{
  "schema": "semiagora.ler-lwr-variability.v1",
  "version": "2026-09-03-v127",
  "workUnitId": "SA-PROC-LER-LWR-VARIABILITY-059",
  "productContractSha256": "C0E4B966AAD12FDE6B41394CD6EB1D7EE19F38F4D871E1529470E38C021BAD9D",
  "title": "LER/LWR To SRAM Variability Chain",
  "proposition": "Two edges can move together, apart, or independently.",
  "userOutcome": "Distinguish LER from LWR and inspect how edge correlation, correlation length, extraction bandwidth, and CD aperture change local-CD dispersion before any bounded device or SRAM proxy.",
  "evidenceClass": "illustrative-original-surrogate",
  "routes": [
    "/learn/line-edge-width-roughness",
    "/simulations/ler-lwr-variability-chain",
    "/labs/ler-lwr-variability-chain"
  ],
  "defaultInput": {
    "seed": 127031,
    "nominalCd": 32,
    "edgeSigma": 1.2,
    "edgeCorrelation": 0.35,
    "correlationLength": 12,
    "measurementLength": 256,
    "localCdAperture": 8,
    "sampleCount": 256,
    "inputUnit": "nm"
  },
  "presets": [
    {
      "id": "default",
      "label": "Default",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 1.2,
        "edgeCorrelation": 0.35,
        "correlationLength": 12,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    },
    {
      "id": "zeroRoughness",
      "label": "Zero roughness",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 0,
        "edgeCorrelation": 0.35,
        "correlationLength": 12,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    },
    {
      "id": "perfectCorrelation",
      "label": "Perfect correlation",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 1.2,
        "edgeCorrelation": 1,
        "correlationLength": 12,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    },
    {
      "id": "independentEdges",
      "label": "Independent edges",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 1.2,
        "edgeCorrelation": 0,
        "correlationLength": 12,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    },
    {
      "id": "antiCorrelatedEdges",
      "label": "Anti-correlated",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 1.2,
        "edgeCorrelation": -1,
        "correlationLength": 12,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    },
    {
      "id": "shortCorrelation",
      "label": "Short correlation",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 1.2,
        "edgeCorrelation": 0.35,
        "correlationLength": 2,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    },
    {
      "id": "longCorrelation",
      "label": "Long correlation",
      "input": {
        "seed": 127031,
        "nominalCd": 32,
        "edgeSigma": 1.2,
        "edgeCorrelation": 0.35,
        "correlationLength": 40,
        "measurementLength": 256,
        "localCdAperture": 8,
        "sampleCount": 256,
        "inputUnit": "nm"
      }
    }
  ],
  "inputRanges": {
    "seed": {
      "min": 1,
      "max": 999999,
      "integer": true
    },
    "nominalCdNm": {
      "min": 12,
      "max": 80
    },
    "edgeSigmaNm": {
      "min": 0,
      "max": 3
    },
    "edgeCorrelation": {
      "min": -1,
      "max": 1
    },
    "correlationLengthNm": {
      "min": 1,
      "max": 64
    },
    "measurementLengthNm": {
      "min": 64,
      "max": 512
    },
    "localCdApertureNm": {
      "min": 1,
      "max": 32
    }
  },
  "synthesis": {
    "prng": "mulberry32",
    "normalTransform": "Box-Muller",
    "spatialProcess": "stationary AR(1)",
    "arCoefficient": "exp(-sampling_pitch_nm / correlation_length_nm)",
    "detrend": "least-squares straight line per edge",
    "normalization": "each detrended edge basis has descriptive sample standard deviation one",
    "crossCorrelation": "Gram-Schmidt orthogonal companion followed by rho*u_left + sqrt(1-rho^2)*u_orthogonal",
    "edgeCoordinates": "left=-nominal_cd/2+sigma*u_left; right=nominal_cd/2+sigma*u_right",
    "circularBoundary": "The synthetic trace wraps only for local-CD aperture averaging; it is not a physical wafer boundary.",
    "traceDigest": "SHA-256 of UTF-8 semiagora.ler-lwr-trace-digest.v1 bytes with canonical inputs and trace columns serialized as fixed-decimal-10 strings.",
    "traceDigestDecimalPlaces": 10
  },
  "metricContract": {
    "ler": {
      "quantity": "edge-position residual",
      "leftAndRightReportedSeparately": true,
      "pooledDefinition": "3*sqrt((var(left residual)+var(right residual))/2)",
      "convention": "3 x descriptive sample standard deviation after straight-line detrend with N-1 divisor",
      "bandwidth": "minimum wavelength=2*sampling pitch; maximum wavelength=measurement length",
      "semNoiseCorrection": false
    },
    "lwr": {
      "quantity": "right edge minus left edge",
      "definition": "3 x descriptive sample standard deviation of linewidth residual with N-1 divisor",
      "exactVarianceIdentity": "var(width)=var(left)+var(right)-2*cov(left,right)",
      "equalVarianceRelation": "LWR_3sigma=LER_3sigma*sqrt(2*(1-rho)) only when left and right variances are equal under this locked convention",
      "universalTwoTimesRule": false,
      "twoTimesCondition": "rho=-1 with equal edge variances under the locked convention"
    },
    "localCd": {
      "quantity": "circular boxcar average of right-minus-left width",
      "aperturePoints": "nearest odd point count to aperture_nm/sampling_pitch_nm, bounded below trace length",
      "histogramBins": 16,
      "histogramCountMustEqualSamples": true
    },
    "statistics": [
      "count",
      "mean",
      "descriptive sample standard deviation",
      "minimum",
      "p05",
      "median",
      "p95",
      "maximum"
    ]
  },
  "bridgeContract": {
    "evidenceClass": "illustrative-original-surrogate",
    "architecture": "unspecified teaching chain",
    "calibration": "none",
    "coefficients": [
      {
        "id": "vt-shift-index",
        "formula": "clamp(-0.45*relative_cd_delta,-0.25,0.25)",
        "unit": "normalized index"
      },
      {
        "id": "dibl-shift-index",
        "formula": "clamp(-0.30*relative_cd_delta,-0.25,0.25)",
        "unit": "normalized index"
      },
      {
        "id": "drive-current-ratio",
        "formula": "clamp(1-0.80*relative_cd_delta-0.25*vt_shift_index,0.5,1.5)",
        "unit": "ratio to synthetic nominal"
      },
      {
        "id": "inverter-delay-ratio",
        "formula": "clamp(1/drive_current_ratio,0.5,1.5)",
        "unit": "ratio to synthetic nominal"
      },
      {
        "id": "snm-sensitivity-ratio",
        "formula": "clamp(1-1.20*abs(relative_cd_i-relative_cd_paired),0.5,1)",
        "unit": "sensitivity ratio, not mV SNM"
      },
      {
        "id": "write-margin-sensitivity-ratio",
        "formula": "clamp(1-0.90*abs(relative_cd_i-relative_cd_paired),0.5,1)",
        "unit": "sensitivity ratio, not mV write margin"
      }
    ],
    "pairing": "Each local-CD sample is paired with the sample half a trace away only to create a deterministic mismatch demonstration.",
    "measuredReplacementSlots": [
      "Matched CD-SEM or scatterometry edge traces with extraction recipe, uncertainty, bandwidth, and genealogy.",
      "Calibrated 3D device simulations or matched I-V data linking local geometry to DIBL, Vt, and drive current.",
      "Qualified compact models and transistor assignment for inverter delay.",
      "Transistor-level SRAM Monte Carlo with architecture, bias, temperature, SNM/write extraction, and measured validation."
    ],
    "prohibitedInterpretations": [
      "physical DIBL or Vt prediction",
      "physical drive-current or delay prediction",
      "SNM or write margin in volts",
      "cell fail probability",
      "yield",
      "process window",
      "recipe recommendation",
      "signoff"
    ]
  },
  "sourceSpine": [
    {
      "id": "nist-ler-lwr-metrology-issues",
      "title": "Issues in Line Edge and Linewidth Roughness Metrology",
      "organization": "NIST",
      "url": "https://www.nist.gov/publications/issues-line-edge-and-linewidth-roughness-metrology",
      "supports": [
        "RMS roughness depends on sampled length and sampling interval.",
        "LER and LWR require explicit extraction and uncertainty conventions.",
        "Roughness-to-device propagation remains incompletely established."
      ],
      "use": "definition and limitation only",
      "rights": "link-only; NIST and publication notices apply"
    },
    {
      "id": "nist-line-edge-width-chapter",
      "title": "Line Edge and Linewidth Roughness",
      "organization": "NIST",
      "url": "https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932010",
      "supports": [
        "Edge/width residual, RMS, PSD, autocovariance, and spatial-frequency vocabulary.",
        "Variance-from-PSD is a consistency relation, not a process qualification."
      ],
      "use": "metric vocabulary and extraction-bandwidth rationale",
      "rights": "link-only; NIST publication notices apply"
    },
    {
      "id": "nist-dimensional-pattern-metrology",
      "title": "Dimensional Metrology for Nanoscale Patterns",
      "organization": "NIST",
      "url": "https://www.nist.gov/programs-projects/dimensional-metrology-nanoscale-patterns",
      "supports": [
        "LWR is variation in line width relative to its average.",
        "Amplitude and frequency content both belong in roughness metrology."
      ],
      "use": "metrology context",
      "rights": "link-only; NIST notices apply"
    },
    {
      "id": "pmc-ler-lwr-correlation",
      "title": "Impact of Line Edge Roughness on ReRAM Uniformity and Scaling",
      "organization": "Scientific Reports / PMC",
      "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC6926851/",
      "supports": [
        "For equal edge variances, LWR variance depends on left-right edge cross-correlation.",
        "The relation is assumption-dependent and does not make LWR universally twice LER."
      ],
      "use": "correlation identity context; no ReRAM result is transferred to CMOS SRAM",
      "rights": "link-only; article license and PMC notices apply"
    },
    {
      "id": "pmc-ler-to-finfet-computational",
      "title": "Line-Edge Roughness from Extreme Ultraviolet Lithography to Fin-Field-Effect-Transistor: Computational Study",
      "organization": "Micromachines / PMC",
      "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC8706712/",
      "supports": [
        "LER-to-device analysis requires an explicit geometry and device-model bridge.",
        "A computational bridge is not measured fab evidence."
      ],
      "use": "bridge-boundary context only",
      "rights": "link-only; article license and PMC notices apply"
    },
    {
      "id": "semiagora-v123-roughness-path",
      "title": "Roughness and local CD to margin causal chain",
      "organization": "SemiAgora",
      "url": "/journeys/causal-chain/roughness-local-cd",
      "supports": [
        "Existing proxy/derived/reproduced/measured distinction.",
        "Existing measured-replacement slots and explicit yield stop."
      ],
      "use": "internal public continuity",
      "rights": "public SemiAgora route"
    }
  ],
  "interactionContract": {
    "runtime": "React state in the current browser tab",
    "presets": [
      "default",
      "zero roughness",
      "perfect correlation",
      "independent edges",
      "anti-correlated edges",
      "short correlation",
      "long correlation"
    ],
    "controls": [
      "seed",
      "nominal CD",
      "edge sigma",
      "left-right correlation",
      "correlation length",
      "measurement length",
      "local-CD aperture"
    ],
    "views": [
      "Trace",
      "Distribution",
      "Metrics",
      "Bridge",
      "Evidence"
    ],
    "charts": [
      "left and right edge trace",
      "local-CD trace",
      "local-CD histogram",
      "bounded proxy summaries"
    ],
    "exports": [
      "json",
      "csv"
    ],
    "deterministicExport": true,
    "resetRequiresExplicitCommand": true,
    "keyboardAccessibleLabels": true,
    "reducedMotionSupported": true,
    "noLocalStorage": true,
    "noSessionStorage": true,
    "noIndexedDb": true,
    "noUrlState": true
  },
  "privacy": {
    "browserTabStateOnly": true,
    "bundledSyntheticInputsOnly": true,
    "networkWrites": false,
    "accounts": false,
    "uploads": false,
    "images": false,
    "productionData": false,
    "privateMetrology": false,
    "processRecipes": false,
    "equipmentControls": false,
    "serverPersistence": false,
    "remoteFreeFormStorage": false,
    "analytics": false,
    "behavioralSignals": false,
    "aiModelCalls": false,
    "cookies": false,
    "localStorage": false,
    "sessionStorage": false,
    "indexedDb": false,
    "queryState": false,
    "fragmentState": false,
    "liveSolver": false,
    "liveMonteCarloService": false,
    "backgroundJobs": false,
    "databaseAccess": false,
    "cloudStorage": false
  },
  "limitations": [
    "All traces and distributions are deterministic synthetic teaching outputs, not fab, wafer, resist, mask, etch, device, circuit, or production data.",
    "The AR(1) process is a convenient stationary correlation model, not a universal physical PSD or stochastic lithography model.",
    "The reported descriptive 3-sigma values depend on the locked detrend, N-1 divisor, measurement length, sampling pitch, aperture, circular boundary, and absence of measurement-noise correction.",
    "The requested correlation length is a synthesis input, not a fitted or uncertainty-qualified metrology result.",
    "The equal-variance LER/LWR relation is conditional; unequal edge variance, different conventions, filtering, and real metrology can change the relation.",
    "The DIBL, Vt, drive-current, inverter-delay, SNM, and write-margin values are original normalized proxies with arbitrary visible coefficients and no calibration.",
    "The product cannot establish physical causality, statistical representativeness, measurement uncertainty, model validity, process capability, recipe transfer, yield, signoff, or production readiness.",
    "Researcher-facing businesses remain deferred to a separately verified V200 contract."
  ]
}