1. Development of front-end electronics for Silicon Photo-Multipliers F. Corsi, A. Dragone, M. Foresta, C. Marzocca, G. Matarrese, A. Perrotta INFN DASiPM Collaboration DEE - Politecnico di Bari and INFN Bari Section, Italy

2. Accurate modelling of the SiPM for reliable simulations at circuit level. Development of an extraction procedure for the parameters involved in the model. Validation of the model accuracy. Comparison of different front-end approaches. Preliminary results of the first version of front-end based on a current buffer. Main activities

3. Electrical model of a SiPM R q : quenching resistor (hundreds of k  ) C d : photodiode capacitance (few tens of fF) C q : parasitic capacitance in parallel to R q (smaller than C d ) I AV : current source modelling the total charge delivered by a microcell during the avalanche  C g : parasitic capacitance due to the routing of the bias voltage to the N microcells, realized with a metal grid. Example: metal-substrate unit area capacitance 0.03 fF/mm2 metal grid = 35% of the total detector area = 1mm2  Avalanche time constants much faster than those introduced by the circuit: I AV can be approximated as a short pulse containing the total amount of charge delivered by the firing microcell Q=  V(C d +C q ), with  V=V BIAS -V BR Cg  10pF, without considering the fringe parasitics

4. Extraction of R q Forward characteristic of the SiPM, region in which  V/  I is almost constant and equal to R q /N. _____ Measured characteristic _____ Least square linear fit Forward characteristic of a SiPM produced by ITC-irst. Slope = 1.59 mS R q /N = 629  N = 625 Rq = 393 k 

5. Extraction of V br and C d +C q Charge associated to a single dark count pulse as a function of the bias voltage: Q=(C d +C q )(V bias -V br ) C d +C q and, by extrapolation, V br V bias [V] Q [C] * Measured points __ Least square linear fit Example of a single dark count pulse for the ITC-irst SiPM (obtained by reading the pulse with a 50  resistor and using a 140 gain, fast voltage amplifier) Charge contained in a single dark count pulse vs. bias voltage

6. Extraction of C d, C q and C g  CV plotter measurements near the breakdown voltage: Y M and C M  According to the SiPM model, Y M and C M are expressed in terms of C dtot =NC d, C qtot =NC q, R qtot =R q /N and the frequency  of the signal used by the CV plotter. YMYM CMCM C qtot CgCg C dtot R qtot Y M [  S] C M [pF] V bias [V] CV plotter measurement results for the same device from ITC-irst. The signal frequency is 1 MHz. C d,C q CgCg

7. Results of the extraction procedure  Extraction procedure applied to two SiPM detectors from different manufacturers.  The table summarizes the main features of the devices and the results obtained.  Good agreement with the expected parameter values estimated on the basis of technological and geometrical parameters. Model ParameterSiPM ITC-irst N=625, Vbias=35V SiPM Photonique N=516, Vbias=63V RqRq 393 kΩ774 kΩ V br 31.2 V61 V Q175.5 fC127.1 fC CdCd 34.6 fF40.8 fF CqCq 12.2 fF21.2 fF CgCg 27.8 pF18.1 pF

8. Front-end electronics: different approaches RSRS SiPM Vbias ISIS k I S = I OUT Charge sensitive amplifierVoltage amplifierCurrent buffer - + SiPM Vbias CFCF V OUT + - RSRS SiPM Vbias V OUT A I-V conversion is realized by means of R S The value of R S affects the gain and the signal waveform V OUT must be integrated to extract the charge information: thus a further V-I conversion is needed R S is the (small) input impedance of the current buffer The output current can be easily reproduced (by means of current mirrors) and further processed (e.g. integrated) The circuit is inherently fast The current mode of operation enhances the dynamic range, since it does not suffer from voltage limitations due to deep submicron implementation The charge Q delivered by the detector is collected on C F If the maximum  V OUT is 3V and Q is 50pC (about 300 SiPM microcells), C F must be 16.7pF Perspective limitations in dynamic range and die area with low voltage, deep submicron technologies

9. SiPM + front-end behaviour CqCq A) SiPM coupled to an amplifier with input impedance R s The load effects, the grid parasitic capacitance and the value of R s are key factors in the determination of the resulting waveform of V IN and I IN A qualitative study of the circuit can be carried out with reference to the simplified schematic depicted below. The two circuits give very similar results, provided that R s is much lower than R qtot =NR q I AV RqRq CdCd (N-1)C d (N-1)C q R q /(N-1) CgCg RSRS - V IN I IN + I AV RqRq CdCd CqCq IqIq IqIq CgCg C eq - V IN + I IN RSRS B) Simplified circuit

10. SiPM + front-end behaviour Time V IN Responses of the circuits A) and B) to a single dark pulse (160fC) for three different values of Rs and typical parameter values The simulations show that the peak of V IN is almost independent of R s. In fact, a constant fraction Q IN of the charge Q delivered during the avalanche (considered very fast with respect to the time constants of the circuit) is instantly collected on C tot =C g +C eq. The simplified circuit has two time constants:  IN = R s C tot  r =R q (C d +C q ) Decreasing R s, the time constant  IN decreases, the current in R s increases and the collection of the charge is slightly faster, as shown by the simulations. R s =75  R s =50  R s =20  _____ Circuit A) _____ Circuit B)

11. Bandwidth of the amplifier Amplifier output voltage for a single dark pulse: same gain and different bandwidth _____ BW=500MHz _____ BW=100MHz Time V OUT R s =20  _____ BW=500MHz _____ BW=100MHz Time V OUT R s =75  The simulations show the output of a voltage amplifier for two different R s and bandwidths. The bandwidth of the amplifier directly affects the rise time of the waveform, independently of the value of R S. The peak amplitude of the waveform is strongly dependent on the amplifier bandwidth, especially for low values of R S. In fact, in this case  IN can be very fast compared to the dominant time constant of the amplifier, which is unable to adequately reproduce the input signal. The time needed to collect the charge is just slightly influenced by the amplifier bandwidth. The same conclusions are valid also for the waveform of the output current obtained with a current buffer

12. Experimental validation of the model Two different amplifiers have been used to read-out the ITC-irst SiPM a) Transimpedance amplifier BW=80MHz Rs=110  Gain=2.7k  b) Voltage amplifier BW=360MHz Rs=50  Gain=140 The model extracted according to the procedure described above has been used in the SPICE simulations The fitting between simulations and measurements is quite good

13. Current buffer: two alternative solutions CMOS 0.35um standard technology Feedback applied to reduce input resistance and increase bandwidth Buffer1 Buffer2

14. Integrated current buffer: two alternative solutions Buffer1 simple structure more bandwidth (≈ 300 MHz) limited dynamic range Buffer2 more complex a little slower (BW  250 MHz) extended dynamic range

15. Experimental setup 8ns V 7V t 4.5ns Input waveform Blue Led SiPM Vbias I out 100Ω 50Ω BNC Pulse Generator Current Buffer Voltage Amplifier Experimental setup Test board

16. Measure Preliminary results: dark count pulses

17. The test board is the bottleneck for the BW of the whole system The total no. of photons is always the same in all measurements The standard deviation of the current peak corresponds to about 1/2 micro-cell Measure Preliminary results: output waveforms Buffer1 Buffer2

18. The first solution exhibits limited dynamic range and gain, as expected Measure Preliminary results: linearity

19. More measurements on the current buffers with known ligth source Definition of the architecture (shaper? current peak detector? on chip ADC?) 9 channel test chip Migration to another technology (for instance 0.18um) Final task: 64 channel ASIC Measure Future work