A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

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110 noise and radiation damage Figure 74: The simultaneous signals from up to three pixels are visible in this oscilloscope trace. Optical cross-talk between adjacent pixels that form a cluster generates these events. The MPHD model described in the text assumes all signals in a cluster to appear at the same time. increasing linearly with the applied bias voltage. The trap lifetime, τ, determines the typical time-scale. SiPM are manufactured so that signal uniformity from pixel to pixel is quite good, typically within 10 % [89]. The small variation, σG, together with the narrow single electron response function of each APD provides excellent photon counting capabilities and as many as 20 photons can easily be resolved in a typical pulse height spectrum [78]. The distance between multi-pixel peaks in the spectrum is a measure of the charge gain, A. Surface leakage currents do not cross the multiplication region. Their fluctuations are merged with other noise sources to define the noise amplitude as measured by the pedestal width, σped. A change in the surface leakage current should also appear as a shift in pedestal position, xped. An avalanche of 10 6 carriers in any of the micro-metric APD forming the SiPM will create around 50 photons via hot carrier luminescence with enough energy to trigger any neighbouring pixel [90]. Devices without trenches filled with opaque material exhibit optical crosstalk, where at least one photon is able to cross the spacing between micro-cells to produce a simultaneous signal (within 100 ps). Fig. 74 shows the effect of optical cross-talk in the SiPM elementary signal. The well defined amplitudes of the multi-pixel events is a result of the simultaneity of the composing signals. Optical cross-talk is modeled by considering the probability, q, of simultaneous activation of two isolated pixels when one of them has been triggered and deducing the probability for all possible clusters in the SiPM pixel matrix. No distinction is made when there is more than one neighbour active. Fig. 75 shows all independent cluster types
6.5 damage characterisation with a monte carlo model 111 (a) 4q 3 (1 − q) 8 (b) 8q 3 (1 − q) 9 (c) 8q 3 (1 − q) 9 (d) 4q 3 (1 − q) 10 (e) 8q 3 (1 − q) 8 (f) 4q 3 (1 − q) 10 (g) 8q 3 (1 − q) 9 (h) 4q 3 (1 − q) 8 (i) 8q 3 (1 − q) 8 (j) 4q 3 (1 − q) 8 (k) 8q 3 (1 − q) 8 (l) 8q 3 (1 − q) 9 Figure 75: Independent clusters in which three pixels have been fired (crossed cells) in addition to the initial one (solid cell) as a consequence of optical cross-talk. Any of the possible 76 patterns can be derived from (a) to (l) by symmetry operations. White cells represent pixels which remain off. The sum of all terms equals P(3) = q 3 [36(1 − q) 8 + 32(1 − q) 9 + 8(1 − q) 10 ], where q is the probability of activation of a single pixel. No distinction is made when there is more than one neighbour active.
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M E A S U R E M E N T O F T H E U N
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A B S T R A C T The new stage of th
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C O N T E N T S i kaon electroprodu
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Part I K A O N E L E C T R O P R O
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4 introduction Lorentz invariance.
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6 introduction appear in the K + Λ
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8 introduction there was almost no
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10 introduction This allows us to w
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12 introduction K ¡p γ ∗ Λ(Σ
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16 introduction amount of resonance
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18 introduction photo and electropr
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20 introduction 1.6 previous experi
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22 introduction Figure 9: Total cro
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E X P E R I M E N TA L S E T U P A
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2.3 target 27 Figure 11: Schematic
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2.4 kaos spectrometer 2.4 kaos spec
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M MWPC L F 2.4 kaos spectrometer 31
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Table 3: Spectrometers properties 2
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2.4 kaos spectrometer 35 Figure 16:
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2.4.5.1 Read out electronics 2.4 ka
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2.4 kaos spectrometer 39 channels.
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2.5 kaos single arm trigger 41 64MB
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2.6 spectrometer b 43 Figure 23: Sc
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2.7 coincidence setting 45 to be im
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2.8 data acquisition and analysis s
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2.9 kinematical setting 49 (GeV/c)
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52 detection efficiencies and data
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A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

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