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Landau Fluctuations

At each step, the total number of electron-hole pairs created is determined. This is done by calculating the number of collisions in $1\mu$m of silicon: a Poisson distribution of mean 4. Then for each interaction, the energy losses are calculated according to [1]. In 90% of all collisions, the energy loss is less than 170eV, and the mean energy loss for these collisions is 30eV. However in 2% of cases, it is greater than 1000eV, and in 0.2% of cases, it is greater than 10000eV. It is these high energy fluctuations which lead to the well known quasi-Landau distribution for the sum of all energy losses in the silicon. Since these large fluctuations occur rarely, they cause biases in the position determination on an event-by-event basis. Over many events, this leads to a broadening in the resolution.



Andrew Galloni
1998-12-14