Q R (1+P CqRq)

1. D.Chokheli, V.Grebenyuk, A.KalininStudy of SiPM with help of transient processes induced by light, dark-noise and current pulses.

2. A SiPM is a solid-state photodetector that is consist of a matrix of independent micro avalanche photodiodes ( micro-pixels), that are operated in limited Geiger mode. The pixels are all connected onto a common substrate.The sizes are about 1*1 mm square.The thin depletion region is in the upper part of device. The film resistor connects the micropixel to a conduction grid on the SiPM top surface.

4. Interest to this devices is explained by the its unique properties: an ability to detect single photons, a high photon detection efficincy, low operating voltage and others. The signal is created, when the hitting photon is converted to electron and hole and the multiplied charge is accumulated on the C. The gain of SiPM G=10^6 as in PMT, but high single photon resolution in vacuum PMT is not possible. The equivalent circuit of SiPM is shown in Fig 1(upper), when the photodiode is not exited. There are resistor Rq in series with diode capacitance in every pixel, but load resistor R is common. .

5. The equivalent circuit of SiPM of course based on the operating principle of one pixel that was been worked up in the end of the last century. It’s essential for us now that the quenching resistor do not be low resistive. It’s about 1 Mom. As a result of this we have to take into account the capacitance Cq. It’s verysimilary because Rq disposes in the upper part of SiPM in the vicinity with ears electrodes. • Down Fig1 shows the case in which only one micropixel at a • time firesi.e. when a single dark-noise pulse is considered. As it seen the signal in this case is the fired cell and the rest of cells together with resistor R are the load, but now the existing voltage is dE= E- Ebr, which has the form of a step. The rise time of the step is small.It is determined by t=RsCd, where Rs- internal resist of itself avalanch. Its value t<<1 ns, and we may it neglect in our consideration.

6. .

8. Q R (1+P CqRq) Uout(p) = --------------------------------------------------------------------------------------- P2RRq(CdC+CqC+CqCd)+P[R(Cd+C)+Rq(Cd+Cq)]+1 Z= -1/CqRq P1= - 1/[R(Cd*+C)+Rq*(Cd*+Cq*)] P2= - 1/R[C+(Cd*Cq*)/(Cd*+Cq*)]

10. The pulse form of SiPM

11. Compemsation of the zero by the pole. • At low R the output signal is the sum of two components A1 and A2. The former is very short (about T=RCq) and big, the last is long and small, but with increasing R it quickly rises. It is may to show when RqCq=RC the output pulse is getting one-exponent form. It is result of the compensation of the zero by the pole. The rise time in this case is nil as before.( we suppose, that the avalanche rise time is equal zero). At the further increasing of the load resistor R the signal form gets • two components again, but the rise time =RC and the pulse duration is increased.

14. The SiPM has the unique resolution of single electron (or the same, of single pixel). It’s result of the outstanding uniformity of the pixels. What possibilities offer this property? First of all, it allows the simple calibration and determination of the photon quantity, hitting on the detector. Besides, the distance between the peaks D (in channels) is proportional to the SiPM gain G. So G= Q/q=D* Q 1ch/ q= 10^4- 10^6. The more, it seems, by operative measuring of the distance between the peaks give an opportunity to restore the gain after any changing of temperature or others conditions, if only this changing is in the limited range. Also, by this method the digital gain system stabilization may be created.

17. N44&4131

19. It is the picture from the only publication (NIM A, 572(2007) where the dark pulse has the clear fast exponent, received with help of fast amplifier (1,8GHz) and LeQroy oscillograph.

22. Conclusion • 1.The SiPM equivalent circuit isproposed and the analitical formulas for the SiPM output signal shape are deduced at different load R. • 2.At low R the signal is the sum of two falling exponents, one very short and high and the other long and small. This signal is preferable for time measurements. • 3.The signal amplitude increases in proportion to increasing R and when RC=RqCq, the compensation of the zero by the pole take plase and the pulse gets a one-exponent shape. In this case the pulse duration may be minimized by introducing the second clipping compensation in the amplifier. It may be useful for minimizing dark-noise, because the gate of Q-COD may be the smallest. • 4 As the resistance R goes on increasing, the signal grows long and the rise time becomes equal to RC. If R is more than 50k, it is possible to use the charge-sensitive preamplifier.In this case the low thermal noise allows one to work with small overvoltage.

23. The noise and the interpixel cross-talk. The noise of SiPM is result of accident excitation of p-n junction by thermal electrons and is determined by reverse current of diode. So, it’s increases with temperature and with voltage. In reality, the resolution worsening from noise is dependent from technology. Usually no more, then 15% at the optimum voltage increasing. The noise pulse count consists about 10-100 kHz/s. The specific effect of the interpixel cross-talk is exciting of the neighbour pixels. It displays the first peaks of spectrum, but at moderate voltage it’s not marked.