Saturation or active mode
While V_{GS} > V_{th} and V_{DS} > (V_{GS} - V_{th})
The switch is turned on, and a channel has been made that allows current to flow between the drain and source. As the drain voltage is higher than as compared to the gate voltage, the electrons spread out, and conduction is not by a narrow channel but by a broader, two- or three-dimensional current distribution extending away from the interface and deeper in the substrate. The onset of this region is as well termed as pinch-off to point out the lack of channel region near the drain. Now the drain current is weakly dependent on drain voltage and controlled primarily through the gate-source voltage, and modeled very approximately like:
I_{D} = (μ_{n} C_{ox} /2) W/L (V_{GS} - V_{th})^{ 2} (1 + λV_{DS})
The additional factor including λ, the channel-length modulation parameter models current dependence on drain voltage because of the early effect or channel length modulation.
As per to this equation, a key design parameter, the MOSFET trans conductance is:
G_{m} = 2I_{D}/V_{GS}-V_{th} = 2I_{D}/V_{ov}
In which the combination V_{ov} = V_{GS} - V_{th} is called the overdrive voltage. One more key design parameter is the MOSFET output resistance r_{out} described by:
r_{out} = 1/ λI_{D}
r_{out} is the inverse of g_{DS}
In which g_{DS} = ∂I_{DS} / ∂V_{DS}. V_{DS} is the expression in saturation region.
If λ is considered as zero, an infinite output resistance of the device results which leads to unrealistic circuit predictions, specifically in analog circuits. Since the channel length becomes extremely short, these equations become quite inaccurate. New physical effects take place. For instance, carrier transport in the active mode may become limited through the velocity saturation. While velocity saturation dominates, the saturation drain current is more nearly linear than as compared to the quadratic in V_{GS}. Even at shorter lengths, carriers transport with near zero scattering, termed as quasi-ballistic transport. Additionally, the output current is influenced by drain-induced barrier lowering of the threshold voltage.