Lilienfeld 1925 Apply the Main Dc Bias

# Apply the Main DC Bias: A Current That Can Feed Back on Itself

Every step through Step 10 built a path and confirmed it would conduct; this step is the first to actually drive current through it, and the first to discover that the compound film doesn't behave like an ordinary wire once it does. A plain metal conductor's resistance rises slightly as it warms, which is self-limiting — more heat, more resistance, less current, less heat. Copper sulfide, like many semiconducting compounds, can behave the opposite way: its conductivity tends to rise as temperature rises, because more thermal energy frees more charge carriers. Applying a steady bias to a conductor with that property is not automatically safe just because Step 9 confirmed the path conducts at all — it opens a feedback loop that a simple metal terminal never has to worry about.

## 1. The Bias Itself Generates the Heat That Can Undermine It

Driving current through the film's own resistance dissipates power directly in the conducting path, following the ordinary Joule heating relationship applied to the resistance Step 5 and Step 9 together established:

For an ordinary metal, this heating raises $R_{\text{film}}$ slightly, which lowers $P_{\text{joule}}$ in turn — a mild, self-correcting effect. For a film whose resistance instead falls as it heats, the same equation describes something more dangerous: more power dissipated, more temperature rise, lower resistance, and at a fixed applied voltage, even more power dissipated than before. Whether that loop settles down or runs away depends on how quickly the device can shed the heat it generates relative to how steeply its own resistance falls with temperature.

## 2. Real Diagram: Two Possible Feedback Loops, Only One of Them Safe

## 3. Whether the Loop Escalates Comes Down to a Single Comparison

A fixed operating point under this feedback loop stays stable only if the device can carry heat away to its surroundings faster than the Joule heating itself grows as temperature rises. Comparing the rate of heat removal to the rate of heat generation gives the actual stability condition:

where $G_{\text{th}}$ is the thermal conductance carrying heat from the film into the glass support beneath it. A device with good thermal contact to a support that conducts heat away efficiently satisfies this comfortably; one with poor contact, or a film whose resistance falls especially steeply with temperature, can fail it — and once it fails, the only things that stop the resulting rise are external, not anything intrinsic to the feedback loop itself: either the bias is removed, or the film reaches a temperature where some other physical limit, like Step 8's own decomposition threshold, finally intervenes.

## Real Diagram: Where Heat Generated Meets Heat Removed

## Apply the Main DC Bias's Place in the Process Lineage

Apply the Main DC Bias follows Step 10, Attach Electrical Connections, which made the external wiring this step's bias is actually applied through; it precedes Step 12, Apply Control-Electrode Bias, which introduces the foil's own voltage on top of whatever operating point this step establishes. It is the eleventh step of this concept's sequence and the first to expose a genuinely new risk that construction alone could never reveal: a conducting path that passed every structural and compositional check Steps 5 through 10 performed can still behave unpredictably the moment it actually carries current, simply because the specific compound this concept depends on does not necessarily share a plain metal's forgiving relationship between heat and resistance.