Crosswise Slicing

# Crosswise Slicing: Cutting Perpendicular to Read Out the Grown Structure

Every slice taken perpendicular to the pull axis, anywhere along the completed ingot's length, is a complete n-p-n transistor cross-section — the device was never assembled, it was read out of a structure that already existed inside the crystal before the saw ever touched it. This is the step that makes the entire grown-junction strategy pay off: because the three regions were laid down one after another along a single growth axis, with boundaries set by elapsed pull time rather than any lateral process, a cut plane oriented perpendicular to that axis intersects all three regions in the correct order every single time, regardless of exactly where along the ingot's length the cut happens to land. The diamond saw doesn't define the device; it only decides where, within the already-fixed boundaries, to separate one wafer's worth of sandwich from its neighbors.

## 1. Cut-Plane Orientation Is the Entire Point

$$\hat{n}_{\text{cut}} \parallel \hat{n}_{\text{pull}}$$

The saw's cut plane has to be oriented perpendicular to the crystal's pull axis — parallel to the growth-front isotherms that defined each dopant region's boundary as it froze — not angled, and not aligned along the pull direction. A cut that drifted even a few degrees off perpendicular would intersect the n-emitter, p-base, and n-collector regions at a slant, which does two damaging things at once: it artificially widens the apparent base region on that slice relative to the true $W_B = v_p \cdot \Delta t_{\text{switch}}$ set back at the second pellet drop, and it makes that widening inconsistent from one edge of the wafer to the other, since a slanted cut traverses a different amount of each layer depending on where across the diameter you measure. Every electrical specification computed from the earlier steps' timing assumes the slice that reads it out is a true perpendicular cross-section — slicing angle is not a cosmetic tolerance, it is the mechanism by which an already-correct crystal can still produce an incorrectly-specified device.

## 2. Real Diagram: One Cut, Many Repeats, Same Structure Every Time

Crosswise Slicing — Perpendicular Cuts Read Out the Same Sandwich n̄_cut ∥ n̄_pull — any cut off this orientation widens the base non-uniformly correct: perpendicular cut both cuts level, W_B identical across the whole wafer diameter incorrect: slanted cut base appears wider on one edge, narrower on the other — same wafer same ingot, same true W_B slicing angle is the mechanism by which a correctly-grown ingot still ships an incorrectly-specified device

## 3. Diamond Sawing Trades Precision Against Kerf Loss

$$L_{\text{usable}} = L_{\text{ingot}} - N_{\text{slices}} \cdot (t_{\text{slice}} + w_{\text{kerf}})$$

Each pass of a diamond saw removes not just the finished slice's thickness $t_{\text{slice}}$ but an additional kerf width $w_{\text{kerf}}$ of crystal lost to the cut itself — material that was grown, correctly doped, and then turned to waste by the blade's own width. A thinner blade reduces kerf loss and recovers more usable slices per ingot, but a blade that's too thin sacrifices the mechanical rigidity needed to hold a true perpendicular orientation across the full wafer diameter, reintroducing the slant risk from §1. This is a direct, quantifiable tradeoff between the yield economics of step four's pull-length decision and the slicing hardware's own mechanical limits — a longer ingot only pays off in proportion to how much of it the saw doesn't throw away getting there.

Usable Slices per Ingot vs. Blade Kerf Width L_usable = L_ingot − N_slices · (t_slice + w_kerf) kerf width, w_kerf → usable slices recovered thinner blade, more slices recovered rigid enough for true perpendicular too thin — slant risk returns the blade chosen trades kerf loss against the orientation accuracy section 1 requires

## Crosswise Slicing's Place in the Process Lineage

Crosswise slicing is step five of the six-step grown-junction transistor device process flow — after ingot completion has produced a cooled, stable crystal, and before lead attachment and final can sealing. It is the step that converts a continuous grown structure into individual device wafers, and the point where a purely geometric error (cut-plane tilt) can still corrupt a device whose doping was already perfectly correct.

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