# Study on SiPM performance at low temperatures between $-60^{\circ}$C and
$-20^{\circ}$C

C. Zhong,11footnotetext: Corresponding author. F. J. Luo  B. Zheng  X. D. Wang
M. Y. Bu  J. Zou  and M. N. Deng

###### Abstract

Radon is the main background source of dark matter and neutrino experiments.
Radon concentration ($\rm mBq/m^{3}$) measurement by liquid scintillation
detector is a highly sensitive method at low temperatures using silicon
photomultipliers (SiPMs) arrays. The SiPM performance characteristics are
closely related to the lower detection limit of the detector. In this study,
we built an automatic and accurate low-temperature measurement system to study
the single photoelectron (SPE) spectrum, SPE resolution, optical crosstalk,
and after-pulse of the SiPM at different temperatures. As a result, we
obtained the variation trend of the SiPM parameters at different temperatures,
and the SiPM optimal working conditions were obtained, which can improve the
detector’s sensitivity.

##  1 Introduction

Radon is the main background source for many low-background detector
experiments [2, 3, 4, 5]. Currently, the radon measurement methods worldwide
mainly include the ionization chamber, electrostatic adsorption, and liquid
scintillator measurement methods. Among them, due to the advantages of a high
solubility coefficient and a low background, the liquid scintillator
measurement method is widely used in dark matter and neutrino experiments,
such as Jiangmen Underground Neutrino Observatory (JUNO) [6, 7] and China
Jinping Underground Laboratory (CJPL) [8, 9]. Moreover, they all require high
sensitivity for low-background detectors for radon measurements. In liquid
scintillators, radon and its daughters generate photons through the
$\beta-\alpha$ cascaded decay [10, 11], and photon counts are detected using
photomultiplier tubes. However, silicon photomultipliers (SiPMs) are the most
popular photon detection devices in the composition of liquid scintillation
detectors [12]. As novel low-light-sensing optoelectronic conversion devices,
SiPMs have attracted significant attention due to their small size, high gain,
fast response, and low cost. It comprises a high-density diode [13] matrix
with a common output load, each in a finite Geiger-Muller mode for high gain
[15, 14, 16].

Generally, the detection limit of the detector characterizes the sensitivity
in radioactivity measurements [17], which refers to the minimum expected value
of radioactivity that can be detected by a certain measurement method under a
certain confidence level. Based on the measurement of radon and its daughters’
concentrations, the detection limit is defined as the minimum detectable
concentration (MDC) [18], and is presented in Equation 1.1.

$MDC=\frac{4.65\sqrt{n_{b}/t_{b}}}{\epsilon\cdot\eta\cdot V\cdot\zeta},$ (1.1)

where $n_{b}$ is the background count rate (cps), $t_{b}$ is the counting time
of the sample and the background (s), $\epsilon$ is the detection efficiency,
$\eta$ is the total recovery efficiency during the separation and
concentration process, and $V$ is the sample amount ($m^{3}$), $\zeta$ is the
branching ratio of gamma rays or other particles. Therefore, effectively
reducing the background count is the key to achieving high sensitivity of the
detector, $i.e.$, to reduce the noise influence when the SiPM detects the
photon signal in the experiment. We know that the SiPM temperature
characteristics make it easy to generate a lot of thermal noise due to the
excessive operating voltage [20, 19, 21, 22]. So, the temperature can
seriously affect the background count in detection experiments [24, 23].
Moreover, SiPMs have excellent SPE resolution, and very low noise
characteristics at low temperatures, which can effectively reduce the
detection limit of the detector and improve the detection sensitivity of
liquid scintillation detectors to the decay concentration of radon and its
decay daughters.

Moreover, the sensitivity of the detector is also related to the light yield
of the liquid scintillator. In low-temperature experimental environments, the
light yield of the liquid scintillator increases by $2$% when the temperature
decreases by $10^{\circ}$C from room temperature [25]. Therefore, by reducing
the experimental temperature reasonably, the light yield can be effectively be
increased, thereby improving the detector’s sensitivity.

In this study, we design the low-temperature measurement system to
systematically study the SPE [26, 22] spectrum, gain, optical crosstalk,
after-pulse, time resolution, and SPE resolution of the SiPM under different
temperatures. By analyzing the amplitude and charge spectrum of the pulse
signal, we can obtain the low-temperature effects on the performance
characteristics of SiPMs. Moreover, the optimal working conditions of SiPMs
are obtained with lower noise and better SPE resolution.

##  2 Experimental system

###  2.1 Measurement system

Measuring the radon concentration by the liquid scintillator detector of the
SiPM array requires studying the pulse counts obtained on the SiPMs [27, 28,
29]. The pulse count per unit time is proportional to the radon concentration
so that the radon concentration can be determined. Also, a low-temperature
measurement system was designed to study the SiPM performance characteristics
(Fig. 1). In the system, two low-voltage power supplies provide the working
voltage for the SiPM and the preamplifier. Also, the preamplifier amplifies
the output signal by 30 times. The SiPM is placed on the support plate (Fig.
2), and they are placed together in a dark room. Then, the dark room is placed
in an automatic control cryostat. The SiPM model used here is the
S13360-6050CS from Hamamatsu; the working voltage is 54.86 V at room
temperature, and the size is 6 mm $\times$ 6 mm $\times$ 6 mm. Its effective
photosensitive area is 26.64 $\rm mm^{2}$, and its spectral response range is
$270$–$900$ nm.

When measuring the SPE spectrum, a pulse generator (pulser) drives the light
source to illuminate the photocathode of the SiPM and outputs a pulse signal
from the anode, which is driven at a frequency of $1$ kHz. Among them, a blue-
emitting LED ($\lambda$ = 420 nm) is used as the light source coupled with the
pulser. The pulse signal is used as the measurement signal after the fan-in
fan-out. Using the synchronous triggering method, the pulser simultaneously
outputs a trigger signal that passes through the low-threshold discriminator
(LT-Dis). The model of this LT-Dis is N840 from CAEN. Then, a FlashADC (FADC,
DT5751) from CAEN was used to sample the waveforms [30].

During the experimental preparation, we measured the preamplified baseline
signal from the support plate where no SiPM was placed, which was 2mv
displayed on the oscilloscope. We measure the breakdown voltage of the first
clear signal of the SiPM at room temperature, that is, the minimum voltage at
which the SiPM can operate normally at room temperature. Also, to reduce
electrical interference and noise from the LED, the LED and its circuits are
wrapped with shielding materials, such as tin foil, and fixed near the SiPM
surface. The measurement of the SPE spectrum requires the pulse waveform to
have a stable single photoelectron signal. It is defined as the occurrence of
a single photoelectron signal once in ten pulses, $i.e.$, the probability of a
single photon is $10$%.

In the experiments, we measured the SPE spectra with the LED through an
automated cryostat to control the temperature of the experimental environment.
During the data taking, the cryostat temperature and the SiPM voltage vary
from $-60^{\circ}$C to $-20^{\circ}$C and 51 V to 56 V, respectively. This
experiment mainly provides some reference data for the performance
characteristics of SiPMs at low temperatures for developing low-background
detectors for measuring the concentration of radon and its daughters and
selecting the best working conditions for SiPMs to obtain high detection
sensitivity.

Figure 1: The low temperature measurement system. Figure 2: SiPM and support
plate.

###  2.2 SPE spectrum of SiPM

The SiPM waveforms are sampled by the FADC waveform automatic acquisition
system, which is then calibrated. During the calibration experiment, the
standard input signal is set as a standard square wave sent by the pulser,
which is collected by the oscilloscope through LabVIEW [31], and the FADC
digital acquisition system collects the output signal. Next, data sampling and
analysis are performed according to the amplitude from $0$–$100$ mV, with a
step size of $10$ mV. Their amplitude spectra are shown in Fig. 3, and they
are fitted with a Gaussian function to obtain the mean value as the amplitude
value. Figure 4 shows the result of the FADC calibration. The associated
calibration factor obtained is $0.91$. The charge conversion equation is given
as follows:

$q=\frac{V_{\rm Fixed}}{V_{\rm FADC}\times R}\times t_{0},$ (2.1)

where $V_{\rm Fixed}$ is the standard amplitude value corresponding to each
channel ($1$ mV), and $V_{\rm FADC}$ is the amplitude value of each channel
after calibration by the FADC ($0.91$ mV). $R$ is the load resistance ($50$
$\Omega$), and $t_{0}$ is the $1$ GHz sampling rate of the FADC. Based on the
FADC calibration results, Equation 2.1 was used to estimate the corresponding
charge value for each channel to be $21.98$ fC to analyze the charge spectrum
for subsequent SPE spectrum measurements.

Figure 3: Amplitude spectrum with oscilloscope (left) and FADC (right). Figure
4:  FADC calibration result using amplitude spectra. Here $V_{\rm os}$ and
$V_{\rm DT}$ are the mean values obtained after fitting the amplitude spectra
collected by the oscilloscope and the FADC with a Gaussian function,
respectively.

The photoelectrons generated by the photon incident on the SiPM photocathode
in the detector conform to the Poisson distribution after photomultiplication
[26],

$P(n)=\mu^{n}e^{-\mu}/n!,$ (2.2)

where $P(n)$ is the probability that the pulse collected on the SiPM contains
$n$ photons, $\mu$ is the average photon number of the pulse, and $n$ is the
number of photons in the pulse. The light intensity of the LED was adjusted to
ensure that $90$% and $10$% of the probability are a step and a signal,
respectively. At this time, the ratio of the single photoelectron to the
multiphoton in the signal is 1:21, $i.e.$,

$P(n=1)/p(n>1)=21.$ (2.3)

Also, the probability of a single photon is about $9.5$%. Moreover, when the
pulse count is large, the Poisson distribution can be approximated to a
Gaussian distribution, so a Gaussian function can be used to fit the data.
Fig. 5 shows the charge distribution of the SPE based on log coordinates,
which eliminates the effect of baseline deviation and can be fitted with a
multiGaussian function to obtain the peak (mean) and width (sigma) of the
pulse waveform. Among them, $Q_{1}$ is a step mainly derived from electronic
circuits and noise, $Q_{2}$ is a single photoelectron signal, and $Q_{3}$ is a
two photoelectron signal. The ratio of the single photoelectron signal to the
total signal can be estimated as

$R=\frac{N_{sig}}{(N_{sig}+N_{bkg})}=9.1\%,$ (2.4)

where $N_{sig}$ and $N_{bkg}$ are the counts of steps and signals,
respectively. The results show that the signal measured in the experiment is
basically the SPE, and a small amount of multiphoton signal is mixed. The
amplitude and charge spectrum of the SPE at different temperatures are
analyzed in Fig. 6, where the charge spectrum can be obtained by a simple
superposition of the integral areas. Also, for the rigor of the experiment, we
also examined the relationship between steps, single photoelectrons, and two
photoelectrons for all acquired pulse waveforms.

$Q=Q_{2}-Q_{1},$ (2.5)

with

$Q_{3}=2\cdot Q+Q_{1}.$ (2.6)

Here, $Q$ is the channel of the single photoelectron charge. When the channels
satisfy this equation, one can be sure that the data samples collected in the
experiment are reasonable. Using the calibrated SPE spectra, we further
investigated the performance parameters of the SiPM at different temperatures,
such as gain, optical crosstalk, after-pulse, time resolution, and SPE
resolution,.

Figure 5: The charge spectra of SPE at $-20^{\circ}$C.

Figure 6: Amplitude (left) and charge (right) $vs.$ SiPM operating voltage
distribution at different temperatures. They were fitted separately with
polynomials at different temperatures.

##  3 Results and discussion

###  3.1 Gain

We evaluated the gain by illuminating the SiPM with low photon flux. SPE
spectra with clearly distinguishable peaks were obtained from the SiPM anode.
The gain of the SiPM is defined as follows:

$Gain=\frac{(q_{2}-q_{1})}{e\times A},$ (3.1)

where $q_{2}$ is the charge of the single photoelectron ($q_{2}$ = $Q_{2}$
$\times$ $q$), $q_{1}$ is the charge of the electronic noise, $e$ is the
charge of a single electron, and $A$ is the magnification of the preamplifier.
Through the low-temperature measurement system, the temperature of the
cryostat was controlled to change the working conditions of the SiPM to study
the relationship between the gain and the working voltage of the SiPM at
different temperatures and analyze the temperature effect on the SiIPM gain.
Figure 7 (left) shows the variation of the SiPM gain with voltage under
different temperatures; an obvious linear relationship exists between them.
Also, as the temperature decreases, the gain increases accordingly.

Over-voltage is defined as the difference between the SiPM operating voltage
and the breakdown voltage. According to the gain analysis results, the
breakdown voltage of the SiPM at different temperatures can be estimated by
extending the fitted line shape outwards in the Fig. 7 (left), and calculating
their corresponding over-voltages in the Fig. 8. Figure 7 (right) shows the
variation trend of breakdown voltage with temperatures. It can be found that
the decrease of temperature can reduce the corresponding breakdown voltage.

Figure 7: Gain dependence $vs.$ operating voltage of SiPM at different
temperatures (left), and breakdown voltage $vs.$ temperatures (right). Figure
8: Gain dependence $vs.$ over-voltage of SiPM at different temperatures.

###  3.2 Optical crosstalk

During the avalanche process, the photons emitted by the carrier have a
certain probability to reach the adjacent cell diode and trigger a second
avalanche. The probability of an avalanche caused by this mechanism is called
optical crosstalk probability [33, 32]. The optical crosstalk limits the
photon counting resolution of SiPMs. Therefore, the optical crosstalk
probability is an important SiPM property that should be reduced as much as
possible. Methods for determining optical crosstalk are based on the SPE
spectrum analysis. We estimate the optical crosstalk probability as,

$P_{ct}=N_{1.5p.e.}/N_{0.5p.e.},$ (3.2)

where $N_{1.5p.e.}$ is the count of optical crosstalk in all single
photoelectron pulses, $i.e.$ above the $1.5$ photoelectron ($p.e.$) threshold,
and $N_{0.5p.e.}$ is the count of all pulses after step removal, $i.e.$ above
$0.5p.e.$ threshold.

In the experimental analysis, it is usually difficult to distinguish the
optical crosstalk and the after-pulsing. A two-dimensional histogram of the
charge and time corresponding to the maximum peak in the pulse waveform were
used to study them (Fig. 9). Evidently, a single photoelectron after-pulse
signal and a small amount of optical crosstalk signal are observed. To
estimate the counts of the optical crosstalk above the $1.5$ $p.e.$ threshold,
the time must be within the pulse signal range (between 400 and 470 ns), and
the charge must be a smear to the right of the single photoelectron peak. We
calculated the optical crosstalk rate of a single photon at different
temperatures (Fig. 10) and found that although the optical crosstalk
probability is very low. It has a clear law of increasing change with the
increase of temperature in Fig. 10 (left) and Fig. 11. Especially when the
temperature is from $-20^{\circ}$C to $-40^{\circ}$C, this change is very
clear, that is, as the temperature decreases, the optical crosstalk
probability also decreases accordingly. However, the probability of optical
crosstalk at temperatures below $-40^{\circ}$C is less affected by
temperature. That is, the optical crosstalk tends to saturate under the
influence of low temperature conditions. Therefore, the low-temperature
environment can greatly reduce the optical crosstalk interference of SiPMs.
Moreover, when the over-voltage is lower, the probability of optical crosstalk
is relatively lower, especially when the over-voltage is lower than 3V.

Figure 9: The charge $vs.$ time corresponding to the maximum peak at
$-40^{\circ}$C. Here, the black dashed box is the signal of the SPE, 1$p.e.$,
while the red box is the after-pulse signal in the SPE and the pink box is the
optical crosstalk signal in the SPE.

Figure 10: Optical crosstalk (left) and after-pulse (right) at different
temperatures. Figure 11: Optical crosstalk $vs.$ temperature at different
over-voltage.

###  3.3 After-pulse

The measurement of the after-pulse rate is also based on the SPE spectrum
analysis. After-pulses are electrons generated during the avalanche that are
captured and released again after a delay lasting from nanoseconds to
microseconds, resulting in a new secondary current pulse with a smaller
amplitude than the original secondary current, $i.e.$, a “small pulse” whose
the pulse amplitude will be less than the real signal [33, 32, 35].
Unfortunately, the after-pulse signals cannot be separated from the true
single photoelectron signal, reducing the photon counting resolution.
Therefore, the effect of different temperatures on the after-pulse rate must
be studied to minimize its interference with the real signal.

Fig. 9 clearly distinguishes the step (0$p.e.$), single photoelectron
(1$p.e.$), and two photoelectron signals (2$p.e.$). To estimate the after-
pulse count of a single photoelectron, the time must exceed 470 ns, and the
charge must be within the range of the channel corresponding to the valleys on
both sides of the single photoelectron peak, $i.e.$ between 0.5$p.e.$ and
1.5$p.e.$. By estimating the fraction of after-pulse counts in 0.5$p.e.$
photoelectron counts, we obtained the after-pulse rates at different
temperatures in Fig. 10 (right). From the behaviour observed, the after-pulse
probability has no dependence on the temperature change when the temperature
is between $-60^{\circ}$C and $-20^{\circ}$C.

###  3.4 SPE resolution

When the single photoelectron signal is measured, most of the signal obtained
by the FADC is the electronic noise, which overlaps with the single
photoelectron signal and even other multiphoton signals. As many photons are
detected on the SiPM, the mean value of the single photoelectron peak obtained
by fitting the estimated charge distribution deviates from the mean value of
the real single photoelectron distribution, thus affecting the SPE resolution
of the charge measurement. The SPE resolution of a single photoelectron is
defined as

$\delta=\frac{\sigma_{\rm\tiny SPE}}{mean_{\rm\tiny SPE}},$ (3.3)

where $\sigma_{\rm\tiny SPE}$ is the sigma value after fitting the SPE charge
spectrum. And $mean_{\rm\tiny SPE}$ is the mean value after fitting the SPE
charge spectrum after deducting steps. The measured SPE resolution results at
different temperatures are shown in Fig. 12. The result analysis revealed that
the SPE resolution is affected by temperature. It can be clearly found that
when the over-voltage is between 0V and 3V, SPE resolution is improved rapidly
with the increasing of over-voltage. However, when the over-voltage is between
3V and 8V, the SPE resolution is slightly improved with the increasing of
over-voltage. Therefore, the SPE resolution of SiPM can be improved by
reasonably controlling the temperature and the over-voltage.

Figure 12: SPE resolution distribution at different temperatures.

Figure 13: Time distribution of the SPE at 51V with $-20^{\circ}$C (left), and
the time resolution at different temperatures (right).

###  3.5 Time resolution

SiPMs are photodetection devices with fast time responses. In the experiments,
the transit time and transit time dispersion, which characterize the temporal
characteristics, were studied. They refer to the time from the light incident
event on the photocathode surface to the appearance of the output pulse and
fluctuations in the transit time of all single photoelectron pulses on the
photocathode surface, respectively.

During the pulse waveform analysis, the transit time was challenging to
estimate because the baseline shifted generally. Therefore, the time
resolution was used to study the time characteristics of the SiPM in the pulse
analysis. In Fig. 13 (left), it is the time distribution corresponding to the
maximum amplitude value of each pulse waveform. However, time resolution is
defined as the sigma value obtained by fitting the time distribution with a
Gaussian function. In this paper, the time resolution depends only on the
readout scheme without considering the effect of the electronics on the SiPM
alone. In the figure, the photon signal is mainly concentrated between the
time 400–480 ns, and the SiPM time resolution of SiPM is $(9.4\pm 0.2)$ ns. By
studying the time resolution of different temperatures, it was observed that
the time parameter is not affected by temperature (Fig. 13 (right)).

##  4 Conclusion

In conclusion, we study how to realize the high sensitivity of liquid
scintillation detector for very low concentration radon measurement by
reducing the influence of SiPM noise and improving the light yield of liquid
scintillation. In order to obtain the optimal working conditions of SiPM to
improve its parameter performance and reduce the impact of its noise, we built
an automatic and accurate low-temperature measurement system to study the SPE
spectrum, SPE resolution, optical crosstalk, and after-pulse of SiPM at
different temperatures.

In the experiment, we found that the low temperature environment can
effectively improve the performance of SiPM. When the temperature is lower
than $-40^{\circ}$C and the over-voltage is less than 3V, the optical
crosstalk probability of SiPM is low, and the SPE resolution is relatively
better. Therefore, we take it as the optimal condition, and can reduce the
noise of SiPM by reasonably controlling it. Moreover, we can also know that
there is a strong dependence between temperature and the light yield of liquid
scintillation. When the experimental temperature is lower than room
temperature, the light yield of liquid scintillation will increase
accordingly. Therefore, when the temperature is lower than $-40^{\circ}$C, we
can obtain a higher light yield, thus improving the liquid scintillation
sensitivity. By rationally utilizing this optimal working condition, we can
effectively reduce the noise of SiPM, improve the light yield of liquid
scintillation, and thus improve the sensitivity of the detector and meeting
the experimental requirements of extremely low-background detection.

##  5 Acknowledgment

The authors wish to thank all teachers and classmates of the School of nuclear
science and technology, University of South China. This work is supported by
the State Key Laboratory of Particle Detection and Electronics, SKLPDE-
KF-202203; Special funds for the construction of innovative provinces in Hunan
under contract No. 2020RC3054; Hunan Postgraduate Research Innovation Project
in 2021, CX20210914.

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