Alpha-power law: definition · Chip Field Guide

Beginner

A formula that fits real, tiny transistors better than the textbook rule, because their current grows more gently.

Novice

A MOSFET model in which saturation current grows as $(V_{\mathrm{GS}} - V_{\mathrm{t}})$ to a power $\alpha$ between 1 and 2 instead of exactly 2. $\alpha = 2$ gives back the square law; $\alpha$ near 1 means strong velocity saturation.

Expert

$I_{\mathrm{Dsat}} = P_{\mathrm{c}} (\beta/2)(V_{\mathrm{GS}} - V_{\mathrm{t}})^{\alpha}$ and $V_{\mathrm{DSAT}} = P_{\mathrm{v}} (V_{\mathrm{GS}} - V_{\mathrm{t}})^{\alpha/2}$ , with $\alpha$ , $P_{\mathrm{c}}$ and $P_{\mathrm{v}}$ fitted to measured or simulated curves. Sakurai and Newton’s $n$ th-power-law form also fits the linear region; $\alpha \approx 1.3$ is a typical value for a 65 nm process.