effective dielectric constant

Dear all,

I have a multi-layered substrate which I want to simulate in EM solver.
Since the layers are pretty thin, it will very likely create so many meshes. How can I find a kind of effective dielectric constant to make a single layer substrate? Can anyone refer me to any paper?

Most of the papers talk about effective dielectric constant for typical structures e.g. CPW, microstrip. Effective dielectric constant indeed depends on the shape of the structure.

But I would like to have an effective dielectric constant to use it in my EM solver.

thanks

The simplest and ,as it practically turns out in ICs, also accurate thing is
use equivalent series plate capacitor model.

For instance :
C_total = C1||C2 (C=E_o*E_r*A/t)

E_r_total/t_total= (E_r_1/t_1)||(E_r_2/t_2)

E_r_total - is your effective diel.

Enjoy :)

If you are using a commercial planar simulator, e.g. Ansoft Designer, Sonnet, Momentum, you do not need to worry about using an effective dielectric constant. All of the planar simulators will account for very thin layers dielectric layers in the Green's function. Hence, you do need an effective dielectric constant, and in fact, I would discourage you from trying to use one.

Layered media can provide several different coupling mechanisms that are not present in a uniform effective dielectric. For example, surface waves, leaky waves, and dielectric waveguides. Depending on the stack and the geometry, you could get very wrong results.

Wiley - I want to see you simulating in HFSS 40 layer stackup with
some layers of 100nm while your simulated instances 500um.

Basically Wiley is right but it depends on problem.
In the field of RFICs it is common to use effective dielectric.

Note that I wrote "planar simulators". :D

Ansoft Designer - never used

Momentum - yes it's correct after substrate calculation the green fuction exist
and layers height doesn't bother you anymore.

Sonnet - I think 100nm(which are common in sub-micron processes) height layers will slow down the simulator and you will not get actually much accurate results if you unified(with eff Er) them.
I think it's better ,at least, unify all layers between each X and X-1 Metal layer .

IE3D - also likes more unified dielectrics for time simulation enhancing.

I agree Wiley,that HFSS was very radical example :)

Hi, GoaGosha:

One thing you can try on IE3D to speed up the simulation is to use finite dielectrics for the thin layers. If you have multiple thin layers, it certainly will slow down the simulation. IE3D V12 has much improvement on it. However, it will still be much slower for multiple thin infinite layers. However, as an alternative, you can try to model some thin layers and finite substrates on IE3D. For many cases, finite substrates will slow down the simulation. However, for multiple thin layers, I think it may speed up the simulations. Regards.

There is a link that might help you. It is basically for "optical" problems, but looking in it might give information you need.

http://wwwhome.math.utwente.nl/~hammer/oms.html