EDN: Measuring Nanoamperes

Except they never actually count electrons.

I've always wanted to build a circuit that could clearly resolve single electrons. 1 electron into 1 pF is about 160 nV, hard to dig out of the noise.

I think maybe you could use an eprom cell to demonstrate single-electron steps. Or possibly some sort of varicap-based parametric amplifier.

John

How about a field emitter and a Channeltron? They're easier to measure when they arrive with 1 keV to announce them.

Cheers,

Phil Hobbs

Oh sure, that's easy. I've done that with PMTs and microchannel plates. But I meant a circuit that measures the charge on a node, and detects single electrons leaking in or out.

If you take, say, a mosfet and float the gate, cool it a bit maybe, the leakage rate can be below an electron per second. You'll get random bias jumps but I'm thinking the noise will overwhelm the steps, and I can't think of a way to analyze the fet output to clearly resolve the steps.

An eprom has a tiny gate capacitance, fF range, and leakage rates are very low. A zot of UV will change the gate charge in e quanta, so all we need to do is find a way to measure floating gate voltage. I think you can do that by sweeping Vcc and looking for logic transitions on cells that are right on the 0/1 borderline.

John

If you can get down to a couple of millidegrees K, an RFSet probably can do the trick.

Here's a c > "John Lark >> It is possible to produce electrical currents that have little or >> no random shot noise, to literally dispense exactly one (or >> more!) electrons a second, rigidly periodically. SETs (single >> electron transistors) are one way to do this.

A Radio Frequency Single Electron Transistor (RFSet) can have a bandwidth greater than 100MHz and extreme sensitivity. It is described as a fraction of the charge on an electron.

Here's one that runs at 700MHz with a sensitivity of 3.63 * 10-5 e/RootHz. They show how it is measured:

Schoelkopf has a bunch of papers on them:

Here's one that operates at 1.7GHz with a sensitivity of 1.2 * 10-5 e/Roothertz. Fig. 1 shows a SEM photo of the device.

Fig. 3 shows the time-domain response for a large (~5.5 electrons peak-to-peak) signal, 10 kHz triangle-wave applied to the gate. The SNR looks very good:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Regards,

Mike Monett

Actually, looking at Fig. 3A again shows each electron arriving at the gate. Here's the text:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The rapid response of the RF-SET in the time domain can be seen by examining the amplified output of the rectifying diode on a digitizing oscilloscope. The average of 2048 individual traces, taken with a large amplitude (Dqg 5 CgVg ' 5.5 e peak-to-peak) 10-kHz triangle-wave signal applied to the gate, is shown (Fig. 3A).

The output indeed follows the sinusoidal transfer function, passing through five successive maxima (one for each electron added to the island), and then reversing at the turning points of the gate signal (dotted line). The S/N ratio is also quite high.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Averaging 2048 waveforms improves the SNR by

so an individual electron may not be visible in a single sample.

Regards,

Mike Monett

What about a "micro cell" that has an oil drop and field plates - to make a minature version of the infanous Millikan oil drop experiment?

I still want to do it with an uncooled electronic circuit that can be made with available parts.

John

The EDN article also references a "Low level measurements handbook"

You can make CCDs have sub-electron readout noise just by reading them lots of times before dumping them--which you and I would call "bandwidth narrowing".

Another approach would be to make a two-well structure with a FET gate in each well, and shunt the single electron back and forth between them. That would get you out of the 1/f noise, and doing it repeatedly would let you reduce the bandwidth.

The usual way to measure things way below the circuit noise is by cross-correlation of M independent measurements of the same thing, e.g. using M MOSFETs lets you make M*(M-1)/2 independent cross-correlations, which brings the noise voltage down by about M/sqrt(2) times. That's hard to arrange with single electrons, because the capacitance would go up as M as well, so the gate voltage would go down as 1/M, and the SNR would be roughly constant with M.

One interesting fact is that free electrons are stable in pure nitrogen, so you could probably do the equivalent of an ion trap experiment in an N2 atmosphere. Classical equipartition of energy would predict that the electron would move around with a mean velocity of about 300 times the sound velocity (an electron is about 50000 times lower in mass than a nitrogen molecule, and the velocity of sound is [iirc] about half the mean thermal velocity), so you could sort it out from the air ions pretty readily. Of course, it wouldn't take too long to diffuse out of your trap.

Cheers,

Phil Hobbs

I think it might be possible to demonstrate single electron detection using a small capacitor vibrating at a few KHz and an isolated charge pickup capacitively coupled to a small area JFET. The problem is not the voltage noise in the JFET but the low frequency drift of the gate, which cannot be distinguished from the voltage at the charge pickup. If there is a way to keep the gate at a controlled potential, maybe it is doable. Probably some cooling is needed to reduce the gate leakage and the drift. I hope to do such an experiment some day. I'll report it to the list if I succeed.

Tell us what happens regardless - even if you don't succeed it would still be interesting!

Regards,

Mike Monett

That only works if the averaged measurments are available faster than the average electron leakage rate, and if there's not a lot of slow drift, 1/f and temperature and stuff. Ideally, you'd like a plot to show the distinct steps as you lose electrons. Not as good would be some statistical analysis that demonstrates the step property even if you can't see the individual ones. Either seems to me to have serious noise problems in real life. It helps a lot of the electron hops aren't random in time, which is why something like UV zots are useful. That's what Millikan did, with x-rays.

But you have access to IC fabs, and I don't.

Electrons packed in nitrogen, like tuna in spring water?

I still think the eprom thing might work. It's getting so that the difference between a 1 and a 0 is thousands of electrons, and the floating gate capacitances are in the 1 fF sort of range.

Maybe a mems tuning fork capacitor thing?

Hey, maybe a charged quartz fiber, like an old dosimeter.

John

If you flash some light, or uv, or xrays at the rig, you can force most of the charge changes to happen at known times. So you could plot the detector output versus time, along with the flashes, and maybe see the jumps. Or do a statistical analysis of signal before and after the flashes, and demonstrate the quantization levels.

If you had a cantelever, like a quartz fiber or a SEM tip, that was deflected by charge, you could maybe do the laser thing like the SEM people do, or use the capacitance to shift an LC oscillator or something. Maybe a mechanical intermediary would be more sensitive than using pure electronics, which would be sort of ironic.

John

Ironic? O, thou master of understatement! It could open the door to astounding new breakthroughs in metaphysics! %-}

Cheers! Rich