Surface Barrier 1953 Monitor Etch Current Endpoint

# Monitor Etch Current to Endpoint: Reading the Base's Own Resistance as It Disappears

Step thirteen started both jets together, but neither that step nor any step before it gives this process a direct way to see the base thinning in real time — the wafer sits inside a fixture, submerged in electrolyte, completely inaccessible to visual inspection while etching proceeds. This step solves that blindness electrically rather than optically: the remaining germanium between the two etch fronts is itself part of the circuit carrying etch current, and that circuit's own electrical behavior changes measurably as the base thins — giving this process a way to detect its own endpoint without ever seeing the wafer directly.

## 1. The Remaining Base Adds Its Own Resistance to the Etch Circuit

$$R_{\text{total}} = R_{\text{electrolyte}} + R_{\text{Ge}}(d) = R_{\text{electrolyte}} + \rho\,\frac{d}{A}$$

The full circuit's resistance is the electrolyte path's resistance, which stays roughly constant through the etch, plus the remaining germanium's own resistance $R_{\text{Ge}}(d)$ — directly proportional to the base's own resistivity $\rho$, set all the way back in step two of this series, and to the remaining thickness $d$ divided by the conducting area $A$. As $d$ shrinks toward zero, $R_{\text{Ge}}(d)$ shrinks toward zero as well, meaning the base's own contribution to total circuit resistance falls as it thins, not rises — a specific, predictable signature this step's monitoring circuit is built to detect.

## 2. Real Diagram: Current Rises as the Base's Own Resistance Drops Out

A Thinning Base Removes Resistance From Its Own Etch Circuit the signal this process reads comes from the wafer itself, not an external sensor etch time → measured etch current, I I rises as R_Ge(d) falls endpoint — approaching target d thick base, high R_Ge no camera, no probe touching the active region — the current itself is the measurement

## 3. The Endpoint Is a Calibrated Current Threshold, Not a Fixed Etch Time

$$I_{\text{endpoint}} = \frac{V}{R_{\text{electrolyte}} + \rho\,d_{\text{target}}/A}$$

Rather than relying on step thirteen's elapsed time alone — which step thirteen's own analysis showed is already sensitive to current and start-time variation — this step reads the circuit's current directly and halts etching when $I$ reaches the value $I_{\text{endpoint}}$ corresponding to step six's target base width $d_{\text{target}}$, calculated from this step's own resistance relationship using step two's known resistivity $\rho$. This closes a loop running all the way back to this series' earliest steps: the resistivity decision made in step two, originally justified by its effect on base-spreading resistance, now also supplies the calibration constant this step needs to detect when etching has reached its intended depth.

A Resistivity Decided in Step Two Calibrates This Step's Threshold endpoint current is computed, not guessed, from numbers fixed early in this series step 2: resistivity ρ step 6: target depth d_target I_endpoint = V / (R_electrolyte + ρd_target/A) a computed threshold, not an assumed etch duration a number decided twelve steps ago now controls when this step stops

## Monitor Etch Current to Endpoint's Place in the Process Lineage

Monitoring etch current to endpoint is step fourteen of Philco's surface-barrier process, running continuously once step thirteen's simultaneous etching begins and ending only when this step's own threshold is reached. It is the step that gives this process a way to see a wafer it cannot see, turning the base's own thinning resistance into the measurement that controls the process, and it is the first step to directly reuse step two's resistivity decision for a purpose — calibration — that step two's own narrative never anticipated. Step fifteen, halting etching at the target base thickness, is the mechanical action this step's detected threshold actually triggers.

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