diffusion length

Diffusion length in photolithography refers to the average distance that chemically active species — primarily photoacid molecules in chemically amplified resists (CARs) — migrate during the post-exposure bake (PEB) step. This diffusion length directly determines the trade-off between resist sensitivity amplification and resolution blur.

Acid Diffusion in CARs

• When a CAR is exposed to UV or EUV light, photoacid generator (PAG) molecules absorb photons and produce strong acid molecules.
• During PEB (typically 60–120 seconds at 90–130°C), these acid molecules diffuse through the resist and catalyze chemical reactions (deprotection of the polymer backbone), changing the polymer's solubility.
• Each acid molecule can catalyze hundreds of deprotection events as it diffuses — this is the "chemical amplification" that gives CARs their high sensitivity.

Why Diffusion Length Matters

• Signal Amplification: Longer diffusion length → each acid catalyzes more reactions → higher sensitivity (lower dose needed).
• Image Blur: Longer diffusion length → the chemical image is smeared over a larger area → worse resolution and higher line edge roughness.
• Shot Noise Smoothing: Diffusion averages out statistical variations in acid generation (from photon shot noise) → reduces stochastic defects. This is beneficial.
• Trade-Off: Optimal diffusion length balances sufficient amplification and noise smoothing against acceptable blur.

Typical Values

• DUV CARs: Diffusion lengths of 10–30 nm during standard PEB conditions.
• EUV CARs: Target 5–15 nm — shorter diffusion for better resolution, but need to maintain adequate amplification.
• Metal-Oxide Resists: No acid diffusion mechanism — chemical change is localized to the absorption site, achieving ~0 nm "diffusion length."

Controlling Diffusion Length

• PEB Temperature: Higher temperature accelerates diffusion — diffusion length increases approximately as $\sqrt{D \cdot t}$ where D is the diffusion coefficient (temperature-dependent) and t is bake time.
• PEB Time: Longer bake → more diffusion. But PEB time also affects quench reactions and acid loss.
• Quencher: Base additives in the resist neutralize acid, effectively reducing the distance acid can travel before being quenched. More quencher → shorter effective diffusion length.
• Polymer Matrix: The resist polymer's free volume and glass transition temperature affect how easily acid diffuses.

Diffusion length is one of the key tuning knobs in resist engineering — it directly controls the tradeoff between sensitivity, resolution, and roughness that defines resist performance.