Electron-Beam Lithography Writer

1. Theory

• Definition: An electron-beam writer exposes resist directly with a focused or shaped electron beam, without a mask, so it writes masks and research patterns at nanometre resolution but serially (Waterloo; IMS; ECE 695 L21).
• Throughput: Writing time is dose times area divided by beam current, which is why multi-beam writers were developed (IMS).
• Proximity effect: Forward scattering broadens the beam slightly and backscattering from the substrate exposes a wide halo, described by a double Gaussian (van de Kraats).
• Resolution: Spots below 3 $\mathrm{nm}$ are possible at 100 $\mathrm{kV}$, but forward scattering in thick resist and backscatter in dense patterns limit printed features (Waterloo; ECE 695 L21).

2. Working Principle

• Column: A field-emission column forms a nanometre spot at 20 to 100 $\mathrm{kV}$ (Waterloo; ECE 695 L21; Electron Optics page).
• Deflection and stage: The beam is deflected within a field and the stage moves between fields, which are stitched to within about 9 to 20 $\mathrm{nm}$ (Waterloo).
• Pattern generator: Pixels are exposed at up to 50 $\mathrm{MHz}$ (Waterloo).
• Multi-beam: Hundreds of thousands of programmable beams write a mask in parallel (IMS).
• Correction: Dose or shape is adjusted for proximity (van de Kraats).

3. Applications

• Photomask writing: Masks, including curvilinear ILT masks, on multi-beam writers (IMS; Resolution Enhancement page).
• Research and prototyping: Nanometre patterns, gratings and devices (ECE 695 L21).
• Direct write: Small-volume patterning where masks are not justified (ECE 695 L21).

Writing Strategy and Throughput

Name	Formula	Related Formulae	Variables/Constants
Writing time	$t=\frac{DAf}{I}$	$Q_{pixel}=D{p}^2,t_{dwell}=\frac{Q_{pixel}}{I}$	$D:areadose$ $A:fieldarea$ $f:patternfillfraction$ $I:beamcurrent$ $\begin{array}{r}p:pixelsize;dose-chargebalance\\ (computed);Waterloo:50\mathrm{MHz}pattern\\ generator;IMS:upto1\mu \mathrm{A}totalin262\\ thousandbeams\end{array}$ $\begin{array}{r}(assumed:300\mu C/c{\mathrm{m}}^2,5\mathrm{nm}pixels,20ns\\ dwell;computed:3.75\mathrm{nA}beam,800sper\\ m{m}^{2}atfullfill,83hperc{m}^{2}at1\mathrm{nA})\end{array}$
Multi-beam mask writing	$t_{mask}=\frac{D{A}_{mask}f}{I_{total}}$	$I_{total}\le 1\mu \mathrm{A},N_{beams}\approx 2.6\times 10^5$	$\begin{array}{r}IMS:20\mathrm{nm}beams,full100x130\mathrm{mm}mask\\ under10h,throughputindependentof\\ patterncomplexity,curvilinearILT\\ patterns,resistsabove100\mu C/c{\mathrm{m}}^2\end{array}$ $\begin{array}{r}(computed:100\mu C/c{\mathrm{m}}^{2}over130c{m}^{2}atfull\\ filland1\mu \mathrm{A}takes3.6hofbeamtime,\\ consistentwithunder10h)\end{array}$
Fields and stitching	${\Delta }_{stitch}\le \pm 9\mathrm{nm}(62.5\mu \mathrm{m}\text{field})$	${\Delta }_{stitch}\le \pm 20\mathrm{nm}(0.5\mathrm{mm}\text{field})$	$\begin{array}{r}Waterloo:JBX-6300FSfields,stitchingand\\ overlay,2.9\mathrm{nm}spotat100\mathrm{kV}\end{array}$ $\begin{array}{r}(myreading:asmallerdeflectionfield\\ tradesareaperstagemoveforlower\\ deflectiondistortion)\end{array}$

Proximity Effect

Name	Formula	Related Formulae	Variables/Constants
Double-Gaussian proximity function	$f\left(r\right)=\frac{1}{\pi \left(1+\eta \right)}\left[\frac{e^{-r^2/{\alpha }^2}}{{\alpha }^2}+\eta \frac{e^{-r^2/{\beta }^2}}{{\beta }^2}\right]$	$\eta =\frac{E_{back}}{E_{forward}}$	$\alpha :forward-scatteringrange$ $\begin{array}{r}\beta :backscatteringrange;vandeKraats:\\ Eq.3,\eta =0.74onSi,doubleGaussian\\ insufficientforcomplexstacks\end{array}$ $\begin{array}{r}(computed:at100keV,\beta /\alpha =31.2/0.007=\\ 4460)\end{array}$
Energy dependence	$\alpha :1.33\to 0.007\mu \mathrm{m},\beta :0.18\to 31.2\mu \mathrm{m}(5\to 100\mathrm{keV})$	$\text{backscatter negligible below about 10 keV}$	$\begin{array}{r}vandeKraats,TableI(Si,0.5\mu \mathrm{m}resist,\\ bracketedvaluesextrapolated);ECE695\\ L21:forwardwidthfallswithenergyand\\ riseswithresistthickness;\\ Electron-MatterInteractionpageforthe\\ rangephysics\end{array}$ $\begin{array}{r}(myreading:highvoltagesharpensthe\\ forwardbeambutspreadsthebackscatter\\ backgroundovertensofmicrometres)\end{array}$
Proximity correction	$D_{dense}\approx \frac{D_{iso}}{1+\eta }(\text{dose modulation})$	$\text{shape modification, GHOST background}$	$\begin{array}{r}vandeKraats:dosemodulationbypixel,\\ shapemodificationwithruletables\\ (PYRAMID),GHOSTinverseexposureforthe\\ backscatterpart;dense-areascaling\\ (computedfromthenormalizedPSF;my\\ reading)\end{array}$ $\begin{array}{r}(computed:with\eta =0.74alargepad\\ receives1.74timesthedoseofan\\ isolatedfineline)\end{array}$

Resists, Resolution and Charging

Name	Formula	Related Formulae	Variables/Constants
Resist doses and contrast	$D_{PES}\approx 200\mu C/c{\mathrm{m}}^2(10\mathrm{keV})$	$D>3000\mu C/c{\mathrm{m}}^2\Rightarrow \text{PMMA cross-links}$	$\begin{array}{r}ECE695L21:PESsensitivity,PMMA\\ contrastabout0.8,colddevelopmentnear\\ -15{}^{\circ }Csteepest,ZEPsensitivityfalling\\ withcolddevelopment;IMS:resistsabove\\ 100\mu C/c{\mathrm{m}}^2\end{array}$ $\begin{array}{r}(myreading:PMMAswitchesfrompositive\\ tonegativetoneatveryhighdose)\end{array}$
Resolution	$d_{spot}\le 2.9\mathrm{nm}(100\mathrm{kV})$	$p=9\mathrm{nm}\text{in 25 nm HSQ (small area)}$	$\begin{array}{r}Waterloo:measuredspot;ECE695L21:\\ Raith-1503to4\mathrm{nm}at20\mathrm{kV},9\mathrm{nm}pitch\\ overabout50\mathrm{nm},proximitypreventingit\\ onlargegratings,forwardscattering\\ limitingthickresists;ElectronOptics\\ pageforspotformation\end{array}$ $\begin{array}{r}(myreading:thespotsetsresolutionin\\ thinresistandforwardscatteringin\\ thickresist)\end{array}$
Charging	$E_2\approx 1.3\mathrm{keV}(65\mathrm{nm}\text{PMMA on glass})$	$t_{metal}\approx 10\mathrm{nm}\text{Al}$	$\begin{array}{r}ECE695L21:chargingminorbelow500\mathrm{nm}\\ resistat30\mathrm{kV},10\mathrm{nm}AlpreferredtoAu\\ oninsulators;Electron-MatterInteraction\\ pagefor{E}_2\end{array}$ $\begin{array}{r}(myreading:Alispreferredbecauseits\\ lowerZscattersless)\end{array}$

Important Questions

Ques: Why is electron-beam lithography so slow, and how does multi-beam writing help?

Because charge must be delivered pixel by pixel. Writing time is $DAf/I$ (computed from charge balance): at an assumed 300 $\mu C/c{\mathrm{m}}^2$ a 1 $\mathrm{nA}$ beam needs about 83 h per cm${}^2$ of fully written area, and with 5 $\mathrm{nm}$ pixels at the 20 ns dwell of a 50 $\mathrm{MHz}$ generator (Waterloo) the beam must carry 3.75 $\mathrm{nA}$ and still takes 800 s per mm${}^2$ (computed). IMS’s MBMW-101 splits up to 1 $\mu \mathrm{A}$ among about 262 thousand programmable 20 $\mathrm{nm}$ beams; 100 $\mu C/c{\mathrm{m}}^2$ over a full 100 x 130 $\mathrm{mm}$ mask is then 3.6 h of beam time (computed), consistent with their under-10 h figure. Its throughput is independent of pattern complexity, which suits curvilinear ILT masks (IMS; Resolution Enhancement and Multiple Patterning page). Reference: C. Klein and E. Platzgummer (IMS Nanofabrication), ‘MBMW-101: World’s 1st High-Throughput Multi-Beam Mask Writer’, Proc. SPIE 9985 (2016): 262 thousand programmable 20 nm beams, up to 1 uA total current at up to 1 A/cm2, full 100 x 130 mm mask in under 10 h, throughput independent of pattern complexity, curvilinear ILT patterns printed, designed for resists above 100 uC/cm2, conventional 50 keV VSB for comparison (fetch-tool summary); University of Waterloo QNFCF, ‘E-Beam litho 100kV [JEOL-EBL]’: JEOL JBX-6300FS at 100 kV, measured minimum spot 2.9 nm or less, fields 0.5 mm (high speed) and 62.5 um (high resolution), stitching and overlay +/-9 nm (high resolution) or +/-20 nm (high speed), 50 MHz pattern generator, stage steps 0.125 and 1 nm (fetch-tool summary); Resolution Enhancement and Multiple Patterning page of this vault.

Ques: What is the proximity effect and how is it corrected?

Exposure of nearby areas by scattered electrons. Van de Kraats models the deposited energy as a double Gaussian, a narrow forward term of width $\alpha$ and a wide backscatter term of width $\beta$ weighted by $\eta$, the backscatter-to-forward energy ratio. On silicon with 0.5 $\mu \mathrm{m}$ resist, $\eta$ is 0.74, so a large pad receives 1.74 times the dose of an isolated fine line (computed from the normalized function; my reading). He lists three corrections: dose modulation per pixel, which is superior but computationally heavy; shape modification from rule tables such as PYRAMID; and GHOST, a second inverse exposure that levels the background but lowers throughput. ECE 695 L21 shows the consequence: a 9 $\mathrm{nm}$ pitch prints over 50 $\mathrm{nm}$ but not over large gratings. Reference: A. van de Kraats (modified by R. Murali), ‘Proximity Effect in E-beam Lithography’, Georgia Tech nanolithography group: double-Gaussian PSF f(r) = [exp(-r^2/alpha^2)/alpha^2 + eta exp(-r^2/beta^2)/beta^2]/(pi(1 + eta)), Si with 0.5 um resist alpha 1.33, 0.39, 0.12, 0.024, 0.007 um and beta 0.18, 0.60, 2.0, 9.5, 31.2 um at 5, 10, 20, 50, 100 keV with eta 0.74, backscatter negligible below about 10 keV, low-Z substrates and polymer underlayers backscatter less, corrections by dose modulation, shape modification (PYRAMID) and GHOST background exposure (fetch-tool summary); ECE 695 Nanometer Scale Patterning and Processing, Lecture 21, Spring 2016, nanoHUB resource 24952: PES negative resist about 200 uC/cm2 at 10 keV, PMMA contrast about 0.8, cold development steepest near -15 C, PMMA cross-linking above about 3000 uC/cm2, forward-scattering width falling with energy and rising with resist thickness, Raith-150 3 to 4 nm at 20 kV, 9 nm pitch in 25 nm HSQ over about 50 nm but proximity limiting large gratings, charging minor below 500 nm resist at 30 kV, 10 nm Al for insulators, E2 1.3 keV for 65 nm PMMA on glass (fetch-tool summary).

Ques: How does beam energy change resolution and proximity?

It trades forward blur against backscatter range. Van de Kraats tabulates forward ranges on silicon of 1.33, 0.39, 0.12, 0.024 and 0.007 $\mu \mathrm{m}$ and backscatter ranges of 0.18, 0.60, 2.0, 9.5 and 31.2 $\mu \mathrm{m}$ at 5, 10, 20, 50 and 100 keV, with backscatter negligible below about 10 keV. At 100 keV the backscatter halo is 4460 times wider than the forward beam (computed), so it becomes a nearly uniform background that dose modulation can level (my reading). ECE 695 L21 adds that forward scattering grows with resist thickness and limits resolution above a critical thickness. Low-Z substrates and polymer underlayers backscatter less, consistent with the yield trends on the Electron-Matter Interaction page. Reference: A. van de Kraats (modified by R. Murali), ‘Proximity Effect in E-beam Lithography’, Georgia Tech nanolithography group: double-Gaussian PSF f(r) = [exp(-r^2/alpha^2)/alpha^2 + eta exp(-r^2/beta^2)/beta^2]/(pi(1 + eta)), Si with 0.5 um resist alpha 1.33, 0.39, 0.12, 0.024, 0.007 um and beta 0.18, 0.60, 2.0, 9.5, 31.2 um at 5, 10, 20, 50, 100 keV with eta 0.74, backscatter negligible below about 10 keV, low-Z substrates and polymer underlayers backscatter less, corrections by dose modulation, shape modification (PYRAMID) and GHOST background exposure (fetch-tool summary); ECE 695 Nanometer Scale Patterning and Processing, Lecture 21, Spring 2016, nanoHUB resource 24952: PES negative resist about 200 uC/cm2 at 10 keV, PMMA contrast about 0.8, cold development steepest near -15 C, PMMA cross-linking above about 3000 uC/cm2, forward-scattering width falling with energy and rising with resist thickness, Raith-150 3 to 4 nm at 20 kV, 9 nm pitch in 25 nm HSQ over about 50 nm but proximity limiting large gratings, charging minor below 500 nm resist at 30 kV, 10 nm Al for insulators, E2 1.3 keV for 65 nm PMMA on glass (fetch-tool summary); Electron-Matter Interaction page of this vault.

Ques: What resolution and placement do research e-beam writers achieve?

A few nanometres in spot and about ten in stitching. Waterloo’s JEOL JBX-6300FS at 100 $\mathrm{kV}$ has a measured spot of 2.9 $\mathrm{nm}$ or less, 62.5 $\mu \mathrm{m}$ high-resolution and 0.5 $\mathrm{mm}$ high-speed fields, stitching and overlay of plus or minus 9 and plus or minus 20 $\mathrm{nm}$, and stage steps of 0.125 and 1 $\mathrm{nm}$. ECE 695 L21 quotes 3 to 4 $\mathrm{nm}$ for a Raith-150 at 20 $\mathrm{kV}$ and a 9 $\mathrm{nm}$ pitch in 25 $\mathrm{nm}$ HSQ. Smaller fields reduce deflection distortion at the cost of more stage moves (my reading). The spot is formed by the same source, aberration and diffraction trade-offs described on the Electron Optics and the SEM Column page. Reference: University of Waterloo QNFCF, ‘E-Beam litho 100kV [JEOL-EBL]’: JEOL JBX-6300FS at 100 kV, measured minimum spot 2.9 nm or less, fields 0.5 mm (high speed) and 62.5 um (high resolution), stitching and overlay +/-9 nm (high resolution) or +/-20 nm (high speed), 50 MHz pattern generator, stage steps 0.125 and 1 nm (fetch-tool summary); ECE 695 Nanometer Scale Patterning and Processing, Lecture 21, Spring 2016, nanoHUB resource 24952: PES negative resist about 200 uC/cm2 at 10 keV, PMMA contrast about 0.8, cold development steepest near -15 C, PMMA cross-linking above about 3000 uC/cm2, forward-scattering width falling with energy and rising with resist thickness, Raith-150 3 to 4 nm at 20 kV, 9 nm pitch in 25 nm HSQ over about 50 nm but proximity limiting large gratings, charging minor below 500 nm resist at 30 kV, 10 nm Al for insulators, E2 1.3 keV for 65 nm PMMA on glass (fetch-tool summary); Electron Optics and the SEM Column page of this vault.

Ques: Which resists and charge-control steps are used?

High-contrast polymer resists and conductive layers. ECE 695 L21 reports a PES negative resist at about 200 $\mu C/c{\mathrm{m}}^2$ at 10 keV, PMMA contrast of about 0.8 with the steepest contrast for cold 3:1 IPA:MIBK development near -15 ${}^{\circ }\mathrm{C}$, and PMMA cross-linking into a negative resist above about 3000 $\mu C/c{\mathrm{m}}^2$; IMS designed its writer for resists above 100 $\mu C/c{\mathrm{m}}^2$. For charging, the lecture notes that resists below about 500 $\mathrm{nm}$ rarely charge at 30 $\mathrm{kV}$, that 10 $\mathrm{nm}$ of aluminium is preferred over gold on insulators because it scatters less, and that 65 $\mathrm{nm}$ PMMA on glass has a second crossover of 1.3 keV, the quantity that sets charge polarity on the Electron-Matter Interaction page. Reference: ECE 695 Nanometer Scale Patterning and Processing, Lecture 21, Spring 2016, nanoHUB resource 24952: PES negative resist about 200 uC/cm2 at 10 keV, PMMA contrast about 0.8, cold development steepest near -15 C, PMMA cross-linking above about 3000 uC/cm2, forward-scattering width falling with energy and rising with resist thickness, Raith-150 3 to 4 nm at 20 kV, 9 nm pitch in 25 nm HSQ over about 50 nm but proximity limiting large gratings, charging minor below 500 nm resist at 30 kV, 10 nm Al for insulators, E2 1.3 keV for 65 nm PMMA on glass (fetch-tool summary); C. Klein and E. Platzgummer (IMS Nanofabrication), ‘MBMW-101: World’s 1st High-Throughput Multi-Beam Mask Writer’, Proc. SPIE 9985 (2016): 262 thousand programmable 20 nm beams, up to 1 uA total current at up to 1 A/cm2, full 100 x 130 mm mask in under 10 h, throughput independent of pattern complexity, curvilinear ILT patterns printed, designed for resists above 100 uC/cm2, conventional 50 keV VSB for comparison (fetch-tool summary); Electron-Matter Interaction page of this vault.

References

1. A. van de Kraats, modified by R. Murali, “Proximity effect in e-beam lithography,” Georgia Institute of Technology. Available: https://www.nanolithography.gatech.edu/proximity.pdf
2. ECE 695 Nanometer Scale Patterning and Processing, Lecture 21, Spring 2016, nanoHUB resource 24952. Available: https://nanohub.org/resources/24952/download/2016.03.02-ECE695Q-L21.pdf
3. University of Waterloo Quantum-Nano Fabrication and Characterization Facility, “E-Beam litho 100kV [JEOL-EBL].” Available: https://uwaterloo.ca/quantum-nano-fabrication-and-characterization-facility/node/19
4. C. Klein and E. Platzgummer, “MBMW-101: world’s 1st high-throughput multi-beam mask writer,” Proc. SPIE 9985, 2016. Available: https://www.ims.co.at/wp-content/uploads/2019/01/2016-10-17_BACUS-2016_IMS_MBMW-101_998505.pdf
5. Electron Optics and the SEM Column page of this vault.
6. Electron-Matter Interaction page of this vault.
7. Resolution Enhancement and Multiple Patterning page of this vault.

Related pages in this vault: Electron Optics and the SEM Column, Electron-Matter Interaction, Resolution Enhancement and Multiple Patterning, Photoresist and Process Window, Focused Ion Beam (FIB), Nanoimprint Lithography Tool, Laser Direct-Write and Interference Lithography System, Electron-Beam Evaporator.