The linear model correctly predicts the MOSFET behavior for small drain-source voltages, where the MOSFET acts as a variable resistor.

The quadratic model includes the voltage variation along the channel between source and drain.

This model is most commonly used despite the fact that the variation of the depletion layer charge is ignored.

The variable depletion layer model is more complex as it includes the variation of the depletion layer along the channel.

As the name suggests, the linear model, describes the MOSFET acting as a linear device.

More specifically, it can be modeled as a linear resistor whose resistance is modulated by the gate-to-source voltage.

In this regime, the MOSFET can be used as a switch for analog and digital signals or as an analog multiplier.

If the velocity of the carriers is constant between source and drain, the transit time equals.

This leads to the following expression for the drain current.

We also assume that the basic assumption described in section 6.3.2 applies, namely that the charge density in the inversion layer equals minus the product of the capacitance per unit area and the gate-to-source voltage minus the threshold voltage.

Replacing the inversion layer charge density in the expression for the drain current yields the linear model.

Also note that the drain current is zero if the gate-to-source voltage is less than the threshold voltage.

The linear model is only valid if the drain-to-source voltage is much smaller than the gate-to-source voltage minus the threshold voltage.

This insures that the velocity, the electric field and the inversion layer charge density is indeed constant between the source and the drain.

The slope of the curves equals the conductance of the device, which increases linearly with the applied gate voltage.

However, this model allows the inversion layer charge to vary between the source and the drain.

The current is also related to the local channel voltage, IV C.

The linear model as described by equation ( 7.3.6 ), still applies to such section, yielding.

Both sides of the equation can be integrated from the source to the drain, so that y varies from 0 to the gate length, L, and the channel voltage V C varies from 0 to the drain-source voltage, V DS.

According to the above equation the current would even decrease and eventually become negative.

The charge density at the drain end of the channel is zero at that maximum and changes sign as the drain current decreases.

As explained in section 6.2, the charge in the inversion layer does go to zero and reverses its sign as holes are accumulated at the interface.

However, these holes cannot contribute to the drain current since the reversed-biased p-n diode between the drain and the substrate blocks any flow of holes into the drain.

Gate Mosfet Signal Shape Modulation