effect of shot noise on measurement

Shot noise arises from ordinary sqrt(N) fluctuations due to the counting statistics of electrons, unless the electrons are forced to be correlated. A given current can have no shot noise, partial shot noise, or full shot noise (i.e. i_n = sqrt(2eIdc) amps per hertz). After amplification, it can even have more than full shot noise.

Not all measurements exhibit shot noise. Most purely electronic ones do not, e.g. strain gauges, accelerometers, capacitive gauges, and most kinds of temperature sensors. Most measurement folks run into shot noise primarily in photocurrents, i.e. the output current of a photodiode. Photocurrents have exactly full shot noise essentially always.(*) There's no way to get round this limit, except by narrowing the bandwidth (i.e. using a lock-in amplifier or trace averaging) or finding some more light from somewhere.

Shot noise in circuits usually arises from conduction in transistors--the collector current of a bipolar transistor with no feedback applied will have full shot noise. That sort of problem is fixed using feedback, and enough feedback can suppress it to any degree you like. Photocurrents are another matter.

Cheers,

Phil Hobbs

(*)There are a very few instances, using quantum measurement techniques, where the noise can be a couple of dB less, and if you're looking at the long-wavelength tail of an extremely hot and extremely small thermal source, the noise can be a few percent more. Otherwise, any unamplified photocurrent will exhibit exactly full shot noise.

Any kind of noise amounts to fluctuations. When measuring a constant value, you can easily compensate by filtering (averaging).

As to shot noise, it isn't going to be a factor in a 1.5 meter wire:

"However, shot noise is absent in a macroscopic, metallic resistor because the ubiquitous inelastic electron-phonon scattering smoothes out current fluctuations that result from the discreteness of the electrons, leaving only thermal noise."

What are you actually trying to do?

If you are measuring a current of - say - 100 electrons per second, or

- to be more realistic - a light intensity that only delivers 100 photons per second to your detector - that 100 electrons or photons in any one second is merely the number that you are most likely to see.

In fact, over a long series of one second measurements you will get a distribution of numbers.

The mean number of hits per second will average out to one hundred, but the standard deviation of the distribution will be ten - more generally, the square root of average number of hits over the measurement period.

The fluctuations from one measurement to the next look exactly like random noise. The only way you can compensate for it is to average a lot of observations.

This does assume that successive photons or electrons are not correlated - the electrons are not coming from some of charge pump that spits one one electron every ten milliseconds, on the ticks of of a 100Hz clock. This true for most situations where one wants to take a measurement, but there are occasional exceptions - electrons coming from a photocathode or a electron gun can be emitted a bit more regularly than you'd expect, because the space charge of the last electron emitted can make it less likely that the next electron to be emitted while its predecessor is still close to the source.

-- Bill Sloman, Nijmegen

Ahhhhhhhh ok...so it is somehow related to the Poisson distribution and hence probably truly random.

I suppose one could argue that there is always the shot noise of the individual electrons. Or is shot noise defined so as to exclude this component? ("Quantization" noise?)

It's true that you can't have a fractional number of electrons, and this sets the lower limit of charge granularity. But that's not a _measurement_ issue, really, it's a question of whether what you want to measure is itself actually a well-defined quantity. Both feedback and bandwidth-narrowing have effects on circuit operation (i.e. reduced gain and slow measurements) that eventually limit how well you can do in any practical case.

Cheers,

Phil HObbs

Not necessarily. An electron can be anywhere on a wire, and there needn't be an integral number of electrons, say, on the gate of a FET: there could be electrons *near* the gate (or its connections), changing the electric field a continuous amount.

Tim

-- Deep Fryer: A very philosophical monk. Website @

The lack of shot noise is (I think?) some sort of e-e interaction in metallic conductors. Is that some phonon thing, like the Cooper pair effect? If it is, wouldn't it stop working at low currents, as the moving electrons start to get very far apart on average? I've googled this issue a fair amount and found little good stuff. It's not even clear what sorts of conductors have zero shot noise... metal films for sure, but what about cermets, or carbon film?

I put together a semi-crude setup to measure shot noise in various resistors, and tried metal/cermet/carbon, and couldn't see shot noise in any of them, in a setup that should have easily measured full shot noise.

Hmmm, if you split up a thinfilm resistor into many narrow paths,

|-----------------| | | |-----------------| | |

-------|-----------------|-------- | | |-----------------| | | |-----------------|

might that increase shot noise?

John

That's not how low currents work in metallic conductors - there are still a lot of electrons around, but the net rate of movement becomes very slow.

Carbon film resistors do have "excess" noise - more than you would expect from Johnson noise in an ideal resistor having the same resistance - but it isn't due to shot noise. The stuff I've read seems to suggest this has to do with the negative temperature coefficient of the carbon film, which leads to a certain amount of "current channeling". This doesn't lead to visible instability at at low currents (actually low self-heating) but does make the resistance slightly unpredictable.

No. Thin film resistors don't exhibit shot noise - the electrons interact and smooth out the effects of their discrete nature.

-- Bill Sloman, Nijmegen

You are quite right. It is a Poisson distribution (which looks rather like the normal distribution when you've got more than a few electrons/ photons per sampling period).

-- Bill Sloman, Nijmegen

Think of a carbon composition bulk resistor. It is a semi-conductor material. There is going to be friction.

I wonder what the shot noise of the guys in the pool in Germany with the power strip floating by is.

According to our late solid state guru, Rolf Landauer, the shot noise suppression in a resistor is equal to the mean free path divided by the length of the resistor. Inelastic electron-electron scattering smears out the clumps. Putting wires in parallel shouldn't do anything one way or another.

Cheers,

Phil Hobbs

But summing a large number of zero-shot-noise but uncorrelated current sources won't cause shot noise? It's not as if the electron streams from the various paths are cooperating.

John

I would think it would average whatever shot noise was emerging from each stream, and the result would be sqrt(n) times the noise from one, while the current would be n times.

Both vacuum tubes and semiconductor diodes have shot noise associated with current flow, because the electrons that flow are localized in these devices. FETs, on the other hand, have a continuous channel, and the electrons aren't constrained to have local position well-determined in that channel. So some amplifier types have shot noise, and others don't.

Shot noise is just the phenomenon of movement statistics in discrete charge packages, i.e. electrons. You can't compensate for it, only swamp the noise with statistically large numbers of charges. There are LOTS of things that require statistically large quantities of charge, it's very unusual to find shot noise to be a limitation.

I don't see why it would. If you have N identical currents, then since their residual fluctuations aren't correlated with each other, the current goes up by N and the fluctuations by sqrt(N) times the RMS value of the individual fluctuations. That means that if the individual currents have epsilon times full shot noise, the sum also has epsilon times what its full shot noise would be.

Cheers,

Phil Hobbs