UNIVERSIT . . AT BONN Physikalisches Institut - Prof. Dr. Norbert ...

2.4. Signal formation in direct converting pixel detectors 13
In most cases the upper limit of the charge collection time for a detector of thickness D
at a bias V can be estimated by the following formula.
t e/h = D2
µ e/h · V
(2.13)
The formula neglects sensor effects like the build-up of space charge, which can cause
large deviations of the electric field from the externally applied one. Still, typical charge
collection times in thin Si detectors (300 µm at 100 V) are on the order of 3 ns for electrons
and 9 ns for holes. Thicker CdZnTe sensors typically have transit times on the order of
several dozen nanoseconds.
Parallel plate detector
Fig. 2.8(a) shows the signal generation for a parallel plate detector under the assumptions
of a constant electric field and an electron mobility, which is three times higher than
the respective value for holes. In this particular detector geometry the weighting field is
constant as indicated by the evenly spaced equipotential lines in Fig. 2.8(a). If a photon
creates a number of electron hole pairs right in the middle of this detector, the resulting
mirror charge Q(t) at the cathode has a quickly rising electron and a slowly rising hole
component (see Fig 2.8(a) middle). The current flowing through the anode is shown in
the bottom left plot in Fig 2.8(a) and it consists of a short-lived but strong electron
a) b)
+ +
-
I
Q
total
e
h
Φ w
-
+
Read
out
total
e
h
t
t
Fig. 2.8: Weighting potential (top), induced mirror charge Q(t) (middle) and generated
signal current i(t) (bottom) in a parallel plate detector (a) and a pixel detector (b). Both (a)
and (b) assume a constant electric field inside the sensor. The three images in (a) illustrate
the different duration and magnitude of the electron and hole components of the sensor
signal, if the charge carriers are created in the middle between the detector electrodes. (b)
shows the small pixel effect using the example of two different electron trajectories through
the detector. In this case hole signals are neglected.
-
Q
I
B
-
-
A
Φ w
A
B
A
B
Read
out
t
t