Thin sheet of semiconductor in a dielectric-filled capacitor

[SinglePhotonGuy]

Hi all,

I have a question regarding modifications to a "standard" plate-capacitor with plate area A, plate distance d and filled with a dielectric.
The equations for capacitance and electric field in this case are well known.

I found examples for what happens when inserting a thin conductor parallel to the plate, namely that it just "splits" the capacitor, resulting in two capacitors in a series with either reduced distance d1 and d2, depending where the conductor is inserted in relation to the plates. The respective capacitances can be calculated accordingly.

Is the inside of this conductor actually considered free of the eletric field of the capacitor in this case? Or does the electric field penetrate the inserted conductor? I remember something in the way of surface charges forming, which basically screen the inner part of the conductor? But I might also mix something up here.

The actual question to which this is leading up to:

What happens if I insert a thin slab of undoped semiconductor, let's say GaAs, into the capacitor, so that it is surrounded by the dielectric and is parallel to the plate? Can it be considered a dielectric, as long as the resulting field strength is not causing any charge carriers in the semiconductor to get into the valence band?

And would that mean, that the electric field of the capacitor is penetrating the semiconductor?

Thank you very much for your insights!

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In general I would be interested if this could be a possibility to have an electric field in a semiconductor without having a p-i-n junction in reverse bias, which is often used to observe the (Quantum-Confined) Stark Effect.

 

[rjenkinsgb]

The external charge would influence electrons within the metal plate. (Not sure what it would do with the semiconductor).

If an electrostatically charged item is brought near a conductive plate, electrons are either attracted or repelled from the near surface, causing an inverse charge to appear on the opposite surface.

If the opposite surface is discharged before the charged item is removed, the plate will have a charge afterwards.

That's "Electrostatic induction", and how such as a Wimshurst electrostatic machine works.

Electrostatic induction - Wikipedia

en.wikipedia.org

 

[Tony Stewart]

The thin metalized layer in the middle of a dielectric of uniform E field will now have two capacitors with twice the original value in series yielding almost the same as the original capacitance with just 2 electrodes, if you neglect the relatively thin middle conductor replacing dielectric material.

Changing that middle conductive layer to another dielectric insulator will not change the overall capacitance if the dielectric constant is much larger but will reduce it if smaller. The bandgap material, such as a GaAs, when doped, has the ability to increase the capacitance and conductivity at the same time with a positive PN potential and reduce capacitance with a negative potential. Undoped, it might be just another dielectric with insulation properties.

 

[SinglePhotonGuy]

Thank you for the two answers so far! It says in the linked wikipedia article by rjenkinsgb, that the conductor (the metal plate) in this case is free of an electric field inside - thank you for clearifying!

According to your answer Tony Stewart, it is then legit to conclude that there would be an electric field in the undoped semiconductor, as long as it behaves as a dielectric, i.e. if nothing excites enough charge carriers to bridge the band-gap? Since there would be an electric field in any other dielectric in a regular capacitor.

 

[Tony Stewart]

Yes an electric field implies it must be an insulator and there must be a gradient [V/m] E-field, whereas for conductors the voltage is constant (except for resistive losses).

Then for a semiconductor you have both insulation and conductance variables. Adding more capacitance to a semiconductor is not usually desirable unless one leg is a connected to a voltage source as that would reduce the GBW attribute for transconductance.

For any series or cascade of dielectrics, the largest potential energy will occur across the lowest dielectric constant material or smallest C. [pF]