Surface Barrier 1953 Final Tests Classify and Release

# Final Tests, Classify, and Release: Twenty-Four Steps of Variation, Resolved Into a Frequency Number

Every step in this series introduced some small, real amount of uncertainty — step five's purity margin, step ten's shrunk accept band, step fourteen's endpoint-current calibration, step twenty-four's temperature-capped conditioning. None of those individual uncertainties ever resolved into a single number until now. Classification is the step where all twenty-four of them, accumulated across jet-etching, electroplating, bonding, and sealing, finally show up together as a measured spread — not primarily in current gain, the number the alloy-junction route sorted by, but in the frequency response this entire process existed to deliver.

## 1. Base-Width Uncertainty Propagates Into Frequency Response, Not Just Gain

$$f_{\alpha}\approx \frac{D_n}{2\pi W_B^{2}},\qquad \sigma_{f_\alpha}^2\approx\left(\frac{\partial f_\alpha}{\partial W_B}\right)^2\sigma_{W_B}^2$$

Because transit-time-limited frequency response $f_\alpha$ scales as $1/W_B^2$, uncertainty in base width — accumulated from step six's thickness ceiling, step ten's margin, step thirteen and fifteen's timing tolerances, step fourteen's endpoint calibration — propagates into frequency response more sharply than it would into gain alone, which scales more gently with $W_B$. This is why final testing on this device weighs a frequency-domain measurement at least as heavily as the gain measurement every earlier series in this project emphasized: the quantity this whole process was built to deliver, tens of megahertz of useful response, is exactly the one most sensitive to every upstream tolerance this series has carried.

## 2. Real Diagram: Twenty-Four Small Uncertainties Converge on One Frequency Spread

Upstream Uncertainties Converging on a Frequency Spread each step's own tolerance feeds into W_B, and W_B feeds sharply into f_alpha step 5-10: purity, margin step 13, 15: timing step 14: endpoint calibration step 24: conditioning stress σ_W_B squared σ_f_alpha², amplified by 1/W_B² this is the first point where every prior step's tolerance is combined into one number

## 3. Grading Sorts by Frequency Response, Rejects on Either Spec

$$z_f=\frac{f_{\alpha,\text{measured}}-\bar f_\alpha}{\sigma_{f_\alpha}}, \qquad \text{reject if } \alpha_{\text{measured}}<\alpha_{\min}\ \text{OR}\ f_\alpha<f_{\alpha,\min}$$

A finished unit is graded primarily by where its measured frequency response $f_{\alpha,\text{measured}}$ falls within the batch distribution Section 1 predicted, expressed as a standard score $z_f$ — the same statistical sorting principle this project's alloy-junction series used for gain, applied here to the parameter this device actually competes on. Rejection still happens on either spec independently: a unit with excellent frequency response but gain below $\alpha_{\min}$ is scrapped exactly as readily as one with strong gain but $f_\alpha$ below the minimum useful threshold, because step twenty-one already established that neither specification alone certifies a working device.

Sorting the Finished Batch by Frequency Response z_f measures where each unit sits in the distribution this step's own propagation predicted measured frequency response, f_alpha rejected, below f_alpha,min z_f threshold RF grade standard grade

## Final Tests, Classify, and Release's Place in the Process Lineage

Final tests, classify, and release is step twenty-five of Philco's surface-barrier process — the last of the twenty-five steps, and the final disposition of every unit that has survived this entire sequence. It closes the series by resolving the base width this process began constraining in step six, narrowed by two opposing electrolyte jets through steps eleven to fifteen, contacted by two asymmetric metal-semiconductor barriers in steps seventeen and eighteen, and conditioned under a thermally-capped acceleration test in step twenty-four, into the one measurement — frequency response, not gain alone — that determines whether a finished surface-barrier transistor actually delivers the tens-of-megahertz capability this whole project's first article, and this series' very first step, identified as the entire point of leaving mechanical thinning behind.

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