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Square Law Model (MOSFET)

Describes the drain current (IDI_D) of a MOSFET in the saturation region, simplifying the complex physics to ID≈K′(W/L)(VGS−Vth)2/(2 (1+lambdaVDS))I_D \approx K' (W/L) (V_{GS} - V_{th})^2 / (2 \ (1 + \\lambda V_{DS})).
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The statement of the theorem

For a MOSFET operating in the saturation region (VDS≥VGS−VthV_{DS} \ge V_{GS} - V_{th}), the drain current IDI_D is modeled by the square law approximation, incorporating the channel length modulation effect (λ\lambda):\nID≈K′2(WL)(VGS−Vth)2(1+λVDS)−1I_D \approx \frac{K'}{2} \left( \frac{W}{L} \right) (V_{GS} - V_{th})^2 \left( 1 + \lambda V_{DS} \right)^{-1}\nWhere K′K' is the process transconductance parameter, W/LW/L is the aspect ratio, VGSV_{GS} is the gate-source voltage, VthV_{th} is the threshold voltage, and λ\lambda is the channel length modulation parameter.
Source: Wikipedia