MOS Capacitor Inversion Mode
In Strong inversion electrons that move through gate contain electrons in Drain and source and minority carriers of substrate as well.
These all depend on the charge of surface.



All of this happens when the voltage of the gate increase to the level that gather enough hole above channel area in metal part to gather enough electrons in channel area for Symmetry of charges.

The thing is that changing p-type substrate to n-type happen only through the channel of FET, due to gathering most of the electrons of the substrate in the channel region, matter in fact bottom of the p-type substrate has a major increase in the number of acceptors(NA) while it's in strong inversion mode.