Confused on MOSFET terms (velocity limited, mobility limited, constant mobility)

Question

So we're learning about transistors, but we don't much of the physics behind how they work (yet) so these terms are quite strange to me. The models we've used are "velocity limited", "mobility limited", and "constant mobility". In some models, the relation between drain current and gate-source voltage is linear and in others it's based on a square law. What do these terms mean, and where do the square or linear relationships come from?

Here's the equation for velocity-limited characteristics: \$I_d=V_{sat} C_{ox} W_g (V_{gs}-V_t) (1+\lambda V_{ds})\$

And this is for mobility limited (which they also refer to as constant mobility): \$I_d=\frac{1}{2} \mu C_{ox} \frac{W_g}{L_g} (V_{gs}-V_t)^2 (1+\lambda V_{ds})\$

Answer 1

Although MOSFET are linear voltage control switches, the gate charge during transition means you have to dump current from the driver to the gate capacitance during transition. Since you know the square law of V for the Cap current, it is quadratic during transition and linear beyond that. My rule of thumb is assume 50:1 impedance ratio for driver on gate to load on drain or source. For faster transition times they use Diacs to dump a capacitor storage into the gate or low impedance MOSFETs to drive even lower power MOSFETs. eg 50mΩ drive to gate with 1mΩ output. 100:1 is also possible. Anything where Source does not match line and load will lead to skew, ringing from mismatched impedances from source to load.

The same holds true for high power IGBT's.