line width roughness measurement

**LWR** (Line Width Roughness) measurement is the **quantification of random fluctuations in the width (CD) of a patterned line along its length** — capturing how much the line width varies from point to point, which directly affects transistor performance variability. **LWR Measurement Details** - **Definition**: $LWR = 3sigma$ of the line width measured at many points along the line. - **Relation to LER**: $LWR^2 = LER_{left}^2 + LER_{right}^2 - 2 ho cdot LER_{left} cdot LER_{right}$ where $ ho$ is the correlation between left and right edges. - **Uncorrelated**: If edges are uncorrelated ($ ho = 0$): $LWR = sqrt{2} cdot LER$. - **CD-SEM**: The standard measurement tool — measures width at hundreds of points along the line. **Why It Matters** - **Electrical Impact**: LWR directly causes Vth variation — wider sections have different threshold voltage than narrower sections. - **Performance**: LWR causes drive current ($I_{on}$) and leakage ($I_{off}$) variability — degrades circuit performance margins. - **IRDS Targets**: The IRDS targets <12% LWR/CD ratio — increasingly difficult at sub-5nm nodes. **LWR** is **the waviness of the line width** — measuring how much a patterned line's CD fluctuates along its length, driving transistor variability.