LER (Line Edge Roughness) measurement is the quantification of random fluctuations in the position of a line edge in a patterned feature — measuring how much the actual edge deviates from the intended straight (or smooth) edge, typically using CD-SEM (Critical Dimension Scanning Electron Microscopy).

LER Measurement Methods

• CD-SEM: Scan the line edge at multiple points along its length — the standard deviation of edge positions is the LER.
• 3σ LER: LER is reported as 3σ of the edge position — $LER_{3sigma} = 3 sqrt{frac{1}{N}sum_i (x_i - ar{x})^2}$.
• PSD: Compute the power spectral density of edge fluctuations — reveals the spatial frequency content of roughness.
• Correlation Length: The characteristic length scale over which edge positions are correlated.

Why It Matters

• Scaling: LER does not scale with feature size — 2nm LER on a 20nm line is 10%, but on a 5nm line is 40%.
• Variability: LER causes transistor-to-transistor threshold voltage variation — a dominant variability source at advanced nodes.
• Yield: High LER causes shorts and opens — directly impacts manufacturing yield.

LER is the roughness of the pattern edge — measuring how much actual line edges deviate from the intended smooth design.