local cd uniformity (lcdu)

Local CD Uniformity (LCDU) measures the critical dimension (CD) variation of features at very small length scales — specifically the CD variation between nominally identical features within a small area (typically within a single die or even within a single field). It captures the random, feature-to-feature dimensional variability that cannot be corrected by scanner or process adjustments.

What LCDU Measures

• Consider a row of 100 nominally identical lines. Measure each line width. The standard deviation of these widths is the LCDU (usually reported as 3σ).
• LCDU captures the random component of CD variation — the part that varies from one feature to the next even under identical processing conditions.
• It is distinct from global CDU (variation across the wafer) or field CDU (variation within an exposure field), which are systematic and correctable.

Why LCDU Matters

• At advanced nodes, transistor performance is extremely sensitive to gate length variation. LCDU directly affects Vt (threshold voltage) variation, which determines circuit speed and power uniformity.
• For SRAM cells, LCDU in gate or fin dimensions determines the minimum operating voltage (Vmin) — worse LCDU means the chip must run at higher voltage, wasting power.
• Yield: Extreme LCDU outliers can cause functional failures — features too wide cause shorts, features too narrow cause opens.

What Drives LCDU

• Photon Shot Noise: The dominant contributor at EUV. Random photon arrival creates random exposure dose, leading to random CD variation.
• Resist Chemistry: Random distribution and activation of photoacid generators, diffusion variability.
• Line Edge Roughness (LER): Closely related — roughness on each edge of a feature contributes to CD variation when measured at any single point along the feature.
• Etch Contributions: Plasma etch adds its own random component to LCDU through microloading and ion angular variations.

Typical Values

• Target LCDU at advanced nodes: 1.0–1.5 nm (3σ) for critical gate or fin patterning layers.
• Current EUV capability: ~1.2–2.0 nm (3σ), depending on resist, dose, and feature type.

Improvement Approaches

• Higher Dose: More photons reduce shot noise contribution. Moving from 30 mJ/cm² to 60 mJ/cm² reduces photon noise by ~30%.
• New Resist Materials: Metal-oxide resists and other non-CAR materials may provide better LCDU at equivalent dose.
• Etch Optimization: Reducing etch-related contributions through process tuning.

LCDU is the key lithographic metric at advanced nodes — it directly connects patterning capability to transistor performance variability and circuit yield.