# Talk:Shot noise

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## nature of shot noise

i thought shot noise was to do with electrons passing over a junction between two different conducting materials? ill go else where and check... mark_metcalfe@hotmail.com —Preceding unsigned comment added by 158.125.1.23 (talkcontribs)

I think that's called a flicker noise... kuevis@hotmail.com —Preceding unsigned comment added by 150.150.77.68 (talkcontribs)

Hi,

You are absolutely right, and this page needs some editing. I think I or someone with more detailed knowledge should do this.

Briefly speaking, the granular nature of charge is not responsible for shot noise by itself. Shot noise occurs when charge carriers must cross a junction.

So for instance, a copper wite carrying current will exhibit only thermal noise but not shot noise, while a semiconductor junction will exhibit both.

Flicker noise is an altogether different phenomenon, and while there are several theories and models regarding flicker noise, there is no universally accepted physical model to explain it yet (perhaps a Nobel Prize waiting for someone), despite and perhaps owing to its universal nature. It is seen in phenomena from microscopic scale to the astronomical scale.

Vivek vivkr .at. yahoo . com —Preceding unsigned comment added by 62.218.180.1 (talkcontribs)

I believe you are rong. Shot noise occours in copper wires. Some discussion could take place due to the less deffined position of electrons in copper, but this only reduces the bandwith of the noise and not the its power.
I believe flicker noise is usually due to electron traps in the potential barrier beetwen conductors and isolators.
--Paclopes 19:37, 18 January 2007 (UTC)

According to Horowitz and Hill (2nd eddition) There is less than the expected shot noise in resisotrs and other conductors. (how much less is not specified) This is becasue the electrons in a conductor are coorelated, (I assume by the electric field), when an electron leaves on end of the conductor the other electrons "know" about it. For PN junctions the charge carriers move by diffusion, they are uncoorelated and show shot noise. I find the case of photon noise to be more confusing. All light sources have shot noise, but there can be excess noise from an incoherent light source (light bulb) under certain rather extreme conditions See Hanbury-Brown and Twiss Gherold 18:25, 9 February 2007 (UTC)

## shot and thermal noise

Shot noise is directly dependent on current while thermal noise is indepedent of the applied voltage or current, they don't seem to be related.

>> See the paper by Sarpeshkar, Delbruck, and Mead referenced in the main article. Apparently, they are related through Einstein's relation $D_n = \mu_n\,kT/q$.

Treat an open circuited resistor as having a pair of balanced diffusion currents in opposite directions, so that the DC current is zero. Since the diffusion currents in opposite directions are uncorrelated, take the sum of the two noise power terms. Then substitute Einstein's relation and combine conductance terms to get $i_n^2 = 4\,kT\,G\,\Delta{}f$ and multiplying both sides by $R^2$ and taking the square root, obtain the classic forumula for Nyquist-Johnson noise: $e_n = \sqrt{4\,kT\,R\,\Delta{}f}$

Shot noise only depends on fluctuations in the number of carriers arriving in a given interval, assumed to be Poisson-distributed for most purposes, and not on any specific properties of the medium. Contact noise, 1/f noise, popcorn noise, etc., are all examples of excess noise.

## references on noise

Hi,

I forgot to post some references at the end of my mail. I am adding these here. There are bound to be many sources on the web too, which are more accessible to those who are not electrical engineers or have a good library nearby.

Ref. 1 has an excellent introduction on this topic in the Chapter on Noise, (Chap. 10). Ref. 2 is also decent, although their treatment of flicker noise is not perfectly satisfying, even if it is technically correct.

1. "The Design of CMOS Radio Frequency Integrated Circuits" by Thomas H Lee, Cambridge University Press.

2. "Analysis & Design of Analog Integrated Circuits" by Gray, Meyer, Hurst & Lewis, John Wiley & Sons (Chap. 11).

There exist many more references of course ...

Vivek —Preceding unsigned comment added by 62.218.180.1 (talkcontribs)

## examples at top

Say at the top how shot noise might mess up one's life or experiments. --Jidanni 2006-04-16

## formulas

Why there are no formulas for shot noise?! The page is only talk.... Somethink like

$I_{sh} = \sqrt{2 q I_{dc} \Delta f}$

Agree PAR 03:43, 5 November 2006 (UTC)

Agree Dr Lind 12:34, 20 December 2006 (ETC) (Shot noise being the more common term)

## Deletion of content

Can someone fact check these edits? I don't understand the changes that were made or why some of the content was deleted. — Omegatron 00:59, 15 November 2006 (UTC)

Hmmmm! I suggest we revert pending me finding my book on Noise ! 8-)--Light current 01:48, 15 November 2006 (UTC)

## simple analogy for non specialists

The article launches into the topic in a fairly technical manner and never explains why it's called 'shot' noise. The way I was introduced to the phenomenon was to imagine the difference between a cup of molten lead being poured onto a surface vs a cup of lead shot. This can also be extended to cover the phenomenon's relevance to extremely low level signals with a bit of imagination. Does someone more eloquent than me want to tackle this before I make a hash of it? :) MagnusL (talk) 11:21, 21 November 2007 (UTC)

I took a shot at an explanation along those lines. I typically explain this to students using light photons but sugar grains / lead shot are perhaps more accessible. That was reverted because it was 'unsourced/POV' -- that's a function of any explanation meant to give intuition. I'm not going to persist, use an edited version of this if you like. Mhisted (talk) 15:49, 24 July 2008 (UTC) 04:34, 1 June 2008 (UTC)

## Wrong SNR

The wrong SNR is given. You don't have to deal with the signal amplitude and the standard deviation, but with powers/energys, i.e. with the squared amplitude and the variance. Hence, the signal-to-noise ratio of shot noise is N. —Preceding unsigned comment added by 65.202.28.10 (talk) 22:42, 13 December 2007 (UTC)

## Shot noise in conductors?

I thought it was only when crossing junctions of some type. This page also seems to say, at least, that shot noise formulas are not applicable to conductors. — Omegatron (talk) 23:15, 3 May 2008 (UTC)

Here's another. — Omegatron (talk) 23:19, 3 May 2008 (UTC)

"Shot noise is present in any conductor — not just a semiconductor. Barriers in conductors can be as simple as imperfections or impurities in the metal. The level of shot noise, however, is very small due to the enormous numbers of electrons moving in the conductor, and the relative size of the potential barriers. Shot noise in semiconductors is much more pronounced." "Opamps for Everyone" — Omegatron (talk) 22:34, 4 May 2008 (UTC)

To summarize the analog.com article and Horowitz and Hill (who they quote): to have shot noise, you must have 1. small numbers of quanta and 2. independence between the arrival times of the quanta. Metal conductors violate #2 because they have long-range correlations between carriers. So you could still see shot noise in a long tube filled with a salt solution, but not in a long metal wire. Mhisted 05:05, 1 June 2008 (UTC)

I'm going to correct the article based on this discussion Mhisted (talk) 15:51, 24 July 2008 (UTC)

Imagine light coming out of a laser pointer and hitting a wall. That light comes in small packets, or photons. When the spot is bright enough to see, there are many billions of light photons that hit the wall per second. Now, imagine turning down the laser brightness until the laser is almost off. Then, only a few photons hit the wall every second. But the fundamental physical processes that govern light emission say that these photons are emitted from the laser at random times.

Actually, the fundamental physical process behind lasing is stimulated emission. It's quantum mechanical, and hence probabilistic, not random. If laser physics were truly random, then laser light couldn't be coherent. Phase coherence is arguably the single defining characteristic of a laser!

Now, on a one-second time scale, yes, there is a most-likely number of photon arrivals. Naturally, if you measure the photon arrivals in many one-second intervals, you'll find a statistical distribution around this value. I'll grant you that this distribution probably qualifies as shot noise in that it looks random, but it's a question of time scale.

Also, I should point out that this distribution exists regardless of the laser's brightness -- i.e., the "shot noise" still exists even if there are billions of photons hitting a wall per second. It's just that the SNR is much higher than when the laser is dim.

Also, no links to photon or laser articles? --Firstorderapproximation (talk) 10:21, 29 January 2010 (UTC)

## origin of the term "shot noise"?

The term "shot noise" comes from looking at what happens to lead shot in a shot tower, right? That is, the arrival times of the shot (when they hit the water) are exponentially distributed, and the number in any given time period is Poisson distributed. Can anyone find a quick reference? cheers, 38.111.20.226 (talk) 19:44, 11 May 2010 (UTC)

I'd always assumed (without evidence) that it was named after buckshot because it scatters 'randomly' if not actually Poissonly. A quick Google search finds me one source claiming it's named after Schottky who first analysed it, and another saying it's named after "the sound made by a fistful of gunshot dropped on the floor... not the name of its discoverer". Perhaps a bit more research is needed.
Either way we should probably add some mention of Schottky to the article. Olaf Davis (talk) 20:31, 11 May 2010 (UTC)

## Formulas for photography

Suppose I were taking a picture and wanted to compute the shot noise. Assuming 100% QE and FF, and no other noise, I think I'd compute the luminous intensity on each pixel (based on the luminance of the subject, the magnification, subject distance, and entrance pupil diameter), then figure out the radiant intensity at the given wavelength, then use Planck's law to get the photon flux, and multiply by the exposure time to get the number of photons. Finally, using the Poisson distribution to find $\sigma = \sqrt{n}$.

Does that sound right?

If so, then if I image a candle flame at 1m with an entrance pupil diameter of 10mm so it covers 100x100 pixels, then we are talking a solid angle of 2.5×10-5 steradians. So at 1/683 W/sr at 540×1012Hz (=555nm), we are talking 3.66e-8 W.

At that wavelength, each photon is 3.58e-19 J, so the photon flux is 1013 photons per second, or 1e10 photons for a 1/1000-second exposure, and so I get one million photons per pixel, so the standard deviation should be 1000 photons, or 0.1%.

If I throw in QE*FF=0.3 I get 0.18%, which, for an 8-bit sensor near its max looks like sigma = 0.5 counts.

Is that right? —Ben FrantzDale (talk) 15:00, 21 June 2010 (UTC)

## Before Schottky there was Campbell

I don't think Schottky was the first to study shot-noise. According to the point process literature[1] [2], it was the work[3][4] by Norman R. Campbell on shot noise[2], which was partly inspired by the work of Ernest Rutherford and Hans Geiger on alpha particle detection, where the Poisson point process arose as a solution to a family of differential equations by Harry Bateman. In Campbell's work, he presents the moments and generating functions of the random sum of a Poisson process on the real line, but remarks that the main mathematical argument was due to G. H. Hardy, which has inspired some to say that the result should be called the Campbell-Hardy theorem. [5].