Looking everywhere for a simple 1 attofarad capacitor. Tried Ebay, Amazon, Aliexpress, Mouser, but none of them seem to have any available. Surely someone manufactures these things—I mean, how hard could it possibly be to make a 10^-18F capacitor?

HINT: This could be a trick question.

 

Looking everywhere for a simple 1 attofarad capacitor.

If you find one, I'll give you an attoboy.

 

Are you serious?
1 pF = 1 x 10^-12 F
1 aF = 1 x 10^-18 F
The lowest you will ever get is 10000 aF.
Stray capacitance alone is greater than 100,000 aF.

If you really need a 1 aF capacitor, maybe this will help:
https://docs.quantumatk.com/tutorials/atomic-scale_capacitance/atomic-scale_capacitance.html

 

Twist two wires together.....

 

Looking everywhere for a simple 1 attofarad capacitor. Tried Ebay, Amazon, Aliexpress, Mouser, but none of them seem to have any available. Surely someone manufactures these things—I mean, how hard could it possibly be to make a 10^-18F capacitor?

Well, let's consider a really simple model and see what it tells us.

The equation for the capacitance of a parallel plate capacitor, ignoring fringing fields (which can become dominant in small geometries) is

\(
C\; = \;\frac{\kappa \epsilon A}{d}
\)

where ε0 is the permittivity of free space, which is 8.85e-12 F/m, or 8.85 aF/µm and κ is the relative permittivity constant, which for normal materials is always greater than 1, and since we want small capacitances, we'll just use 1.

This means that, in this simple model, a capacitor made with a place that is 1 µm x 1 µm and separated by 1 µm would have a capacitance of about 10 aF.

So making a capacitor that small is actually going to be quite difficult, if for no other reason than you have to mitigate against all (as in EVERY) source of parasitic capacitance that could contribute any stray capacitance on that scale, which would include your interconnects to it, which likely have parasitic capacitances that are thousands to millions of times larger. If you did do it, it would almost certainly be anything but a "simple" capacitor.

EDIT: Fix LaTeX typo.

 

Twist two wires together.....

This normally results in capacitances in the range of ~50 pF/m. Let's say that you managed to get that down to 1 pF/m somehow (probably wouldn't be too easy). Your length would still need to be just 1 µm long before you've exceeded 1 aF.

 

This means that, in this simple model, a capacitor made with a place that is 1 µm x 1 µm and separated by 1 µm would have a capacitance of about 10 aF.


So making a capacitor that small is actually going to be quite difficult, if for no other reason than you have to mitigate against all (as in EVERY) source of parasitic capacitance that could contribute any stray capacitance on that scale, which would include your interconnects to it, which likely have parasitic capacitances that are thousands to millions of times larger. If you did do it, it would almost certainly be anything but a "simple" capacitor.

In fact, the hypothetical capacitor that you just described would only be capable of storing a single electron!

Hence the point of this thread: You literally cannot construct a 1 attofarad capacitor simply because the lowest capacitance possible is roughly 6.28aF. Anything below that would not be able to store any electrons whatsoever. =)

 

would only be capable of storing a single electron!

Interesting though.

I have a meter for measuring pF caps. I cannot use any leads. I have to subtract out the environment. Just moving tools around on the bench changes the reading.

 

Theoretically, two 1 cm^2 plates spaced 885 meters apart would have a capacitance 1 aF, and would require 7 electrons to raise the voltage to 1.122V.

But it would be completely swamped by parasitic effects and fringing fields. So, there's that.

 

And the question begs: why would you even need a 1 Af capacitor in the first place?

 

And the question begs: why would you even need a 1 Af capacitor in the first place?

A target for my "electron gun"?

 

You literally cannot construct a 1 attofarad capacitor simply because the lowest capacitance possible is roughly 6.28aF. Anything below that would not be able to store any electrons whatsoever.

It is possible.
Use 2 plates 1 sq. mm each, at distance between them 885.4 cm (in air) and capacitance will be exactly 0.000001 pF (1 aF).
ADDED:
@joeyd999 already calculate it in post #9.

 

It is possible.
Use 2 plates 1 sq. mm each, at distance between them 8.854 m (in air) and capacitance will be exactly 0.000001 pF (1 aF).

I want one to put into my 1 x 1 nm op amp.

 

In fact, the hypothetical capacitor that you just described would only be capable of storing a single electron!

Based on what?

What is the voltage across it when it is storing one electron?

What happens to the number of electrons on it if the voltage is increased by a factor of ten?

Hence the point of this thread: You literally cannot construct a 1 attofarad capacitor simply because the lowest capacitance possible is roughly 6.28aF. Anything below that would not be able to store any electrons whatsoever. =)

Again, based on what?

Capacitance is NOT a measure of how many electrons can be stored, but rather the ratio of the number of electrons stored to the resulting voltage across the capacitor. Look at the units -- 1 farad = 1 coulomb/volt

For example, if you have 10 electrons that have been moved from one plate to the other and the plates are separated by enough distance such that there it takes 100 V across them to make that happen, you have a capacitance of

C = Q/V = (10 e)(1.602e-19 C/e) / (100 V) = 1.602e-20 C/V = 0.016 aF

 

Based on what?



What is the voltage across it when it is storing one electron?



What happens to the number of electrons on it if the voltage is increased by a factor of ten?





Again, based on what?



Capacitance is NOT a measure of how many electrons can be stored, but rather the ratio of the number of electrons stored to the resulting voltage across the capacitor. Look at the units -- 1 farad = 1 coulomb/volt



For example, if you have 10 electrons that have been moved from one plate to the other and the plates are separated by enough distance such that there it takes 100 V across them to make that happen, you have a capacitance of



C = Q/V = (10 e)(1.602e-19 C/e) / (100 V) = 1.602e-20 C/V = 0.016 aF

OK in retrospect that really was a pretty bone-headed claim. Guess I'm just gonna have to take a mulligan on this one....

 

And the question begs: why would you even need a 1 Af capacitor in the first place?

BTW: It's 1 aF, not 1 Af.

One application is electron counting. I don't know what the capacitance was, but back when I was working at NIST (late 80s time frame) they had developed a system that counted charge by gating single electrons through a circuit. It worked by having a capacitance so small that a single electron resulted in a high enough voltage across the gap to suppress further charge movement until that charge was drawn off. I forget the specifics beyond that.

Another place where we work in capacitances on that order is in IC design where plate and fringing capacitances are sometimes specified in aF and µm dimensions, though the actual resulting capacitances are seldom much less than a femtofarad (at least back when I was designing ICs, which has been quite some time now).

 

BTW: It's 1 aF, not 1 Af.

One application is electron counting. I don't know what the capacitance was, but back when I was working at NIST (late 80s time frame) they had developed a system that counted charge by gating single electrons through a circuit. It worked by having a capacitance so small that a single electron resulted in a high enough voltage across the gap to suppress further charge movement until that charge was drawn off. I forget the specifics beyond that.

Another place where we work in capacitances on that order is in IC design where plate and fringing capacitances are sometimes specified in aF and µm dimensions, though the actual resulting capacitances are seldom much less than a femtofarad (at least back when I was designing ICs, which has been quite some time now).

In my younger years, I developed a spectrophotometer using a photodiode array. The entire four orders of magnitude of linear dynamic range fit on a 10pF cap.