Crewe,.
1979).
A.deinite.trade-off.exists.between.dose.and.image.idelity,.due.in.part.to.the.electron.
statistics.of.the.exposure.process.(Kruit.et.al.,.2004)..Most.commercial.resist.materials.are.
able. to. provide. good. resolution. with. moderate. speed. at. 100.nm. minimum. feature. size..
Lithographic.patterning.in.the.20-100.nm.range.is.readily.accomplished.with.several.com-
mercial.materials.(Koshelev.et.al.,.2011)..Below.20.nm,.the.number.of.resist.materials.that.
deliver. satisfactory. performance. over. a. broad. range.of. patterning. conditions. is. severely.
limited.(Singh.et.al.,.2011)..At.the.CAD.level,.all.elements.of.the.pattern.are.binary—every.
point. is. either. inside. a. pattern. or. not.. In. an. ideal. lithography. system. this. would. hold.
TABLe 12.2
Impact.of.Beam.Energy.on.Diffraction.Limited.
Resolution.and.Depth.of.Focus.(DOF)
Electron
Energy (kV)
Wavelength
λ (Å)
δ
d
(nm)
a
= 5 mrad
±DOF
(nm)
10
0.123
1.50
246
50
0.056
0.68
112
100
0.041
0.50
82
125
0.038
0.46
76
200
0.031
0.38
62
