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EDN: Measuring Nanoamperes

Discussion in 'Electronic Design' started by Mike Monett, May 4, 2007.

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  1. Mike Monett

    Mike Monett Guest

    To All,

    Paul Rako has an interesting article in the April 26 issue of EDN,
    titled "Measuring nanoamperes". He measures the 1uA current in a
    32,768 Hz watch crystal using a Tektronix CT-1 current probe. (This
    is beyond the max frequency spec, but additional calibration
    indicates it may be ok. Also see my article below on analyzing
    crystal oscillators in SPICE.)

    The main part of the article is a companion to the articles Bob
    Pease wrote on measuring the input current of the National LMC662.
    They are "What's All This Teflon Stuff, Anyhow?":,1562,4,00.html

    and "What's All This Femtoampere Stuff, Anyhow?":,1562,5,00.html

    He includes additional circuit details by Paul Grohe, plus photos of
    the actual setup.

    There are two reference sections with some good links, including
    "Counting Electrons: How to measure currents in the attoampere
    range", by Adam Daire, Keithley Instruments:

    The EDN article is at


    Mike Monett

    SPICE Analysis of Crystal Oscillators:
    Noise-Rejecting Wideband Sampler:
  2. John Larkin

    John Larkin Guest

    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.

  3. Phil Hobbs

    Phil Hobbs Guest

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


    Phil Hobbs
  4. John Larkin

    John Larkin Guest

    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.

  5. Mike Monett

    Mike Monett Guest

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

    Here's a copy of a post I made earlier with info on RFSet, including
    the waveforms on a 5.5 electron triangle wave. (They don't show how
    a triangle wave can be made using 5.5 electrons:)

    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:


    Mike Monett
  6. Mike Monett

    Mike Monett Guest

    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

    20 * log(sqrt(2048)) = 33.1dB,

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


    Mike Monett
  7. Robert Baer

    Robert Baer Guest

    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?
  8. John Larkin

    John Larkin Guest

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

  9. john jardine

    john jardine Guest

    The EDN article also references a "Low level measurements handbook"
  10. Phil Hobbs

    Phil Hobbs Guest

    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

    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.


    Phil Hobbs
  11. 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
  12. Mike Monett

    Mike Monett Guest

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


    Mike Monett
  13. John Larkin

    John Larkin Guest

    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.

  14. Rich Grise

    Rich Grise Guest

    Schrödinger's electron? ;-)

  15. John Larkin

    John Larkin Guest

    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.

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

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