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Madeline Horn edited subsection_Shot_Noise_The_concept__.tex
over 8 years ago
Commit id: bc023f5e38da57c45cb1b693ef46b18495c60feb
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\subsection{Shot Noise:}
The concept of shot noise was first introduced in 1988 by Walter Schottky who described the noise generated in the form of Poisson Statistics. The Poisson Statistics show that the randomized events of an imbalance of electrons across the resistor are significant and not ignorable. Instead, these fluctuations are measurable and produce the charge of the electron if measured correctly.
To find the charge Schottky's prediction of
a fundamental relation between the
electron, you need to find size of the
fluctuations $<\delta i^2(t)>$ in a current
($V_{sq}$) across the resistor, find $\Delta f$ (Bandwidth), and you need to know the different gains from the amplifiers ($G_1$ of uncorrelated (randomly emitted) electrons of average magnitude $i_{dc}$ is produced by a photo-diode illuminated by a light bulb and
$G_2$). To find the
charge, you can use the following equation: amount of charge $e$ carried by an individual electron in that current:
\begin{equation}
10 V_{sq} \label{eq:SchottkyPredictionForShotNoise}
<\delta i^2(t)> =
\left( 2 e i_{dc} (2 e) \left(i_{\textrm{dc}} \Delta f
\right) \left( G_1 G_2 R \right)^{2} \right).
\end{equation}
where
$e$ $\Delta f$ is the
charge of the electron ENBW, as before, and would explain that
we are looking for, R is the resistance of the resistor used.
Or, you
rewrite the shot equation as $<\delta i^2> / \Delta f $ vs $2 i_{dc}$ with a slope could determine $e$ from measurements of
$e$. $<\delta i^2(t)>$ and $i_{dc}$.