Multi-patterning techniques — Hinglish notes

4.3.9 · Hardware › Semiconductor Fabrication

Multi-patterning EXISTS kyun karta hai?

Yeh formula kyun? Diffraction. Pitch $p$ ki ek grating, light ko $sin θ_{m} = mλ / p$ angles par orders mein diffract karti hai. Image banane ke liye lens mein kam se kam 0th aur 1st orders capture karne padte hain. Lens $sin θ = NA$ tak accept karta hai, isliye $λ / p \leq NA$ chahiye, yaani minimum pitch $p_{m i n} = λ / NA$ aur half-pitch $HP = p_{m i n} /2 = 0.5 λ / NA$ . Clever illumination (off-axis, dipole) se $k_{1}$ ko $0.25$ ke paas squeeze kar sakte hain.

Numbers plug karo: single exposure best case $HP_{m i n} = 0.25 \times \frac{193 nm}{1.35} \approx 36 nm .$

Toh agar design rules mein 20 nm half-pitch ki demand hai aur EUV available nahi hai, toh ek shot mein yeh possible nahi → pattern split karna hi padega. Yahi poora motivation hai.

KAISE: main techniques

1. LELE — Litho-Etch-Litho-Etch (Double Patterning, DPT)

Kyun kaam karta hai: har individual exposure ek relaxed pitch $2 p$ dekhta hai (tool ki limit ke andar), lekin final composite pitch $p$ hoti hai.

Effective $k_{1}$ : kyunki do exposures interleave karte hain, achievable half-pitch aadha ho jaata hai → $k_{1}^{eff} \approx 0.125.$

Weakness — overlay: mask B ko mask A ki lines ke bilkul beech mein land karna padta hai. Koi bhi misalignment (overlay error) pitch walking (alternating wide/narrow spaces) ka kaaran banta hai. Yeh LELE ki Achilles heel hai aur yeh average out nahi hoti.

2. SADP — Self-Aligned Double Patterning (Spacer)

Self-aligned aur superior kyun: spacer ki width deposited-film thickness se set hoti hai, na ki kisi doosre exposure se — isliye final pitch ke dono edges ek hi lithography step se aate hain. Isse LELE ka overlay-driven pitch walking khatam ho jaata hai. Line width ko film deposition thickness se control kiya jaata hai, jo doosre mask alignment se kahin zyaada uniform hoti hai.

Cost: ab lines har jagah aati hain; layout ek regular grating hona chahiye aur unwanted spacer loops hataane ke liye extra cut/block masks chahiye (spacers, mandrel ends ke around closed loops banate hain).

3. SAQP — Self-Aligned Quadruple Patterning

Spacer trick do baar karo: spacers-of-spacers. Final pitch = mandrel pitch / 4. $p_{final} = \frac{p _{mandrel}}{2 ^{N}} (N = spacer generations)$ SAQP: $N = 2 \Rightarrow$ pitch/4. ~10 nm-class fins/metal ke liye use hota hai.

4. LELELE / triple, aur SAOP (octuple)

LELE ko 3+ colors tak extend karo (LELELE) → pitch/3, jiske liye layout coloring chahiye (graph coloring: same mask par adjacent features itne door hone chahiye). SAOP = spacer trick ×3 → pitch/8.

Worked examples

Common mistakes

Flashcards

Single-exposure resolution floor kya set karta hai?

Rayleigh limit

HP = k_{1} λ / NA

jisme

k_{1} \to 0.25

λ = 193

nm,

NA \leq 1.35

⇒ ~36 nm.

Shorter wavelength ki jagah multi-patterning kyun use karte hain?

Jab shorter-

λ

tool (EUV) unavailable/too costly ho, layout ko sparse sub-patterns mein split karo jo har ek 193i par printable ho.

LELE ka full form kya hai?

Litho-Etch-Litho-Etch: do exposure+etch passes interleave karke pitch half karte hain.

LELE ki main weakness kya hai?

Do masks ke beech overlay error → pitch walking (uneven alternate spaces).

SADP "self-aligned" kyun hai?

Final pitch, EK exposure ki spacer film thickness se set hoti hai, na ki doosre mask alignment se → koi pitch-walking overlay term nahi.

SADP ke steps kya hain?

Mandrels print karo → conformal deposit → etch-back karke sidewall spacers chhodo → mandrels remove karo (2 spacers/mandrel).

SAQP mein pitch reduction kitna hota hai?

Pitch/4 (do spacer generations,

p_{mandrel} / 2^{2}

N spacer generations ke liye general pitch formula kya hai?

p_{final} = p_{mandrel} / 2^{N}

Spacer processes ko cut/block masks kyun chahiye?

Spacers, mandrel ends ke around closed loops banate hain aur har jagah print hote hain; cut masks unwanted loops/lines trim karte hain.

Double patterning ka effective

k_{1}

single ke mukable mein?

~0.125 vs 0.25 (half-pitch halved).

Recall Feynman: 12-saal ke bache ko samjhao

Socho tumhare paas ek stamp hai jo sirf itni hi paas-paas stripes print kar sakta hai — zyaada press karo toh woh blur ho jaati hain. Tum double close stripes chahte ho. Trick: pehle odd stripes stamp se print karo (aasaan, woh door-door hain), phir even stripes doosri press se gaps mein print karo. Ab paper par double stripes hain, chahe tumhara stamp better nahi hua! Aur bhi smart trick (spacers): mote blocks print karo, unke sides par thin coat spray karo, phir blocks dissolve karo — baaki bachi paint ki edges tumhari super-thin stripes hain, aur unki width sirf itni hai jitna tumne spray kiya. Koi doosra aiming nahi = koi tedhi lines nahi.

Connections

Photolithography — woh $λ$ /NA baseline set karta hai jo multi-patterning ko force karta hai.
EUV Lithography — 13.5 nm light jo multi-patterning ki zaroorat kam karti hai.
Overlay and Alignment — woh error source jo LELE ko destroy karta hai.
Etch and Deposition (CVD/ALD) — conformal ALD, SADP mein uniform spacers enable karta hai.
Design Rule Check and Layout Coloring — LELELE ke liye graph-coloring mask decomposition.
Rayleigh Criterion — first-principles resolution physics.