Surface Barrier 1953 Slice the Germanium

# Slice the Germanium: The Same Ceiling, Now Approached From Both Faces by Etching Instead of One Pair of Firing Depths

Slicing here is the same pure geometry-and-yield problem the alloy-junction route already solves — this crystal is uniformly N-type with no junctions anywhere in it yet, so there is nothing structural to read out, only a thickness to choose and a kerf loss to pay for every cut. What differs is what this step's single chosen number becomes the ceiling for. In the alloy-junction route, that ceiling is spent by two alloyed junctions firing inward from each face. Here, the same ceiling will instead be spent by two electrolyte jets dissolving inward from each face — a different downstream mechanism reaching for the identical thickness budget this step fixes once and never revisits.

## 1. Thickness and Kerf Loss Still Trade Off Directly Against Wafer Count

$$N_{\text{wafers}} = \left\lfloor \frac{L_{\text{usable}}}{t_{\text{slice}} + w_{\text{kerf}}} \right\rfloor$$

As in the alloy-junction route, every saw pass removes kerf width $w_{\text{kerf}}$ as pure waste alongside the wafer thickness $t_{\text{slice}}$ itself, so wafer count falls as either number rises. A thinner target wafer still buys more pieces from the same crystal at the cost of a more fragile slice through every later mechanical step — unchanged economics, because nothing about jet-etching versus alloying affects how a diamond saw interacts with germanium.

## 2. Real Diagram: The Same Cut Geometry, a Different Mechanism Waiting to Spend It

Wafer Thickness and Kerf, Unchanged From the Alloy-Junction Route the saw and the kerf loss do not know which process will later consume this thickness usable length from step five t_slice kerf four wafers shown, three kerf losses between them chosen once here later spent by etching, not firing same trade as alloy-junction — thinner wafers, more pieces, more fragility through every later step

## 3. The Ceiling Is the Same Form, Now Spent by Two Etch Depths Instead of Two Firing Depths

$$W_B \approx t_{\text{slice}} - d_{\text{top}} - d_{\text{bottom}}$$

Where the alloy-junction route's base width is whatever survives after emitter and collector firing depths are each subtracted from $t_{\text{slice}}$, this process's base width is whatever survives after the top and bottom electrolyte etch pit depths, $d_{\text{top}}$ and $d_{\text{bottom}}$, are each subtracted from the identical $t_{\text{slice}}$. The algebraic shape of the ceiling is unchanged; only the mechanism approaching it from below has changed, from a thermally driven alloy front to an electrochemically driven dissolution front. Nothing about how precisely the etch current or etch time is controlled roughly a dozen steps from now can produce a base thinner than this step's own thickness choice ultimately permits once both pits are fully cut — exactly as $t_{\text{slice}}$ was already the hard ceiling in the alloy-junction route, just reached by a different route.

One Fixed Ceiling, Now Approached by Two Etch Pits t_slice is set now; d_top and d_bottom won't be set until roughly steps twelve through sixteen time, across later process steps → thickness consumed t_slice, fixed this step d_top, etched later d_bottom, etched later W_B, what's left W_B can only shrink below this step's ceiling — etching cannot raise it back

## Slice the Germanium's Place in the Process Lineage

Slicing the germanium is step six of Philco's surface-barrier process, immediately after usable crystal sections have been selected and before the individual slices are ground or lapped — mechanically identical to the equivalent step in this project's alloy-junction series, right down to the kerf-versus-thickness tradeoff governing wafer count. What this step fixes is still a single number nothing downstream can exceed; what changed, three steps before this process diverges from the alloy-junction route's own sequence, is only which mechanism will later spend that number down. Step seven, grinding or lapping the slices, turns this step's rough-cut thickness into the precise final geometry both routes depend on equally.

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