Name the quantity
Edge position, linewidth, local CD, read margin, and a normalized profile response are different quantities. A shared word such as sigma does not make them comparable.
METROLOGY / VARIABILITY / UNCERTAINTY
Keep the contract attached to the number.
An uncertainty budget becomes useful only after the quantity, unit, measurement grain, denominator, evaluation method, correlation, and evidence boundary are visible.
observed spreadALEATORICmissing knowledgeEPISTEMICmeasurement systemMEASUREMENTmodel discrepancyMODEL
BUDGET ANATOMY
Four questions come before combination.
The V136 fixtures are original teaching values. They expose bookkeeping and refusal behavior; they do not imitate a fab distribution or transfer a source result.
Lock grain and denominator
A trace segment, wafer site, cell-condition observation, condition row, AFM-like map, and Gauge R&R study represent different counted units.
Separate the class
Observed stochastic spread, missing knowledge, measurement-system effects, and model discrepancy answer different questions and stay visible as separate components.
Declare evaluation
Type A and Type B describe how a component is evaluated. They do not rename aleatoric, epistemic, measurement, or model uncertainty.
COMBINE ONLY AFTER COMPATIBILITY
Variance terms plus named covariance
Every component must describe the same output quantity, unit, grain, denominator, and evidence class. An explicit sensitivity coefficient maps each standard uncertainty to that output.
u_c^2 = sum((c_i u_i)^2) + 2 sum(rho_ij c_i u_i c_j u_j)k = 2 is shown only as a teaching interval. It is not a universal confidence level, coverage statement, acceptance limit, or disposition rule.
ONE DISCIPLINE / DIFFERENT GRAINS
The same reading order travels across domains.
LER/LWR and PSD
Sampling pitch and trace length define the visible spatial band. Edge correlation changes linewidth variance.
Open V127Hierarchical variation
Condition, lot, wafer, site, replicate, and residual components do not gain independent samples at the same rate.
Open V128Plasma-etch uncertainty
Condition-dependent spread remains a normalized teaching signal, not a recipe or transferable process window.
Inspect signalHybrid-bonding metrology
Surface and mechanical characterization requires map identity, aperture, uncertainty, and replacement evidence before readiness claims.
Inspect signalREADING ORDER
Move from definition to a visible stop.
- 01Define
Quantity, unit, sign convention, extraction method, operating condition, grain, and denominator.
- 02Decompose
Aleatoric, epistemic, measurement, and model components, including unknown or zero states explicitly.
- 03Correlate
Named covariance terms only; no hidden independence assumption and no rho outside the declared component pair.
- 04Filter
Sampling pitch, measurement length, PSD band, aperture response, detrend, and finite degrees of freedom.
- 05Stop
Refuse mixed dimensions, cross-case ranking, missing classes, insufficient samples, and production requests.
No physical calibration, universal uncertainty budget, process recipe, acceptance threshold, qualification, material disposition, silicon correlation, production readiness, or signoff follows from this lesson or its deterministic lab.