Lilienfeld 1925 Deposit Thin Copper

# Deposit Thin Copper: A Flat Film Over a Surface That Isn't Flat

Every step so far has treated the assembly as a flat plane to be measured and positioned against — a gap, a clearance, a flush edge. Depositing copper across it for the first time exposes a problem none of those earlier measurements anticipated: the surface this film has to cover is not actually flat. It steps up and down at the terminal coatings' own edges, and it steps again at the exposed foil edge Step 4 fixed flush with the glass. A thin film deposited by a directional process struggles at exactly these steps, and if it struggles badly enough, the continuous conducting path Step 9 needs never actually forms — not because anything upstream was done wrong, but because physical vapor arriving from one direction simply cannot reach every part of a stepped surface equally well.

## 1. A Step Casts a Shadow the Deposition Flux Can't Reach

Material arriving at the surface from a roughly fixed direction deposits less thickness on a sidewall facing away from that direction than it does on a flat, directly-exposed surface — the sidewall sits partly in the source's own geometric shadow. A simple line-of-sight model relates the sidewall thickness to the flat-surface thickness through the angle between the incoming flux and the sidewall normal:

where $\theta$ is the angle between the dominant deposition direction and the sidewall's own surface normal at the step. At the foil's edge, and at each terminal coating's own edge, $\theta$ can be large enough that the sidewall receives only a fraction of the thickness depositing everywhere else — precisely at the two locations this entire device most needs a continuous film to actually exist.

## 2. Real Diagram: The Flat Top Deposits Freely; the Step Doesn't

## 3. Even a Thin Sidewall Deposit Has to Clear Its Own Continuity Threshold

A thinned sidewall is not automatically a broken one — a metal film is continuous as soon as its growing islands of deposited material coalesce into a single connected path, and that coalescence happens above a characteristic percolation thickness rather than at some vanishingly small deposit. The sidewall deposit this step actually produces has to clear that threshold even after Section 1's shadowing reduces it:

Below $t_{\text{percolation}}$, the deposited material sits as isolated islands rather than a connected film, and no amount of Step 8's sulfurization chemistry can create continuity across a gap that was never electrically connected metal in the first place. This is the real requirement behind the roadmap's own instruction to cover "the exposed foil edge" explicitly, rather than assuming a blanket deposition automatically succeeds everywhere it is aimed: the flat regions have comfortable margin above $t_{\text{percolation}}$ by construction, but the stepped regions — the only places this device's continuity actually depends on — do not get that margin for free.

## Real Diagram: The Sidewall's Margin Shrinks as the Angle Grows

## Deposit Thin Copper's Place in the Process Lineage

Deposit Thin Copper follows Step 6, Preserve Metal Separation, which confirmed the geometry this blanket deposition now has to cover without ever letting the foil touch a terminal directly; it precedes Step 8, Sulfurize the Deposited Copper, which can only produce a working compound film wherever this step's copper deposit already cleared the percolation threshold on its own. It is the seventh step of this concept's construction sequence and the first point where the device's topology — not just its in-plane geometry — becomes something this concept actually has to engineer around, rather than simply measure.