Alloy Junction 1952 Select Usable Crystal Sections

# Select Usable Crystal Sections: Why the Accept Band Has to Be Narrower Than the Spec Band

Step four handed over a measured resistivity curve and a structural pass/fail — this step is where that data actually becomes a keep-or-discard line drawn through the rod, and drawing that line naively at the spec boundary itself is a mistake this step exists to avoid. The probe measurement that produced step four's curve has its own uncertainty, and a section measured right at the edge of the tolerance band could just as easily be a genuinely marginal section or a perfectly good section whose measurement happened to land low. Treating the two cases the same — accepting anything that reads inside the nominal band — lets measurement noise alone determine whether out-of-spec material slips through, which is exactly the risk this step is built to close off.

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

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

A section only counts as usable if it clears both of step four's independent checks at once — the electrical resistivity condition and the mechanical structural-integrity condition — because either one failing alone is sufficient to make that section unusable regardless of how well the other performed. A structurally flawless section with resistivity outside the band is just as unusable as a structurally cracked section with perfect resistivity; this step does not average the two checks together or let a strong result on one compensate for a weak result on the other.

## 2. Real Diagram: The Rod, Sectioned by Status

Step Four's Curve, Converted Into a Keep/Discard Line each segment gets one of three outcomes — not a single accept/reject split accepted guard-band, discarded accepted rejected, cracked accepted seed end tail end a section just inside the resistivity band, next to a cracked section, is still discarded on its own merits three outcomes, not two — "measured as in-spec" is not the same decision as "accepted"

## 3. The Accept Band Has to Shrink Inside the Spec Band by the Measurement's Own Uncertainty

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

The probe measurement itself carries uncertainty $\sigma_{\text{meas}}$ — repeatability of contact resistance, probe spacing, and thermal drift during the sweep all contribute — so a raw reading sitting exactly on step three's tolerance boundary carries roughly equal odds of belonging to either side of that boundary. Pulling the accept criterion in from both edges by a guard margin $k\sigma_{\text{meas}}$ converts "measured as roughly in-spec" into "confidently in-spec," at the acknowledged cost of discarding some genuinely good material that happened to measure near the edge — a trade this step accepts deliberately, because shipping a section that is actually out of specification is a far more expensive mistake than discarding one that happened to measure conservatively.

Accept Band Sits Inside the Nominal Spec Band the guard margin on each side is set by the probe's own measurement uncertainty position along rod → resistivity nominal spec band, step three accept band, shrunk by kσ_meas nominally in spec, still rejected this point reads inside the spec band but outside the accept band — too close to call reliably

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

Selecting usable crystal sections is step five of RCA's forty-two-step alloy-junction manufacturing sequence — immediately after the crystal has been cooled and inspected, and before it is sliced into individual wafers. It is the step that converts step four's continuous measured data into a discrete keep-or-discard decision, deliberately drawing that line inside the nominal specification rather than exactly on it, to keep the probe's own measurement uncertainty from becoming an unintended source of out-of-spec material downstream. Step six, slicing the germanium, only ever touches the sections this step actually retained.

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