Surface Barrier 1953 Select Usable Crystal Sections

# Select Usable Crystal Sections: The Same Guard Band, Now Protecting a Doubled Stake

This step draws the same keep-or-discard line through the rod that the alloy-junction route already draws, using the same two independent conditions and the same deliberately shrunk accept band — and the cost of drawing that line carelessly is now the doubled penalty step four already established. A section let through at the edge of the nominal band is not risking one downstream spec here; it is risking both base body resistance and base-spreading resistance at once, the moment a later etch step multiplies this same resistivity by a confined geometry.

## 1. Selection Is Still Two Independent Conditions, Not One

$$\text{usable}(x) = \mathbb{1}\big[\rho_{\text{meas}}(x) \in \text{band}\big] \;\wedge\; \mathbb{1}\big[\text{structurally sound}(x)\big]$$

As in the alloy-junction route, a section only counts as usable if it clears the electrical and structural checks simultaneously — a resistivity in-band but structurally cracked is unusable, and a structurally sound section outside the band is unusable too. Neither condition can compensate for the other, and nothing about surface-barrier processing changes that logic; the two checks are independent because the two failure mechanisms behind them — thermal stress and segregation drift — are themselves independent.

## 2. Real Diagram: The Same Three-Outcome Sectioning, a Sharper Reason to Be Conservative

Step Four's Curve, Still Converted Into Keep or Discard identical three-outcome sectioning to the alloy-junction route — the stakes behind it are what changed accepted guard-band, discarded accepted rejected, cracked accepted seed end tail end a marginal section here risks body R and spreading R together, not one spec alone same sectioning logic as alloy-junction — a wrong call now costs twice, not once

## 3. The Accept Band Still Shrinks by the Measurement's Own Uncertainty, Now Guarding a Doubled Risk

$$\rho_{\text{accept}} \in \left[\rho_0(1-\delta_{\text{tol}}) + k\sigma_{\text{meas}},\ \rho_0(1+\delta_{\text{tol}}) - k\sigma_{\text{meas}}\right]$$

The guard margin $k\sigma_{\text{meas}}$ pulled in from both edges of the nominal band is computed exactly as in the alloy-junction route — the probe's own measurement uncertainty is a property of the measurement technique, not of what the measured material will later become. What changes is only the asymmetry of the mistake this margin is protecting against: discarding a genuinely good section near the edge still costs yield, same as always, but shipping a section that is actually out of band now risks compounding error across two multiplied specs rather than one. That asymmetry is exactly why this step holds the same conservative guard margin the alloy-junction route uses, rather than loosening it on the reasoning that "etching happens later anyway" — the margin decided here is banked before the etch geometry that will multiply its consequence is even chosen.

The Same Accept Band, Guarding a Doubled Downstream Risk the guard margin is unchanged; what it now protects against is not position along rod → resistivity nominal spec band, step three accept band, shrunk by kσ_meas nominally in spec, still rejected rejecting this point costs yield once; accepting it would have risked two specs downstream

## Select Usable Crystal Sections's Place in the Process Lineage

Selecting usable crystal sections is step five of Philco's surface-barrier process, immediately after the crystal has been cooled and inspected and before it is sliced — mechanically and logically identical to the equivalent step in this project's alloy-junction series. The accept band, the guard margin, and the two-condition selection logic all carry over unchanged. What this step hands to step six, slicing the germanium, is material that has now cleared a selection process calibrated against a stake this series has quietly doubled since step two, even though the selection criterion itself never had to be rewritten to account for it.

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