🧪 Module 2 · Chemistry and Materials Science · Chapter 2.5 · 13 min read

Lithography Chemistry

How do you print 28 nm features with 193 nm light? — the story of photoresist chemistry.

Prerequisites

2.4 — Thin-Film Deposition: ALD, PVD, CVD

What you'll learn here

List the three steps of photolithography (coat, expose, develop)
Explain the chemical difference between positive and negative photoresists
Use the Rayleigh criterion ($\mathrm{CD} = k_1 \lambda / \mathrm{NA}$) to compute the minimum printable feature
Show why chemical amplification is critical for EUV-dose stability
Summarize thermal and chemical constraints of lithography in the SIDRA 28 nm flow

Hook: Printing 28 nm with 193 nm Light

Think of a photographer: lens resolution is bound by the wavelength of light. With visible light (400-700 nm) you can resolve features around ~200 nm. So how do you print a 28 nm MOSFET gate with 193 nm light? You cheat — but only with the chemical cheats that physics allows.

SIDRA Y10 places BEOL memristor stacks on a 28 nm CMOS base. That 28 nm is patterned with ArF immersion lithography: 193 nm light + water-immersion lens + chemically amplified resist + multi-patterning. Each step is an engineering tradeoff, and each tradeoff is realized as a chemical reaction.

This chapter explains why fabricating a chip takes an enormous amount of chemistry — and why EUV (13.5 nm) is not “just a shorter wavelength”.

Intuition: Light → Chemistry → Shape

Photolithography has three stages:

Coat (spin coating): liquid photoresist is dropped on the wafer and spun at 3000 rpm → 50-200 nm film. Solvent evaporates; resist remains.
Expose: 193 nm light passes through a photomask (template); only certain regions of the resist get illuminated. In those regions, the chemistry changes.
Develop: a chemical bath dissolves one class of resist and leaves the other. The mask pattern remains on the wafer — 4× shrunk.

Positive resist: the illuminated region dissolves (like a photographic negative). The opened windows expose the underlying layer to etch or implant.

Negative resist: the illuminated region hardens. Only the dark regions dissolve in develop.

SIDRA uses 95% positive resist (sharp edges, less contamination). Negative is reserved for special cases.

Formalism: Rayleigh Criterion and Chemical Amplification

L1 · Başlangıç

Simple rule: the smaller the wavelength $\lambda$ , the smaller the printable feature. But there’s an optical floor:

\mathrm{CD} = k_1 \cdot \frac{\lambda}{\mathrm{NA}}

$\mathrm{CD}$ — Critical Dimension (the smallest printable feature)
$\lambda$ — wavelength
$\mathrm{NA}$ — Numerical Aperture (lens opening)
$k_1$ — process constant (0.25–0.5)

193 nm, NA = 1.35 (immersion), $k_1 = 0.3$ → $\mathrm{CD} \approx 43$ nm. The single-patterning floor.

L2 · Tam

How do we reach 28 nm? Three tricks:

Immersion: put water between the lens and the wafer. Effective NA rises 1.44× (water’s refractive index). Ceiling: $\mathrm{NA}_{max} = n_{medium}$ .
Off-axis illumination + OPC (Optical Proximity Correction): the mask isn’t a plain rectangle — it’s distorted to pre-compensate diffraction. $k_1$ drops to ~0.25.
Multi-patterning (LELE, SAQP): split one mask into 2 or 4 steps. LELE (Litho-Etch-Litho-Etch) → half the effective pitch. SAQP (Self-Aligned Quadruple) → quarter.

SIDRA 28 nm is satisfied by LELE. Below 7 nm requires SAQP or EUV.

Chemical amplification (CAR):

A 193 nm photon carries $= hc/\lambda = 6.4$ eV. Enough to break a C-C bond (~3.6 eV) — but not enough to transform the whole resist. So:

The resist contains PAG (Photoacid Generator) molecules.
A photon cleaves a PAG → releases one H⁺ (proton).
The proton acts as a catalyst — each deprotects 100-1000 resist monomers.
A Post-Exposure Bake (PEB, 100-130°C, 60 s) drives diffusion + reaction.

Net effect: 10³ chemical events per photon. Sharp contrast at low dose.

Typical SIDRA parameters:

Resist thickness: 80 nm (thick → doesn’t collapse, but resolution drops)
Exposure dose: 30 mJ/cm²
PEB: 110°C × 60 s
Develop: TMAH 2.38%, 30 s

L3 · Derin

Shot noise (EUV’s silent killer): a 13.5 nm photon carries 92 eV — one photon can cleave ~10 bonds. Good, but few photons is the new problem.

At a 10 × 10 nm pixel, 30 mJ/cm² EUV → ~2000 photons per pixel. Pure photon shot noise: $\sigma/\mu = 1/\sqrt{2000} \approx 2.2\%$ .
Real-world LER is 2-3 nm (industry data). Why? Resist stochastics dominate at volumes smaller than the photon-dose scale:
- PAG density ~0.05/nm³ → a 10 × 10 × 50 nm critical volume holds ~250 PAG molecules. Count fluctuation alone gives σ/μ = $1/\sqrt{250} \approx 6.3\%$ — about 3× worse than the 2.2% photon shot noise.
- Photoacid diffusion range ~3-5 nm: each acid deprotects ~20-50 monomers with Poisson spread.
- Finite polymer chain length → develop yields jagged, not crisp, edges.
Net result: observed LER is not photon shot noise-limited; it’s set by molecular-scale resist chemistry. At CD = 10 nm, LER 2-3 nm means 20-30% deviation.

Fixes: higher dose (hurts throughput), metal-oxide resists (more photon absorption + less chain-scission spread), stochastics-aware OPC, longer PEB.

Numerical example — Rayleigh + LELE:

193 nm immersion, NA 1.35, $k_1 = 0.28$ : $\mathrm{CD} = 0.28 \cdot 193/1.35 = 40$ nm. LELE halves the pitch → effective $\mathrm{CD} = 20$ nm. Plenty for SIDRA 28 nm logic + 15 nm SRAM.

DSA (Directed Self-Assembly): block copolymer (PS-b-PMMA) self-organizes into periodic phases. Lithography supplies a guide pattern; DSA fills the space between. Cheap sub-10 nm lines. A candidate for SIDRA Y100.

Nanoimprint (NIL): the mask is physically pressed onto the resist. No optics — pure mechanical contact + UV cure. Sub-10 nm is easy, but defect rates are high; now in NAND Flash production.

Experiment: Thought Experiment — The Contrast Curve

A resist’s contrast curve plots dose (mJ/cm²) vs remaining resist thickness (%). For positive resist:

  remaining
  100% ├──╲
       │   ╲
   50% │    ╲
       │     ╲╲
    0% │      ╲──────
       └─────┴─────────── dose
             D₀   (threshold)

Steps:

Dose below $D_0$ : resist remains intact (no development). Contrast = 0.
Cross $D_0$ : sharp drop. Steeper drop → higher γ (contrast coefficient).
High dose: resist dissolves fully. $D_{100\%}$ .

$\gamma = 1/\log_{10}(D_{100}/D_0)$ . CAR resists reach $\gamma \approx 6-10$ (very sharp). Older DNQ resists: $\gamma \approx 3$ .

Sketch it on paper. SIDRA targets $\gamma > 5$ — below that, LER explodes.

Quick Quiz

1/5What are the three core steps of photolithography?

Lab Exercise

Lithography plan for SIDRA 28 nm logic:

(a) 193 nm, NA = 1.35, $k_1 = 0.28$ → single-patterning CD? (b) With LELE on the same system, what’s the effective CD? (c) Dose 30 mJ/cm², 10 nm × 10 nm pixel area. How many 193 nm photons land per pixel? ( $E_{photon} = hc/\lambda$ , $h = 6.63 \times 10^{-34}$ J·s) (d) What is shot noise σ/μ? Is LER a problem?

Answers

(a) CD = 0.28 · 193 / 1.35 = 40 nm.

(b) LELE halves the pitch → effective CD = 20 nm. Ample margin for SIDRA 28 nm.

(c) $E_\gamma = hc/\lambda = (6.63 \times 10^{-34})(3 \times 10^{8})/(193 \times 10^{-9}) = 1.03 \times 10^{-18}$ J = 6.4 eV. Pixel area 100 nm² = $10^{-12}$ cm². Energy = 30 mJ/cm² × $10^{-12}$ cm² = $3 \times 10^{-14}$ J. Photon count = $3 \times 10^{-14} / 1.03 \times 10^{-18}$ = ~29,000 photons/pixel.

(d) σ/μ = $1/\sqrt{29000} \approx 0.59\%$ . Photon shot noise is negligible at 193 nm. At EUV (13.5 nm, same dose) the photon is 92 eV → ~14.3× fewer photons (~2000) → σ/μ ≈ 2.2%. Pure photon shot noise would give only ~0.2-0.5 nm LER; but real EUV systems show 2-3 nm LER because of resist stochastics (PAG count, photoacid diffusion, chain length). At small CDs this is 20-30% variance — critical.

Cheat Sheet

Litho 3 steps: spin coat → expose (mask + light) → develop.
Rayleigh: $\mathrm{CD} = k_1 \lambda / \mathrm{NA}$ . SIDRA 28 nm: 193 nm + NA 1.35 + LELE.
CAR (chemical amplification): PAG → H⁺ → 10³ catalytic reactions. Low dose, sharp contrast.
Positive vs negative resist: positive — illuminated region dissolves (SIDRA 95%); negative — illuminated region hardens.
SIDRA chemical budget: 80 nm resist, 30 mJ/cm², 110°C PEB, 2.38% TMAH develop.
Shot noise: negligible at 193 nm; critical at EUV (~50 photons/pixel → LER 2-3 nm).

Vision: The Future of Lithography

High-NA EUV (NA 0.55): ASML Twinscan EXE:5000 (2024-25), for N2/A14. Single-patterning 8 nm.
Hyper-NA EUV (NA 0.7+): 2030+ research, sub-5 nm features.
DSA (Directed Self-Assembly): block copolymer + litho guide. Cheap sub-10 nm lines.
Nanoimprint (NIL): mechanical press + UV cure. Canon FPA-1200NZ2C drives NAND production.
Metal-oxide resists (MOR): Inpria’s ZrO₂-based — ~3× better photon absorption at EUV; LER drops.
Attosecond lithography: x-ray laser (still research, 2035+).
Electron-beam direct write (EBL): maskless, very slow but ultra-fine. Used for mask-making and research.
Photon-crystal self-assembly: template-free pattern formation; research phase.

Biggest lever for post-Y10 SIDRA: a High-NA EUV + DSA hybrid. EUV for critical logic at 8 nm, DSA for intermediate fill at 5 nm. Mask count drops 3×, wafer cost ~40% lower. 2028–2030 horizon.

Prerequisites

What you'll learn here

🪝 Hook: Printing 28 nm with 193 nm Light

🧭 Intuition: Light → Chemistry → Shape

📐 Formalism: Rayleigh Criterion and Chemical Amplification

🧪 Experiment: Thought Experiment — The Contrast Curve

📝 Quick Quiz

🛠️ Lab Exercise

🗂️ Cheat Sheet

🔮 Vision: The Future of Lithography

📚 Further Reading