Do not count shared shifts as independent cells
Every cell in one lot inherits the same synthetic lot component. More rows do not create more independent lots.
MEMORY / SRAM / VARIABILITY
SRAM variation and corner coverage
A sigma without hierarchy and coverage can mix fixed condition shifts, lot-to-lot movement, wafer structure, local mismatch, measurement noise, and missing observations into one ambiguous number.
01Conditionfixed direction
02Lotshared shift
03Wafer + sitenested structure
04Replicatemeasurement layer
READ THE HIERARCHY
Shared causes create shared observations.
The V128 dataset is synthetic and known-ground-truth: four conditions, four lots, three wafers per lot, a 5 x 5 site grid, and two replicate rows. Its purpose is to expose attribution and denominator choices, not to imitate a foundry distribution.
Keep location attached
A 5 x 5 coordinate grid preserves smooth spatial structure separately from cell-local mismatch.
Separate reading noise from cell state
Paired replicate rows share the cell-condition state while carrying opposite-sign synthetic measurement-noise terms.
VARIANCE CLOSURE
Total = component variances + pairwise covariance remainder
Summing only diagonal component variances is incomplete whenever component vectors co-vary in the selected analysis set. V128 reports the remainder and the absolute closure error instead of hiding it.
FOUR ANALYSIS SETS
Name the rows before comparing sigma.
Condition matched
- Numerator
- Valid replicate rows at one condition
- Denominator
- Cells represented in all four conditions
- Question
- What varies inside one declared condition?
Pooled total
- Numerator
- All valid replicate rows
- Denominator
- Every eligible condition and valid observation
- Question
- How much spread appears when fixed shifts remain pooled?
Common set
- Numerator
- Valid replicate means
- Denominator
- Only cells represented in all four conditions
- Question
- What changes after equalizing cell coverage?
All valid
- Numerator
- Every valid cell-condition mean
- Denominator
- All observed cell-condition pairs
- Question
- What does the available dataset say without common-set filtering?
FIXED CONDITION BOUNDARY
Fixed condition is not sigma.
Nominal, read-stress, write-stress, and inverter-skew directions are deterministic PD/PG/PU offsets in this teaching model. No percentile, occurrence probability, or foundry-corner equivalence is assigned.
- DeclareName the condition and role offsets.
- SeparateKeep fixed shifts out of within-condition spread.
- Map only with evidenceAdd sigma meaning only when an independent statistical definition supports it.
SOURCE SPINE
Methods, uncertainty, and semiconductor context
These are link-only anchors. The hierarchy, coefficients, rows, missingness, and numerical outputs in V128 are original synthetic teaching artifacts.
NIST/SEMATECH: nested variationOpen source ->NIST/SEMATECH: variance componentsOpen source ->NIST/SEMATECH: confidence interval for standard deviationOpen source ->NIST TN 1297: reporting uncertaintyOpen source ->IEEE: Matching Properties of MOS TransistorsOpen source ->IEEE: Analysis and Decomposition of Spatial VariationOpen source ->ACM: Statistical Analysis of SRAM Cell StabilityOpen source ->SemiAgora upstream variability chainContinue ->
No PDK parameter, physical SRAM margin, silicon Vmin, failure probability, array yield, process capability, recipe recommendation, qualification, production readiness, or foundry signoff follows from this lesson or its synthetic lab.