Lilienfeld 1925 Sulfurize the Deposited Copper
# Sulfurize the Deposited Copper: The Thinnest Spots Inherit a Second Weakness
Step 7 left a copper film of uneven thickness — comfortable everywhere flat, thinned at the sidewalls, barely above the percolation threshold at the foil edge and the terminal steps. Sulfurizing that film does not treat every point on it equally. The reaction has to progress inward from the exposed surface, converting metallic copper into the copper-sulfur compound this device actually depends on for conduction, and the depth that reaction reaches in a given exposure time is the same everywhere — which means the thinnest regions Step 7 already flagged as marginal are the first to either convert all the way through, or the first to fail to, depending on how this step's own timing is chosen.
## 1. The Reaction Front Advances the Same Way Everywhere, but the Film Doesn't Start Even
Sulfur has to diffuse into the copper and react with it, and like most solid-state reaction-diffusion processes this series has already encountered in other materials, the depth that reaction front reaches grows with the square root of exposure time:
For a region to convert fully into the conducting compound, this depth has to reach at least the local copper thickness — but Step 7 established that thickness is not uniform. The flat regions, with their full deposited thickness, need the least additional time to convert completely; the sidewalls, already thinned by shadowing, convert completely sooner — unless the exposure is cut short to avoid something else, in which case those same sidewalls are also the first regions left only partially converted, with unreacted metallic copper still sitting underneath a thin sulfurized skin.
## 2. Real Diagram: One Reaction Front, Two Different Starting Thicknesses
## 3. How Fully It Converts Determines What Kind of Conductor Remains
Whether a given region ends up fully converted matters beyond simple completeness, because the copper-sulfur compound's own conductivity depends sensitively on how far the sulfur incorporation actually proceeded — copper sulfides are well known to form a range of non-stoichiometric compositions between pure copper and the fully sulfurized compound, with conductivity varying across that range rather than switching on at some fixed threshold:
where $x_S$ is the local sulfur fraction actually achieved and $f$ captures how strongly the compound's conductivity depends on that composition. A region converted just enough to clear Section 1's full-thickness requirement, but no further, can carry a noticeably different conductivity than a region given more reaction time at the same temperature — which means this step's exposure duration is not simply a pass/fail choice between "converted" and "not converted," but a continuous control over the actual electrical character of the conducting path Step 9 inherits.
## Real Diagram: Conductivity Tracks Composition, Not Just Completion
## Sulfurize the Deposited Copper's Place in the Process Lineage
Sulfurize the Deposited Copper follows Step 7, Deposit Thin Copper, whose uneven thickness this step's reaction front has to contend with directly, converting the thinnest regions soonest and the thickest regions last; it precedes Step 9, Complete the Conducting Path, which depends on every point along that path having reached a composition that actually conducts, not merely having been exposed to sulfur for some amount of time. It is the eighth step of this concept's construction sequence and the point where the device's main current path stops being a deposited metal and becomes, for the first time, the specific compound this entire concept is actually built around.