Lilienfeld 1926 Apply Control Bias Test Modulation
# Apply Control Bias and Test for Modulation: The Modulation Statistic Must Wait Out the Decay Step 8 Characterized
Step 8 established that this construction's I₁₃ response to a step bias has two components: a decaying capacitive transient (Path A) and, if present, a non-decaying conduction plateau (Path B). Step 9 applies the actual bias schedule intended to test for field-effect modulation, and the same decay structure now governs how the modulation statistic itself must be computed. Reading ΔI₁₂ too early after each bias step risks attributing part of Path A's settling transient to genuine control-induced modulation — a confound this construction's fracture-mounted geometry makes more severe than the 1925 specimens ever faced.
The settling wait is not optional overhead — it is what makes the statistic meaningful. Step 8 measured this construction's decay time constant τ for the capacitive transient at the control electrode. Step 9 reuses that same τ as the minimum wait time before reading I₁₂ at each nonzero bias point. A measurement taken before this wait elapses mixes a decaying, non-field-effect transient into what should be a clean measure of steady-state modulation — exactly the failure mode the dwell-time test in Step 8 was designed to characterize and now exists to prevent.
The pass criterion combines the 1925 modulation threshold with this construction's own leakage bound. As in the 1925 protocol, a pass requires |ΔI₁₂(V₁₃)| > δI_min simultaneously with f_leak(V₁₃) ≤ f_leak,max. But because Step 8 already established this device's f_leak at the specific bias magnitudes planned for Step 9's schedule, the leakage check here is a confirmation that f_leak remains stable at the planned test points — not a fresh, unconstrained measurement. A significant upward shift in f_leak between Step 8 and Step 9 would itself be diagnostic of something changing in the device between tests, independent of whether modulation is observed.
Consistency across repeats matters as much as the magnitude itself. As in the 1925 protocol, the bias order is randomized across at least three full repeats, and the result must show consistent sign and comparable magnitude across those repeats — not merely an average that happens to clear δI_min while individual repeats scatter unpredictably. A result that passes on average but fails the consistency check is not evidence of genuine, repeatable field-effect modulation; it is evidence of an unstable measurement.
| Step | Process operation | Input | Output | Specification | Constraint |
|---|---|---|---|---|---|
| 9.1 | Confirm Step 8's τ and f_leak,max values are available for this device | Leakage record from Step 8 | Confirmed test parameters | τ and f_leak,max recorded with uncertainty from Step 8 | Testing without these values defeats the purpose of Step 8's characterization |
| 9.2 | Define pre-registered bias schedule: zero-bracketed nonzero points, randomized order per repeat | Confirmed parameters from 9.1 | Bias schedule, locked before testing begins | At least 3 full repeats; bias magnitudes within the range validated in Step 8 | Testing at bias magnitudes outside Step 8's validated range means f_leak at those points is unknown, not merely assumed low |
| 9.3 | Apply first bias point per schedule, hold for at least 3τ before reading | Bias schedule from 9.2 | Settled bias point measurement | Wait time ≥ 3τ (from Step 8 fit) before recording I₁₂ | Shorter wait leaves measurable residual Path A transient in the reading |
| 9.4 | Record I₁₂ at settled bias, and I₁₃ to confirm f_leak remains within Step 8 bound | Settled measurement from 9.3 | Per-point I₁₂, I₁₃ pair | f_leak at this point consistent with Step 8 value, within measurement noise | A shifted f_leak invalidates this point's modulation reading until the shift is explained |
| 9.5 | Return to zero bias, wait ≥ 3τ, record I₁₂(0) before the next nonzero point | Measurement from 9.4 | Zero-bias reference point | Same settling discipline as nonzero points | Skipping the zero-bias settling wait corrupts the baseline half of the ΔI₁₂ comparison |
| 9.6 | Repeat 9.3-9.5 for all scheduled bias points, all repeats | Schedule from 9.2 | Complete raw dataset | All points collected per the locked schedule; no post-hoc point additions or removals | Adding or dropping points after seeing results defeats the pre-registration discipline |
| 9.7 | Compute ΔI₁₂(V₁₃) per point, averaged across repeats | Raw dataset from 9.6 | Modulation statistic per bias level | Formula: ΔI₁₂(V₁₃) = I₁₂(V₁₃, plateau) − [I₁₂(0⁻) + I₁₂(0⁺)]/2 | Using unsettled readings in this formula reintroduces the Path A confound Step 9.3's wait time was meant to eliminate |
| 9.8 | Plot each result on the scoring plane; apply pass/fail against δI_min and f_leak,max simultaneously | Statistics from 9.7 | Final modulation test verdict | Pass requires every repeat, not just the average, inside the pass region | A result that passes on average but scatters across the pass/fail boundary is not a reliable detection |
Step 9 is where this 1926 construction either demonstrates genuine field-effect modulation or does not. Every step before this one built, sealed, and characterized the baseline and leakage properties of a specific physical device. Step 9 is the first point at which the control electrode's intended function — modulating the film's conductance through the glass dielectric — is actually tested against a pre-registered, falsifiable threshold, using exactly the settling discipline that Step 8's decay characterization made necessary for this fracture-mounted geometry.