Re: Shot noise

From: John Larkin (jjlarkin_at_highSNIPlandTHIStechPLEASEnology.com)
Date: 08/31/04 

Date: Tue, 31 Aug 2004 15:52:07 -0700

On Tue, 31 Aug 2004 10:54:44 -0400, Phil Hobbs
<pcdhSpamMeSenseless@us.ibm.com> wrote:

>Mike wrote:
>> On Tue, 31 Aug 2004 13:37:01 +0200, Christian Rausch wrote:
>>
>>
>>>Hello everybody,
>>>
>>>Q1.
>>>Shot noise, as stated in Horowitz&Hill, ch7.11, p.432, shows a noise current
>>>of
>>>
>>>Inoise(rms) = sqrt(2*q*Idc*B)
>>>with q:electron charge, B:bandwidth and Idc:the DC current,
>>>
>>>but this formula "assumes that the charge carriers making up the current act
>>>independently. This is indeed the case for charges crossing a barrier, as
>>>for example the current in a junction diode...but is not true for the
>>>important case of metallic conductors, where there are long-range
>>>correlations between charge carriers..."
>>>
>>>Does anybody know what the exact criterion for this 'independence of the
>>>charge carriers' is?
>>>Are there situations with 'partial' shot noise?
>>
>>
>> This page describes noise in metal resistors of various lengths:
>>
>> http://www.ilorentz.org/beenakkr/mesoscopics/topics/noise/noise.html
>>
>> From the paper:
>> ------------
>> Shot noise results from the fact that the current is not a continuous flow
>> but the sum of discrete pulses in time, each corresponding to the transfer
>> of an electron through the conductor. Its spectral density is proportional
>> to the average current, I, and is characterized by a white noise spectrum
>> up to a certain cut-off frequency, which is related to the time taken for
>> an electron to travel through the conductor. In contrast to thermal noise,
>> shot noise cannot be eliminated by lowering the temperature.
>>
>> In devices such as tunnel junctions the electrons are transmitted randomly
>> and independently of each other. Thus the transfer of electrons can be
>> described by Poisson statistics, which are used to analyse events that are
>> uncorrelated in time. For these devices the shot noise has its maximum
>> value at 2eI, where e is the electronic charge.
>>
>> 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. But recent progress in nanofabrication technology has
>> revived the interest in shot noise, particularly since nanostructures and
>> "mesoscopic" resistors allow measurements to be made on length scales that
>> were previously inaccessible experimentally.
>> ------------
>>
>> -- Mike --
>>
>
>Shot noise in metallic resistors is suppressed by a factor of the mean free
>path of the electrons in the metal divided by the physical length of the
>resistor. Most of the time this is a very small number.
>

OK, humor me here: hang a metal-film resistor across a power supply,
and we get a current with low shot noise. What happens if we put two
equal-value resistors in series across the supply, one metal-film and
one something crummy, carbon film or something? Will this just act
like a voltage divider between a noisy resistor and a quiet one,
giving half the shot noise current as an all-carbon circuit?

John

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