Surface Barrier 1953 Halt Etching Target Base Thickness

# Halt Etching at Target Base Thickness: Why Stopping Has the Same Timing Problem Starting Did

Step fourteen's monitoring circuit detects the moment current reaches $I_{\text{endpoint}}$, but detecting that moment and actually stopping both jets at that moment are two different operations, separated by whatever delay this step's own shutdown mechanism takes to act. Step thirteen already established that a start-time mismatch between the two jets produces an asymmetric base. Stopping is the mirror of that same problem, arriving at the single most sensitive point in the entire process: the base is now at its thinnest, so the same absolute timing error that mattered little when the base was thick now consumes a proportionally much larger fraction of what little material remains.

## 1. A Stop-Time Mismatch Costs More Now Than It Would Have Earlier

$$\delta_d^{\text{(stop)}} = \frac{dd}{dt}\,\Delta t_{\text{stop}}, \qquad \frac{\delta_d^{\text{(stop)}}}{d_{\text{target}}} \gg \frac{\delta_d^{\text{(start)}}}{t_{\text{slice}}}$$

The absolute depth error from a stop-time mismatch $\Delta t_{\text{stop}}$ has the identical form to step thirteen's start-time error — both scale with the instantaneous etch rate $dd/dt$. What has changed is the denominator this error is measured against: step thirteen's error was a small fraction of the full starting thickness $t_{\text{slice}}$, while this step's identical absolute error is now a fraction of the much smaller $d_{\text{target}}$ itself, making the same hardware tolerance proportionally far more consequential at this specific moment than at any earlier point in the process.

## 2. Real Diagram: The Same Timing Error, Measured Against a Shrinking Denominator

The Same Δt Costs Far More at the Thinnest Point step thirteen's timing error and this step's are identical in form, not in consequence step 13 — starting t_slice, full thickness Δt error — small fraction of t_slice step 15 — stopping d_target, thin remaining base same Δt error — large fraction of d_target the hardware's timing tolerance did not get worse — what it is measured against got much smaller

## 3. Halting Also Has to Outrun Diffusion-Limited Etching That Current Alone Does Not Control

$$d_{\text{residual}} = d_{\text{target}} - k_{\text{diff}}\,[\text{electrolyte}]\,\Delta t_{\text{flush}}$$

Cutting the etch current does not instantly stop all dissolution — electrolyte already in contact with the surface can continue removing germanium at a slower, diffusion-limited rate for a brief interval after current ceases, governed by a rate constant $k_{\text{diff}}$ and the local electrolyte concentration, until this step's flush actually clears the electrolyte away. This step therefore has two sequential actions, not one: cut the current fast enough to satisfy Section 1's symmetric-stop requirement, then flush fast enough to satisfy this section's requirement that residual, current-independent dissolution not consume additional base thickness beyond what the current-based endpoint already measured.

Two Sequential Actions, Not One Instantaneous Stop current stops the controlled etch; flushing stops the uncontrolled residual etch cut current stops the controlled, Faraday-governed etch flush electrolyte stops residual diffusion-limited dissolution d_residual = d_target − k_diff·[electrolyte]·Δt_flush a slow flush erodes the target this step just reached both actions must complete before the base is considered finished this step's real endpoint is after the flush, not after the current cuts off

## Halt Etching at Target Base Thickness's Place in the Process Lineage

Halting etching at target base thickness is step fifteen of Philco's surface-barrier process, triggered by step fourteen's detected current threshold and completed only once both current and residual electrolyte dissolution have stopped. It is the mirror image of step thirteen's start-time requirement, arriving at the point in this process where the same absolute timing tolerance costs the most, and it adds a second, current-independent failure mode — diffusion-limited residual etching — that step fourteen's purely electrical monitoring could not see coming. Step sixteen, rinsing the etched wafer, takes over once this step confirms the base has actually stopped thinning, not merely that the current has stopped flowing.

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