Lilienfeld 1926 Stability Under Sustained Operation
# Characterize Stability Under Sustained Operation: The Fracture Margin Adds a Fourth Timeline
The 1925 protocol tracked three independent timescales of drift: operational (device under continuous bias), storage (unbiased shelf life), and cycling (repeated power on/off). This construction needs a fourth: whether the fracture-margin leakage component Step 8 identified as Path B grows over time as the Step 6 seal ages at that specific interface. Path B's magnitude is not guaranteed to stay fixed at whatever value Step 8 first measured — if the seal is slowly failing at the fracture margin specifically, rather than degrading uniformly across all four sealed interfaces, Path B will grow while the device's other characteristics remain stable, and only a timeline that isolates this one path will catch it.
The fracture-margin timeline requires a specific re-measurement, not a general health check. Operational, storage, and cycling drift can all be caught by periodically re-running Step 7's baseline I-V test — a general-purpose check. Fracture-margin drift requires re-running Step 8's specific dwell-time decay fit at each checkpoint, because only that measurement separates the decaying Path A component from the Path B plateau. A checkpoint that only re-measures baseline conductance could show a perfectly stable device while Path B silently grows underneath, because Path B's conduction only shows up distinctly in the control-electrode leakage measurement, not in the film's own terminal-to-terminal resistance.
Saturating exponential trend fitting applies here exactly as in the 1925 protocol, but to a different quantity. Where the 1925 series fit X(t) = X₀ + ΔX(1 − e^(−t/τ)) to baseline conductance and leakage drift, this construction fits the same functional form to the Step 8 plateau value itself, tracked across checkpoints. A growing plateau that saturates at some elevated value indicates a seal that is degrading toward a new, worse steady state rather than one that will continue degrading indefinitely — the same distinction the 1925 protocol drew between a bounded settling process and genuine ongoing failure.
| Step | Process operation | Input | Output | Specification | Constraint |
|---|---|---|---|---|---|
| 12.1 | Establish checkpoint schedule across all four timelines | Reproducibility-confirmed population from Step 11 | Locked checkpoint schedule | Checkpoints spaced to resolve expected drift timescales; schedule fixed before monitoring begins | Adaptive checkpoint spacing based on early results undermines the pre-registration discipline used throughout this series |
| 12.2 | At each checkpoint, re-run Step 7 baseline I-V test | Device from prior checkpoint | Baseline trend point | Same four-wire protocol and settling discipline as original Step 7 | Deviating from the original test procedure introduces a confound separate from genuine drift |
| 12.3 | At each checkpoint, re-run Step 8 dwell-time decay fit | Device from prior checkpoint | τ and plateau I₁₃ trend point | Same bias magnitude and dwell duration as original Step 8 | A different bias magnitude at checkpoint time changes the comparison basis for Path B's plateau value |
| 12.4 | Fit saturating exponential to each of the four timeline's checkpoint series | Trend points from 12.2, 12.3, and operational/storage/cycling logs | Four independent trend fits | X(t) = X₀ + ΔX(1 − e^(−t/τ_trend)) fit to each series | Fitting a single combined trend across all four timelines would mask which specific mechanism is drifting |
| 12.5 | Compare each ΔX against the repeatability bounds established in Steps 7 and 8 | Trend fits from 12.4 | Pass/fail per timeline | ΔX within original measurement repeatability counts as stable; beyond it counts as drift | Using an arbitrary drift threshold instead of the device's own measured repeatability bound invites inconsistent judgment across specimens |
| 12.6 | For any timeline showing drift, determine whether the trend has saturated or is still rising | Pass/fail results from 12.5 | Drift classification: settled vs. ongoing | Saturated trend (flattening ΔX) classified separately from unbounded rising trend | Treating all drift as equally severe ignores the practical difference between settling to a new stable state and ongoing failure |
| 12.7 | For fracture-margin drift specifically, cross-check against Step 6.7's original pre-seal and post-seal resistance values | Fracture-margin trend from 12.6 | Seal-degradation root-cause estimate | Compare current plateau trajectory against the gap (if any) already present between Step 6.7's before/after values | A device that already showed a small gap at Step 6.7 is a better candidate for eventual fracture-margin drift than one that showed none |
| 12.8 | Record final stability classification per device, per timeline, with supporting trend fits | All prior results | Complete stability characterization record | All four timelines reported individually; no single combined "stability" verdict that obscures which mechanism is responsible | A single pass/fail stability number discards exactly the diagnostic structure this four-timeline approach was built to preserve |
Step 12 is where the population-level reproducibility result from Step 11 gets a time dimension. A construction method that reproduces well at a single point in time (Step 11) but drifts unpredictably at the fracture margin over weeks or months is not yet a trustworthy construction — it is one whose failure mode has simply not yet had time to appear. Tracking the fracture-margin timeline separately from the three mechanisms the 1925 protocol already tracked is what lets this distinction surface before it becomes an unexplained field failure.