Metal–oxide–semiconductor field-effect transistor

The mechanism

The MOSFET is the central controllable device of CMOS logic. An insulated gate changes the electric potential in the semiconductor channel, regulating current between source and drain. A body or substrate is also part of the device, even when a simplified circuit symbol emphasizes only three terminals. Real operation is continuous and analog: digital circuits choose voltage ranges that stand for zero and one. The atlas cross section separates gate, dielectric, channel, terminals, and body so each function can be inspected. Its dimensions are explanatory rather than a vendor cross section. Moving outward reveals how complementary devices form gates, then memory and arithmetic, through their wiring relationships.

Apply a gate voltage relative to the other transistor terminals.
Use the gate field to change the mobile charge and potential in the channel.
Allow the resulting controlled source–drain current to charge or discharge a circuit node.

Science and assumptions

Long-channel linear-region current

I_D\approx\mu_n C^{\prime}_{\mathrm{ox}}\frac{W}{L}\left[(V_{GS}-V_T)V_{DS}-\frac{V_{DS}^2}{2}\right]

Long-channel triode current is mobility times oxide capacitance per area times width-to-length ratio, multiplied by gate overdrive times drain voltage minus half the squared drain voltage.

Applicable here for strong inversion and $0 ≤ V_{DS} < V_{GS} − V_{T}$ ; it is not a modern short-channel device predictor.

Symbols and units

I_D: Drain current
A
μₙ: Electron mobility
m²/(V·s)
C′_ox: Gate oxide capacitance per area
F/m²
W: Channel width
m
L: Channel length
m
V_GS: Gate-to-source voltage
V
V_T: Threshold voltage
V
V_DS: Drain-to-source voltage
V

Gate overdrive creates channel charge; drain bias drives it along the channel. Mobility, gate capacitance per area, and width-to-length ratio set the ideal current scale.

Assumptions Long-channel nMOS, strong inversion, $0 ≤ V_{DS} < V_{GS} − V_{T}$ , constant mobility, gradual-channel approximation; not a predictive compact model for modern short-channel FinFETs or GAA devices.

Engineering example

In the long-channel expression, raising $V_{GS}$ above $V_{T}$ increases the overdrive term; velocity saturation and short-channel effects limit the extrapolation.

Distinctions and tradeoffs

A MOSFET is an analog physical device; zero and one are voltage-range conventions established by the surrounding digital circuit.

Stronger drive can reduce delay. Capacitance and leakage constrain the associated power benefit.

CMOS circuits combine these devices into digital machinery. No isolated transistor implements a neural-network concept by itself.

Specifications and interfaces

Electrical terminals: Gate, source, drain, body
Body may be implicit in simplified diagrams.
Control variable: Gate-to-source voltage
Operating behavior also depends on other terminal voltages.
Device behavior: Continuous current–voltage relation
Binary logic is a circuit-level abstraction.

Interfaces

Gate Input: Control voltage and charging current
Source/drain path Output: Controlled conduction current

Check your understanding

What primarily controls a MOSFET channel?

The gate electric field
A mechanical gate that swings open
A software token stored in the silicon atom

Answer and reasoning

The gate electric field

The insulated gate changes the channel’s electrostatics. Real current varies continuously with terminal voltages.

Historical context

1960 · Kahng files the insulated field-effect device patent

The patent records a controllable semiconductor device with an insulated electrode, an early foundational step toward MOS integrated circuits. The date is the filing year, not the 1963 grant year.

Kahng — US3102230A

Evidence and scope

The equation is a first-order regime model, not a modern node compact model.

Vary gate and drain bias in the long-channel current model; geometry, doping and short-channel behavior are not adjustable here.