- Fano factor
In

probability theory andstatistics , the**Fano factor**[Fano, 1947] , like thecoefficient of variation , is a measure of the dispersion of aprobability distribution .Fano factor is defined as

:$F=frac\{sigma\_W^2\}\{mu\_W\}$

where $sigma\_W^2$ is the variance and $mu\_W$ is the mean of a

random process in some time window $W$. The Fano factor can be viewed as a kind of noise-to-signal ratio; it is a measure of the reliability with which therandom variable could be estimated from a time window that on average contains severalrandom event s.For a

Poisson process , the variance in the count equals the mean count, so $F=1$Fano factor is similar to the

variance-to-mean ratio if the time window is chosen to be infinity.In detector systems, the Fano Factor results from the energy loss in a collision not being purely statistical. The process giving rise to each individual charge carrier is not independent as the number of ways an atom may be ionized is limited by the discrete electron shells. The net result is a higher energy resolution than predicted by purely statistical considerations.

The Fano factor is a material specific value. Theoretical values (according to Alig, Bloom and Struck, 1980) are:

Si: 0.115

Ge: 0.13

GaAs: 0.10

Diamond: 0.08**ee also***

Coefficient of variation

*Ugo Fano

*Variance-to-mean ratio (or VMR)**References*** Fano, U. (1947). Ionization yield of radiations. II. The fluctuations of the number of ions. "Phys. Rev.", 72:26-29.

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