intermediate Semiconductor Physics

MOSFET Operation

Visualise the MOSFET cross-section and I-V characteristics. Explore cutoff, linear (triode), and saturation regions interactively.

Vgs1.50 V

Vds0.50 V

SATURATIONId = (kn/2)·(Vgs−Vth)² = 0.188 mA

Id–Vds family (Vgs = 1.5/2.0/2.5/3.0 V) — operating point ●

Vth = 1 V. Green layer = inversion channel. Dashed curve = saturation boundary (Vds = Vgs−Vth).

Set Vgs = 0 V. The device is in CUTOFF — no inversion layer forms, no drain current flows. The gate voltage is below the threshold voltage Vth = 1.0 V.

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The threshold voltage Vth is the minimum gate voltage needed to form a conductive channel between source and drain.
Increase Vgs above 1.0 V. A thin green inversion layer appears — a channel of electrons induced by the positive gate field. This is the ON state.

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The inversion layer is a sheet of electrons at the Si/SiO₂ interface. Its conductance is proportional to (Vgs - Vth).
With Vgs = 2.0 V, increase Vds from 0 to 3 V. At low Vds, the device is in the LINEAR region — Id increases roughly linearly with Vds.

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In the linear region: Id ≈ kn·(Vgs-Vth)·Vds for small Vds. The MOSFET behaves like a voltage-controlled resistor.
Continue increasing Vds past Vgs - Vth (the overdrive voltage). You'll see the channel pinch off near the drain. The device enters SATURATION — Id becomes nearly independent of Vds.

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Pinch-off occurs when the local gate-to-channel voltage at the drain drops below Vth. Beyond this point, current saturates at Id = (kn/2)(Vgs-Vth)².
Examine the family of I-V curves in the lower panel. Each curve corresponds to a different Vgs. The dashed curve is the saturation boundary (Vds = Vgs - Vth). The orange dot is your current operating point.

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IC designers use these curves to choose the bias point (Vgs, Vds) for a given drain current. The slope in saturation (output resistance) ideally is zero.