Spin Coater and Resist Track

1. Theory

• Definition: A resist track is a linked cluster that primes, coats, bakes and develops wafers before and after exposure; its spin coater sets resist thickness by balancing centrifugal flow against viscosity and solvent evaporation (EPFL; Hall et al.).
• Spin physics: The Emslie-Bonner-Peck equation gives thinning as $-2\rho {\omega }^2{h}^3/(3{\eta }_0)$, and the final thickness scales as ${\eta }_0^{1/3}{\omega }^{-1/2}$ (Hall et al.).
• Thin-film optics: Reflection from the substrate forms standing waves with period $\lambda /(2n)$ in the resist, and dose to clear swings with thickness; TARC and BARC suppress these reflections (MicroChemicals note; AZ data sheet).
• Bakes: Soft bake drives out solvent and post-exposure bake drives acid-catalysed reactions in chemically amplified resists (AZ data sheet; Photoresist and Process Window page).

2. Working Principle

• Prime: HMDS vapour promotes adhesion (EPFL).
• Coat: BARC and resist are dispensed and spun, with edge-bead removal and back-side rinse (EPFL; AZ data sheet).
• Bake and chill: Hot plates bake and chill plates cool each wafer, with multi-zone plates for PEB (EPFL; Hansson and Boyd).
• Develop: A puddle of 0.26 N TMAH develops for about 60 s, followed by a DI rinse (AZ data sheet; EPFL).
• Link to scanner: Wafers pass between track and exposure tool (EPFL; High-NA DUV Immersion Scanner page).

3. Applications

• All lithography layers: Every patterned layer is coated and developed on a track (EPFL).
• CD uniformity control: Thickness, bake and develop uniformity set across-wafer CD (MicroChemicals note; Hansson and Boyd).
• Antireflective stacks: BARC and TARC for reflective substrates and small features (AZ data sheet).

Spin Coating

Name	Formula	Related Formulae	Variables/Constants
Spin-off thinning	$\frac{dh}{dt}=-\frac{2\rho {\omega }^2{h}^3}{3{\eta }_0}$	$h\left(t\right)=\frac{h_0}{\sqrt{1+\frac{4\rho {\omega }^2{h}_0^{2}t}{3{\eta }_0}}}$	$h:filmthickness$ $\rho :density$ $\omega :angularspeed$ $\begin{array}{r}{\eta }_0:viscosity;Halletal.:\\ Emslie-Bonner-Peckequation;solutionfor\\ constantviscosity(computedby\\ integration)\end{array}$ $\begin{array}{r}(assumed:toluene\rho =870kg/m^3,\nu =0.1553\\ c{m}^2/s,3000\mathrm{rpm},h_0=50\mu \mathrm{m};computed:{\eta }_0=\\ 13.5mPas,initialrate530\mu m/s,10.6\mu \mathrm{m}\\ after1sand2.0\mu \mathrm{m}after30swithout\\ evaporation)\end{array}$
Final thickness scaling	$h_f\propto {\eta }_0^{1/3}{\omega }^{-1/2}$	$E=k\left(x_I-x_e\right)$	$E:evaporationrate$ $k:mass-transfercoefficient$ $\begin{array}{r}{x}_I,x_e:initialandequilibriumsolvent\\ fractions;Halletal.:{\omega }^{-1/2}withinerror\\ forallcases,modelwithinabout10per\\ cent,under-predictingaboveabout10wt\%\\ andwithvolatilesolvents\end{array}$ $\begin{array}{r}(computed:goingfrom1000to4000\mathrm{rpm}\\ halvesthethickness)\end{array}$
Viscosity grades	$\frac{h_2}{h_1}={\left(\frac{{\eta }_2}{{\eta }_1}\right)}^{1/3}(\text{Hall})$	$14\mathrm{cP}\to 1.08\mu \mathrm{m},29\mathrm{cP}\to 1.73\mu \mathrm{m}$	$\begin{array}{r}AZMiR701datasheet:twogradesandthe\\ 0.6to2.5\mu \mathrm{m}range(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:the29/14viscosityratio\\ predicts1.27timesthicker;thesheet\\ shows1.60times,anapparentexponentof\\ 0.65)\end{array}$

Optics and Chemistry of the Film

Name	Formula	Related Formulae	Variables/Constants
Standing waves and swing curve	${\Lambda }_{sw}=\frac{\lambda }{2n}$	$\Delta d_{swing}=\frac{\lambda }{4n}$	${\Lambda }_{sw}:standing-waveperiodintheresist$ $\begin{array}{r}\Delta d_{swing}:thicknesschangebetweenswing\\ maximaandminima;MicroChemicalsnote:\\ halfthewavelengthinresist,114\mathrm{nm}for\\ i-linewithnabout1.6,57\mathrm{nm}thickness\\ forahalf-wavepathchange\end{array}$ $\begin{array}{r}(assumed:ArFresistn=1.7;computed:{\Lambda }_{sw}\\ =57\mathrm{nm}and\Delta d=28\mathrm{nm}at193\mathrm{nm})\end{array}$
Antireflective coatings	$\text{TARC: top reflection}\downarrow ,\text{BARC: substrate reflection}\downarrow$	$D_{TARC}=180,D_{none}=220mJ/c{\mathrm{m}}^2$	$\begin{array}{r}MicroChemicalsnote:TARCremovedin\\ development,BARCbakedat200{}^{\circ }Cand\\ removedbydryetch,afewtensofnm\\ thicknesschangeshiftingdosebyseveral\\ tensofpercent;AZdatasheet:about65\\ \mathrm{nm}AquatarTARCloweringthedose,BARC\\ below0.5\mu \mathrm{m}\end{array}$ $\begin{array}{r}(computed:TARClowersthenominaldoseby\\ 18percent)\end{array}$
Developer concentration	$0.26\mathrm{N}\mathrm{TMAH}=2.38\%$	$c_w\approx \frac{0.26\times 91.15}{1000}$	$\begin{array}{r}TMAH:tetramethylammoniumhydroxide,molar\\ mass91.15g/mol(assumed);AZdatasheet:\\ 0.26N(2.38percent)standard,60s\\ puddleorimmersion;EPFL:TMA238WA\\ developer\end{array}$ $\begin{array}{r}(computed:23.7g/L,2.37percentbymass\\ forunitdensity,matching2.38)\end{array}$

Track Sequence and Control

Name	Formula	Related Formulae	Variables/Constants
Bake sequence	$\text{HMDS}\to \text{coat}\to \text{soft bake}\to \text{chill}\to \text{expose}\to \text{PEB}\to \text{chill}\to \text{develop}$	$T_{SB}=90\text{to}100{}^{\circ }C,T_{PEB}=110\text{to}115{}^{\circ }C$	$\begin{array}{r}EPFL:HMDSvapour,coaterswithedge-bead\\ removalandback-siderinse,hotplates,\\ chillplates,8-zonePEBplates;AZdata\\ sheet:softbakeandPEBtemperaturesand\\ 60to90stimes\end{array}$ $\begin{array}{r}(myreading:chillplatesreturnthewafer\\ toafixedtemperaturesothenextstep\\ startsfromthesamestate)\end{array}$
PEB temperature control	$\text{optimal: heat and cool at maximum rate}$	$\Delta CD=\frac{\partial CD}{\partial T}\Delta T$	$\begin{array}{r}HanssonandBoyd:optimalPEBprofile;\\ EPFL:8-zonePEBplates;Photoresistand\\ ProcessWindowpage:acid-catalysed\\ deprotectionduringPEB;CDsensitivity\\ form(myreading)\end{array}$ $\begin{array}{r}(myreading:ashort,fast-rampedbake\\ fixestheacidreactiontime,whichiswhy\\ multi-zoneplatesandfastchillareused)\end{array}$
Edge bead and substrate flatness	$\text{EBR solvent at the edge, back-side rinse}$	$TTV<2\mu \mathrm{m}$	$\begin{array}{r}AZdatasheet:EBRsolvents;EPFL:EBR\\ needle,back-siderinse,waferswithTTV\\ below2\mu \mathrm{m}\end{array}$ $\begin{array}{r}(myreading:thebeadthickenedbysurface\\ tensionattherimisremovedsoitcannot\\ contaminatechucksorflake)\end{array}$

Important Questions

Ques: What sets the thickness of a spin-coated resist film?

Spin speed, viscosity and solvent evaporation. Hall et al. use the Emslie-Bonner-Peck equation, $dh/dt=-2\rho {\omega }^2{h}^3/(3{\eta }_0)$, until thinning slows to the evaporation rate $k(x_I-x_e)$, after which the film only loses solvent; they find the final thickness scales as ${\eta }_0^{1/3}{\omega }^{-1/2}$ within error from 12 $\mathrm{nm}$ to 33 $\mu \mathrm{m}$. Going from 1000 to 4000 $\mathrm{rpm}$ therefore halves the thickness (computed). For a toluene-like liquid at 3000 $\mathrm{rpm}$ starting at 50 $\mu \mathrm{m}$, flow alone thins it to 10.6 $\mu \mathrm{m}$ in 1 s and 2.0 $\mu \mathrm{m}$ in 30 s (computed), so most thinning happens in the first seconds. Their model is within about 10 per cent but under-predicts concentrated or volatile solutions. Reference: D. B. Hall, P. Underhill and J. M. Torkelson, ‘Spin Coating of Thin and Ultrathin Polymer Films’, Polym. Eng. Sci. 38, 2039 (1998): Emslie-Bonner-Peck thinning dh/dt = -2 rho omega^2 h^3/(3 eta_0), evaporation E = k(x_I - x_e), flow ending when thinning equals evaporation, h proportional to eta_0^(1/3) omega^(-1/2) within error, 12 nm to 33.2 um films, 500 to 4500 rpm for 60 s, toluene nu 0.1553 cm2/s and rho 0.87 g/cm3, model within about 10 per cent, underprediction above about 10 wt% and with volatile solvents, overprediction at low concentration (fetch-tool summary).

Ques: Does the one-third-power viscosity law explain resist viscosity grades?

Not fully. Hall et al. report $h\propto {\eta }_0^{1/3}$ for polymer solutions, but warn that their model under-predicts thickness above about 10 wt% and with volatile solvents, because evaporation during spin-off raises viscosity. The AZ MiR 701 data sheet lists 14 $\mathrm{cP}$ giving about 1.08 $\mu \mathrm{m}$ and 29 $\mathrm{cP}$ about 1.73 $\mu \mathrm{m}$. The one-third law predicts only 1.27 times thicker for the 2.07 times higher viscosity, whereas the sheet shows 1.60 times, an apparent exponent of 0.65 (computed). Since resists are concentrated solutions in the regime where Hall et al. find under-prediction, and the data sheet does not state that both grades were spun at the same speed, the data-sheet curves are the more reliable guide for real resists (my reading). Reference: D. B. Hall, P. Underhill and J. M. Torkelson, ‘Spin Coating of Thin and Ultrathin Polymer Films’, Polym. Eng. Sci. 38, 2039 (1998): Emslie-Bonner-Peck thinning dh/dt = -2 rho omega^2 h^3/(3 eta_0), evaporation E = k(x_I - x_e), flow ending when thinning equals evaporation, h proportional to eta_0^(1/3) omega^(-1/2) within error, 12 nm to 33.2 um films, 500 to 4500 rpm for 60 s, toluene nu 0.1553 cm2/s and rho 0.87 g/cm3, model within about 10 per cent, underprediction above about 10 wt% and with volatile solvents, overprediction at low concentration (fetch-tool summary); MicroChemicals / Merck, ‘AZ MiR 701 Series’ technical data sheet (University of Arizona clean-room copy): positive resist for 0.5 and 0.35 um nodes on i-line steppers, 14 cP giving about 1.08 um and 29 cP about 1.73 um, range 0.6 to 2.5 um, soft bake 90 to 100 C for 60 to 90 s, PEB 110 to 115 C for 60 to 90 s, 0.26 N (2.38 per cent) TMAH developers, 60 s puddle or immersion, doses 220 mJ/cm2 (0.35 um lines) and 180 mJ/cm2 with AZ Aquatar TARC at 0.56 NA, TARC about 65 nm, BARC for patterns below 0.5 um, n = 1.63365 at 633 nm, EBR solvent (fetch-tool summary).

Ques: Why does dose to clear swing with resist thickness, and how is it suppressed?

Because light reflected from the substrate interferes with the incoming wave. The MicroChemicals note explains that standing waves form with a period of half the wavelength in the resist, about 114 $\mathrm{nm}$ for i-line with $n$ near 1.6, so a thickness change of about 57 $\mathrm{nm}$ moves the film from a swing maximum to a minimum; variations of a few tens of nanometres can shift the needed dose by several tens of per cent. At 193 $\mathrm{nm}$ with an assumed index of 1.7, the corresponding values are 57 and 28 $\mathrm{nm}$ (computed). A top antireflective coating reduces the air-resist reflection and dissolves in the developer, and a bottom coating absorbs the substrate reflection. The AZ data sheet quotes 220 $mJ/c{\mathrm{m}}^2$ without and 180 $mJ/c{\mathrm{m}}^2$ with a 65 $\mathrm{nm}$ TARC, 18 per cent less (computed). Reference: MicroChemicals, ‘Anti-reflective coating of photoresist’ application note: standing-wave period half the wavelength in the resist, about 114 nm for i-line with n about 1.6, about 57 nm thickness for a half-wave path change, stronger standing waves for reflective substrates and weakly absorbing resists, thickness variations of a few tens of nm shifting dose by several tens of per cent, TARC reducing top reflection and removed in development, BARC reducing substrate reflection and baked at 200 C, broadband exposure smoothing (fetch-tool summary); MicroChemicals / Merck, ‘AZ MiR 701 Series’ technical data sheet (University of Arizona clean-room copy): positive resist for 0.5 and 0.35 um nodes on i-line steppers, 14 cP giving about 1.08 um and 29 cP about 1.73 um, range 0.6 to 2.5 um, soft bake 90 to 100 C for 60 to 90 s, PEB 110 to 115 C for 60 to 90 s, 0.26 N (2.38 per cent) TMAH developers, 60 s puddle or immersion, doses 220 mJ/cm2 (0.35 um lines) and 180 mJ/cm2 with AZ Aquatar TARC at 0.56 NA, TARC about 65 nm, BARC for patterns below 0.5 um, n = 1.63365 at 633 nm, EBR solvent (fetch-tool summary).

Ques: What does a resist track contain and in what order are wafers processed?

Coating, baking and developing modules joined by a robot. The EPFL TEL Clean Track ACT 8 has an HMDS vapour prime, a BARC coater and a resist coater with edge-bead-removal needles and back-side rinse, a developer with high-flow DI rinse, low- and high-temperature hot plates, high-speed chill plates and 8-zone precision plates for post-exposure bake, with track temperature and humidity controlled. The AZ data sheet gives a typical recipe: soft bake at 90 to 100 ${}^{\circ }\mathrm{C}$ for 60 to 90 s, exposure, PEB at 110 to 115 ${}^{\circ }\mathrm{C}$, then 60 s in 0.26 N TMAH. That normality corresponds to 2.37 per cent by mass (computed), matching the quoted 2.38 per cent. Chill plates reset temperature between steps (my reading). Reference: EPFL Center of MicroNanoTechnology, ‘TEL Clean Track ACT 8’ equipment page: 100 mm cluster, BARC coater with edge-bead-removal needle and back-side rinse, resist coater with four pump lines, developer with high-flow DI rinse, HMDS vapour adhesion, low- and high-temperature hot plates, high-speed chill plates, 8-zone precision PEB plates with cooling arm, temperature and humidity controller, JSR M108Y and M35G resists, TMA238WA developer, wafers with TTV below 2 um (fetch-tool summary); MicroChemicals / Merck, ‘AZ MiR 701 Series’ technical data sheet (University of Arizona clean-room copy): positive resist for 0.5 and 0.35 um nodes on i-line steppers, 14 cP giving about 1.08 um and 29 cP about 1.73 um, range 0.6 to 2.5 um, soft bake 90 to 100 C for 60 to 90 s, PEB 110 to 115 C for 60 to 90 s, 0.26 N (2.38 per cent) TMAH developers, 60 s puddle or immersion, doses 220 mJ/cm2 (0.35 um lines) and 180 mJ/cm2 with AZ Aquatar TARC at 0.56 NA, TARC about 65 nm, BARC for patterns below 0.5 um, n = 1.63365 at 633 nm, EBR solvent (fetch-tool summary).

Ques: Why is post-exposure bake control so important?

Because the chemistry that forms the image runs during the bake. In chemically amplified resists, the photoacid catalyses deprotection during PEB, so bake time and temperature set how far the reaction and acid diffusion proceed (Photoresist and Process Window page). Hansson and Boyd found that the optimal PEB profile is to heat and cool at maximum speed, which fixes the effective reaction time; the EPFL track uses 8-zone precision plates with an integrated cooling arm for the same reason (my reading). Any CD change then follows $\partial CD/\partial T$ times the plate temperature error (my reading). Exposure itself happens on the scanner linked to the track (High-NA DUV Immersion Scanner page), so the track controls everything before and after the image is printed. Reference: A. Hansson and S. Boyd, ‘Optimal Temperature Profiles for Post-Exposure Bake of Photoresist’, Proc. SPIE 3332, 271 (1998), abstract: optimal PEB strategy to heat and cool with maximum speed (fetch-tool summary); EPFL Center of MicroNanoTechnology, ‘TEL Clean Track ACT 8’ equipment page: 100 mm cluster, BARC coater with edge-bead-removal needle and back-side rinse, resist coater with four pump lines, developer with high-flow DI rinse, HMDS vapour adhesion, low- and high-temperature hot plates, high-speed chill plates, 8-zone precision PEB plates with cooling arm, temperature and humidity controller, JSR M108Y and M35G resists, TMA238WA developer, wafers with TTV below 2 um (fetch-tool summary); Photoresist and Process Window page of this vault; High-NA DUV Immersion Scanner page of this vault.

References

1. D. B. Hall, P. Underhill and J. M. Torkelson, “Spin coating of thin and ultrathin polymer films,” Polymer Engineering and Science, vol. 38, no. 12, pp. 2039-2045, 1998. Available: https://gnusha.org/~nmz787/pdf/Spin_Coating_of_Thin_and_Ultrathin_Polymer_Films.pdf
2. Merck / MicroChemicals, “AZ MiR 701 Series” technical data sheet, University of Arizona copy. Available: https://wp.optics.arizona.edu/osccleanroom/wp-content/uploads/sites/66/2024/09/tds_az_mir701_series.pdf
3. MicroChemicals, “Anti-reflective coating of photoresist,” application note. Available: https://microchemicals.com/dokumente/application_notes/anti_reflective_coating_photoresist.pdf
4. EPFL Center of MicroNanoTechnology, “TEL Clean Track ACT 8.” Available: https://www.epfl.ch/research/facilities/cmi/equipment/photolithography/tel-cleantrack-act-8/
5. A. Hansson and S. Boyd, “Optimal temperature profiles for post-exposure bake of photoresist,” Proc. SPIE 3332, pp. 271-281, 1998 (abstract read). Available: https://web.stanford.edu/~boyd/papers/peb.html
6. Photoresist and Process Window page of this vault.
7. High-NA DUV Immersion Scanner page of this vault.

Related pages in this vault: Photoresist and Process Window, High-NA DUV Immersion Scanner, Spectral Reflectometer, Light-Matter Interaction for Optical Inspection, Contact and Proximity Mask Aligner, Laser Direct-Write and Interference Lithography System.