Properties of large SiPM at room temperature

We present in this paper the comparison of methods to measure parameters to characterize a large SiPM of area of about 1 cm$^2$. We also explain the challenges of operating it with continuous light and at room temperature. We present a method to compensate for the voltage drop induced by emission to continuous illumination in order to control its response stability. This is important for applications where illumination changes with time, such as when they are employed in cameras of gamma-ray telescopes.


The Hamamatsu S10943-2832(X) large area SiPM
The sensor used for the studies illustrated in this document ranks among the world's largest monolithic sensors. It has been developed by the University of Geneva group in cooperation with the Hamamatsu company and is named S10943-2832(X). The work presented here is also the object of detailed papers [1,2]. The main characteristics of the sensor are detailed in Tab Table 1: S10943-2832(X) SiPM main characteristics at T = 25 • C an Vop = V BD + 2.8 V, including the dark count rate, DCR, and the capacitance of the µcell, C µcell .
It is currently employed in two SiPM-based cameras of the SST-1M gamma-ray telescopes (see Fig. 1 and Ref. [3]), that will be used in the LHAASO experiment. The telescope has been originally built for the Cherenkov Telescope Array (CTA) by the University of Geneva and a Consortium of Polish and Czech Institutions. To achieve the de-sired performance with the chosen optics, a mirror of 4 m diameter, the camera of the SST-1M is composed by 1296 pixels, each of an angular opening of about 0.24 • . This translates into a pixel linear size of about 2.32 cm (more details on camera and its design and performances can be found in ref. [3]).
The sensor, shown in Fig. 2-top is built with the LCT2 (Low Cross Talk) standard technology of Hamamatsu [4] with microcell (µcell) square size of 50 µm. Hamamatsu has further improved this technology (LCT5) and introduced the LVR (Low Reverse Voltage), which has much reduced cross-talk (XT) and increased photodetection efficiency (PDE), but substantially longer pulse shape and higher gain. The hexagon is the best possible shape to achieve a uniform trigger response with minimum dead space, thanks to the fact that the pixel centres are equidistant. The pixel size to achieve the required angular resolution is achieved through this large SiPM coupled with light funnel. The light funnel, approaching the ideal Winston cone geometry, has been designed by the University of Geneva group to be coupled to SiPMs and achieve the desired pixel size. The light funnel has entrance and exit hexagonal area and has a compression factor of about six [5]. Its internal surface is coated in order to maximise reflection of UV Cherenkov light produced by the cosmic rays when traversing the atmosphere, and also to have a good reflectivity for light with a direction almost parallel to cone surface. A module of 12 pixels with the frontend electronics and the slow control board, replicated 108 times, makes up the full camera shown in Fig. 2-middle. This has linear dimension of about 1 m. It is shown partially assembled in Fig. 2

-bottom.
Remarkably when using SiPM it is necessary to adopt filters reducing the contribution of the night background at waveglenths beyond ∼ 550 nm. The SST-1M adopted The large area of the SiPM sensors can be a limiting factor in many applications, due to the large capacitance and dark-count rate (DCR). Large devices tend to have longer output signals and be more noisy. However, as shown by the SST-1M camera [3], with the proper associated electronics, such a large device can achieve the desired performances in specific applications. The sensor capacitance is directly related to its active area and this has an impact on the signal recharge time. In this case, signals would have typical duration of about hundred ns, a too long time for the desired bandwidth of 250 MHz. This readout frequency of the fully digitizing electronics has been chosen taking into account the typical time duration of atmospheric showers induced by gamma-rays and cosmic rays.
To reduce the effect of the capacitance, the sensor has four independent anodes and a common cathode as shown in Fig. 2-top. This configuration allows to readout the 4 channels independently, but there is a single bias for the whole sensor. Nonetheless, in order to achieve the desired bandwidth, a shaping of the signal is needed. The four channels are summed by two in order to reduce the equiva-Thermistor B1 B2 A2 A1 Figure 2: Top: Hamamatsu S10943-2832(X) with its electric model. The NTC probe is indicated, which monitors the temperature variations affecting SiPM working parameters [6]. Bottom: A module of 12 pixels partially assembled. lent capacitance and pulse length. The summed signals are further summed up in a differential amplifier, which feeds the output signal into the digital readout system. The adopted solution [6] is a transimpedance amplifier topology with low noise amplifiers (OPA846) as it can achieve the required event rate with the best signal-to-noise ratio and gain/bandwidth ratio.
Another important characteristic of the camera architecture is the fact that the front-end and the digital readout are DC coupled. This is important to easily measure on an event by event basis the level of Night Sky Background (NSB), meaning the moonlight and human-induced light background, which changes with time. As a matter of fact, the variation of the NSB change the real working point of the device, relevant to correctly extract the number of photons from the signal. An example of NSB variation measured by the SST-1M camera is shown in Fig. 3.

Characterisation of the sensor
All the laboratory measurements (i.e. static, dynamic and optical) are performed at room temperature T = 25 Spikes are due to airplanes, being the telescope in Krakov close to the airport.
• C at the premises of IdeaSquare 2 at CERN, where an experimental setup has been installed.

Static characterisation
The static characterization (i.e. reverse and forward current-voltage (IV) curves), is performed using a Keithley 2400 [7] pico-ammeter for bias supply and current measurements. Static means that a constant current is read. The advantage of these measurements is that they are simple and fast, while the disadvantage is that they provide only limited information, namely the breakdown voltage V BD , the working range and R q .
Forward IV:. As shown in Ref. [2] the forward IV (See Fig. 4) can be used to calculate the quenching resistor R q as: where N µcell number of SiPM micro-cells and b is the slope parameter extracted by the linear fit (red line in Fig. 4). For this SiPM, the fit gives R q = 182.9 ± 0.3 (stat.) ±31 (sys.) kΩ.
Reverse IV:. The reverse IV measurements is commonly used for fast calculation of breakdown voltage V BD and SiPM working range. Different methods might be used to calculate V BD , such as the "relative logarithmic derivative" [4], the "inverse logarithmic derivative" [8], the "second logarithmic derivative" [9], the "third derivative" [10] and "IV Model" methods [11,12]. The V BD calculated from various methods are presented in Fig. 5. They are spread over a range of less than 1 V due to the model assumptions made to approximate the IV curve with simple equations.

Dynamic characterisation
For the dynamic measurements presented here (also called AC measurements), instead of the standard preamplification topology used in the real camera [6], each SiPM channel is connected to an operational amplifier OPA846 and readout independently. This is done to improve precision in the measurement reducing the pile up probability. The SiPM device is illuminated with low intensity light of different wavelengths (e.g. 405 nm, 420 nm, 470 nm, 505 nm, 530 nm and 572 nm) produced by pulsed LEDs. For each operating voltage of the LED providing a certain light level, 10'000 waveforms are acquired on an oscilloscope and sampled at 500 MHz. Each one is 10 µs long. The signal used to pulse LEDs is produced by a pulse generator and it is also used to trigger waveform acquisition.
The readout window is adjusted in such a way to have the trigger signal in the middle of the waveform. i.e. at 5 µs from the window start, in order to have: • a "Dark " interval from 0 to 5 µs, when the device is operated in dark conditions. Only uncorrelated DCR enhanced by correlated noise, i.e. cross-talk (prompt and delayed) and afterpulses, are present; • "LED" interval, from 5 to 10 µs, when the device is illuminated by LED light pulses. In this case, both signals pulses due to the light and uncorrelated SiPM noise pulses are present. Both types of pulses are further affected by SiPM correlated noise (i.e. prompt and delayed cross-talk and afterpulses). Dark intervals are used to calculate the SiPM Gain, the breakdown voltage V AC BD , the dark count rate (DCR) and the optical cross-talk probability P XT , while LED intervals are used to calculate the SiPM photon detection efficiency P DE. To measure the afterpulse probability, P AP , an additional data run is performed. The data acquisition system used for these measurements, consists of a transimpedance amplifier based on OPA846, an oscilloscope Lecroy 620Zi for the waveform acquisition (a bandwidth of 20 MHz is used to reduce the influence of the electronic noise) and a Keithley 6487 to provide bias voltage to the SiPM. For each LED of different wavelengths, the over-voltage ∆V = V bias − V AC BD is varied in the range 1 V < ∆V < 8 V, to cover the full working range of the device.
Gain and breakdown voltage V BD :. The SiPM gain is calculated from the time integration of the signals of a device: where G Amp is the amplifier gain, I(t) is the current generated by SiPM (I(t) = V (t)/R). As expected, G increases linearly with increasing V bias (see Fig. 6). Since no avalanches take place before breakdown, the V BD is calculated as the intersection of linear fits with the x-axis and V BD = 54.699 ± 0.017 (stat.) ± 0.035 (sys.) V is found. Knowing V BD , the overvoltage parameter, defined as ∆V = V bias − V BD , can be determined and will be used further instead of V bias .
Uncorrelated and correlated noise:. Two main categories of the SiPM noise can be identified: the DCR or primary uncorrelated noise, which is independent from light conditions, and the secondary or correlated noise of optical cross-talk and afterpulses. From the experimental point of view, the DCR can be determined by counting all SiPM pulses with amplitude exceeding a given threshold (see Fig. 7). This counting method is affected by correlated noise (i.e. cross-talk and afterpulses). Due to this, the cross-talk can be also calculated as: Figure 7: DCR vs. threshold for different values of the overvoltage ∆V for S10943-2832(X). The blue and green vertical lines represent the DCR at 0.5 p.e. and 1.5 p.e. thresholds, respectively.
To overcome the effect of correlated noise, the Poisson Figure 8: DCR vs. ∆V for S10943-2832(X) for the 0.5 p.e. counting method (blue), Poisson statistics method (red) and the 1.5 p.e. threshold (green). Also shown the difference between the experimental data and the fit, normalized to experimental data, for the 0.5 (blue), 1.5 (green) p.e thresholds and Poisson statistics (red). Fit parameters for the Poisson method are given.
statistic method can be used to calculate pure uncorrelated SiPM noise at 0.5 p.e. threshold as: where P dark (0) is the Poisson probability not to have any SiPM pulse and −ln(P dark (0)) is the average number of detected SiPM pulses within the time interval L. The P dark (0) can be calculated as: where N dark (total) represents the total number of analyzed waveforms and N dark (0) is the number of waveforms without any SiPM pulse within the given time interval L. As shown in Ref. [2], L should be long enough to include all after pulses corresponding to the primary pulse, otherwise the DCR would be overestimated. The comparison of the DCR calculated from the counting and Poisson statistic methods are presented in Fig. 8. As is expected, the counting method shows slightly overestimated results due to afterpulses. From Eq. 3 the cross-talk P XT is calculated and presented in Fig. 9. Using a standard approach [1], the P XT is corrected for the pile up effect and also presented in Fig. 9.
The afterpulse probability is measured by acquiring 20 µs long waveforms, triggering their acquisition and using a pulse with an amplitude larger than 0.5 p.e. This Figure 9: P XT vs ∆V of S10943-2832(X) with (P Corrected XT in green) and without correction for the pile up effect (P XT in blue). In the bottom plot the difference between experimental data and fit normalized to data errors is shown.
pulse, called in the following primary pulse, is adjusted to fall in the center of the waveform (i.e. at 10 µs). To ensure that pulses are either afterpulses related to the primary pulse or randomly generated dark pulses, waveforms without any signal within the 5 µs preceding the primary pulse are selected and analyzed in the following. Details of the measurement are in Ref. [1]. Fig. 10 is a two-dimensional histogram of the amplitude in p.e. of the first pulse following a primary pulse of 1 p.e. vs the time difference between the two. This plot shows the various SiPM noise components. The population of dots around amplitude of 1 p.e and time delay larger than 50 ns are typically dark pulses and afterpulses. The population with amplitude lower than 1 p.e. and delay smaller than 50 ns are afterpulses produced when the µcell has not yet recovered. The population at time delay less 50 ns and amplitude 1 p.e. might be mostly delayed optical cross-talk, and some dark pulses or afterpulses related to avalanches happened more than 5 µs before the primary avalanche. The other populations at larger amplitude than 1 p.e. are of similar nature than what described for 1 p.e. but further enhanced by optical cross-talk. In the plot, the red solid line is calculated from: where A 1p.e. is the single photoelectron (p.e.) amplitude, τ rec. = R q · C µcell is the recovery time constant since the afterpulsing occurs in the same µcell as primary avalanche, hence its amplitude A AP strongly depends on the recovery state of the µcell.

Optical characterisation
The photon detection efficiency P DE is one of the most important parameters describing the sensitivity of a SiPM as a function of wavelength of the incident light λ and the applied overvoltage ∆V : where QE(λ) is the quantum efficiency, P G is the Geiger probability, and the micro-cell fill factor (the percentage of it that is sensitive to light). More details about each P DE component can be found in the Ref. [13]. To study the P DE, our experimental setup at IdeaSquare at CERN is used (more details can be found in Ref. [1]).
Absolute PDE:. For the absolute P DE measurements, LEDs of six different wavelengths λ are operated in a pulsed mode (pulse width from 2 to 5 ns, depending on the LEDs type). The so-called Poisson statistic [14] [15] [16] [17] method is used for data analysis and the results are presented in Fig. 11.
Relative PDE:. The absolute P DE measurements require a pulsed light source, as an LED or a laser, so it is possible only for a limited number of wavelengths. Therefore, to measure the P DE in a wide wavelength range, from 260 nm up to 1150 nm, a second method, the so called "Relative PDE", is used. Using the method described in Ref. [1] and [15], the relative P DE is calculated in a wide λ   range from 260 nm up to 1150 nm and presented in Fig. 12 for all four SiPM channels. By combining the the absolute and relative P DE measurements the P DE as a function of ∆V and λ can be obtained and it is presented in Fig. 13.

SiPM cross-talk in SST-1M camera
SiPM cross-talk is already discussed in Sec. 2.2. Different optical elements can dramatically increase the crosstalk. To study this effect, we measured the cross-talk for four different conditions: only SiPM device, SiPM covered by a reflecting mirror, SiPM covered by sample of a coated window used in SST-1M camera, SiPM connected to a coated lightguide. The results are presented in Fig. 14. As expected, the mirror and coated window (by reflecting the photons created during the avalanche multiplication process) increase the cross-talk with respect to its initial values. However, after introducing the light funnel between the SiPM and the coated window, the cross-talk decreases back to its initial value. This effect is obtained due to the lightguide design, which is hollow inside. Such cross-talk reduction might not be achievable with solid (i.e. quartz) light funnels, such as those adopted in the FACT camera [18].

SiPM behavior under continuous light (CL)
In order to protect a SiPM from drawing too high current, a resistor is connected in series to it in its bias circuit. Consequently, the resistor introduces a voltage drop when the SiPM draws a steady current. This happens when it is illuminated by constant light. This reduces the actual SiPM bias and then its sensitivity to light. As a matter of fact, this effect changes all relevant SiPM features, both electrical (i.e. breakdown voltage, gain, pulse amplitude, dark count rate and optical crosstalk) and optical Figure 14: P XT vs ∆V of S10943-2832(X) measured for the SiPM (black), the SiPM covered by the coated window (green), the SiPM connected to the lightguide and covered by the coated window (blue) and the SiPM covered by the mirror (red).
(i.e. photon detection efficiency). Of course the intensity of the effect is more prominent for larger resistors and sensors with high gain (i.e. current).
We have characterized the Hamamatsu device under light rates raging from 3 MHz up to 5 GHz of photons per sensor at room temperature (T = 25 • C). Then, we developed a model in order to derive the parameters needed to correct for the voltage drop effect (for more details see Ref. [2]).
In Fig. 15 the effect on the P DE and G as a function of time is shown from the model for two different values of the resistor. The time interval before the steady state is achieved increases with the rate of photons F light on the sensors and gain G. For this particular example, it is reached after 100 ns and with noticeably changed parameters.
The proposed model was implemented in a Monte Carlo and validated using the SST-1M camera and its Camera Test Setup (CTS) [3]. The CTS is equipped with two LEDs (λ = 468 nm) per each SST-1M camera pixel: one in pulsed mode (AC LED) and the other in continuous mode (DC LED). An AC/DC scan, described in Ref. [2], has been performed for all 1296 camera pixels at ∆V = 2.8 V. For each pixel, AC and DC LED values, the baseline and signal amplitude are calculated. Results are presented in Fig. 16. Here the variation of the average amplitude A rel. of the AC LED signal on top of the baseline due to the rate of CL F light is shown. We can observe that almost for all pixels A rel. decreases with increasing baseline shift light illumination.
The drop of the SiPM parameters under CL may be compensated by increasing the bias voltage by some correction voltage V Cor. bias in order to keep constant the overvoltage ∆V . This can be implemented in a compensation loop. The V Cor.
bias as a function of the baseline shift is presented in Fig. 17 for two values of R bias of 10 kΩ and 2.4 kΩ with CL of 2 × 10 9 photons/s and with compensation loop (dashed lines) and without (solid lines) (top). We can observe, that to compensate by V drop ∼ 0.9 V, the V bias should be increased by 1.7 V, as shown in Fig. 17 (bottom). As a drawback, the detected NSB rate increases as well as the SiPM power consumption.

Conclusions
We have characterized for realistic operation at an astronomical site a large area SiPM sensor. The work done can be used for any SiPM used at room temperature and in the presence of continuous light.