1. Theory

  • Definition: The photoresist converts the scanner’s aerial image into a relief pattern, and the process window is the range of dose and focus over which that pattern stays within its CD, resist-loss and sidewall specifications (Kirchauer).
  • Image quality: The normalized image log-slope, , measures how sharply the image changes at the edge and sets exposure latitude, (Kirchauer; Mack).
  • Resist response: The development-rate gradient equals resist contrast times the image log-slope, so both the image and the resist set resolution (Kirchauer).
  • Mask errors: At low , mask CD errors are amplified on the wafer by the MEEF, which can exceed the 4x reduction for contacts (Lin; Sharp patent).
  • Stochastics: Line edges are rough; for uncorrelated edges , and roughness redistributes between line-width roughness and CD uniformity as lines get shorter (Brunner et al.).

2. Working Principle

  • Exposure: In a non-amplified resist the photoactive compound is consumed at a rate (Kirchauer); in a chemically amplified resist the exposure releases a photoacid (Georgia Tech lecture; Houle et al.).
  • Post-exposure bake: The acid catalyses deprotection of the polymer over a long catalytic chain, while base quencher neutralizes acid and limits blur (Houle et al.).
  • Development: Exposed, deprotected regions dissolve in an aqueous base developer (Georgia Tech lecture).
  • Characterization: A focus-exposure matrix is printed and measured, shown as Bossung plots, and the exposure latitude is plotted against DOF (Kirchauer).

3. Applications

  • Process setup: Choosing dose and focus at the centre of the window (Kirchauer; Lin).
  • Mask specifications: Setting mask CD tolerance from the MEEF (Sharp patent; Lin).
  • Roughness control: Measuring unbiased LWR and PSD on the CD-SEM before and after etch (Cutler et al.; CD-SEM page).
  • Contamination control: Limiting airborne amines that poison chemically amplified resists (Houle et al.).

Image and Resist Response

NameFormulaRelated FormulaeVariables/Constants
Normalized image log-slope


Exposure latitude

Lithographic imaging equation


Process Window and Mask Errors

NameFormulaRelated FormulaeVariables/Constants
Process window


Mask error enhancement factor
Dill exposure model


Roughness and Resist Chemistry

NameFormulaRelated FormulaeVariables/Constants
Line-edge and line-width roughness

Roughness spectrum and line length
Chemically amplified resist

Important Questions

Ques: What sets exposure latitude, and how much NILS is needed?

The image log-slope at the edge. Kirchauer defines and gives , with = 10 and = 0 for an ideal resist. Mack measures EL over a plus or minus 10 per cent CD range, fits real data with , and notes that 15 per cent EL needs NILS of about 2.2; the fit gives 15.1 per cent (computed). A two-beam image, as formed by dipole illumination on the scanner (High-NA DUV Immersion Scanner page), has NILS of (Giannopoulos et al.), which is 31 per cent EL ideally but 23.5 per cent with Mack’s fit (computed). Brunner et al. recommend an image log-slope above 130 at 36 pitch, which is NILS 2.34 for 18 lines (computed), close to Mack’s threshold. Reference: H. Kirchauer, PhD thesis, Institute for Microelectronics, TU Vienna (1998), sections 3.2.1 and 3.2.2: focus-exposure matrix shown as Bossung plots, process window as the focus and exposure region keeping linewidth, resist loss and sidewall angle in specification, exposure latitude against DOF from fitted rectangles or ellipses, lithographic imaging equation d ln r/dx = gamma d ln I/dx, NILS = w d ln I/dx, EL = alpha (NILS - beta) with alpha = 10 and beta = 0 for an ideal resist, resolution and DOF not independent (fetch-tool summary); C. A. Mack, ‘Using the Normalized Image Log-Slope, part 2’, The Lithography Expert, Spring 2001 (FINLE Technologies, KLA-Tencor): %EL about 10 NILS for an ideal resist on a +/-10 per cent CD range, %EL = a(NILS - b) in general, calibrated %EL = 8.9(NILS - 0.5), 15 per cent EL requiring NILS 2.2, NILS 2.5 giving best DOF for 0.25 um lines at NA 0.6 (fetch-tool summary); I. Giannopoulos, I. Mochi, M. Vockenhuber, Y. Ekinci and D. Kazazis, ‘Extreme ultraviolet lithography reaches 5 nm resolution’, arXiv:2402.18234 (PSI): NILS = (1/I)(dI/dx) w, contrast (I_max - I_min)/(I_max + I_min), two-beam monochromatic NILS = pi independent of pitch (fetch-tool summary); T. A. Brunner, X. Chen, A. Gabor, C. Higgins, L. Sun and C. A. Mack, ‘Line-Edge Roughness performance targets for EUV Lithography’, Proc. SPIE 10143, 101430E (2017): LWR = 3 sqrt(Var(X_R - X_L)) = sqrt2 LER and PPR = sqrt2 LER/2 for uncorrelated edges, LER described by 3 sigma, correlation length and roughness exponent, 36 nm pitch values LWR 3.76, LER 2.58, PPR 1.77 nm, L_C 8.02 nm, exponent 0.82, LCDU(L) and LWR(L) adding in quadrature, crossing near 25 nm, open below 5 nm and short above 30 nm local CD, LWR below 4 nm and ILS above 130 per um recommended, fat-tailed CD distributions (fetch-tool summary); High-NA DUV Immersion Scanner page of this vault.

Ques: How is a process window read from a focus-exposure matrix?

From the region where every specification holds. Kirchauer describes printing a focus-exposure matrix, plotting CD against focus at several doses as Bossung curves, and taking the window as the focus and exposure region that keeps linewidth, resist loss and sidewall angle in specification. Fitting the largest rectangles or ellipses inside it and plotting their height against width gives exposure latitude against DOF. Lin evaluates DOF at 8 per cent EL with plus or minus 15 CD bounds, while Mack uses plus or minus 10 per cent of CD; for a 150 line both are the same plus or minus 15 (computed), but for smaller lines Lin’s fixed bound would be the looser criterion (my reading). Kirchauer stresses that resolution and DOF cannot be defined independently. Reference: H. Kirchauer, PhD thesis, Institute for Microelectronics, TU Vienna (1998), sections 3.2.1 and 3.2.2: focus-exposure matrix shown as Bossung plots, process window as the focus and exposure region keeping linewidth, resist loss and sidewall angle in specification, exposure latitude against DOF from fitted rectangles or ellipses, lithographic imaging equation d ln r/dx = gamma d ln I/dx, NILS = w d ln I/dx, EL = alpha (NILS - beta) with alpha = 10 and beta = 0 for an ideal resist, resolution and DOF not independent (fetch-tool summary); B. J. Lin, Optical Lithography: Here Is Why, 2nd ed., SPIE Press (2021), sample chapter PM329: E-D DOF based on 8 per cent EL and +/-15 nm CD bounds, MEEF more than 4 for contact holes negating 4X reduction, line ends up to 10, k1 0.227 for 32 nm at 134 nm and NA 0.95 (fetch-tool summary); C. A. Mack, ‘Using the Normalized Image Log-Slope, part 2’, The Lithography Expert, Spring 2001 (FINLE Technologies, KLA-Tencor): %EL about 10 NILS for an ideal resist on a +/-10 per cent CD range, %EL = a(NILS - b) in general, calibrated %EL = 8.9(NILS - 0.5), 15 per cent EL requiring NILS 2.2, NILS 2.5 giving best DOF for 0.25 um lines at NA 0.6 (fetch-tool summary).

Ques: How large can the MEEF be, and does it really exceed the reduction ratio?

It depends on the feature, and the sources span a wide range. The Sharp patent defines MEEF as the wafer CD change divided by the mask CD change converted to 1x, quotes about 1.5 to 4 for features at or below the wavelength, and measures 5.0 for positive and 2.2 for negative resist on a KrF halftone mask, falling to 1.7 with multiple exposure. Lin reports more than 4 for contact holes, which negates the 4x reduction, and up to 10 at line ends. A 2 mask error at 4x, 0.5 at 1x, therefore becomes 2 on the wafer at MEEF 4 and 5 at MEEF 10 (computed). The values are compatible: dense lines sit near 1.5 to 4, while contacts and line ends, with lower image slope, exceed 4 (my reading). Reference: Sharp Kabushiki Kaisha, ‘Mask pattern and method for forming resist pattern using mask pattern thereof’, US publication 2004/0025139 (Justia): MEEF as wafer resist CD fluctuation divided by mask CD fluctuation converted to 1x, prior values about 1.5 to 4 at or below the wavelength, 5.0 positive and 2.2 negative resist on KrF halftone masks, 1.7 with multiple exposure (fetch-tool summary); B. J. Lin, Optical Lithography: Here Is Why, 2nd ed., SPIE Press (2021), sample chapter PM329: E-D DOF based on 8 per cent EL and +/-15 nm CD bounds, MEEF more than 4 for contact holes negating 4X reduction, line ends up to 10, k1 0.227 for 32 nm at 134 nm and NA 0.95 (fetch-tool summary).

Ques: Is LWR exactly root two times LER?

Only if the two edges are uncorrelated. Brunner et al. give under that assumption and warn it may break down. Their own 36 pitch values are LWR 3.76 and LER 2.58 , while is 3.65 (computed), 3 per cent lower. Writing would need a slight anti-correlation of about -0.06 (computed; my reading of the general form), and the PPR of 1.77 against a predicted 1.82 (computed) points the same way. The difference is small, so the uncorrelated rule is a good approximation here, but it should be checked from both edges rather than assumed (my reading). Reference: T. A. Brunner, X. Chen, A. Gabor, C. Higgins, L. Sun and C. A. Mack, ‘Line-Edge Roughness performance targets for EUV Lithography’, Proc. SPIE 10143, 101430E (2017): LWR = 3 sqrt(Var(X_R - X_L)) = sqrt2 LER and PPR = sqrt2 LER/2 for uncorrelated edges, LER described by 3 sigma, correlation length and roughness exponent, 36 nm pitch values LWR 3.76, LER 2.58, PPR 1.77 nm, L_C 8.02 nm, exponent 0.82, LCDU(L) and LWR(L) adding in quadrature, crossing near 25 nm, open below 5 nm and short above 30 nm local CD, LWR below 4 nm and ILS above 130 per um recommended, fat-tailed CD distributions (fetch-tool summary).

Ques: How does roughness change through etch and with line length?

Etch smooths high-frequency roughness, and short lines turn roughness into CD variation. Cutler et al. found that PSD(0) stays roughly constant through etch while unbiased LWR fell from 3.5 to 2.6 , a 26 per cent drop (computed), and correlation length rose from about 7 to 13 . PSD(0) comes from uncorrelated events such as photon shot noise, and correlation from acid reaction-diffusion. Brunner et al. show that LCDU and LWR for lines of length L add in quadrature to the long-line LWR, crossing near 25 , about three correlation lengths. They recommend LWR below 4 and note that open and short failures come from fat-tailed local CD distributions. CD-SEM measurement noise must be removed to obtain unbiased values (Cutler et al.; CD-SEM page). Reference: C. Cutler et al. (with C. Mack), ‘Roughness Power Spectral Density as a Function of Resist Parameters and Its Impact Through Process’, Proc. SPIE 10587, 1058707 (2018): variance as the PSD area set by PSD(0), correlation length and roughness exponent H, PSD(0) from uncorrelated random events including shot noise, correlation from acid reaction-diffusion, unbiased LWR 3.5 to 2.6 nm through etch while correlation length rose from about 7 to 13 nm and PSD(0) stayed constant, ASML 1900i and CG4000 CD-SEM (fetch-tool summary); T. A. Brunner, X. Chen, A. Gabor, C. Higgins, L. Sun and C. A. Mack, ‘Line-Edge Roughness performance targets for EUV Lithography’, Proc. SPIE 10143, 101430E (2017): LWR = 3 sqrt(Var(X_R - X_L)) = sqrt2 LER and PPR = sqrt2 LER/2 for uncorrelated edges, LER described by 3 sigma, correlation length and roughness exponent, 36 nm pitch values LWR 3.76, LER 2.58, PPR 1.77 nm, L_C 8.02 nm, exponent 0.82, LCDU(L) and LWR(L) adding in quadrature, crossing near 25 nm, open below 5 nm and short above 30 nm local CD, LWR below 4 nm and ILS above 130 per um recommended, fat-tailed CD distributions (fetch-tool summary); CD-SEM page of this vault.

Ques: Why are chemically amplified resists sensitive but prone to blur and contamination?

Because one acid triggers many reactions. The Georgia Tech lecture explains that the photoacid catalyses changes without being consumed, cutting the dose needed at deep-UV wavelengths. Houle et al. describe a very long catalytic chain in PTBOCST resists, so even little acid deprotects strongly at the image edge, which they identify as the main blur mechanism; diffusion dominates only for very mobile acids, erasing lines near 170 with TBI-T but only near 25 with TBI-PFBS. Base additives trap acid but lower contrast. Airborne amines at 3.5 to 15 , 7 on average, suppressed deprotection and caused up to 30 per cent model discrepancies. In a non-amplified resist, by contrast, the Dill model consumes the photoactive compound at (Kirchauer). The amplification that gives sensitivity therefore also amplifies blur and contamination (my reading). Reference: Georgia Tech ECE 6450 Lecture 8, ‘Photoresists and Non-optical Lithography’ (lecturer not named): contrast gamma = 1/log10(D100/D0), Dill alpha = A m + B, critical modulation transfer function, DNQ-novolac chemistry, chemically amplified resists with catalytic acid lowering dose for deep UV, standing waves from substrate reflection (fetch-tool summary); F. A. Houle, W. D. Hinsberg, M. I. Sanchez and J. A. Hoffnagle, ‘The influence of resist components on image blur in a patterned positive-tone chemically amplified photoresist’, IBM Research Report RJ10223 (2001): PTBOCST with TBI-T or TBI-PFBS PAG at 0.045 mol/kg, base additive TBAH, very long catalytic chain length, blur mainly from efficient deprotection at the image edge, PEB 85 C for 1 to 10 min, diffusion causing image loss near 25 nm (PFBS) and 170 nm (TBI-T), base lowering available acid and contrast, airborne amines 3.5 to 15 ppb (average 7) causing up to 30 per cent discrepancies (fetch-tool summary); H. Kirchauer, PhD thesis, TU Vienna (1998), section 5 (node 69): Dill model alpha = A m + B, A = (alpha_M - alpha_P) M_0, dm/dt = -C I m, P = M_0 - M, parameters measured per resist (fetch-tool summary).

References

  1. H. Kirchauer, PhD thesis, Institute for Microelectronics, TU Vienna, 1998, sections 3.2.1 and 3.2.2. Available: https://www.iue.tuwien.ac.at/phd/kirchauer/node41.html and https://iue.tuwien.ac.at/phd/kirchauer/node42.html
  2. H. Kirchauer, PhD thesis, Institute for Microelectronics, TU Vienna, 1998, Dill exposure model. Available: https://www.iue.tuwien.ac.at/phd/kirchauer/node69.html
  3. C. A. Mack, “Using the normalized image log-slope, part 2,” The Lithography Expert, Spring 2001. Available: https://lithoguru.com/scientist/litho_tutor/TUTOR33%20(Spring%2001).pdf
  4. I. Giannopoulos, I. Mochi, M. Vockenhuber, Y. Ekinci and D. Kazazis, “Extreme ultraviolet lithography reaches 5 nm resolution,” arXiv:2402.18234. Available: https://arxiv.org/pdf/2402.18234
  5. Georgia Institute of Technology, ECE 6450 Lecture 8, “Photoresists and Nonoptical Lithography.” Available: https://alan.ece.gatech.edu/ECE6450/Lectures/ECE6450L8-Photoresists%20and%20Nonoptical%20Lithography.pdf
  6. F. A. Houle, W. D. Hinsberg, M. I. Sanchez and J. A. Hoffnagle, “The influence of resist components on image blur in a patterned positive-tone chemically amplified photoresist,” IBM Research Report RJ10223, 2001. Available: https://dominoweb.draco.res.ibm.com/reports/RJ10223.pdf
  7. T. A. Brunner, X. Chen, A. Gabor, C. Higgins, L. Sun and C. A. Mack, “Line-edge roughness performance targets for EUV lithography,” Proc. SPIE 10143, 101430E, 2017. Available: https://lithoguru.com/scientist/litho_papers/2017_LER_Performance_Targets_for_EUV.pdf
  8. C. Cutler, J. W. Thackeray, J. DeSisto, J. Nelson, C.-B. Lee, M. Li, E. Aqad, X. Hou, T. Marangoni, J. Kaitz, R. Rena and C. Mack, “Roughness power spectral density as a function of resist parameters and its impact through process,” Proc. SPIE 10587, 1058707, 2018. Available: https://www.fractilia.com/s/SPIE2018_Roughnesspowerspectraldensityasafunctionofresistparameters.pdf
  9. Sharp Kabushiki Kaisha, “Mask pattern and method for forming resist pattern using mask pattern thereof,” US Patent Application 2004/0025139. Available: https://patents.justia.com/patent/7032209
  10. B. J. Lin, Optical Lithography: Here Is Why, 2nd ed. Bellingham, WA: SPIE Press, 2021, sample chapter. Available: https://photonicsforenergy.spiedigitallibrary.org/samples/PM329.pdf
  11. High-NA DUV Immersion Scanner page of this vault.
  12. CD-SEM page of this vault.

Related pages in this vault: High-NA DUV Immersion Scanner, CD-SEM, Optical CD Scatterometer (OCD), Patterned-Wafer Optical Inspection, Resolution Enhancement and Multiple Patterning, Spin Coater and Resist Track, Contact and Proximity Mask Aligner, EUV Scanner, Electron-Beam Lithography Writer, Plasma Asher (Barrel and Downstream).