Surface Barrier 1953 Verify Finished Slice Dimensions

# Verify Finished Slice Dimensions: Closing the Shared Phase With One Combined Gate

Four separate steps have each quietly set their own requirement on this wafer — step six's thickness ceiling, step seven's parallelism tolerance, step eight's damage-free depth, step nine's wettable surface — and this step is still the first point where all four get checked together, on the actual finished piece, exactly as in the alloy-junction route. What this step hands forward differs for the first time since step one: rather than feeding two pellet-placement steps, this usable-area map now feeds the opposing jet fixture that step eleven assembles, and the margin it has to clear is sized against two aligned jets instead of two placed disks.

## 1. The Same Four Requirements, Checked Together for the First Time

$$\text{accept}(\text{wafer}) = \mathbb{1}[t_0 \in [t_{\min}, t_{\max}]] \wedge \mathbb{1}[\Delta t_{\text{wedge}} \le \delta_{\text{wedge}}] \wedge \mathbb{1}[A_{\text{usable}} \ge A_{\text{min}}]$$

As in the alloy-junction route, a wafer only passes if measured thickness falls inside step six's window, wedge error stays under step seven's tolerance, and enough defect-free, properly wettable surface survives steps eight and nine to actually support the process ahead. This step still does not re-derive any upstream limit — it refuses to assume that a wafer clearing each prior step's own process-level check still clears all of them together on the one physical piece this process will actually etch.

## 2. Real Diagram: The Same Usable-Area Map, Now Feeding a Jet Fixture Instead of Pellet Placement

Measuring Where the Requirements Hold, Now for Two Opposing Jets this wafer passes overall, but not every point on its surface qualifies equally usable region excluded local defect site edge-zone wedge excess clear this map now sizes where two opposing jets, not two placed disks, can safely land

## 3. Usable Area Still Has to Clear a Margin, Now Against an Alignment Instead of a Placement

$$A_{\text{usable}} \ge A_{\text{jet-pair}} \cdot (1 + m_{\text{alignment}})$$

The usable area this step maps still has to exceed the two jets' combined footprint inflated by a margin — but where the alloy-junction route's margin $m_{\text{placement}}$ accounts for a fixture positioning one disk after another, this process's margin $m_{\text{alignment}}$ accounts for something stricter: the top and bottom jets must stay registered to each other across the wafer, not merely each individually placed within tolerance, because the base this process is building depends on both jets converging on the same point from opposite faces. A jet pair positioned exactly where its combined footprint fits on paper can still fail if the fixture holding both jets has any real-world misalignment between the two sides — exactly the failure mode step eleven's fixture design exists to prevent, and exactly the margin this step's measurement has to anticipate before that fixture is ever built.

Usable Area Still Has to Clear the Footprint Plus Margin now protecting jet-to-jet registration, not disk-to-disk placement wafers, sorted by usable area → usable area, A_usable bare jet-pair footprint footprint with alignment margin rejected — below margin line accepted the gap between the two dashed lines is still this step's whole point

## Verify Finished Slice Dimensions's Place in the Process Lineage

Verifying finished slice dimensions is step ten of Philco's surface-barrier process — the last step of this process's shared preparation phase, identical in every requirement and governing equation to the equivalent step in this project's alloy-junction series, since both processes have now spent nine steps on the same bulk-material physics without either one yet touching anything specific to how its final junction geometry will be formed. This is also the last step where that is true. Step eleven, assembling the electrolyte jet-etch fixture, is where this process's own distinctive sequence actually begins — the point ten steps of shared physics have been building toward since step one first noted that a membrane a few micrometers thick demands a tighter purity margin than a fired alloy junction ever did.

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