How inversion layer shields electric field?

[anhnha]

This question is somewhat relating to electronics but I think it fits better with physics.

The leccture here (slide 13) shows that the gate to body capacitance (Cgb) in linear region is 0. However, there is no explanation at all.

I tried to find the explanation from the reference book and got this:

In linear-mode operation, the inverted channel extends across the MOSFET, between the source and the drain (Fig. 3.31(b)). This conducting inversion layer on the surface effectively shields the substrate from the gate electric field; this Cgb = 0.

With the shielding, does this mean the electric field in substrate is 0?

Is there a way to prove that Cgb = 0 mathematically?

Thank you.

 

[BigJDubs]

Yes, the electric field in the substrate is zero when the inverted channel extends across the MOSFET. This is because the electric field is generated by the gate voltage and the capacitance between the gate and the body (Cgb). When the channel is extended across the MOSFET, the capacitance between the gate and the body is effectively reduced to zero, since there is no longer an insulating layer between them. To prove that Cgb = 0 mathematically, you can use the formula for the capacitance of a parallel-plate capacitor: C=ε0εrA/dWhere C is the capacitance, ε0 is the permittivity of free space, εr is the relative permittivity, A is the area of the plates, and d is the distance between the plates. When the channel is extended across the MOSFET, d=0, so Cgb=0.