Track each edge separately
Subtract a fitted straight line from each edge, then report three times the descriptive sample standard deviation. The sample length, pitch, detrend, divisor, and filtering belong with the number.
PROCESS / METROLOGY / VARIABILITY
Line-edge and linewidth roughness
LER asks how one edge wanders. LWR asks how the distance between two edges changes. Correlation decides whether those two observations rise together or separate.
same edge sigma
different width response
different width response
THE DISTINCTION
Two rough edges do not imply one universal linewidth rule.
Track right minus left
Linewidth is the distance between the edges. Common-mode edge motion can leave width unchanged; opposing motion can magnify its variation.
Declare the aperture
An aperture average suppresses short spatial components. A local-CD distribution is therefore inseparable from its Extraction bandwidth and boundary convention.
CONDITIONAL RELATION
LWR = LER x sqrt(2 x (1 - rho))
This only holds for equal left and right edge variances under the same locked convention. At rho = +1, LER can remain nonzero while LWR is zero. At rho = 0, the ratio is sqrt(2). The 2 x case occurs only at rho = -1.
READING ORDER
Carry the measurement contract before the causal story.
- DefineName edge position, width, or aperture-averaged local CD and the 3-sigma convention.
- BoundRecord sampling pitch, measurement length, detrend, aperture, circular synthetic boundary, and missing SEM-noise correction.
- CompareInspect requested and realized edge correlation, then verify the width-variance identity.
- BridgeKeep device, delay, SNM, and write outputs as visible normalized sensitivities until calibrated replacement evidence exists.
SOURCE SPINE
Definition anchors and model boundaries
These are link-only references. The V127 generated traces are original synthetic teaching artifacts, not extracted publication data.
NIST: Issues in Line Edge and Linewidth Roughness MetrologyOpen source ->NIST: Line Edge and Linewidth RoughnessOpen source ->NIST: Dimensional Metrology for Nanoscale PatternsOpen source ->Scientific Reports / PMC: LER correlation contextOpen source ->Micromachines / PMC: computational LER-to-device bridgeOpen source ->SemiAgora roughness-to-margin causal chainContinue ->
No physical device prediction, process window, recipe recommendation, cell-fail probability, yield, production readiness, or signoff follows from this lesson or its synthetic lab.