Lilienfeld 1925 Measure Control Electrode Leakage

# Measure Control-Electrode Leakage: Quantify the Current the Field Effect Must Outrun

Step 20 measures how much current flows into or out of control foil 13 when that foil is held at the biases Step 22 intends to use. Step 18 screened for forbidden bridges at deliberately low stress and could only bound gross or latent shorts. Step 19 established the unmodulated 11↔12 characteristic with the foil held at a declared potential. Neither of them measured what the control electrode itself does once it is driven to its working bias, and that is the quantity which decides whether a later change in terminal current may be attributed to the field effect at all.

The separating barrier here is not an engineered dielectric. Foil 13 is kept out of direct contact with the copper coatings by a thin native oxide and by the compound film's own coverage, neither of which was deposited to a specification or verified for uniformity. Leakage should therefore be expected to be non-ideal, bias dependent, history dependent, and capable of degrading under stress. Step 20 exists to measure that honestly rather than to assume an insulator.

## 1. Leakage is a three-terminal measurement, not a two-terminal one

A single ammeter in the control lead reports a total. It does not say which main terminal the current reached, and it cannot distinguish a real conduction path from charge flowing into the structure's own capacitance. Measure all three terminal currents simultaneously and enforce conservation,

$$ I_{11}+I_{12}+I_{13}=0, $$

with every current referred to the same sign convention and the same measurement common. A residual larger than the combined uncertainty is not noise to be averaged away — it means current is leaving through a path that is not being measured, such as the fixture, a guard, a shield, or a surface film across the glass.

Then resolve the control current into its two destinations,

$$ I_{13}=I_{13\rightarrow 11}+I_{13\rightarrow 12}, $$

because a one-sided leakage points to a specific physical defect at a specific mapped coordinate, while a symmetric leakage is more consistent with distributed barrier conduction. Step 18 already recorded which side, if either, was marginal; a leakage that concentrates on that same side is corroboration, not coincidence.

Three-terminal current accounting for Lilienfeld control-electrode leakage A schematic places an ammeter in each of the three terminal leads of the Lilienfeld structure, with the control foil driven to a forced potential, and requires the three measured currents to sum to zero so that leakage can be resolved into a left-side and a right-side component. LEAKAGE IS A THREE-TERMINAL MEASUREMENT Measure all three currents and require that they sum to zero within uncertainty CURRENT ACCOUNTING AT THE CONTROL ELECTRODE V13 FORCED A I13 13 11 12 A I11 A I12 left leakage path right leakage path A residual in the current sum means an unmeasured path, not noise to be averaged away. single measurement common WHY THIS IS NOT STEP 18 AGAIN STEP 18low-stress screen for a forbidden bridge; a pass only bounds gross or latent shortsSTEP 20full intended control bias, with magnitude, polarity, time dependence and stabilitySTEP 22inherits both; a modulation claim is void if leakage can account for the observed change

## 2. Separate displacement current from conduction

The control foil and the compound film form a capacitor. Any change in control potential therefore injects a transient that has nothing to do with leakage:

$$ I_{meas}=I_{cond}+C_{13}\frac{\mathrm{d}V_{13}}{\mathrm{d}t}. $$

This term is the single most common way a leakage measurement is overstated, and it is also the most common way a modulation measurement is faked, because a step applied to the foil produces a terminal transient on both main leads that decays. Step 20 must characterize it deliberately: apply a small step, record the full decay, and extract the effective capacitance and time constant rather than waiting an arbitrary delay and sampling once.

A nominal parallel-plate estimate,

$$ C_{13}\approx\frac{\varepsilon_{0}\varepsilon_{r}A}{d}, $$

is useful only as an order-of-magnitude expectation. In this structure the overlap area $A$ is set by the mapped film-over-foil coverage from Step 16 and the separation $d$ is a native oxide of unknown and probably nonuniform thickness, so the measured capacitance should be treated as the datum and the formula as a sanity check. A measured capacitance far above the estimate suggests thinner or locally breached separation; far below suggests the film is not covering the foil as the coverage map claimed.

## 3. Drive a bounded bias-stress staircase and watch for progression

Step up the control bias in small increments toward the intended operating point, recording the complete current transient at each step against a declared settling criterion. Dwell at the operating point for a stated time. Step back down. Reverse polarity and repeat. Return to zero and re-measure the zero-bias condition.

Bound the exposure before starting. The relevant stress is field, not voltage, and the field is unknown because $d$ is unknown, so use measured quantities as the budget: cap the integrated charge delivered through the barrier,

$$ Q_{13}=\int \left|I_{13}\right|\,\mathrm{d}t, $$

and cap the dwell power. Abort on compliance, on an abrupt current increase, on instability, or on a current that creeps upward during a constant-bias dwell. Progressive leakage under constant bias is the signature of barrier degradation, and continuing the sweep converts a measurable device into a shorted one.

Three dwell behaviors must be distinguished and are easy to confuse: a decaying current is displacement or dielectric absorption; a flat current is steady conduction and is the quantity Step 22 needs; a rising current is degradation and disqualifies the operating point.

Control-electrode leakage magnitude and dwell behavior A log-scale plot of leakage current against control bias magnitude shows both polarities against an instrument and fixture floor with a soft-breakdown knee, beside a current-versus-time plot that distinguishes displacement decay, steady conduction, and progressive degradation during a fixed dwell. THE LEAKAGE FLOOR SETS WHAT STEP 22 MAY CLAIM Separate displacement current from conduction, and watch for progressive degradation MAGNITUDE VERSUS CONTROL BIAS onset of soft breakdown 1e-61e-91e-12 magnitude of control bias leakage current, log scale instrument and fixture floor positive control bias negative control bias unresolved: report a bound BEHAVIOR DURING A FIXED DWELL time at the operating bias control-electrode current displacement decay steady conduction progressive degradation A creeping dwell current voids the operating point. ACCEPTANCE RULE BEFORE STEP 22 PASSleakage resolved, stable through the dwell, and far below the terminal change Step 22 will claimHOLDunresolved above the floor, slow settling, or polarity and history dependence not yet boundedREJECTsoft or hard breakdown, creeping dwell current, or a shifted Step 19 baseline after stress

## 4. Report a bound when the leakage is not resolved

At low bias the honest result is usually that the leakage is below what the fixture and instrument can resolve. That is a successful outcome and must be written as an inequality rather than as a small number. Carry forward the Step 18 discipline: run the open fixture and the insulating blank through the identical cables, switches, and voltage sequence, and subtract with uncertainty,

$$ \left|I_{13}\right|\le\left|I_{meas}-I_{blank}\right|+U_{meas}+U_{blank}, $$

reporting the right-hand side as the bound. Never record zero, and never record infinity for the equivalent barrier resistance. If the bound is too loose to support the later modulation claim, the fixture must be improved before Step 22 is attempted, because a leakage bound that is larger than the effect being sought makes the experiment unfalsifiable rather than merely imprecise.

## 5. Tie the acceptance limit to the modulation claim, not to convenience

The purpose of this step is to pre-commit to a threshold. Step 19 published a resolvable-change threshold $\delta I_{min}$ for the terminal current. Step 22 will look for a terminal change $\Delta I_{12}$ when the foil is biased. Define in advance the fraction of that change which leakage could explain,

$$ f_{leak}=\frac{\left|I_{13}\right|}{\left|\Delta I_{12}\right|}, $$

and declare the maximum $f_{leak}$ that will still permit a field-effect interpretation. Require simultaneously that the expected modulation exceed the baseline repeatability, $\left|\Delta I_{12}\right| > \delta I_{min}$, and that the leakage be small on this ratio at every bias and polarity to be used.

This ordering matters. If the limit is set after an encouraging trace appears, the experiment has no power to reject the leakage explanation, and the result will be indistinguishable from the historical pattern of claimed solid-state amplification that could not be reproduced.

## 6. Re-establish the Step 19 baseline after the stress

Control-bias stress can change the device even when leakage stays within limits. Ionic rearrangement in the compound film, charge trapping at the barrier, or local heating under the foil can all shift the 11↔12 path. Therefore the final action of Step 20 is to re-run the Step 19 baseline protocol unchanged and compare.

Compare the zero-bias conductance $g(0)$, the symmetry, and the normalized loop area against the pre-stress values using the thresholds Step 19 published. A baseline that no longer matches means the device that enters Step 22 is not the device that was characterized, and the baseline must either be re-established and re-published or the specimen set aside. A shifted post-stress baseline is a reject condition, not a footnote.

## 7. Minimum Step 20 record

Retain:

  • device genealogy and the registered Step 15–19 geometry, coverage, material, isolation, and baseline results;
  • full three-terminal wiring diagram, sign conventions, single measurement common, guard topology, and the state of every shield;
  • instrument models, calibration state, ranges, integration time, compliance, and the current-sum residual at every bias point;
  • open-fixture and insulating-blank traces through identical cables, switches, and sequences;
  • declared maximum control bias, charge budget $Q_{13}$, dwell power limit, and abort criteria, all set before the first step;
  • complete transients for every step, both polarities, both directions, with settling criteria and zero returns;
  • extracted effective capacitance and time constant, and the measured-versus-estimated comparison;
  • resolved left-side and right-side leakage components and their correlation with Step 16 and Step 18 coordinates;
  • leakage values or bounds with full uncertainty budgets, and the declared $f_{leak}$ limit fixed in advance;
  • temperature, humidity, illumination, elapsed time, and cable-motion controls;
  • the post-stress Step 19 baseline re-measurement and its comparison against the published thresholds;
  • every abort, compliance event, breakdown signature, and the final pass, hold, or reject disposition.

The historical geometry is grounded in [J. E. Lilienfeld, US Patent 1,745,175](https://patents.google.com/patent/US1745175A/en), in which the aluminum control member is separated from the copper terminal coatings while the compound film covers it. The low-current measurement discipline — guarding, fixture and blank subtraction, settling, displacement-current handling, and the reporting of bounds rather than zeros — follows the [Keithley Low Level Measurements Handbook](https://www.tek.com/en/documents/product-article/keithley-low-level-measurements-handbook---8th-edition).

## Measure Control-Electrode Leakage’s Place in the Process Lineage

Step 18 removed devices with forbidden bridges and Step 19 fixed a reference characteristic for the intended film path. Step 20 now measures what the control electrode actually does at working bias, resolves that current into its destinations, separates it from the structure's own displacement current, proves the barrier does not degrade during the dwell, and publishes the leakage bound together with the maximum fraction of any future terminal change that leakage would be permitted to explain. Step 21 can then apply the control bias as an experimental variable, and Step 22 can test for modulation against thresholds that were fixed before the data existed.

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