Point Contact 1947 Apply Copper or Gold to the Underside

# Apply Copper or Gold to the Underside: The Same Formula, Pointed the Other Way

Step two's spreading-resistance equation set the scale this entire block had to be cut to, and this step is where that same formula gets used for the opposite purpose — instead of a small contact concentrating current into a localized region, this step builds a contact deliberately as large as the underside allows, specifically to drive that same resistance term toward zero. Where the point contacts still to come will be made as small and sharp as practical, this base electrode is made broad on purpose, because a point contact's whole value is its localized interaction with the germanium beneath it, while a base electrode's whole value is adding as little series resistance as possible to every signal this device will ever pass.

## 1. The Same Spreading-Resistance Law, Minimized Instead of Accepted

$$R_{\text{spread}} = \frac{\rho}{2\pi r}$$

This is the identical relationship step two introduced to explain why the block itself had to be sized generously relative to the point contacts it would host — but here, $r$ is the base electrode's own effective contact radius, and the design goal is the opposite of a point contact's: make $r$ as large as the underside physically allows, which drives $R_{\text{spread}}$ down toward a small, manageable value rather than accepting whatever resistance a small, deliberately localized contact would produce. The two faces of this same block use the same physics to opposite ends — concentration on top, spreading-resistance minimization on the bottom.

## 2. Real Diagram: Small on Top for Localization, Broad on the Bottom for Low Resistance

Two Contacts, One Block, Opposite Design Goals small r concentrates current; large r minimizes resistance to it N-type germanium block future point contacts, small r (not yet placed) copper or gold base electrode, large r — this step the whole underside becomes the contact, minimizing R_spread by design

## 3. The Metal Film's Own Thickness Adds a Second, Independent Resistance Term

$$R_{\text{sheet}} = \frac{\rho_{\text{film}}}{t_{\text{film}}}$$

Spreading resistance in the germanium is only one contribution to the base connection's total resistance — the metal film itself, however it's applied, has its own sheet resistance set by its resistivity $\rho_{\text{film}}$ divided by its thickness $t_{\text{film}}$, and for very thin evaporated layers that resistivity can run measurably higher than the same metal's bulk value, because electrons in a sufficiently thin film scatter off the film's own surfaces and grain boundaries far more often than they would in bulk material. This is part of why both copper and gold appear as options here rather than one obvious best choice: copper offers lower bulk resistivity, but gold resists the oxidation that would otherwise degrade this electrode's conductivity over the working life of the device — a genuine trade between minimizing resistance today and keeping it low over time.

Thin-Film Resistivity Rises Above the Bulk Value very thin evaporated layers scatter electrons more than bulk metal does film thickness, t_film → film resistivity, ρ_film bulk resistivity value very thin film, elevated resistivity a thicker deposit approaches the bulk value this step's resistance target assumes

## Apply Copper or Gold to the Underside's Place in the Process Lineage

Applying copper or gold to the underside is step five of the twenty-five-step sequence documenting the original 1947/48 Bell Labs point-contact transistor — immediately after the germanium was chemically etched, and before any lead is attached or the germanium is mechanically supported. It is the step that resolves the spreading-resistance concern step two first raised, doing so by maximizing contact area rather than minimizing it, the opposite strategy the point contacts still to come will use, and it layers a second, metal-film-specific resistance consideration on top of the geometric one. Step six, attaching a base lead and supporting the germanium mechanically, is what finally gives this electrode its third, external terminal connection.

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