Problem with total energy in Electrostacis/StatElecSolve model

Numerical methods and mathematical models of Elmer
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iguaz
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Problem with total energy in Electrostacis/StatElecSolve model

Post by iguaz »

Hello!

I’m new in Elmer and I have a problem with the energy calculation in the Electrostatics model.

I have a created a complex geometry with gmsh + ElmerGrid composed of:
1) A germanium volume of 4 mm thickness divided in two pieces.
2) 7 hexagonal germanium pixels (1 central & 1 ring of six around) situated on the top side of the germanium volume.
3) 7 cylindrical copper bars at the center of each pixel.
4) Different vacuum/air volumes in the interspace of pixels & around the copper bars.
5) A ceramic volume on top of the copper bars.

My goal is to estimate the capacitance of each pixel, using as a reference the bottom side of the germanium volume. This seems to work when I use the “capacitance matrix” and values are ~1.2-1.5 pF, which are more or less what I expect.

I have then tried to verify the correctness of these values using the total energy, as it should be the sum of 0.5 x C x V^2 terms. With this aim, I have first set all electrodes to 0 V and I have then consecutively set the pixels (with its corresponding copper bar) to 100 V.

However, the values I obtain are non-sense:

Pixels to 100 V -------------> Energy (10^-8 x J)
----------------------------------------------------------
Central ------------------------> 0.698
Central + 1 pixel -------------> 1.004
Central + 2 pixel -------------> 1.032
Central + 3 pixel -------------> 1.038
Central + 4 pixel -------------> 1.025
Central + 5 pixel -------------> 0.973
Central + 6 pixel -------------> 0.661

I don’t know if any boundary condition is missing or anything else.

I have also tried not to mesh the copper bar volumes, with the same results.

I attach you the .geo and .sif files, as well as three images for illustration. I’m using the last version of Elmer.

Many thanks in advance for any help & advice.

Best regards,

Paco Iguaz
Attachments
Geometry description
Geometry description
Geom5_Description.png (602.96 KiB) Viewed 1869 times
case.sif
Elmer configuration file
(5.83 KiB) Downloaded 210 times
HPGeDSL12.geo
Geometry created by GMSH
(100.33 KiB) Downloaded 205 times
raback
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Re: Problem with total energy in Electrostacis/StatElecSolve model

Post by raback »

Hi

What is the problem? Can the cross-capacitance of the pixels not explain this. If you have potential at either 0 or 100 I would guess that a mix would result to the highest energy.

Note that you may introduce electrostatic energy when you set any Dirichlet condition, be it 0 or 100. Comparing just cross capacitance of two parts you should have only those set.

Btw, the far field potential model does not work with given potential, but assumess spherical decay and hence it might not be applicable to many cases.

-Peter
iguaz
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Joined: 20 Jun 2019, 16:23
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Re: Problem with total energy in Electrostacis/StatElecSolve model

Post by iguaz »

Hello Peter,

Many thanks for your replay.

I understand your point that the electrostatics energy may decrease when switching on several electrodes if the inter-pixel capacitance values are of the same order as self-capacitance values. However, as you can check in the capacitance matrix output file, this is not the case: ~10^-10 pF vs 1.2-1.5 pF.

For the second point, what could I do to get a good cross-check? Should I define vacuum volumes all around my geometry and set the external surfaces to "Electric Infinity BC = Logical True"?

Best regards,

Paco
Attachments
capamatrix.txt
Capacitance matrix
(847 Bytes) Downloaded 208 times
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