Saturation

Saturation and mobility are two separate ideas that both describe how current behaves once it's already flowing through a transistor's channel — mobility is how easily a carrier moves through silicon under a given electric field, and saturation is the operating region where a transistor's drain current stops increasing with drain voltage and instead levels off, controlled almost entirely by the gate instead. Together they explain why a transistor's current-voltage behavior isn't a straight line, and why "faster silicon" and "a transistor acting like a good switch" turn out to be the same underlying physics viewed two different ways.

Mobility measures how fast a carrier drifts through silicon per unit of electric field, and it's a property of the material and the carrier type, not of any particular device. Silicon's atomic lattice constantly scatters moving carriers — off vibrating atoms, off dopant impurities, off crystal defects — and mobility is essentially the net result of how much of that scattering a carrier experiences before it can build up speed. Electron mobility in bulk silicon runs roughly two to three times higher than hole mobility, which is why PMOS transistors are routinely built wider than matching NMOS transistors just to deliver comparable drive current. Mobility also drops as doping concentration rises, because more dopant atoms means more scattering sites — which is exactly the tradeoff that makes heavily-doped source/drain regions great conductors but a comparatively poor choice for the channel itself.

In the linear (or "triode") region, drain current rises roughly in proportion to drain voltage, and mobility directly sets how steep that rise is. At small drain voltages, the channel behaves almost like an ordinary resistor whose resistance is set by the channel's carrier density and mobility — higher mobility means a lower-resistance channel and more current for the same voltage. This is the region where mobility-boosting techniques pay off most directly: strained silicon, high-mobility channel materials like silicon-germanium or indium-gallium-arsenide, and crystal-orientation choices all aim squarely at improving this linear-region slope, because a faster channel here means a faster-switching transistor overall.

Saturation begins at the pinch-off point, where the channel's effective length shrinks to zero at the drain end and the current simply can't rise with drain voltage anymore. As drain voltage increases past a certain threshold, the voltage drop across the channel near the drain side becomes large enough that it depletes the channel from that end entirely — the channel "pinches off" right at the drain, even though a conductive path still exists back toward the source. Past this point, any further increase in drain voltage gets absorbed by a small high-field region right at the pinch-off location rather than pulling more current through the rest of the channel, so drain current levels off into a plateau. This is the single most important operating region for digital logic, because a transistor that's "fully on" in a digital circuit is almost always sitting in saturation.

Saturation current is controlled almost entirely by gate voltage, which is exactly the behavior a good digital switch needs. Once in saturation, drain current depends strongly on how far the gate voltage sits above the threshold voltage, and only weakly on drain voltage itself — meaning the transistor acts like a voltage-controlled current source rather than a simple resistor. That weak drain-voltage dependence is what lets digital circuits treat a transistor as a clean, predictable switch instead of a voltage-divider whose behavior shifts with every downstream load; it's also, not coincidentally, the regime amplifier designers rely on for predictable gain.

At very short gate lengths, a second, independent flattening effect called velocity saturation kicks in and changes the story. Mobility describes how carriers respond to a weak field, but under the very strong fields present in a short-channel transistor, carrier velocity stops increasing linearly with field strength and saturates at a maximum "scattering-limited" velocity well before pinch-off would otherwise occur. This means short-channel transistors reach their current plateau earlier and at a lower current than simple long-channel theory predicts, and it's one of the core reasons transistor scaling below roughly 100 nm required a wholesale rewrite of the equations engineers use to predict device behavior — mobility alone stopped being enough to describe what the carriers were actually doing.