## Plate materials in capacitors

Hi
I was wondering about an issue i thought about while attending a masters thesis dissertation earlier

does the material of the plate (not the filling dielectric) affect capacitance (even if in the fringing level) ?
Check the attached picture , for a better explanation
Attached Thumbnails

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 The conductive material will not effect capacitance so long as: 1 - Each conductor enforces an equipotential condition across its surface. 2 - The conductive material is well behaved in the presense of the required E-field. A violation of (1) would be a capacitor with 1 square foot plate used for 1GHz signal. A violation of (2) would be very high surface charge density, say from combination of high voltage and sharp edge on conductor, causing corona discharge.
 But isnt aluminum a "better conductor" ? isnt having a higher conductivity something that will upset the electric field distribution, since more charges will accumulate on the metal than on the silicon ?

## Plate materials in capacitors

"Better conductor" only matters if current is flowing through the conductor.

Capacitance is an electrostatic quantity. Charges are not in motion; they have arrived at their equilibrium positions which, in turn, creates the E field distribution that leads to the measured voltage between plates.

If your frequency is low enough that the charges are able to be, at any frozen moment in time, close to their electrostatic equilibrium positions, then the capacitance will be correspondingly close to the electrostatic capacitance ("quasi-static" approximation).

If your frequency is high enough that the charges are not able to keep up and reach their electrostatic equilibrium positions, then you no longer have equipotential surfaces.

Perhaps what you are saying is that we can extend the quasi-static approximation to higher frequencies in a given geometry if we use better conductors. This is true, but only to a certain extent. Part of the issue is finite propagation velocity. If I had a parallel plate capacitor made with superconducting plates 1 square foot in area, I would not expect to have equipotential surfaces at 1GHz.

Check out the free field solvers available at: http://www.fastfieldsolvers.com. or http://www.rle.mit.edu/cpg/research_codes.htm.
 So for micrometer level dimensions , running at the KHz speed : The only issue I will see is a "series" resistance with the silicon part that is about 0.5 ohms ( Aluminum has resistivity 28.2 nΩ·m, while silicon 1KΩ·m) more than that of the aluminum part which will mean each part will behave as a low pass filter , with cutoff frequencies in the THz (RC=0.5*C , and Cap is ~ 10^-11 ) , so ... no difference at running in the KHz BTW my calculations are just rough estimates Am I right ?