Velocity Saturation and Mobility Degradation

Ideal model assumes carrier velocity increases linearly with electric field. In reality, at high and vertical electric fields, carrier velocity saturates, and mobility degrades due to scattering

Saturation Current with Velocity Saturation

$$ I_{\text{dsat}} = W C_{ox} v_{sat} \frac{V_{GT}^{2}}{V_{GT} + V_c} $$

• Where $V_{GT} = V_{gs} - V_t \text{ and }V_c = E_c L$ is the critical voltage where velocity saturates

Full Velocity Saturated Limit

$$ I_{\text{dsat}} \approx W C_{ox} v_{sat} V_{GT} $$

• Current depends linearly on $V_{gs}$

Alpha-Power Law Model

$$ I_{\text{dsat}} = P_c \frac{\beta}{2} V_{GT}^{\alpha} $$

• $\alpha$ is the velocity saturation index between 1 (fully saturated) and 2 (long-channel)
  • nMOS transistors typically have a lower $\alpha$ than pMOS

Channel Length Modulation

Depletion region around the drain grows with $V_{ds}$, shortening the channel length

• In saturation, $I_{ds}$ is not constant bu increases with $V_{ds}$

Early Voltage Model

$$ I_{ds} = \frac{\beta}{2} V_{GT}^2 \left( 1 + \frac{V_{ds}}{V_A} \right) $$

• Where $V_A$ is the early voltage

Threshold Voltage Effects

Body Effect