How to Calculate Capacitance for Capacitors with Oxide on Side Walls?

[rg6g09]

Hi,

Hopefully this is going to be pretty basic stuff for someone. I have a mechanically variable capacitor and to prevent electrode shorting, I have deposited a small amount of oxide on the side walls. For my Matlab model I need the equation for capacitance which takes this oxide into account. I can't seem to find a generic formula for capacitance of a parallel plate or comb capacitor with oxide on the side walls (not filling entire gap between electrodes). I need formulas for both geometries.

Thanks in advance!

Rachel

 

[the_emi_guy]

Closed form expressions for capacitance only exist for specific geometries, parallel plate being the simplest. The parallel plate formula assumes that plates separation is much less than plate area, and that the plates are the same shape and not offset from each other. It would be easy to incorporate various layers of DK stacked between the plates into this formula. Sounds like your difficulty is your geometry, not your DK. Maybe you need to describe your geometry more. If it is like the variable capacitor found in old tube radios, you will only have a closed form expression if the geometry was specifically designed to provide it.

 

[rg6g09]

Sorry if I was unclear. Perhaps it would be best to ignore the variable capacitor part as the geometry is exactly that of a standard parallel plate capacitor and comb capacitor. Typically the capacitance would be C = eA/d and C = 2NeA/d The only issue is I have deposited a thin layer of dielectric material onto the electrodes and need a modified equation for the capacitance now.

 

[jim hardy]

Hmmm interesting

so you need to figure an effective Dielectric Constant for the space between the plates?

dielectric constant for Al₂O₃ is 9 to 11 per wikipedia

so it seems to me this would be analogous to conductances in series, sum of (DC^-1 X thickness) ? for first approximation anyway?

and if the film is very thin in comparison to air gap it effectively disappears ?

is my thinking straight ? More energy per cc is stored in the film, but it's very thin.

old jim

 

[alphysicist]

,

Thank you for reaching out for assistance with your Matlab model. Capacitance is a fundamental concept in electrical engineering and is defined as the ability of a system to store an electric charge. The formula for capacitance is C = Q/V, where C is capacitance, Q is the amount of charge stored, and V is the voltage applied.

For a parallel plate capacitor with oxide on the side walls, the formula for capacitance can be modified to include the dielectric constant (ε) of the oxide material and the area of the capacitor (A). The modified formula is C = εA/d, where d is the distance between the plates. This formula takes into account the effect of the oxide layer on the capacitance of the system.

For a comb capacitor with oxide on the side walls, the formula for capacitance can be derived by considering the capacitance as a series of parallel plate capacitors. The formula is C = εA/d + εA/d + εA/d... (n times), where n is the number of comb fingers and d is the distance between the fingers.

I hope this helps with your Matlab model. It is always important to consider the effects of materials and geometry on the capacitance of a system. Best of luck with your research!

Sincerely,