# Can electrical conductivity be made anisotropic by geometry (similar to fluids)?

Some basics about the flow of electrical current are often compared to the flow of fluids. In many cases this is quite a good model, for more in depth theory the model begins to fall apart.

When I read through the wikipedia article on microvias I stumbled across this picture of a void in such a microvia:
Source: https://commons.wikimedia.org/wiki/File:MicroviaVoiding.png

The void in this picture is formed in such a way, that a question came to my mind: Is this conductor geometry affecting electrical conductivity anisotropically like it would for fluids? With fluids flowing from bottom to the top (in the picture), quite a reasonable part of the pressure vector would point orthogonally at the obstacle and only a small part would result in actual flow (the part at the side of the obstacle). With a flow from top to bottom the downwards part of the vector would partially be deflected to the side and resistance to flow would be lower.

Is a similar effect observable for electrical current? If not, why?

## 1 Answer

It depends on the stuff you change the geometry with. If electrons on the boundary of that stuff are given a higher resistance to flow then it will have influence but small. If you place an air bubble inside a conductor, then on the inside surface the electrons may flow less easily. But compared to the rest of the flow, this surface reduction is negligible.
If you place small parallel insulating plates close to each other in a piece of metal, then the combined surface reductions in flow will add up to a volume reduction and this can influence the electric resistance significantly. Again, if there is increased resistance. Resistance decrease can't appear. If this were the case, the electrons would be still flowing like in the metal without geometric interveniance. Local decrement will not result in a decrement of total resistance while local increment will result in total increment (of resistance).
If electrons somehow get piled up (like on the flat side of the bubble in the picture above) this will result in an increase of resistance. The electrons generate an electric field that opposes the incoming electrons before them. But this building up, piling up, or accumulating of charges is negligible, because they repel each other, so the charge distribution will stay constant.

• So if I understand you correctly, your last paragraph says that a directional effect on resistance might be observable, but will be very small? Jun 17, 2021 at 16:48