Investigations of self-heating effects in Silicon-Photomultipliers

1. Introduction

Silicon Photomultipliers (SiPMs) are the detector of choice for numerous applications in high-energy physics, astroparticle physics and space research, medical imaging, and societal applications. The operating conditions in these applications largely vary, e.g. temperatures can range from cryogenic [1] to 100 °C. Usually, the devices are operated in the dark, and visible photons are the signal to be detected, but in applications such as LiDAR systems (Light Detection and Ranging), SiPMs need to be operated in the presence of ambient light background [2,3]. At collider experiments, SiPMs are operated in a harsh radiation environment. The principal effect of radiation damage already at moderate fluences of ${\mathsf{\Phi }}_{\mathrm{eq}}={10}^{10}$ cm⁻² is an increase of dark current [4,5]. For the Phase 2 Upgrade the CMS collaboration at LHC plans two new detectors equipped with SiPMs [6]. In the High Granularity Calorimeter (HGCAL) plastic scintillator tiles with SiPM readout will equip the rear active layers which, during the detector lifetime will accumulate a 1 MeV neutron equivalent fluence ${\mathsf{\Phi }}_{\mathrm{eq}}=5·{10}^{13}$ cm⁻² [7]. Even worse will be the operation condition in the barrel MIP Timing Detector (MTD) which will reach a fluence of ${\mathsf{\Phi }}_{\mathrm{eq}}=2·{10}^{14}$ cm⁻² [8]. Understanding the SiPM’s response after radiation exposure is crucial for these applications. While the dark count rate (DCR) of non-irradiated SiPMs is typically in the range of 10-500 kHz/mm when operating in a dark environment at room temperature, it has been shown that the DCR increases by five orders of magnitude to above GHz/mm after a fluence ${\mathsf{\Phi }}_{\mathrm{eq}}={10}^{13}$ cm⁻² even with cooling to $-30$ °C [8,9,10,11]. The same high (photo-)current is registered by SiPMs operated with background ambient light. These elevated currents result in significant power dissipation, potentially causing a rise in the SiPM temperature, an effect known as self-heating.

To maintain stable SiPM temperatures in such high dark count rate conditions, it is crucial to ensure a small thermal resistance between the SiPM and the heat sink [12]. Efficient heat dissipation is necessary to prevent self-heating and subsequent variations in the breakdown voltage of the SiPM, which changes its performance parameters such as gain and photon detection efficiency.

This research seeks to devise a method for gauging the temperature increase in SiPM caused by the dissipation of power in its amplification layer.

The SiPM’s performance depends on the temperature T. The photocurrent measured at a constant bias voltage and photon rate decreases with increasing temperature, expressed as $I_{\mathrm{photo}}\propto PDE\left(T\right)·G\left(T\right)·ECF\left(T\right)$, where $PDE$ is the photodetection efficiency, G is the gain, and $ECF$ is the excess charge factor [13]. The temperature sensitivity of the $PDE\propto FF·QE\left(\lambda \right)·P_{Geiger}(V_{\mathrm{bias}},T)$ is introduced via the voltage-dependent Geiger-breakdown probability, $P_{Geiger}$, with $FF$ the device fill factor, and $QE$ the wavelength-dependent quantum efficiency. An increase of T reduces the carriers’ velocity due to increased scattering on the lattice. The ionization coefficients for holes and electrons decrease with T. Consequently, $P_{Geiger}$ at a fix $V_{\mathrm{bias}}$ decreases, and the breakdown voltage, $V_{\mathrm{bd}}$ increases. An increase in $V_{\mathrm{bd}}$ with temperature leads to a decrease in gain, described by the relation: $G=C_{\mathrm{pix}}·(V_{\mathrm{bias}}-V_{\mathrm{bd}}\left(T\right))/q_0$.

In the study by Lucchini et al. [14], a method is proposed to evaluate the heating of SiPMs in various package configurations and to evaluate changes in temperature during operation at elevated dark count rates. The SiPM current ($I_{\mathrm{SiPM}}$) is measured under constant illumination, and changes in $T_{\mathrm{SiPM}}$ are inferred from alterations in $I_{\mathrm{SiPM}}$ when the bias voltage is changed or the thermal conditions are changed by the air flow from a fan. This paper uses a similar approach for deducing temperature variations from current measurements. However, in our method, which we have introduced in [15], $I_{\mathrm{SiPM}}$ is measured in a cycle at a constant bias voltage while varying the intensity of light. This prevents abrupt variations in the SiPM working condition and parameters (G, $PDE$, $ENF$). The primary assumption underlying our analysis is that $I_{\mathrm{SiPM}}$ under constant illumination is solely dependent on $V_{\mathrm{bias}}-V_{\mathrm{bd}}\left(T\right)$. As part of this study, we crosscheck that both methods, Lucchini and ours, measure a consistent temperature increase in the SiPM, independently if the power increase is induced by a light intensity or a bias voltage increase.

The investigated SiPMs and the setup are described in Section 2. The analysis method and its application to determine the increase in SiPM temperature are explained in Section 4. The main results are given in Section 5, followed by the conclusions in Section 6.

2. SiPMs investigated and experimental setup

Two types of SiPMs were investigated. First, an R&D SiPM from KETEK [16] type MP15V09, with $V_{\mathrm{bd}}=27.60\left(0.02\right)\mathrm{V}$ at 25 °C [17], pixel size of 15 x 15 $\mathsf{\mu }{\mathrm{m}}^2,$ and number of pixels $N_{\mathrm{pix}}=27367$. The active region is circular with a radius $r_{\mathrm{SiPM}}=1.4\mathrm{m}\mathrm{m}$. This SiPM is manufactured on a 700 $\mathsf{\mu }$$\mathrm{m}$ thick silicon wafer and does not have a specially manufactured entrance window. The bare silicon sensor is glued on an alumina (Al₂O₃) substrate, with area 20 x 25 $\mathrm{m}{\mathrm{m}}^2$ and thickness $0.6$ $\mathrm{m}$$\mathrm{m}$. The second sample is produced by Hamamatsu Photonics K.K. (HPK) [18] MPPC S14160-9769, with an active area of 3.0 x 3.0 $\mathrm{m}{\mathrm{m}}^2,$ pixel size 10 x 10 $\mathsf{\mu }{\mathrm{m}}^2,$ number of pixels: 89600 and $V_{\mathrm{bd}}=38.19\left(0.02\right)\mathrm{V}$ at 25 °C. It is delivered as a surface-mount package with a silicon resin and glass-epoxy entrance window and has an overall thickness of 0.8 mm. This sample is tested both soldered on a flexible PCB, and on the same alumina as the KETEK sample to compare the different substrates. The information is summarised in Table 1.

The current of the samples, mounted on a temperature-controlled chuck ($\Delta T\approx$ $0.1$ $\mathrm{K}$), is measured using probe needles connected to a Keithley 6517B voltage source/current meter [19]. The alumina or PCB substrate is fastened to the chuck using a vacuum pump. For good thermal contact, the substrate is placed directly on the surface of the chuck. To emulate a degraded thermal contact of the SiPM, two polyoxymethylene (POM) layers of different thicknesses (1.5 and 3.0 ±0.1 mm) are placed between the substrate and the cold chuck, increasing the thermal resistance. The thermal conductivity of POM $k=0.3\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ is close to that of commercially available PCB materials. The thermal contact between POM and Al2O3/HPK-housing is simply via an air-gap and may not be optimal. Three temperature sensors (PT-100) glued with a thermal foil are used. Two sensors record the temperature on the surface of the substrate, $T_{\mathrm{sensor}1}$ and $T_{\mathrm{sensor}2}$, and a third that of the chuck, $T_{\mathrm{sensor}3}$, according to the sketch of Figure 1.

The illumination is provided with light of a wavelength $\lambda =470\mathrm{n}\mathrm{m}$ from an LED operated in DC mode, and surrounded by a diffuser. The setup is located in a light-tight and electrically shielded box.

3. Method

Two sets of data are recorded. The calibration data set, with the substrate in direct contact with the chuck, $I_{\mathrm{cal}}(V_{\mathrm{bias}},T_{\mathrm{chuck}},I_{\mathrm{LED}})$ is taken at several LED intensities, $I_{\mathrm{LED}}$, with $V_{\mathrm{bias}}$ ranging from below $V_{\mathrm{bd}}$ to about 10 $\mathrm{V}$ overvoltage ($OV$), and $T_{\mathrm{chuck}}$ varied in five steps of $2.5$ °C centred at 25 °C and $-30$ °C respectively. From the calibration data, the sensitivity function described in Section 4 is extracted. The sensitivity function is applied to the second set of data, the measurement cycle, used to determine the increase in the SiPM temperature from its measured current, in conditions with good and degraded thermal contact.

Figure 2 exemplary presents the measurement cycles performed on the KETEK SiPM in three different thermal contact configurations. $I_{\mathrm{SiPM}}$ is recorded at constant $T_{\mathrm{chuck}}$ and $V_{\mathrm{bias}}$, in three time intervals of 320 $\mathrm{s}$ each. This time interval is sufficient for reaching thermal equilibrium. The light intensity is set to zero in the first and third intervals, and the dark current, $I_{\mathrm{dark}}$, is measured. In the second interval, the light intensity is set via the current value $I_{\mathrm{LED}}$, previously tuned to induce 25, 50, 75, and 100 $\mathrm{m}$$\mathrm{W}$ of dissipated power in the SiPMs. These particular values of dissipated powers are chosen for this study to mimic a non-irradiated SiPM the power observed after neutron irradiation of the HPK SiPM to a fluence ${\mathsf{\Phi }}_{\mathrm{eq}}={10}^{13}$ cm⁻² operated at $-30$ °C and 2 V overvoltage. The I-V curves used for this consideration are shown in Figure 3. Compared to a fresh SiPM, the irradiated HPK SiPMs demonstrate an increase in the dark current after irradiation by a factor ${10}^5$ at the excess bias voltage $OV$ = 2 V. The same photo-current is induced on a fresh KETEK SiPM by illumination with LED light adjusted to $I_{\mathrm{LED}}$ = 0.47 mA, and operating the SiPM at $OV$ = 10 V. Other combinations of $I_{\mathrm{LED}}$ and $OV$ would also be possible to induce the same power.

The photo-current is defined as $I_{\mathrm{photo}}\left(I_{\mathrm{LED}}\right)=I_{\mathrm{SiPM}}\left(I_{\mathrm{LED}}\right)-I_{\mathrm{SiPM}}\left(I_{\mathrm{dark}}\right)$.

4. Analysis

From the calibration data, $I_{\mathrm{photo}}^{\mathrm{cal}}(V_{\mathrm{bias}},T_{\mathrm{chuck}},I_{\mathrm{LED}})$, the photo-current sensitivity $S_{\mathrm{photo}}$ is obtained using the formula:

$$S_{\mathrm{photo}}(V_{\mathrm{bias}},T_{\mathrm{chuck}})=\frac{1}{I_{\mathrm{photo}}^{\mathrm{cal}}}·\frac{d{I}_{\mathrm{photo}}^{\mathrm{cal}}}{d{V}_{\mathrm{bias}}}·\frac{d{V}_{\mathrm{bd}}}{d{T}_{\mathrm{chuck}}}\left[\frac{1}{\mathrm{K}}\right]$$

(1)

for different $I_{\mathrm{LED}}$ values. The sensitivity gives the relative change of $I_{\mathrm{photo}}$ for a temperature change of 1 $\mathrm{K}$. In Eq. 1 it is assumed that the sensitivity for a given photon flux $I_{\mathrm{photo}}$ only depends on the excess voltage $OV=V_{\mathrm{bias}}-V_{\mathrm{bd}}\left(T\right)$. The sensitivity curves obtained from the calibration data for various LED currents as a function of $OV$ are shown in Figure 4 for KETEK (left) and for HPK (right). The HPK measurements were taken at temperatures of 25 °C and $-30$ °C. In the range of interest of the measurements, the sensitivity is between 0.004 and $0.01$ K⁻¹. As expected, $I_{\mathrm{photo}}$ increases with $I_{\mathrm{LED}}$ for a constant $T_{\mathrm{chuck}}$, since the current is proportional to the rate of converted photons producing a Geiger discharge ($R_{\gamma }$) and the $PDE$, $I_{\mathrm{photo}}=q_0·G·R_{\gamma }·PDE·ECF$ [13]. But it can be seen that $S_{\mathrm{photo}}$ does not depend on $I_{\mathrm{LED}}$. Effects of heating and occupancy can be ignored when extracting this calibration function. The T-dependence of the breakdown voltage is derived from the calibration data recorded at different $T_{\mathrm{chuck}}$, yielding to the $d{V}_{\mathrm{bd}}/dT$ values presented in Table 1.

Once the sensitivity curve is known, the change in SiPM temperature during a measurement cycle (or during operation in an experiment) is calculated from the relative change in photo-current, divided by the sensitivity:

$$\Delta T_{\mathrm{SiPM}}=\frac{1}{S_{\mathrm{photo}}}·\frac{\Delta I_{\mathrm{photo}}}{I_{\mathrm{photo}}},$$

(2)

where $\Delta I_{\mathrm{photo}}=I_{\mathrm{photo}}\left(t_1\right)-I_{\mathrm{photo}}\left(t\right)$, is defined as the (time-dependent) difference of the photo-current to the first measured value after the LED is switched on. If the time $t_1$ is sufficiently close to the time of the LED switching, it is assumed that the temperature before and after the switch is still the same. This can be used to impose continuity constraints on the measured temperature profile during a scan. In Figure 5 the temperature changes induced on the SiPM after switching on the LED in the second interval of the cycles reported in Figure 2 are calculated using Eq. 2. The first points of the blue curve show that the main change is in the first step, therefore the assumption of no T change for the first point after the switching on the LED is not completely fulfilled. This may induce the largest error in the calibration of the temperature increase. The temperature of SiPM mounted directly on the alumina increases only by half a degree, while the SiPMs isolated via POM experience an increase of 3-4 K, depending on the thickness of the substrate.

The cycle presented in Figure 2 assumes that the SiPM parameters at fixed bias voltage are not instantaneously varied by the increase of light intensity in the second step (B). To evaluate the difference between our assumption and the one applied by Lucchini et al. [14], we performed a second cycle scan, depicted in Figure 6, where the LED intensity is kept fixed and the SiPM bias voltage is changed from a value below to above breakdown, to generate in step B exactly the same power as in the previous cycle.

The the temperature changes induced on the SiPM in step B of both cycles shown in Figure 6, are compared in Figure 7. The values obtained and the temperature gradients are the same for both scans, indicating that the change in SiPM parameters from below to above breakdown do not influence significantly the measurements of self-heating.

In the following section $\Delta T_{\mathrm{SiPM}}$ values for long enough times are quoted for which the current has reached a steady state after the switch.

5. Determination of Self-Heating

The procedure described in Section 3 and the analysis of Section 4 are applied to investigate the two SiPMs under study, described in Table 1. Four LED light intensities are chosen to study the temperature increase of the SiPMs in the relevant power range in the dark expected after irradiation. The value of 50 $\mathrm{m}$$\mathrm{W}$ is marked as a reference in the plots, which corresponds to the power of a HPK SiPM irradiated to a fluence ${\mathsf{\Phi }}_{\mathrm{eq}}$ = 1 × 10¹³ cm⁻² and operated at $OV=$ 2 $\mathrm{V}$ and $T=$ $-30$ °C.

As expected, $\Delta T_{\mathrm{SiPM}}$ is proportional to the power, as demonstrated in Figure 8, for measurements performed at $T_{\mathrm{chuck}}=25$ °C.

The best thermal contact is obtained for the SiPM mounted on the alumina substrate and directly placed on the chuck. In this configuration, the increase in temperature calculated using Eq. 2 is $\Delta T_{\mathrm{SiPM}}=1.5\mathrm{K}$. The $1.5$ $\mathrm{m}$$\mathrm{m}$ thick POM layer degrades the thermal contact of the SiPM on the alumina substrate to the same level as the flexible PCB. For both configurations $\Delta T_{\mathrm{SiPM}}=3.0\mathrm{K}$. This demonstrates the significant influence of the thermal contact on the self-heating of SiPMs, the better the thermal contact the lower the increase on $\Delta T_{\mathrm{SiPM}}$.

Figure 9 compares the results for the two SiPM types investigated: At best thermal contact the minimum temperature increase by self-heating is measured for the KETEK sample, $\Delta T_{\mathrm{SiPM}}=0.2\mathrm{K}$. This value is considerably lower than that obtained for the HPK sample tested in the same condition. This may be attributed to the thermal property of the HPK package, which has a higher thermal resistance than the bare thermal contact compared to the bare KETEK silicon sensor. The same is observed when comparing the temperature increase of HPK on PCB with that of KETEK on alumina plus $1.5$ $\mathrm{m}$$\mathrm{m}$ thick POM layer, which according to the result shown in Figure 8 should lead to the same thermal increase. The increase of $\Delta T_{\mathrm{SiPM}}$ is not scaling linearly with the thickness of POM indicating that maybe the thermal coupling via air gap is not ideal or that a more complex volume effect has to be considered. To confirm this effect, detailed 3D finite element simulations of the experimental setup are ultimately required, including the correct boundary conditions.

Table 2 summarizes the $\Delta T_{\mathrm{SiPM}}$ values at 50 $\mathrm{m}$$\mathrm{W}$ with the corresponding breakdown voltage increase, $\Delta V_{\mathrm{bd}}$, which is proportional to the increase in temperature and is determined using the $d{V}_{\mathrm{bd}}/dT$ reported in Table 1.

Measurements taken at 25 °C and at $-30$ °C with the HPK sample soldered on PCB are compared in Figure 10, and analysed using Eq. 2. The results are reported in Figure 11.

The $\Delta T_{\mathrm{SiPM}}$ values for 50 $\mathrm{m}$$\mathrm{W}$ are summarised in Table 3. The induced temperature increase by self-heating at $-30$ °C is slightly higher than at 25 °C. While the relative change in current $\left(\frac{\Delta I_{\mathrm{photo}}}{I_{\mathrm{photo}}}\right)$ is the same at high and low temperatures, the sensitivity is at $-30$ °C ($S_{\mathrm{photo}}=0.6\%/\mathrm{K}$) is lower than at 25 °C ($S_{\mathrm{photo}}=0.7\%/\mathrm{K}$).

6. Conclusions

A method is developed to determine the self-heating of a SiPM from the measurement of its photo-current. The method is tested as a function of induced power, thermal contact, and two different substrates on two SiPM models with different packages. Self-heating causes an increase in breakdown voltage and a decrease in SiPM photo-current operated at fixed bias voltage. In these measurements, the SiPM is illuminated by a blue LED, and its current transients are measured at constant bias voltage when changing the LED current.

The developed method is used to determine the temperature increase for a SiPM with dissipated power around 50 $\mathrm{m}$$\mathrm{W}$, which is the measured power of an HPK SiPM (MPPC S14160-976X) irradiated to a fluence ${\mathsf{\Phi }}_{\mathrm{eq}}$ = 1 × 10¹³ cm⁻² and operated at 2 $\mathrm{V}$ above breakdown voltage at $-30$ °C, taken as reference. For different thermal resistances between the HPK SiPM and the chuck, the following results are obtained: for ideal thermal contact (SiPM on Al₂O₃ substrate) an increase of between $0.2$ $\mathrm{K}$ and $1.5$ $\mathrm{K}$ is observed depending on the SiPM package; for realistic thermal contact (SiPM mounted on a PCB), the temperature is larger and ranges between 2 - 3 $\mathrm{K}$, corresponding to an increase in $V_{\mathrm{bd}}$ of 50 to 100 $\mathrm{m}$$\mathrm{V}$.

These results demonstrate the importance of a proper investigation of the thermal properties of SiPM package, substrate, and thermal connection to a cooling system when planning to operate at high (dark or photo-) currents. Also, the method proposed in this paper can be used to apply adjustments on the operation voltage depending on the value of the SiPM current during operation.