Square-law (Shockley) model: definition

Beginner

The simplest textbook rule for a transistor: push the gate twice as far past its tipping point and four times as much current flows.

Novice

The classic first-order MOSFET model: zero current below threshold, $I_{\mathrm{D}} = \beta(V_{\mathrm{GS}} - V_{\mathrm{t}} - V_{\mathrm{DS}}/2)V_{\mathrm{DS}}$ in the linear region and $I_{\mathrm{D}} = (\beta/2)(V_{\mathrm{GS}} - V_{\mathrm{t}})^2$ in saturation, where $\beta$ depends on the device size and the process.

Expert

Derived from the gradual-channel approximation with constant mobility. $\beta = \mu C_{\mathrm{ox}} W/L$ . It is SPICE Level 1. It works for long channels but overestimates drive current and its growth with $V_{\mathrm{DD}}$ in short ones, because it ignores velocity saturation and mobility degradation.