line edge roughness measurement

**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.