Lilienfeld 1926 Measure Control Electrode Leakage
# Measure Control-Electrode Leakage: The Fracture Margin Is a Leakage Path the 1925 Geometry Never Had
The 1925 specimens used a continuous control electrode seated against a flat, unbroken glass face — leakage there could only occur through the bulk glass or along its exposed perimeter. This 1926 construction is different: Step 2 deliberately fractured the glass, and Step 3 bonded the electrode into that fracture. Any margin of the fracture not fully covered by the Step 3 bond, or any seam where the Step 6 encapsulant meets the fracture edge, is a second leakage pathway this geometry introduces that the 1925 protocol never had to account for. Step 8 extends the three-terminal leakage measurement from the 1925 series specifically to test for this additional path.
The three-terminal accounting identity still applies. As with the 1925 protocol, I₁₁ + I₁₂ + I₁₃ = 0 must hold at every measurement instant: any current entering the film terminals must be accounted for by current at the control electrode terminal, with no unaccounted path. What changes for this construction is the physical interpretation of a nonzero I₁₃ — it is no longer automatically attributable to the single bulk-glass capacitive path the 1925 geometry had. It could be Path A (bulk glass, same mechanism as 1925), Path B (fracture margin), or some combination of both.
Dwell-time behavior separates the two paths even though the single I₁₃ measurement cannot. Path A, being purely capacitive, produces a displacement current that decays as the bias settles: X(t) = X₀ + ΔX(1 − e^(−t/τ)), with the same exponential form used throughout the 1925 series. Path B, if it exists as a true conduction leakage through residual moisture or an incompletely sealed fracture margin, does not decay — it persists as a constant current for as long as the bias is held. A single-point measurement cannot distinguish them; a dwell-time measurement can.
The leakage ratio f_leak must now be computed against the combined baseline, not a single assumed source. Following the 1925 definition, f_leak = |I₁₃| / |ΔI₁₂|, evaluated at the dwell-time plateau rather than at an early transient point, since the plateau isolates whatever true conduction leakage exists after the capacitive Path A component has fully decayed. This plateau value is the correct quantity for the 1925 series' f_leak,max threshold comparison — using an early-time I₁₃ value would overstate leakage by including decaying displacement current that does not represent a genuine fault.
| Step | Process operation | Input | Output | Specification | Constraint |
|---|---|---|---|---|---|
| 8.1 | Connect four-wire probes to terminals 11, 12, and 13 (film pair and electrode) | Baseline-characterized device from Step 7 | Three-terminal probed device | Separate current-force and voltage-sense leads per the 1925 four-wire standard | Two-wire measurement at any terminal conflates lead resistance with device leakage |
| 8.2 | Apply a step control bias at terminal 13, hold at fixed voltage | Probed device from 8.1 | Biased device, dwell clock started | Bias magnitude matched to planned Step 9 test range; hold time sufficient to resolve full decay | Too short a dwell cannot distinguish Path A's decay from Path B's plateau |
| 8.3 | Record I₁₃(t) continuously through the dwell period | Biased device from 8.2 | I₁₃(t) time series | Sampling fast enough to resolve the initial decay transient | Sparse sampling near t=0 loses the shape needed to separate the two paths |
| 8.4 | Fit decay to X(t) = X₀ + ΔX(1 − e^(−t/τ)) and extract the plateau value | Time series from 8.3 | Fitted decay parameters, plateau I₁₃ | Fit residuals within instrument noise | A poor fit suggests more than one decay time constant, implying a more complex leakage structure than Path A + Path B alone |
| 8.5 | Compute f_leak using the plateau I₁₃ value against ΔI₁₂ from the same bias step | Plateau value from 8.4, Step 7 baseline | f_leak estimate | f_leak reported with uncertainty | Using a transient I₁₃ value instead of the plateau overstates leakage |
| 8.6 | Compare plateau value against Step 6.7/7.2 pre-test terminal-to-electrode resistance | f_leak estimate from 8.5 | Seal-degradation-checked result | Consistent with a high-resistance, mostly-capacitive path if plateau is near the Step 7.2 noise floor | A plateau far exceeding the Step 7.2 isolation check indicates the seal degraded between Step 7 and Step 8 |
| 8.7 | Repeat at a second bias polarity to check for path symmetry | Result from 8.5, 8.6 | Polarity-checked leakage record | f_leak consistent in magnitude across both polarities, within measurement noise | Asymmetric leakage magnitude suggests a directional conduction path (e.g., a partial short with diode-like behavior) rather than simple ohmic leakage |
| 8.8 | Record final f_leak, decay time constant τ, and pass/fail against the 1925-derived f_leak,max threshold | All prior results | Complete leakage characterization record | f_leak ≤ f_leak,max required before proceeding to bias-response testing (Step 9) | A device that fails this threshold cannot yield a trustworthy modulation measurement in later steps, regardless of how large any apparent control response appears |
Step 8 is the gate between construction and the field-effect test proper. If the fracture-margin leakage path is present and significant, any later measurement of control-induced modulation (Step 9) is confounded — an observed current change with applied bias could be partly or entirely a leakage artifact rather than genuine field-effect modulation. Measuring and bounding f_leak here, specifically accounting for the leakage path this fracture-mounted construction introduces, is what makes every subsequent result trustworthy.