MOSFET 1962 Threshold Voltage Minimum Gate Turn on

# Confront the Threshold Voltage: A Turn-On Voltage That Has Nothing to Do With a Diode

## 1. Why the Gate Must First Push Majority Carriers Away Before It Can Pull Minority Carriers In

Every earlier step in this series built the structure Step 1 proved could, in principle, work — a clean interface, a thin exact oxide, two symmetric diffusions, a gate that fully covers the channel between them — but a small gate voltage applied to that finished structure still does not turn the device on, because the first thing a gate voltage does is deplete the silicon surface of its own majority carriers, not supply the minority carriers a conducting channel actually needs. As gate voltage increases from zero, the surface first passes through depletion, pushing the substrate's own majority carriers away from the interface and leaving a region stripped of free charge — a state with no mobile carriers of either kind near the surface, and therefore no conduction. Only once the gate voltage grows large enough to bend the surface potential all the way past a specific point does the surface invert, pulling minority carriers to the interface in a thin layer that is, for the first time, the opposite carrier type from the bulk substrate beneath it — and that inversion layer, not the depletion region beneath it, is the channel this entire series has been building toward.

where $\phi_F$ is the bulk Fermi potential of the substrate, so that $2\phi_F$ marks the surface potential at which strong inversion begins, $Q_{\text{dep}}$ the depletion charge the gate voltage must first supply before any inversion charge can accumulate, and $C_{\text{ox}}$ the same oxide capacitance Step 2 fixed by its own thickness — a larger $Q_{\text{dep}}$ or a smaller $C_{\text{ox}}$ both raise the threshold, meaning the exact gate oxide thickness chosen back in Step 2 directly sets how much gate voltage this device needs before it conducts at all.

## 2. Real Diagram: What the Surface Actually Looks Like, Below and Above Threshold

The two cross-sections below show the identical structure at two different gate voltages — below threshold, where the gate has only pushed majority carriers away, and above threshold, where a thin inversion layer of minority carriers has formed directly beneath the oxide, connecting the two diffused regions for the first time.

## 3. A Turn-On Voltage Every Bipolar Series in This Project Already Has, for a Completely Different Reason

Every bipolar device this project has documented since 1954 also has a voltage below which it does not conduct — the forward voltage needed to turn on a base-emitter junction, below which that junction simply does not inject enough carriers to support meaningful current. It would be easy to assume this step's threshold voltage is the same concept under a different name, but the two have almost nothing in common mechanistically. A bipolar turn-on voltage is a property of carrier injection across a single forward-biased PN junction, set by the junction's own doping levels and present the instant any forward bias is applied, rising smoothly rather than switching on at a sharp point. This step's threshold voltage is a property of an entire surface's electrostatic state, set by how much charge a gate must first displace before the surface's own band structure inverts — no junction is being forward biased at all, and the device sits in two genuinely distinct physical regimes, accumulation-then-depletion and inversion, on either side of that threshold, rather than smoothly increasing current from zero.

Step 5 does not discover that this device, like every bipolar device before it, needs some minimum voltage to conduct; it discovers that the minimum voltage this device needs comes from an entirely different physical mechanism, one this project has never had to name until a gate, an oxide, and a silicon surface replaced a forward-biased junction as the thing standing between zero current and useful current.