Cut a Section Containing Both Junctions

# Cut a Section Containing Both Junctions: Margin Against What the Cut Itself Damages

Step twenty-one located both junctions electrically, but "located" means "known within some uncertainty," and this cut's own saw blade introduces a fresh zone of mechanical damage at every face it touches — which means the margin on each side of this cut has to clear two separate, additive error sources, not just one. This is the first cut made into the ingot: a coarse separation that isolates a short, manageable section containing the complete n-p-n sandwich from the much longer bulk emitter and collector regions on either side, discarding material that carries no junction at all while preserving everything electrically important with room to spare.

## 1. The Margin Budget Has Two Independent Terms

$$M_{\text{min}} = \delta x_{\text{measurement}} + d_{\text{saw damage}}$$

The minimum safe margin on each side of a located junction has to cover the point-probe measurement's own positional uncertainty from step twenty-one — no measurement is infinitely precise — plus the depth of mechanical damage this cut's own saw blade introduces at the face it creates, the same category of cutting damage the eventual lead-attachment bar will need etched away later. These two terms are independent and additive: a cut placed closer to a junction than their sum risks the saw damage zone itself reaching into the junction's depletion region, introducing exactly the kind of junction-proximal dislocation step twenty's cooling-control discussion worked to avoid — except now self-inflicted by this cut rather than left over from thermal stress.

## 2. Real Diagram: Placing the Cut Outside Both Error Sources

Cut Placement Clears Measurement Uncertainty and Saw Damage both terms stack against the same margin budget on each side bulk n₁ discarded here junction-bearing section, preserved bulk n₂ discarded here margin margin cuts placed here, both outside the margin band bulk material is cheap to discard — junction-proximal damage is not

## 3. Why Generous, Not Minimal, Margin Is the Right Choice Here

$$\text{Cost(wasted bulk length)} \ll \text{Cost(damaged junction)}$$

Unlike the pull-length yield decision from ingot completion, where longer pulls traded real furnace time and contamination risk against more devices per ingot, the bulk emitter and collector material discarded at this cut has already been grown — its cost is sunk, and keeping an extra margin of it costs nothing further except a slightly smaller remaining section to work with. Because the asymmetry between "a little wasted bulk material" and "a junction damaged by cutting too close" is so lopsided, this step is one of the few places in the entire process where the economically conservative choice (generous margin) and the electrically conservative choice (generous margin) point in exactly the same direction, with no real tradeoff to balance.

Minimum Margin Budget — Two Stacked Terms M_min = δx_measurement + d_saw damage margin distance δx_measurement d_saw damage M_min, the cut line both terms are independent, so they add rather than overlap

## Cut a Section Containing Both Junctions's Place in the Process Lineage

Cutting a section containing both junctions is step twenty-two of the 1951 grown-junction transistor's full manufacturing sequence — immediately after the junction-bearing section has been located electrically, and before individual rectangular transistor bars are cut from it. It is the step that converts a long, mostly-bulk ingot into a short, manageable section with the complete n-p-n sandwich preserved and a margin sized against both measurement uncertainty and the cut's own self-inflicted damage.

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