Threshold Voltage and the Meaning of On/Off

A MOSFET does not become a perfect switch at one magical instant.

Threshold voltage is the practical boundary where the device begins to form a useful channel.

Gate-to-Source Voltage

MOSFET control is usually described using gate-to-source voltage, written as V_GS.

For a simplified n-channel MOSFET:

• if V_GS is below the threshold voltage V_T, the channel is not strongly formed
• if V_GS is above V_T, the channel can conduct much more easily

The common shorthand is:

nMOS turns on when V_GS > V_T.

This is a useful rule, not a full device model.

On and Off Are Engineering Ranges

In digital logic, “off” means blocked enough for the circuit’s purpose. It does not mean absolute zero current.

“On” means conductive enough for the circuit’s purpose. It does not mean a perfect wire.

Real devices have:

• leakage current when off
• resistance when on
• delay while switching
• capacitance that must be charged or discharged
• variation across manufacturing and temperature

Digital systems work because they design around ranges and margins.

Why Threshold Matters for Logic

Threshold behavior helps connect analog physics to digital interpretation.

The transistor responds continuously to electrical conditions, but digital circuits use regions:

• low input range
• high input range
• transition region

The circuit is designed so stable inputs produce stable outputs that another circuit can recognize.

Boundary

Do not treat V_T as the only thing that determines behavior. Drain voltage, body voltage, geometry, temperature, and process details also matter.

The durable model is:

Threshold voltage marks the control range where a MOSFET becomes useful as a conducting path, but digital on/off is always an engineered approximation.