MOSFET I-V Characteristics: Cutoff, Triode and Saturation

A voltage-controlled valve

A MOSFET (metal-oxide-semiconductor field-effect transistor) is a four-terminal device — gate, source, drain, body — that uses the voltage on the gate to control the current flowing between drain and source, with essentially zero DC current flowing into the gate itself, since it's insulated from the channel by a thin oxide layer. That insulation is the whole point: unlike a bipolar transistor, a MOSFET is controlled by an electric field, not a base current, which is why it's called a field-effect transistor and why it can be driven with almost no static power.

Cutoff: the switch that's off

Below the threshold voltage V_th, not enough gate voltage has been applied to pull mobile charge carriers to the silicon surface beneath the gate oxide, so no conducting channel exists between source and drain — ideally, zero drain current flows regardless of the drain voltage. In real devices a small subthreshold leakage current does flow, and controlling that leakage as devices shrink has become one of the central challenges of modern chip design, but the ideal model treats V_GS < V_th as a clean off state.

Triode (linear) region: a voltage-controlled resistor

Once V_GS exceeds V_th, a channel forms, and for small drain voltages (V_DS < V_GS − V_th) the device behaves almost like a resistor whose resistance is set by the gate voltage — this is the triode or linear region, useful for building analog switches and voltage-controlled resistances:

cutoff:      V_GS < V_th               I_D = 0

triode:      V_GS > V_th, V_DS < (V_GS - V_th)
             I_D = k * [ (V_GS - V_th)*V_DS - V_DS^2/2 ]

saturation:  V_GS > V_th, V_DS >= (V_GS - V_th)
             I_D = k * (V_GS - V_th)^2 / 2

k = mu * C_ox * (W/L)     (transconductance parameter)
mu   = carrier mobility
C_ox = gate oxide capacitance per unit area
W/L  = channel width-to-length ratio

Saturation: the square law that makes it an amplifier

Once V_DS grows past V_GS − V_th (the overdrive voltage), the channel "pinches off" near the drain end, and in the ideal model the drain current flattens out, becoming — to first order — independent of V_DS and dependent only on the gate voltage: I_D = k(V_GS − V_th)²/2. This square law is the reason a MOSFET can amplify: a small change in gate voltage produces a current change proportional to the overdrive voltage, giving a well-defined transconductance g_m = k(V_GS − V_th) that circuit designers use to size gain stages. Real transistors show a mild upward slope in saturation from channel-length modulation (the effective channel shortens slightly as V_DS increases), captured with a correction factor (1 + λV_DS), but the flat square-law approximation captures the essential physics.

Reading a family of curves

Plot I_D against V_DS for several fixed values of V_GS and you get the classic MOSFET "family of curves": each trace rises linearly through the triode region, bends at the V_DS = V_GS − V_th knee, and flattens into saturation at a height set by the square law. Higher V_GS traces sit higher and bend further right, since the overdrive voltage — and therefore the pinch-off point — grows with it. Reading this family tells you everything about how the device will behave in a circuit: whether it's biased in the flat, current-source-like saturation region for amplification, or driven hard into deep triode with V_GS ≫ V_th to act as a low-resistance closed switch.

Frequently asked questions

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