The MOSFET square law is an approximate rule that describes how the current through a long channel MOSFET behaves in the saturation region.

In this region, once the drain voltage is high enough, the current no longer increases much with further increase in drain voltage and instead is controlled mainly by the gate voltage above the threshold.

The square law says that under ideal conditions the drain current grows roughly with the square of the effective gate voltage above threshold.

In simple terms, if you increase the gate voltage a little, the channel formed in the semiconductor becomes much stronger, the charge in the channel increases, and the current rises very quickly, not just in a straight line but in a curved way that follows a square relationship.

This model assumes a uniform channel, constant carrier mobility, no velocity saturation, and negligible short channel effects, which is why it works best for older or larger devices.

In modern very small MOSFETs, effects such as velocity saturation and strong electric fields cause the current to grow more slowly than the square law predicts, so engineers use more advanced models, but the square law idea is still very useful for basic understanding and hand analysis.

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