MOSFET Operation: From Cutoff to Saturation

simulator intermediate ~10 min
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I_D = 4.0 mA in saturation

With V_GS = 3 V, V_th = 1 V, and k = 2 mA/V², the MOSFET operates in saturation with drain current I_D = k(V_GS − V_th)²/2 = 4.0 mA and transconductance g_m = 4.0 mA/V.

Formula

I_D = k × (V_GS − V_th)² / 2 (saturation)
I_D = k × ((V_GS − V_th) × V_DS − V_DS² / 2) (linear)
g_m = k × (V_GS − V_th)
V_DS(sat) = V_GS − V_th

The Transistor That Runs the World

The MOSFET — Metal-Oxide-Semiconductor Field-Effect Transistor — is the most manufactured device in human history. Tens of billions sit on every modern processor chip, switching on and off billions of times per second. The principle is simple: a voltage on the gate electrode creates an electric field through a thin oxide layer, attracting carriers to form a conducting channel between source and drain. No gate current is needed, just voltage — making MOSFETs incredibly energy-efficient switches.

Three Regions of Operation

A MOSFET has three distinct operating regions. In cutoff (V_GS below threshold), no channel exists and the transistor is off. In the linear region (V_GS above threshold, V_DS small), the channel spans from source to drain and current flows proportionally to both V_GS and V_DS — the transistor acts like a voltage-controlled resistor. In saturation (V_DS large enough to pinch off the channel at the drain), current depends mainly on V_GS and is approximately constant regardless of V_DS.

The Square-Law Model

The simplest MOSFET model uses the square-law equations derived from gradual channel approximation. In saturation: I_D = (k/2)(V_GS − V_th)², where k = µn × Cox × W/L combines carrier mobility, oxide capacitance, and channel geometry. This parabolic relationship explains why MOSFET amplifiers have lower linearity than bipolar transistors — but their zero gate current and excellent scaling make them dominant in digital circuits.

Scaling and Modern MOSFETs

Moore's Law has shrunk MOSFET gate lengths from 10 µm in 1971 to under 5 nm today. At these scales, the simple square-law model breaks down — short-channel effects, velocity saturation, quantum tunneling through the gate oxide, and drain-induced barrier lowering all become significant. Modern transistor architectures like FinFETs and gate-all-around nanosheets wrap the gate around the channel to maintain electrostatic control at atomic dimensions.

FAQ

How does a MOSFET work?

A MOSFET uses a gate voltage to control current flow between source and drain. When V_GS exceeds the threshold voltage V_th, an inversion layer (channel) forms beneath the gate oxide, allowing electrons to flow. The gate is electrically insulated by the oxide, so it draws virtually zero current.

What are the three operating regions of a MOSFET?

Cutoff (V_GS < V_th): no channel, no current. Linear/triode (V_GS > V_th, V_DS < V_GS − V_th): channel exists end-to-end, current depends on both V_GS and V_DS. Saturation (V_GS > V_th, V_DS > V_GS − V_th): channel pinches off at the drain, current depends mainly on V_GS.

What is transconductance and why does it matter?

Transconductance g_m = dI_D/dV_GS measures how effectively the gate voltage controls drain current. In saturation, g_m = k(V_GS − V_th). Higher g_m means higher voltage gain in amplifier circuits, making it a key figure of merit for analog design.

Why are MOSFETs used as switches?

MOSFETs are ideal switches because they have near-infinite off-resistance in cutoff and very low on-resistance in the linear region. The gate draws no DC current, so switching requires minimal power. Billions of MOSFETs switch in every microprocessor, toggling between cutoff and strong inversion in picoseconds.

Sources

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