Discussion Forum

I'd like to add some facts to my problem - and some questions.

First I have a general question: When capacitive structures are being modeled in v3.5a, you would usually model the electrodes, then add the surrounding material (e.g. a box of air) and then subtract the electrodes from the air box. In v4 you just add the air box without subtracting the electrodes. Why?

I was able to simulate my capacitor in a time-harmonic analysis in version v3.5a. Calculating the capacitance with the formula given in the microstrip example (C11=imag(Y11)/omega) gives me always the same capacitance, no matter what frequency I apply at the input port. I checked the input signal by drawing it versus the time, so I really see a sinusoidal signal with the desired frequency. This can't be correct, since the capacitance is frequency-dependent. Btw, I went up to 1 GHz.

Then I tried a frequency domain analysis in v4.0a. Again, I simulated up to 1GHz and I calculated the Capacitance with the same formula. Again, I get a frequency-independent capacitance which can't be correct. I plotted the Admittance Y11 which shows a perfectly linear increase with the frequency, but I would expect something else due to fringing fields etc.

So to summarize: No matter if I try a DC analysis, a time-harmonic analysis or a frequency domain analysis, I always get the same capacitance, no matter which frequency I apply at the input port.
In fact I would expect something like on this page: 74.86.124.120/$sitepreview/sonnet-dev.com/images/id-cap.gif where you can see a non-linear increase of the capacitance of an interdigitated capacitor versus the frequency.

Any ideas??

I don't think I can be of much help. However, I noticed that in the figure you linked to, the capacitance has no frequency dependence below 1 GHz whatsoever, just like in your case. So why do you stop your frequency analysis at 1 GHz instead of going higher? After all, the capacitance should be constant in the low-frequency limit, whatever "low frequency" may mean.

By the way, even in v4 I always subtract overlapping volumes, since I prefer my physics à la "two bodies cannot be in the same place at the same time". This may no longer be necessary, though, since Comsol 4 has these features now that allow for overriding domain settings by other domain settings.

Hi,

I don't see why a capacitor should be frequency dependent in the AC/DC approximation, unless you have a frequency dependent permittivity which is not the case for air.

The picture changes in RF as soon as your structural dimensions approach the wavelength you use.

But you used AC/DC didn't you?

Cheers Edgar

Hi John,

You're absolutely right, I also noticed that the Capacitance seems to stay very constant in lower frequencies but I guess this is just a question of resolution. I guess if you zoom in and adjust the axis scaling, the same plot would also show a quadratic increase in the lower frequency region, although its not that big. In my case, a have a perfectly constant value. Besides, I ran the simulation up to 100GHz yesterday and still did not see a difference.

Thanks for explaining the issue with the two bodies, I think I understand now. You can still create non-intersecting domains but you don't have to do it anymore, thanks a lot!!

Hi Edgar, thanks a lot for your reply!

First of all, yes I used AC/DC. So from what I know, the capacitance increases versus the frequency due to an increase in fringing fields between the fingers. I think coupling with the substrate (which doesn't count for me since the capacitor is sourrounded by air) is frequency dependent as well.

Now here's the thing: I'm not a hundred percent sure wether AC/DC is taking things like this into account. But there's this guy from the university of british columbia who has lots of comsol examples for electrostatic problems on his webpage:
www.mina.ubc.ca/konradw_comsol_electrostatics

There he modeled quite simple plate capacitors (DC). He claims, that the difference in capacitance between a hand calculation and the comsol model is only due to the fringing fields (e.g. check out the description below the model called "Capacitor with Uniform Dielectric" on that homepage). That's why I assumed you can model fringing influence on the capacitance with AC/DC model...

Hi,

I don't see why a capacitor should be frequency dependent in the AC/DC approximation, unless you have a frequency dependent permittivity which is not the case for air.

The picture changes in RF as soon as your structural dimensions approach the wavelength you use.

But you used AC/DC didn't you?

Cheers Edgar

[...] there's this guy from the university of british columbia who has lots of comsol examples for electrostatic problems on his webpage:
www.mina.ubc.ca/konradw_comsol_electrostatics

There he modeled quite simple plate capacitors (DC). He claims, that the difference in capacitance between a hand calculation and the comsol model is only due to the fringing fields [...] That's why I assumed you can model fringing influence on the capacitance with AC/DC model...

What he means by that is this: Comsol gives you the actual capacitance, including the fringe field. In the analytical solution (C = eps_0 eps_r S/d), the fringe field was neglected, hence the difference. There is no analytical solution for the value Comsol calculates, so this approximation is the only point of reference.

In his example, there is no time/frequency dependence: the electric field doesn't vary with time, therefore the capacitance doesn't either.

I haven't given it much thought, but the only way I could possibly see a frequency dependence (for constant eps_r in each domain) is if you have at least two different dielectrics. Leakage currents through the dielectrics would then redistribute electric charges over time and change the electric field.

Best,

John

Hi John, thanks a lot for your input, I really appreciate it!

So I had the same idea and what I did was, I simulated the capacitor (14 microns high) on a 100um pyrex substrate (epsilonr=6.4) with another 100um air box on top (epsilonr=1).

The result is almost the opposite from what I would expect, the capacitance gets smaller (see attachment). The frequency range was from 1Hz to 100GHz by going up with a factor of ten (1Hz, 10Hz, 100Hz, ...).

Pretty strange...

And if I now set the mesh to extremely fine, I get what I got in the beginning, a constant capacitance...

Hi Jimbo,

of course COMSOL calculates the stray field (you call it fringing field). The difference between an analytical calculation and COMSOL is that COMSOL cannot calculate the stray field at large distances because the FE model must be finite.
In the AC/DC approximation the field topology does not depend on frequency, also the stray fields are frequency independent.
It is the nature of the quasistatic approximation that the relation of structural dimensions and wavelength are ignored.
You must probably use RF to see those effects you are expecting.

Cheers
Edgar