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.