Laser Direct-Write and Interference Lithography System

1. Theory

• Definition: Laser direct-write systems expose resist with a scanned focused laser or spatial modulator, without a mask, while interference lithography records the fringe pattern of two or more coherent beams (Utah; NIST; Seo et al.).
• Interference: Two beams at half-angle $\theta$ give fringes of period $\lambda /(2\sin \theta )$, down to $\lambda /2$ (Seo et al.).
• Direct write: Resolution, address grid and speed are traded by write mode, from 0.3 $\mu \mathrm{m}$ at a few $\mathrm{m}{\mathrm{m}}^2/min$ to 4 $\mu \mathrm{m}$ at 2000 $\mathrm{m}{\mathrm{m}}^2/min$ (Utah).
• Dose: In interference lithography the duty cycle of the printed grating is tuned by dose (Seo et al.).

2. Working Principle

• Direct write: 405 or 375 $\mathrm{nm}$ diode lasers are focused and scanned, or modulated by an imaging head, while the stage moves; greyscale modes vary dose per pixel (Utah; NIST).
• Alignment: Cameras align to existing marks to 100 $\mathrm{nm}$ to 1 $\mu \mathrm{m}$ (Utah; NIST).
• Interference: A laser beam is split, by a beam splitter or a Lloyd’s mirror, and recombined on the resist; rotating the sample adds a second exposure for 2-D arrays (Seo et al.).

3. Applications

• Mask making and prototyping: Direct writing of masks and small batches (Utah; NIST; Contact and Proximity Mask Aligner page).
• Greyscale micro-optics: Up to 1000 grey levels (Utah).
• Periodic nanostructures: Gratings, photonic crystals, anti-reflection surfaces and colour filters (Seo et al.).

Interference Lithography

Name	Formula	Related Formulae	Variables/Constants
Interference period	$\Lambda =\frac{\lambda }{2\sin \theta }$	${\Lambda }_{min}=\frac{\lambda }{2}$	$\Lambda :fringeperiod$ $\begin{array}{r}\theta :half-anglebetweenthebeams;Seoet\\ al.:theserelations,minimumfeatures\\ 182,178,122and96\mathrm{nm}for364,355,244\\ and193\mathrm{nm}\end{array}$ $\begin{array}{r}(computed:257\mathrm{nm}lightgives257\mathrm{nm}\\ periodat\theta =30degreesand128.5\mathrm{nm}at\\ grazinglimit)\end{array}$
Two-beam intensity	$I\left(x\right)=2A\left[\cos \left(\frac{4\pi x}{\lambda }\sin \theta \right)+1\right]$	$C_{img}=1(\text{equal beams})$	$\begin{array}{r}A:partial-beamamplitude;Seoetal.:\\ thisintensity;contrastforequalbeams\\ (computedfromthecosineform)\end{array}$ $\begin{array}{r}(computed:thecosinerepeatswhen4\pi \\ x\sin \theta /\lambda =2\pi ,giving\Lambda above)\end{array}$
Dose and duty cycle	$w=\Lambda \left[1-\frac{1}{\pi }{\cos }^{-1}\left(\frac{c}{D}-1\right)\right](\text{threshold resist})$	$D:9\to 18mJ/c{\mathrm{m}}^2,w:390\to 190\mathrm{nm}$	$w:patternwidthperperiod$ $\begin{array}{r}c:thresholddoseconstant;Seoetal.:\\ measuredshrinkatabout770\mathrm{nm}pitch;\\ idealthresholdmodel(computed;my\\ reading;seetheQ/A)\end{array}$ $\begin{array}{r}(computed:fittingcto390\mathrm{nm}at9mJ/c{\mathrm{m}}^2,\\ theidealmodelpredicts260\mathrm{nm}at18,not\\ themeasured190\mathrm{nm})\end{array}$

Laser Direct Write

Name	Formula	Related Formulae	Variables/Constants
Direct-write resolution and grid	$w_{min}=0.3\text{to}4\mu \mathrm{m}(\text{modes HiRes to V})$	$\text{address grid}=5\text{to}200\mathrm{nm}$	$\begin{array}{r}UtahDWL66+:sixwritemodes,405or375\\ \mathrm{nm}diodelasers,edgeroughness50to160\\ \mathrm{nm}andCDU60to250\mathrm{nm}(3\sigma );NISTMLA150:\\ 1\mu \mathrm{m}minimum\end{array}$ $\begin{array}{r}(myreading:theaddressgridisfarfiner\\ thanthespot,soedgesareplacedmore\\ finelythanfeaturescanberesolved)\end{array}$
Write time	$t=\frac{A}{v_w}$	$v_w=3\text{to}2000\mathrm{m}{\mathrm{m}}^2/min$	$A:area$ $\begin{array}{r}{v}_w:writespeed;Utah:speedsbymodeat\\ 405\mathrm{nm}and2to110\mathrm{m}{\mathrm{m}}^2/minat375\mathrm{nm};\\ NIST:10to15minfor100x100m{m}^2\end{array}$ $\begin{array}{r}(computed:100x100m{m}^{2}takes56hin\\ HiRes,5mininmodeV,and667to1000\\ \mathrm{m}{\mathrm{m}}^2/minontheMLA150;speedscalesroughly\\ asfeaturesizetothe2.5poweracross\\ DWLmodes)\end{array}$
Alignment and greyscale	${\Delta }_{align}=100\text{to}800\mathrm{nm}(3\sigma )$	$N_{grey}=128,255,1000$	$\begin{array}{r}Utah:alignmentbymodeandgreyscale\\ levels;NIST:overlay500\mathrm{nm}frontand\\ 1000\mathrm{nm}back\end{array}$ $\begin{array}{r}(myreading:greyscaleexposurevaries\\ doseperpixeltosculpt3-Dresist\\ profiles)\end{array}$

Patterns and Method Choice

Name	Formula	Related Formulae	Variables/Constants
Two-dimensional interference patterns	$\text{2 exposures at }90^{\circ }\Rightarrow \text{square array}$	$\text{3 beams}\Rightarrow \text{hexagonal array}$	$\begin{array}{r}Seoetal.:doubleexposureandthree-beam\\ methods,Lloy{d}^{\prime }smirrorfor1-Dpatterns\end{array}$ $\begin{array}{r}(myreading:theLloy{d}^{\prime }smirrorusesone\\ laserbeamsplitbyamirror,sopath\\ matchingisautomatic)\end{array}$
Applications of interference lithography	$R\approx 95\%(1300\mathrm{nm}\text{membrane reflector})$	$R\approx 5\%(\text{anti-reflection})$	$\begin{array}{r}Seoetal.:membranereflectorswithabout\\ 100\mathrm{nm}bandwidth,anti-reflection,\\ plasmoniccolourfiltersover2.5x2.5\\ cm,photoniccrystalsandx-raygratings\end{array}$ $\begin{array}{r}(myreading:interferencesuitslarge\\ periodicareaswithoutamask)\end{array}$
Choosing a maskless method	$\text{periodic: interference}\text{arbitrary: direct write}$	$\text{sub-100 nm arbitrary: e-beam}$	$\begin{array}{r}Seoetal.:periodicpatternsdownto\lambda /2;\\ UtahandNIST:arbitrarypatternsat0.3\\ to4\mu \mathrm{m};Electron-BeamLithographyWriter\\ pagefornanometrearbitrarypatterns(my\\ readingofthedivision)\end{array}$ $\begin{array}{r}(computed:193\mathrm{nm}interferencereaches96\\ \mathrm{nm}features,threetimesfinerthanthe\\ 0.3\mu \mathrm{m}DWLHiResmode)\end{array}$

Important Questions

Ques: How does interference lithography set the grating period?

By the angle between the beams. Seo et al. give the two-beam period as $\Lambda =\lambda /(2\sin \theta )$, with $\theta$ the half-angle, and the intensity as $2A[\cos ((4\pi x/\lambda )\sin \theta )+1]$, whose cosine repeats exactly at that period (computed). The smallest period is $\lambda /2$, and they list minimum features of 182, 178, 122 and 96 $\mathrm{nm}$ for 364, 355, 244 and 193 $\mathrm{nm}$ sources. A 257 $\mathrm{nm}$ laser at $\theta$ = 30 degrees gives a 257 $\mathrm{nm}$ period, and 128.5 $\mathrm{nm}$ at the limit (computed). Lloyd’s mirror setups reflect half the beam off a mirror beside the sample, and two exposures at 90 degrees or three beams give square and hexagonal arrays. Reference: J.-H. Seo, J. H. Park, Z. Ma, J. Choi and B.-K. Ju, ‘Nanopatterning by Laser Interference Lithography: Applications to Optical Devices’, arXiv:1402.2189: two-beam pitch Lambda = lambda/(2 sin theta) with minimum lambda/2, I(x) = 2A[cos((4 pi x/lambda) sin theta) + 1], sources 364, 355, 244, 213 and 193 nm with minimum features 182, 178, 122 and 96 nm, Lloyd’s mirror with one direct and one reflected beam, 515 nm doubled and 257 nm sources used, 90 degree double exposure for square and three beams for hexagonal arrays, 9 to 18 mJ/cm2 shrinking 770 nm-pitch patterns from 390 to 190 nm, applications in membrane reflectors (95 per cent near 1300 nm), anti-reflection (5 per cent), plasmonic colour filters, photonic crystals and x-ray gratings (fetch-tool summary).

Ques: Does a simple threshold model predict how dose changes interference pattern size?

Not well. Seo et al. report that at about 770 $\mathrm{nm}$ pitch, raising the dose from 9 to 18 $mJ/c{\mathrm{m}}^2$ shrank the printed features from 390 to 190 $\mathrm{nm}$, the pitch-to-feature ratio rising from about 2 to 4. For the cosine image and an ideal threshold resist, fitting the threshold to 390 $\mathrm{nm}$ at 9 $mJ/c{\mathrm{m}}^2$ predicts 260 $\mathrm{nm}$ at 18 (computed), so the measured shrink is larger than the ideal model allows. The measurement is more likely right, because real resist contrast, development and the finite slope of the cosine image near its minimum all steepen the response (my reading). Dose is therefore an effective but non-linear duty-cycle control, and should be calibrated for each resist (my reading). Reference: J.-H. Seo, J. H. Park, Z. Ma, J. Choi and B.-K. Ju, ‘Nanopatterning by Laser Interference Lithography: Applications to Optical Devices’, arXiv:1402.2189: two-beam pitch Lambda = lambda/(2 sin theta) with minimum lambda/2, I(x) = 2A[cos((4 pi x/lambda) sin theta) + 1], sources 364, 355, 244, 213 and 193 nm with minimum features 182, 178, 122 and 96 nm, Lloyd’s mirror with one direct and one reflected beam, 515 nm doubled and 257 nm sources used, 90 degree double exposure for square and three beams for hexagonal arrays, 9 to 18 mJ/cm2 shrinking 770 nm-pitch patterns from 390 to 190 nm, applications in membrane reflectors (95 per cent near 1300 nm), anti-reflection (5 per cent), plasmonic colour filters, photonic crystals and x-ray gratings (fetch-tool summary).

Ques: What resolution and speed do laser direct writers offer?

A wide range set by the write mode. The Utah DWL 66+ specification lists minimum features of 0.3, 0.6, 0.8, 1, 2 and 4 $\mu \mathrm{m}$ for its HiRes and I to V modes, with address grids from 5 to 200 $\mathrm{nm}$, speeds from 3 to 2000 $\mathrm{m}{\mathrm{m}}^2/min$ at 405 $\mathrm{nm}$, edge roughness 50 to 160 $\mathrm{nm}$ and CD uniformity 60 to 250 $\mathrm{nm}$ (3$\sigma$). A 100 x 100 mm${}^2$ area takes about 56 h in HiRes but 5 min in mode V, so speed rises roughly as feature size to the 2.5 power (computed). NIST’s MLA150, with 8 W at 405 $\mathrm{nm}$, writes 100 x 100 mm${}^2$ in 10 to 15 min at 1 $\mu \mathrm{m}$, 667 to 1000 $\mathrm{m}{\mathrm{m}}^2/min$ (computed). Reference: University of Utah Nanofab, ‘DWL 66 Specs’ (Heidelberg DWL 66+): 405 or 375 nm diode lasers (375 nm for SU-8 and i-line resists), HiRes and modes I to V with minimum features 0.3, 0.6, 0.8, 1, 2 and 4 um, address grid 5 to 200 nm, write speed 3 to 2000 mm2/min at 405 nm and 2 to 110 mm2/min at 375 nm, alignment 100 to 800 nm, edge roughness 50 to 160 nm, CD uniformity 60 to 250 nm (3 sigma), 128 to 1000 grey levels, up to 200 x 200 mm2 exposure (fetch-tool summary); NIST CNST NanoFab, ‘Heidelberg MLA150 Maskless Aligner’: 8 W at 405 nm and 2.8 W at 375 nm diode lasers, 1 um minimum feature, 10 to 15 min for 100 x 100 mm2, overlay 500 nm front and 1000 nm back side, 6 x 6 to 200 x 200 mm2 substrates, three cameras for alignment (fetch-tool summary).

Ques: How do direct writers align, and what is greyscale exposure?

Cameras align to existing marks, and dose is varied per pixel. Utah’s DWL 66+ gives alignment measurement accuracy from 100 $\mathrm{nm}$ in HiRes to 800 $\mathrm{nm}$ in mode V (3$\sigma$), and NIST’s MLA150 gives 500 $\mathrm{nm}$ front-side and 1000 $\mathrm{nm}$ back-side overlay using three cameras. The DWL offers 128 or 255 grey levels, or 1000 with a professional upgrade, and a 375 $\mathrm{nm}$ laser for SU-8 and i-line resists. Varying dose across a pattern produces sloped or curved resist profiles for micro-optics (my reading). These overlays are similar to the 0.5 to 1 $\mu \mathrm{m}$ of mask aligners (Contact and Proximity Mask Aligner page), so direct writers replace masks for prototypes without losing alignment (my reading). Reference: University of Utah Nanofab, ‘DWL 66 Specs’ (Heidelberg DWL 66+): 405 or 375 nm diode lasers (375 nm for SU-8 and i-line resists), HiRes and modes I to V with minimum features 0.3, 0.6, 0.8, 1, 2 and 4 um, address grid 5 to 200 nm, write speed 3 to 2000 mm2/min at 405 nm and 2 to 110 mm2/min at 375 nm, alignment 100 to 800 nm, edge roughness 50 to 160 nm, CD uniformity 60 to 250 nm (3 sigma), 128 to 1000 grey levels, up to 200 x 200 mm2 exposure (fetch-tool summary); NIST CNST NanoFab, ‘Heidelberg MLA150 Maskless Aligner’: 8 W at 405 nm and 2.8 W at 375 nm diode lasers, 1 um minimum feature, 10 to 15 min for 100 x 100 mm2, overlay 500 nm front and 1000 nm back side, 6 x 6 to 200 x 200 mm2 substrates, three cameras for alignment (fetch-tool summary); Contact and Proximity Mask Aligner page of this vault.

Ques: When is interference or direct write chosen over masks and e-beam?

By pattern type and size. Seo et al. use interference for large periodic areas: membrane reflectors near 95 per cent at 1300 $\mathrm{nm}$, anti-reflection near 5 per cent, plasmonic colour filters over 2.5 x 2.5 cm, photonic crystals and x-ray gratings. Direct writers handle arbitrary patterns at 0.3 to 4 $\mu \mathrm{m}$ without a mask (Utah; NIST). Arbitrary sub-100 $\mathrm{nm}$ patterns need e-beam writing (Electron-Beam Lithography Writer page). Interference at 193 $\mathrm{nm}$ reaches 96 $\mathrm{nm}$ features, three times finer than the DWL HiRes mode (computed), but only for periodic layouts (my reading). Direct writers also make the masks used by aligners (Contact and Proximity Mask Aligner page; my reading). Reference: J.-H. Seo, J. H. Park, Z. Ma, J. Choi and B.-K. Ju, ‘Nanopatterning by Laser Interference Lithography: Applications to Optical Devices’, arXiv:1402.2189: two-beam pitch Lambda = lambda/(2 sin theta) with minimum lambda/2, I(x) = 2A[cos((4 pi x/lambda) sin theta) + 1], sources 364, 355, 244, 213 and 193 nm with minimum features 182, 178, 122 and 96 nm, Lloyd’s mirror with one direct and one reflected beam, 515 nm doubled and 257 nm sources used, 90 degree double exposure for square and three beams for hexagonal arrays, 9 to 18 mJ/cm2 shrinking 770 nm-pitch patterns from 390 to 190 nm, applications in membrane reflectors (95 per cent near 1300 nm), anti-reflection (5 per cent), plasmonic colour filters, photonic crystals and x-ray gratings (fetch-tool summary); University of Utah Nanofab, ‘DWL 66 Specs’ (Heidelberg DWL 66+): 405 or 375 nm diode lasers (375 nm for SU-8 and i-line resists), HiRes and modes I to V with minimum features 0.3, 0.6, 0.8, 1, 2 and 4 um, address grid 5 to 200 nm, write speed 3 to 2000 mm2/min at 405 nm and 2 to 110 mm2/min at 375 nm, alignment 100 to 800 nm, edge roughness 50 to 160 nm, CD uniformity 60 to 250 nm (3 sigma), 128 to 1000 grey levels, up to 200 x 200 mm2 exposure (fetch-tool summary); NIST CNST NanoFab, ‘Heidelberg MLA150 Maskless Aligner’: 8 W at 405 nm and 2.8 W at 375 nm diode lasers, 1 um minimum feature, 10 to 15 min for 100 x 100 mm2, overlay 500 nm front and 1000 nm back side, 6 x 6 to 200 x 200 mm2 substrates, three cameras for alignment (fetch-tool summary); Electron-Beam Lithography Writer page of this vault; Contact and Proximity Mask Aligner page of this vault.

References

1. J.-H. Seo, J. H. Park, Z. Ma, J. Choi and B.-K. Ju, “Nanopatterning by laser interference lithography: applications to optical devices,” arXiv:1402.2189. Available: https://arxiv.org/pdf/1402.2189
2. University of Utah Nanofab, “DWL 66 specs” (Heidelberg Instruments DWL 66+). Available: https://www.nanofab.utah.edu/wp-content/uploads/2022/12/DWL-66-Specs.pdf
3. NIST Center for Nanoscale Science and Technology, “NanoFab tool: Heidelberg MLA150 maskless aligner.” Available: https://www.nist.gov/laboratories/tools-instruments/nanofab-tool-heidelberg-mla150-maskless-aligner
4. Contact and Proximity Mask Aligner page of this vault.
5. Electron-Beam Lithography Writer page of this vault.

Related pages in this vault: Contact and Proximity Mask Aligner, Electron-Beam Lithography Writer, Spin Coater and Resist Track, Nanoimprint Lithography Tool.