Velocity saturation: definition

Beginner

A speed limit for electrons in silicon. Past a certain push they bump into the crystal so often that they can’t go any faster.

Novice

At high electric fields, carriers scatter off the silicon lattice and their speed stops rising, leveling off near $10^7\,\mathrm{cm/s}$ for electrons. In a short channel the field from $V_{\mathrm{DS}}$ is high enough for this to cap the current before pinch-off does.

Expert

Carrier velocity rolls off from $\mu E$ toward $v_{\mathrm{sat}}$ once $E = V_{\mathrm{DS}}/L$ approaches the critical field. The fully saturated limit is $I_{\mathrm{D}} = W C_{\mathrm{ox}} (V_{\mathrm{GS}} - V_{\mathrm{t}}) v_{\mathrm{sat}}$ : linear in overdrive and independent of $L$ . Real devices are partly velocity-saturated, which the $\alpha$ -power law fits.