Transcript Delta_leakage

Probability of d leakage to adjacent pixels
F. Marchetto
INFN - 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.
300 mm
Simulation with a toy
MonteCarlo
•
Determine the probability per
track that a primary d leaks in a
neighbor pixel
200 mm
When a leakage happens then two adjacent pixels
will fire with some consequences:
d
p/K
1. Increase the number of hits to be extracted
2. 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
To estimate that probability I used the following ingredients (cloned by a
program of Heinrich Wahl) :
1. Number of primary deltas:
d 2N
1
Z 1 F (T )
 Kz 2
dxdT 2
A 2 T2
where: z = 1, ~1, K/A = 0.307 MeV gr-1cm2 / A, x = length in
gr cm-2, Z = 14, A = 28 (Si) , F(T)~1
Average number of
delta generated with
kinetic energy above T
in the thickness x
0.1[MeV  gr 1  cm2 ]
 NT 
x[ gr  cm2 ]
T [ MeV ]
From the same formula one can simulate the kinetic energy distribution.
• Electron Range as a function of T:
R  0.412  T (1.2650.0954ln(T ))
3 MeV < T < 30 MeV
R(gr/cm2)
R  0.530  T  0.106
10 keV < T < 3 MeV
T(MeV)
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:
qT  (Te / Pe )  ( Pmax / Tmax )
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