MOSFETs are voltage-controlled devices — the gate voltage creates an electric field that modulates channel conductivity. No gate current flows (in DC), giving extremely high input impedance.

Structure and Physics: The gate is insulated from the channel by a thin oxide layer. Applying $V_{GS} > V_{th}$ creates an inversion layer (channel) between source and drain.

MOSFET cross-section

Operating Regions:

Region	Condition	Drain Current
Cutoff	$V_{GS} < V_{th}$	$I_D \approx 0$
Linear (Triode)	$V_{GS} > V_{th}$ , $V_{DS} < V_{GS} - V_{th}$	$I_D = \mu_n C_{ox} \frac{W}{L}\left[(V_{GS}-V_{th})V_{DS} - \frac{V_{DS}^2}{2}\right]$
Saturation	$V_{GS} > V_{th}$ , $V_{DS} \geq V_{GS} - V_{th}$	$I_D = \frac{1}{2}\mu_n C_{ox} \frac{W}{L}(V_{GS}-V_{th})^2$

The Saturation Equation (Square Law):

$I_D = \frac{1}{2}\mu_n C_{ox} \frac{W}{L}(V_{GS}-V_{th})^2(1 + \lambda V_{DS})$

where $\lambda$ is the channel-length modulation parameter.

MOSFET I-V characteristics

Enhancement vs Depletion:

Enhancement mode (most common): Channel forms when $V_{GS} > V_{th}$
Depletion mode: Channel exists at $V_{GS} = 0$ , removed by negative $V_{GS}$

Why MOSFETs Dominate Digital:

Near-zero static power (no gate current)
Easy to fabricate complementary pairs (CMOS)
Scales well with smaller geometries

For switching applications, the goal is to operate fully in cutoff or deep in the linear region (as a closed switch with low $R_{DS(on)}$).

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