Line Edge Roughness Line Width Roughness Naming
LER and LWR are named by counting edges, one or two, and that count is the entire difference between them — line edge roughness (LER) measures how much a single edge of a line wanders away from its ideal straight path, while line width roughness (LWR) measures how much the line's width, the distance between its two edges, varies along its length. A line can have significant LER on both edges yet modest LWR, if the two edges happen to wander together; the names exist separately because a single-edge number and a width number answer different engineering questions, even though both come from the same wavy line.
A few things explain why keeping these two names distinct matters rather than collapsing them into one roughness number:
LWR depends on whether the two edges wander in correlation, and LER alone cannot tell you that. If both edges of a line happen to bow the same direction at the same point along its length (correlated wander), the width stays nearly constant even though each edge individually shows high LER — in that case LWR is small. If the two edges wander independently or in opposite directions (anticorrelated wander), the width swings wildly even with moderate LER on each edge — LWR is large. Reporting only LER hides this correlation entirely, which is why serious CD-uniformity work reports both numbers side by side rather than picking one.
The two names matter for different downstream failures. LWR is the number that predicts transistor-to-transistor variability directly, since a gate's effective width (and therefore its drive current and threshold voltage) is set by local line width, not by which direction either individual edge happens to be leaning. LER matters most where edge position itself is the concern independent of width, such as how roughness on one edge propagates into an adjacent feature during a tight-pitch double patterning or spacer-defined process, where that edge becomes someone else's spacer-inner-surface.
Where the roughness comes from also differs between the two names, which is why the fix for one doesn't automatically fix the other. LER traces back largely to photon-shot-noise and resist-molecule-size statistical fluctuations at a single edge during exposure and development; LWR inherits that same edge-level noise but is also shaped by whatever etch-transfer step comes after lithography, since an etch can either smooth a resist edge's roughness slightly or amplify it depending on the chemistry's own edge-roughening tendencies. A process that improves resist-level LER can still show disappointing LWR after etch if the etch step itself adds anticorrelated roughness.
Siblings worth distinguishing: this entry covers edge-and-width roughness naming specifically, not CD bias (covered elsewhere), which is about the mean width shifting with local pattern density rather than about random variation along a single line's length — bias is a systematic shift, roughness is a statistical spread, and the two are reported as entirely separate numbers on the same metrology report.
Read LER and LWR as two different questions asked of the same noisy edge data: LER asks "how far does this one edge wander," and LWR asks "how much does the resulting width vary," and because the answer to the second question depends on whether both edges wander together or apart, a fab reports both rather than assuming one predicts the other.