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: $LWR^2 = LER_{left}^2 + LER_{right}^2 - 2\rho cdot LER_{left} cdot LER_{right}$ where $\rho$ is the correlation between left and right edges.
• Uncorrelated: If edges are uncorrelated ($\rho = 0$): $LWR = \sqrt{2} cdot LER$.
• 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.