Create Your Own zF Capacitor | PF

[G Cooke]

Hi PF,

I am in need of a capacitance in the zF (zeptofarad = E-21) range.

Of course, they aren't sold this small, so I was wondering if maybe someone with more physics knowledge could help me create my own zF capacitor.

Thanks in advance!

 

[Tom.G]

Hi PF,

I am in need of a capacitance in the zF (zeptofarad = E-21) range.

Of course, they aren't sold this small, so I was wondering if maybe someone with more physics knowledge could help me create my own zF capacitor.

Thanks in advance!

The formula to calculate capacitance is:

C = 0.224 * (n-1) * K * A / d

C in pf (10[sup}-12[/sup]
n = number of plates
K = dielectric constant (1 for air or a vacuum)
A = area of one side of one plate
d = separation between plates

That says the separation must be 0.224*10⁹ as large as the plate area. For a plate 1 inch sq. the separation would be about 3,535 miles, a little more than the width of the North American continent. That's an awful long wire to the second plate, with its own capacitance to the environment. I suggest you try a different approach.

 

[Nidum]

The capacitance of a plain wire can be much higher .

The only situations that I know of where zeptoFarad levels of capacitance have any tangible meaning or significance are in the very specialised technologies of scanning capacitance microscopy and nano scale sensors .

I suggest you try a different approach

+1

Is there any actual purpose to this question ?

 

[G Cooke]

Thanks for your replies, guys.

Actually, I meant to specify that this is a self-capacitance value I'm referring to. I wrote this really late last night, so I apologize.

I would think that if I just wanted a zF capacitance in the conventional sense, I could just connect 5000000 0.05pF capacitors in series (since they add like resistors in parallel) to get about 10zF, right? (But you couldn't conclude that the self-capacitance of one plate of this zF capacitor would necessarily be in the zF range since it is independent of the distance of separation of the plates, etc.)

I see on Wikipedia that the formula for self-capacitance of a circular disk is 8εa, which requires an area of about an angstrom to get 10zF. I'm hoping maybe there's a practical way to achieve this instead.

 

[G Cooke]

Is there any actual purpose to this question ?

Hi Nidum,

Yes, a zF self-capacitance is necessary to satisfy multiple conditions in order to make it possible to prototype a certain apparatus.

 

[jim hardy]

Yes, a zF self-capacitance is necessary to satisfy multiple conditions in order to make it possible to prototype a certain apparatus.

I'm stumped by the practical matter of how will will connect your leads to it .

A Driven Guard can reduce apparent capacitance,
but how would one even detect the charge on a 10^-21 f capacitor to drive the guard? At a whole volt it's less charge than resides on a single electron.
Best electrometer amplifier i know of has a picofarad or two in its Zin , which would swamp the zetafarad . A single electron at its input would produce only about a microvolt and get lost in the picoamp of input bias current .
http://www.ti.com/lit/ds/symlink/opa128.pdfInteresting problem ... how does one detect Electron Millivolts ? and Atto-Amps?
I'm out of my league here .

http://www.tek.com/sites/tek.com/files/media/document/resources/2648 Counting Electrons1.pdf

Watching with interest... old jim

 

[G Cooke]

At a whole volt it's less charge than resides on a single electron.

Actually, using the exact numbers from my calculations, the charge will be the exact charge of an electron. To be specific, 5V*32.04zF=1.602E-19C.

A Driven Guard can reduce apparent capacitance

I'll take a look into this "driven guard."

I'm stumped by the practical matter of how will will connect your leads to it .

Yes, it's interesting lol. I don't know, maybe surface mount?

http://www.tek.com/sites/tek.com/files/media/document/resources/2648 Counting Electrons1.pdf

That's a very interesting article. Thanks, Jim.

 

[G Cooke]

A Driven Guard can reduce apparent capacitance

So I looked up the driven guard here:

http://www.keysight.com/upload/cmc_upload/All/2-Parametric_Measurement_Basic.pdf?&cc=US&lc=eng

and I see that it reduces effective parasitic capacitance in a triaxial cable by isolating the signal line from the shield.

This would seem not very effective in my setup since what I need is actually an object whose self-capacitance is in the zF range. Perhaps this is only possible with nanotechnology; I was just hoping maybe there were some ingenious physics trick by which I could generate an "effective" zF self-capacitance without actually making the physical size so small, maybe by using an extremely low-density conductor like conductive foam or something (trying to find info on that now).

 

[jim hardy]

and I see that it reduces effective parasitic capacitance in a triaxial cable by isolating the signal line from the shield.

Yes, point being it surrounds the signal cable with a shielding conductor(think Faraday cage) held at same potential
so there's no incentive for current to flow through the capacitance between those two conductors.

 

[Baluncore]

A 10 zF capacitor could never be connected to a circuit so the concept of 10 zF is meaningless without context. You could make a negative capacitance, then adjust it to reduce it's own input capacitance to 10 zF. You would end up with something like a driven guard.

A single atom might have about 10 zF capacitance relative to almost nothing nearby in a vacuum.

To be specific, 5V*32.04zF=1.602E-19C.

You could simulate a 32 zF capacitor with an LED. When one electron flows the voltage drop would need to be 5 V. The LED would produce a photon with a wavelength of 1240 / 5V = 248. nm which is UVC, in the middle of the UV part of the spectrum. The voltage on the UVC LED would rise by 5V when it received a 248 nm photon.

This thread should be closed if you cannot explain the context in which a 10 zF capacitor might be connected or interfaced.

 

[Nidum]

This thread should be closed if you cannot explain the context in which a 10 zF capacitor might be connected or interfaced.

+1

 

[berkeman]

This thread should be closed if you cannot explain the context in which a 10 zF capacitor might be connected or interfaced.

Agreed. Finger hovering over mouse button...

 

[jim hardy]

Second the motion

 

[Baluncore]

What is the radius of a conductive sphere having a self capacitance of 10 zF ?
C = 4 · π · ε · r ; where ε = 8.854x10^-12 and C = 10x10^-21.
r = C / ( 4 · π · ε ) = 90 pm
For comparison, the ionic radius of a lithium 1+ ion is also 90 pm.

https://en.wikipedia.org/wiki/Ionic_radius#Determination_of_ionic_radii
https://en.wikipedia.org/wiki/Capacitance#Single-electron_devices

 

[G Cooke]

The LED would produce a photon with a wavelength of 1240 / 5V = 248. nm

Interesting. Could you explain where the 1240 came from?

I appreciate the many interesting facts and useful suggestions you've provided.

 

[Baluncore]

Interesting. Could you explain where the 1240 came from?

The defined speed of light; c = 299792458. metre/second.
The absolute permeability; Uo = 4×10^-7 * Pi henry/metre.
Absolute permittivity; Eo = 1 / ( Uo * c * c ) farad/metre.
The Planck–Einstein relation gives photon energy E from wave frequency; E = h * f.
Where h = Plank's constant = 6.626070040×10^-34 J·s = 4.135667662×10^-15 eV·s
Converting also between frequency and wavelength in nanometres uses the constant = h * c * 10⁹ = 1239.841973862093 = 1240.
So for an LED that produces radiation of nm wavelength; voltage = eV = 1240 / nm.

 

[G Cooke]

Agreed. Finger hovering over mouse button...

Ok, you can close it now. I got what I needed out of it.