Lilienfeld 1925 Apply Control Bias as Experimental Variable

# Apply Control Bias as the Experimental Variable: Design the Comparison Step 22 Will Test

Step 21 turns the control electrode into a deliberately manipulated variable rather than a fixed boundary condition. Steps 19 and 20 each held foil 13 at a stated, unchanging potential while something else was measured. Step 21 instead defines the sequence of control biases that will be applied, the order in which they will be applied, and the exact main-terminal measurement that will be repeated at each one, so that Step 22 is a comparison against a plan written in advance rather than a search for whichever trace looks the most interesting afterward.

This step is procedural, not exploratory. Nothing here is a claim about field effect. Its only output is a locked protocol: a bias list, an interleaving order, a hold-time rule, and the pass/hold/reject logic that Step 22 must apply to the data this protocol produces.

## 1. Choose a bias set that is bounded by Step 20, not by hope

The candidate control biases must all lie inside the range Step 20 already certified: below the soft-breakdown onset, below the charge budget $Q_{13}$, and at a magnitude where the measured leakage still satisfies the pre-committed ratio

$$ f_{leak}=\frac{\left|I_{13}(V)\right|}{\left|\Delta I_{12,\text{expected}}\right|}\le f_{leak,max}. $$

Build the bias list as a finite, written sequence, for example $V_{13}\in\{0,+V_1,+V_2,0,-V_1,-V_2,0\}$, always returning to zero between nonzero points so that a zero-bias reference measurement brackets every perturbation. Do not choose the sequence adaptively while taking data — an experimenter who adds "one more point" because the last one looked promising has already broken the comparison by letting the result influence the protocol that is supposed to test it.

Record alongside the bias list the expected leakage at each point from Step 20's own data, not a new assumption, so that any leakage drift observed during Step 21 is caught against a known reference rather than discovered for the first time during Step 22's analysis.

Locked bias sequence and interleaved measurement order for Lilienfeld Step 21 A timeline shows a predeclared control-bias sequence returning to zero between every nonzero point, paired with an interleaving diagram that alternates control-on and control-off terminal measurements and randomizes their order to avoid confounding drift with bias. THE PROTOCOL MUST BE WRITTEN BEFORE THE DATA EXISTS A bias sequence that reacts to its own results is no longer a controlled comparison LOCKED CONTROL-BIAS SEQUENCE sequence position, fixed order, written before any data is taken 0+V1+V20-V1-V20 Every nonzero bias is bracketed by a return to a zero-bias reference point. INTERLEAVED MEASUREMENT ORDER Each bias point triggers the identical Step 19 terminal sweep; order is randomized across repeats to separate bias from drift. control OFF control ON control ON control OFF control ON control OFF Randomize this order across repeats so a slow drift cannot masquerade as a control-bias effect. Each box applies the unchanged Step 19 sweep protocol: both polarities, full transients, settling, and a zero return. Three or more repeats of the full interleaved block are required before Step 22 may compute a mean effect.

## 2. Repeat the unmodified Step 19 measurement at every bias point

The quantity Step 22 needs at each control bias is the identical terminal characteristic Step 19 already defined: full two-polarity sweeps with complete settling, not a single current sample at one terminal bias. Changing the main-terminal measurement procedure between the control-off reference and the control-on points would introduce a second variable alongside the one being studied, which defeats the purpose of a controlled comparison. Use the same instrument ranges, the same settling criterion, the same compliance, and the same main-terminal bias points that Step 19 used.

At each control bias, also repeat the Step 20 three-terminal accounting,

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

so that any apparent terminal-current change can be checked immediately against the control-electrode current actually delivered, rather than waiting for a separate leakage re-measurement after an interesting result has already been seen.

## 3. Interleave control-on and control-off measurements, and randomize the order

A single before/after comparison cannot separate a real control-bias effect from a time-dependent drift in temperature, contact state, or film composition. Interleave repeated control-off reference blocks between control-on blocks, and randomize the order of nonzero bias points across repeats of the full sequence. This converts a slow monotonic drift into noise that averages out across the randomized schedule instead of a bias that spuriously correlates with the applied control voltage.

Plan a minimum of three full repeats of the interleaved sequence before any averaging is attempted. A single pass through the bias list, however orderly, cannot distinguish a real effect from a one-time coincidence of drift and schedule.

## 4. Decide the statistic in advance

Define before data collection exactly how a control-bias effect will be computed from the interleaved measurements. A defensible choice is a paired difference against the nearest bracketing zero-bias reference,

$$ \Delta I_{12}(V_{13})=I_{12}(V_{13})-\tfrac{1}{2}\left[I_{12}(0^{-})+I_{12}(0^{+})\right], $$

averaged across repeats, with its own standard error. Decide now, not later, whether the comparison will be made at a fixed main-terminal bias or integrated across the whole sweep, and commit that choice to the written protocol alongside the bias list from §1.

Pre-register the two thresholds this step exists to feed into Step 22:

$$ \left|\Delta I_{12}(V_{13})\right| > \delta I_{min}\quad\text{and}\quad f_{leak}(V_{13})\le f_{leak,max}, $$

using the Step 19 repeatability bound and the Step 20 leakage ratio exactly as they were published, with no retroactive loosening.

Pre-registered comparison statistic and disposition logic for Step 21 A paired-difference diagram shows the terminal current at a nonzero control bias compared against the average of its two bracketing zero-bias references, next to a table of the two thresholds a candidate effect must clear and the pass, hold, or reject disposition for the completed protocol. THE COMPARISON RULE IS FIXED BEFORE THE RESULT IS SEEN A paired difference against bracketing zero-bias references, tested against two pre-registered thresholds PAIRED DIFFERENCE AGAINST BRACKETING ZERO-BIAS POINTS sequence position terminal current I12 I12 at 0- I12 at V1 I12 at 0+ average of bracketing references ΔI12(V1) THRESHOLDS A CANDIDATE EFFECT MUST CLEAR, DECIDED IN ADVANCE 1. Resolvable above baseline repeatability: |ΔI12(V13)| exceeds the Step 19 threshold δImin 2. Not attributable to leakage: f_leak(V13) stays at or below the Step 20 limit f_leak,max PASSboth thresholds cleared, consistent sign across randomized repeats, leakage accounted forHOLDeffect resolved but inconsistent across repeats, or close to either thresholdREJECTeffect unresolved, sign-inconsistent, or explainable by leakage or drift alone

## 5. Guard against the control circuit biasing the main-terminal measurement

Switching the control-bias source can inject transients onto the main leads through shared grounds, shared supplies, or capacitive coupling that has nothing to do with the device. Verify, with the fixture blank from Step 20, that toggling the control source alone — with no device installed — produces no detectable change on the main-terminal measurement channels. If it does, that artifact must be characterized and subtracted, or the switching architecture must be changed, before any device data from this protocol can be trusted.

Also confirm that the settling time allotted after each control-bias change is long enough to let the Step 20 displacement-current transient decay to the declared criterion before the main-terminal sweep begins. A main-terminal reading taken while the control electrode's own capacitive transient is still decaying will show a spurious correlation with control bias that has nothing to do with the film.

## 6. Freeze the protocol and register it before the first device-on run

Once the bias list, interleaving order, repeat count, comparison statistic, and thresholds are set, write them down as the frozen protocol and timestamp it. Any deviation discovered to be necessary after this point — a different bias magnitude, an added repeat, a changed settling time — must be logged as an amendment with a reason, not applied silently, because an unlogged change after seeing partial data reopens exactly the adaptive-protocol problem this step exists to close.

## 7. Minimum Step 21 record

Retain:

  • device genealogy and the registered Step 15–20 geometry, coverage, material, isolation, baseline, and leakage results;
  • the frozen control-bias list, its ordering, and the Step 20 leakage and charge-budget basis for every magnitude chosen;
  • the interleaving schedule, randomization method and seed or log, and the planned repeat count;
  • the exact main-terminal measurement procedure to be repeated at each bias point, confirmed identical to Step 19's protocol;
  • the pre-registered comparison statistic, the $\delta I_{min}$ and $f_{leak,max}$ thresholds carried forward unchanged, and the pass/hold/reject rule;
  • the control-switching artifact check against the Step 20 blank, with no device installed;
  • the settling-time criterion linking control-bias transients to the start of each main-terminal sweep;
  • the timestamp of protocol freeze and a log of any later amendment with its stated reason;
  • temperature, humidity, illumination, elapsed time, and cable-motion controls planned for the run.

The historical geometry is grounded in [J. E. Lilienfeld, US Patent 1,745,175](https://patents.google.com/patent/US1745175A/en), whose claimed effect is a change in the current between the two main terminals caused by a potential applied to the control member. The comparison discipline — pre-registration, interleaving, and bracketing reference points — follows standard practice for separating a small claimed effect from instrumental drift and is applied here specifically to this device's known leakage and displacement-current behavior established in the [Keithley Low Level Measurements Handbook](https://www.tek.com/en/documents/product-article/keithley-low-level-measurements-handbook---8th-edition).

## Apply Control Bias as the Experimental Variable’s Place in the Process Lineage

Steps 19 and 20 established what the device does with the control electrode held fixed. Step 21 now fixes, in writing and before any device-on data exists, exactly how the control electrode will be varied, how the main-terminal measurement will be repeated at each bias, how control-on and control-off points will be interleaved and randomized, and what statistic and thresholds will decide the outcome. Step 22 executes this frozen protocol and reports the result against the rule written here, rather than against a rule chosen after the data was seen.

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