Probability of d leakage to adjacent pixels F. Marchetto INFN - Torino

1. Probability of d leakage to adjacent pixelsF. MarchettoINFN - Torino Motivation Simulation Results Motivation: If one column or fraction of the column, it is served by a single TDC then in case of leakage of a primary d from the crossed pixel to the adjacent one, two hits will be formed in the same timeslot (i.e. 10 ns) and one will be necessarily lost.

2. 300 mm Simulation with a toy MonteCarlo d 200 mm • Determine the probability per track that a primary d leaks in a neighbor pixel • When a leakage happens then two adjacent pixels will fire with some consequences: • Increase the number of hits to be extracted • In the case of the TDC/column configuration if the TDC serves adjacent pixels then one of the two hits will be lost (being in the same timeslot) -> some arrangement is needed p/K To estimate that probability I used the following ingredients (cloned by a program of Heinrich Wahl) : • Number of primary deltas: where: z = 1, b~1, K/A = 0.307 MeV gr-1cm2 / A, x = length in gr cm-2, Z = 14, A = 28 (Si) , F(T)~1

3. Average number of delta generated with kinetic energy above T in the thickness x From the same formula one can simulate the kinetic energy distribution. • Electron Range as a function of T: 10 keV < T < 3 MeV 3 MeV < T < 30 MeV R(gr/cm2) T(MeV)

4. Simulation • Number of delta generated as a Poisson distribution with mean value <NT> • Tracks populate uniformly the pixel • Deltas populate uniformly the pixel thickness • Delta are emitted uniformly around the track and with an angle qT with respect to the track direction where:

5. Results • Leakage probability = 5.2% (no cut on the delta energy left in the adjacent pixel) -> a track has a probability of: 3 stations ·5.2 = 15.6 % of having an extra hit, and • with a configuration where there is a TDC/column then in • 15.6% · 2 adjacent sides / 4 sides ~ 7.8% of the case the hit is potentially assigned to a wrong-by-one pixel way too pessimistic: not all the delta give an extra-hit -> energy cut However, considering that the average energy deposited by a mip in 200 mm of Si is 100 keV then with a threshold at at 0.2 (0.5) mip the fraction of tracks with a double hit is: 12.2 (7.3) % and then considering then in column configuration only half are dangerous we have 6.1 (3.6) %. Notice: column made by interleaved pixels would fix the problem Conclusion: the probability of d-leakage is not negligible. It deserves a full simulation (Geant4) to better evaluate the extent of a possible problem