EC-6.7 The MOS Capacitor and the MOSFET

The standard MOS treatment as taught in semiconductor device and integrated circuit courses, September 2026

What this is and why it exists

Almost every transistor ever manufactured is this one. It is worth meeting properly rather than as a symbol with three terminals.

The device is a capacitor whose lower plate is semiconductor. The whole trick is that changing the plate voltage changes what the semiconductor underneath actually is. First it is pushed away from its own carriers. Then it is emptied. Then it is populated with carriers of the opposite type.

That inverted layer is the channel. The threshold voltage is the voltage at which it appears. Once that is clear, the two operating regions stop being things to memorise and become things you can derive.

The vocabulary

Gate — the upper plate, separated from the semiconductor by an insulator.
Oxide — the insulating layer, which is why no gate current flows.
Accumulation — gate voltage pulling the substrate's own majority carriers to the surface.
Depletion — gate voltage pushing them away, leaving fixed charge.
Inversion — gate voltage strong enough to attract the opposite carrier type to the surface.
Channel — the inverted layer that conducts between source and drain.
Threshold voltage — the gate voltage at which the channel becomes usefully conductive.
Linear region — low drain voltage, where the channel behaves as a controlled resistor.
Saturation region — drain voltage past pinch-off, where current stops rising.
Body effect — the threshold rising when the source sits above the body.

The mental model

Take a p-type substrate, put a thin insulating oxide on it, and put a conducting gate on top. That is a capacitor. Now vary the gate voltage and watch what the surface underneath does.

Negative gate: the substrate's own holes are pulled to the surface. Accumulation.

Slightly positive gate: holes are pushed away, leaving behind the fixed negative acceptor ions they had been neutralising. A depleted zone forms. Depletion.

More positive gate: electrons are attracted to the surface. Those are the *minority* carrier in p-type material, and enough of them arrive that the surface behaves as n-type. Inversion.

That third state is the useful one. The surface has become a thin n-type layer connecting two n-type regions either side of it, and current can flow between them. Those regions are the source and the drain, and the layer is the channel.

Threshold voltage is nothing more than the gate voltage at which that layer becomes inverted enough to conduct meaningfully. It depends on the oxide thickness, the substrate doping and the gate material. All three are chosen during manufacture rather than by whoever uses the device.

The defining consequence: the gate is separated from the channel by an insulator, so it draws no steady current. Control is by field alone. That is the fundamental difference from the bipolar device, and it is why digital logic uses this transistor. A gate that draws no current costs nothing to hold in a state.

Now the two regions.

At low drain voltage the channel is roughly uniform and the device behaves as a resistor whose value the gate controls. This is the linear region, and it is what a switch uses.

As drain voltage rises, the voltage between gate and channel shrinks at the drain end, so the channel gets thinner there. At some point it pinches off at the drain end entirely. Past that, raising the drain voltage does not increase the current much. It moves the pinch-off point slightly instead. This is saturation, and it is what an amplifier uses.

Two further effects matter enough to name.

The body effect: if the source sits at a higher voltage than the body, the threshold rises. So a transistor stacked on top of another conducts less well than the same device would alone. A logic gate with many stacked inputs is slower than one with few. In real logic, transistors are stacked constantly.

And scaling. Making everything smaller worked straightforwardly for decades. Then several effects that had been negligible stopped being so. Current leaks through an oxide only a few atoms thick, the threshold falls as the channel shortens, and carrier velocity saturates so speed stops improving. This is exactly where the fifth-semester integrated-circuit option picks the device up, and why that course exists.

What you should now be able to explain or do

Describe the three surface states and say which one makes a transistor.
Say what threshold voltage is and what it depends on.
Explain why the gate draws no steady current and why that matters for logic.
Describe the linear and saturation regions and where pinch-off comes from.
Explain the body effect and why stacked transistors are slower.

Check yourself

The surface under the gate becomes n-type in a p-type substrate. What is that state called and why is it useful?

Inversion. It forms a conducting channel of the opposite type, connecting the two regions either side, which is what makes the device a transistor.

Why does the gate draw no steady current?

It is separated from the channel by an insulating oxide. Control is entirely by field, which is why holding a logic state costs almost nothing.

What happens at pinch-off, and which region follows it?

The channel closes at the drain end. Beyond that the current stops rising appreciably with drain voltage, which is the saturation region used for amplification.

A logic gate with four stacked transistors is slower than one with two. Why?

The body effect. Each transistor above the bottom has its source above the body, which raises its threshold and makes it conduct less well.

Name one effect that stopped being negligible as devices shrank.

Gate leakage through a very thin oxide, the threshold falling with shorter channels, or carrier velocity saturating so speed no longer improves with size.

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