Introduction

Detector technology with scintillation has been utilized in experiments for a long time, such as the ZnS in the Rutherford experiment. This technology is being rapidly developed, especially considering the various inorganic scintillators, such as BGO, PWO, and LYSO, among others, as well as the new photon detector based on silicon [1, 2]. Detecting technologies with scintillation and photomultipliers are comprehensively used in experiments for particle and nuclear physics. The Belle II experiment [3, 4], which is a super B factory and started its physics run in 2019, uses various photon detection technologies such as the time-of-propagation counter and the Aerogel ring-imaging Cherenkov detector for charged particle identification, the electromagnetic calorimeter for high energy photon detection, and the $K_{\text{L}}^0$ and muon detector (KLM) for identifications of $K_{\text{L}}^0$ and muon [5]. The KLM detector modules in the endcaps and the two inner-most layers of the barrel are based on a combination of an extruded scintillator and a wavelength-shifting fiber and silicon photomultiplier (SiPM), in contrast to the resistive plate chambers (RPCs) used in the Belle KLM. The new technology has demonstrated a good performance; however, the remaining 13 layers of the barrel KLM are still using the legacy RPCs from the Belle. As indicated in the Snowmass Whitepaper [6], Belle II is considering upgrading the KLM with all scintillator modules, which contain approximately 38,000 readout channels. By utilizing the advantage of good timing from the scintillator and SiPM, it is possible to measure the time-of-flight of neutral hadrons, such as $K_{\text{L}}^0$ and the neutron. This is critical for improving the $K_{\text{L}}^0$ identification and furthermore, for measuring the momentum of $K_{\text{L}}^0$ or the neutron. Meanwhile, the scheme of using the SiPM and plastic scintillation system to build a muon detector or a hadron calorimeter is also expected to be used in the proposed Circular Electron Positron Collider (CEPC), which is a Higgs factory [7, 8].

The SiPM is a novel photodetector composed of parallel avalanche diodes that operate in the Geiger mode. It has several advantages, such as its small size, low operation voltage (V_op), excellent time resolution, and resistance to magnetic field interference. The SiPM is commonly used for scientific research, medical diagnosis, and biochemical detection [9-12]. The rise-time (${\tau }_{\text{rise}}$) of a signal from the SiPM is only within hundreds of pico-seconds; therefore, photon detection with SiPM can achieve a very good timing performance with an excellent front-end readout. A signal from the SiPM is always small and needs to be amplified at the front-end, and the timing performance is mainly constrained by the bandwidth and the noise level of the amplifier; this front-end readout is called a preamplifier. Furthermore, as the photosensitive area of the SiPM increases, its dark counting rate significantly increases and becomes an issue for the design of the preamplifier. In practice, detectors in particle and nuclear physics experiments usually need to place hundreds or thousands of channels of front-end readout electronics in a small space. Thus, the preamplifier must be low-cost and compact for multi-channel integration. Certain commercial preamplifiers for SiPM are available [13-15]; however, they typically have large volumes, complex circuits, and it is difficult to match the requirements of a high time resolution and high integration in a large-scale detector.

Considering the R&D for the KLM upgrade in Belle II and the muon detector in CEPC, we designed a compact preamplifier that operates for various SiPMs. This preamplifier has the advantages of a fast rise time, low noise level, low cost, and simple circuit form. In this study, we introduce the design and performance of this preamplifier, followed by the time resolution obtained from the combinations of the preamplifier and different types of SiPMs.

Design of the preamplifier

Figure 1(a) presents the circuit diagram of a SiPM equivalent model [16-18], where C_d, R_d, and R_q indicate the capacitance of the reverse-biased diode, resistance of the diode, and resistance of the quenching resistor; C_q is the parasitic capacitance of R_q, and R_s is the load resistance of SiPM. When the SiPM operating at V_op, $Q=\left(C_{\text{d}}+C_{\text{q}}\right)\left(V_{\text{op}}-V_{\text{br}}\right)$ is related to its gain, V_br is its breakdown voltage. For a SiPM containing N_pixel pixels, the total capacitance is $C_{\text{tot}}=N_{\text{pixel}}\cdot \left(C_{\text{d}}+C_{\text{q}}\right)$. Figure 1(b) demonstrates the LTspice simulation [19] with parameters of S13360-6025PE [20] for a typical SiPM signal, which has a fast rise time ${\tau }_{\text{rise}}=R_{\text{d}}\left(C_{\text{d}}+C_{\text{q}}\right)$ and slow fall time ${\tau }_{\text{fall}}$ that can be described as follows: $i_{\text{d}}\left(t\right)=\frac{Q{R}_{\text{s}}}{C_{\text{q}}+C_{\text{d}}}\cdot \left(\frac{C_{\text{q}}}{{\tau }_{\text{fall}}^{\text{fast}}}{e}^{\frac{-t}{{\tau }_{\text{fall}}^{\text{fast}}}}-\frac{C_{\text{d}}}{{\tau }_{\text{fall}}^{\text{slow}}}{e}^{\frac{-t}{{\tau }_{\text{fall}}^{\text{slow}}}}\right)\mathrm{,}$ (1) where ${\tau }_{\text{fall}}^{\text{fast}}=R_{\text{s}}{C}_{\text{tot}}$ and ${\tau }_{\text{fall}}^{\text{slow}}=R_{\text{q}}\left(C_{\text{d}}+C_{\text{q}}\right)$ are the fast and slow components of ${\tau }_{\text{fall}}$, respectively. When multiple SiPMs are combined in parallel for a large total photosensitive area, both ${\tau }_{\text{rise}}$ and ${\tau }_{\text{fall}}$ increase [21]. A large ${\tau }_{\text{rise}}$ is a disadvantage for a good time resolution, and a large ${\tau }_{\text{fall}}$ usually causes pile-up in fetching a signal and increases the dead time of a detector. This is problematic for an ultra-high luminosity experiment such as Belle II, which was designed for a luminosity of 0.8×10³⁶ cm^-2s^-1. To reduce the long ${\tau }_{\text{fall}}$, we can use the pole zero cancellation (PZC) in the preamplifier; the ${\tau }_{\text{rise}}$ is also reduced by PZC.

Fig. 1Full-screen View

Circuit diagram of the SiPM equivalent model [16] and output signal from the SiPM. The plot (a) demonstrates the equivalent model whereas the plot (b) presents the LTspice simulation with parameters of S13360-6025PE [20] for a typical SiPM signal, which consists of a fast rising edge and falling edge containing a fast component and a slow component.

Considering the requirements of a large bandwidth and low noise level, the operational amplifier chip LMH6629 from TI Company [22] was chosen to design the preamplifier. This chip has a voltage slew rate of 1600 V/μs, an input voltage noise of $0.69\text{ nV}/\sqrt{\text{Hz}}$, and a -3 dB bandwidth of 900 MHz at a stable gain of +10 V/V. LMH6629 is sufficient for a significantly fast ${\tau }_{\text{rise}}$ of the SiPM signal.

Figure 2(a) presents the principle diagram of the preamplifier circuit. It adopts the form of negative feedback to improve the ${\tau }_{\text{rise}}$ of the output signal and the stability of the gain. For applications with multiple channels in the experiment, a power supply board for 8-channel parallel preamplifiers was designed, as shown in Fig. 2(b). The preamplifier units are directly inserted into the power supply board and connected to the SiPM readout boards through RF cables. This design can match different sizes of readout boards and various types of SiPMs, which increases the versatility of the preamplifier.

Fig. 2Full-screen View

(Color online) The compact preamplifier designed for a high time resolution. Plot (a) presents the schematic diagram of the preamplifier, and plot (b) presents an image of the bunch of 8-channel preamplifiers with a common power supply board. The ‘SIG IN’ connector is for the input signal from SiPM, and the ‘SIG OUT’ connector is for the output signal being amplified. The ‘HV’ pins are for the V_op for the SiPM operation. The inserted image in (b) presents the regulators at the bottom of the power supply board.

2.2

PZC to reduce the pile-up

According to Eq. (1), the fast component of the falling edge ${\tau }_{\text{fall}}^{\text{fast}}$ is mainly determined by the load resistance R_s. For certain SiPMs that have a high gain are large size, such as the Hamamatsu MPPC S13360-6025PE [24], the terminal capacitance C_tot is 1280 pF. If R_s = 50 Ω, the ${\tau }_{\text{fall}}^{\text{fast}}$ is approximately 64 ns and the total ${\tau }_{\text{fall}}$ is significantly longer, which may lead to the pile-up in a detector using SiPM.

Adding a PZC in the circuit of a preamplifier is a sufficient method for reducing the ${\tau }_{\text{fall}}$ and avoiding the signal pile-up by attenuating the low-frequency components in the output signal. The PZC also reduces the ${\tau }_{\text{rise}}$, which is useful for increasing the time resolution of the preamplifier according to Eq. (2). Figure 3(a) presents the implementation of the PZC in the preamplifier. The transfer function of the PZC in the frequency domain can be described as follows: $V_0\left(s\right)=\frac{s+{\tau }_1^{-1}}{\left(s+{\tau }_{\text{f}}^{-1}\right)\left(s+{\tau }_2^{-1}\right)}\cdot V_{\text{max}}\mathrm{,}$ (4) where V_max is the maximum amplitude of the output signal from the preamplifier, τ_f = R_qC_d, τ₁ = R₁C₁, and τ₂ = R₁R₂C₁/(R₁+R₂). The signal reaches zero cancellation when τ₁ =τ_f, thus the attenuation time of the output signal changes to τ₂ (τ₂ < τ₁).

Fig. 3Full-screen View

PZC implementation in the preamplifier and its effects on the signal shape and pile-up. Plot (a) presents the circuit of a one-stage or two-stage amplifier with the PZC, and plot (b) presents how the ${\tau }_{\text{rise}}$ and ${\tau }_{\text{fall}}$ of the signals improved by the PZC in laboratory testing. Plot (c) presents the SiPM signals from a preamplifier with or without the PZC and are displayed on an oscilloscope in testing with photons from a pulsed laser [26], which operates at a frequency between 0.8 MHz–20 MHz.

The LTspice simulation demonstrates that the output impedance after the PZC network is no longer a constant 50 Ω and the signal amplitude is reduced. To compensate for the gain lost and ensure an output impedance of 50 Ω, we can use a two-stage amplifier after the PZC, as shown in Fig. 3(a). To demonstrate the effect of PZC on the signal shape, we used DT5810B [25] to simulate SiPM signals with ${\tau }_{\text{rise}}\approx 3\text{ns}$ and ${\tau }_{\text{fall}}\approx 50\text{ns}$ and then input them to the designed preamplifiers. We used the Tektronix MDO3024 oscilloscope to fetch the waveforms of the input and output signals of the preamplifier, as shown in Fig. 3(b). The output signals without the PZC have nearly the same ${\tau }_{\text{rise}}$ and ${\tau }_{\text{fall}}$ as those of the input signals. The signals after the PZC without the two-stage amplifier are ${\tau }_{\text{rise}}\approx 1.2\text{ns}$ and ${\tau }_{\text{fall}}\approx 20\text{ns}$, which are significantly improved; however, their amplitudes are reduced. Compared to these signals, the signals from the preamplifier with the two-stage amplifier after the PZC have nearly the same ${\tau }_{\text{rise}}$ and ${\tau }_{\text{fall}}$, and their amplitudes are significantly larger. The improvement of ${\tau }_{\text{rise}}$ is significantly useful for a good time resolution, and a short ${\tau }_{\text{fall}}$ is important for avoiding the pile-up in a detector operation.

Another test was conducted to study the effect of PZC on the pile-up. We used the ps-level laser MDL-PS-450 [26] as the light source, and tuned its frequency from 0.8 MHz to the maximum 20 MHz. Photons from the laser are detected by two SiPMs, which are connected in parallel to the preamplifiers with or without the PZC. Figure 3(c) presents the signals displayed on the oscilloscope. The ${\tau }_{\text{fall}}$ of signal from the preamplifier without the PZC is approximately 200 ns, and a pile-up appears when the laser operates at a frequency of approximately 2 MHz. When the PZC is implemented in the preamplifier, the ${\tau }_{\text{fall}}$ reduces to approximately 5 ns, and there is no pile-up even when the laser is operating at a frequency of 20 MHz. This testing indicates that the PZC significantly reduces the pile-up in a high signal rate environment.

Performance of the preamplifier

To apply this preamplifier in experiments, such as the possible upgraded KLM in Belle II, we studied the performance characteristics of the preamplifier, including the stability of the gain, dynamic of the output signal, noise level, and measurement of a single photoelectron signal. Based on the performance, we then combined the preamplifier with the SiPM and studied their time resolutions.

3.3

Measurement of a single photoelectron

A typical measurement with the SiPM is that of a single photoelectron peak spectrum, which can be used to determine the performance of the SiPM. Based on the gain and resolution of a single photoelectron obtained from the spectrum, we can estimate the number of photoelectrons (or the number of fired SiPM pixels) in a measurement according to the pulse height of the signal. We measured the signal of a single photoelectron by combining an SiPM and the preamplifier for the basis of further measurements, such as the time resolution versus the number of photoelectrons.

First, the measurements were performed with S13360-1325CS, S13360-1350CS, and S13360-1375CS, which have a common photosensitive area of 1.3 mm × 1.3 mm and different pixel sizes of 25 um, 50 um, and 75 um [24], respectively, as listed in Table 1. Figure 4(a) presents the pulse shapes of the single photoelectrons, for which τ_rise < 1 ns and the amplitudes are higher than 10 mV. Occasionally, the photosensitive area of the S13360-13* series was too small for photon collection in a detector. Our R&D for the KLM upgrade concludes the choice of a large SiPM and the combination of multiple SiPMs for a good time resolution, such as that of the 13360-6025PE from Hamamatsu [20] with a photosensitive area of 6.0 mm × 6.0 mm. Figure 4(b) presents an example of a single photoelectron signal from 13360-6025PE and the average of many signals, which are fetched by an oscilloscope. We obtained ${\tau }_{\text{rise}}\sim 3\text{ ns}$, which is larger than that obtained in previous tests for the small SiPMs owing to the large capacitance of 13360-6025PE. For a small gain amplifier, the signal was able to obtain ${\tau }_{\text{rise}}\sim 2\text{ns}$ in our tests. All the tests were conducted under a weak light. We also established an SiPM circuit model based on LTspice for 13360-6025PE and simulated a single photoelectron signal with a preamplifier or an ideal preamplifier. The results of the simulations and those of the measured pulses were in very good agreement, as indicated in Fig. 4(b).

Fig. 4Full-screen View

(Color online) Pulse shapes of single photoelectron signals from SiPMs with (a) a small photosensitive area of 1.3 mm × 1.3 mm or (b) large area of 6.0 mm × 6.0 mm. The tests were conducted under a weak light. Plot (a) demonstrates τ_rise < 1 ns and the different gains of the small SiPMs with different pixel sizes. In (b), the red curve indicates a typical single photoelectron signal and the black curve indicates the average of many signals fetched in the oscilloscope, while the blue (green) curve indicates the simulation of a single photoelectron signal from the LMH6629 (ideal) amplifier.

Time resolution achieved from the combination of the preamplifier and SiPM

Time resolution is one of the most important characteristic properties of certain detectors. For a scintillation detector using SiPM as the photosensor, the time resolution is determined by the scintillator material, SiPM, and the front-end readout with the preamplifier.

To determine the time resolution of the preamplifier, DT5810B was used to generate pulse signals with different amplitudes, which were then input into two parallel preamplifiers. The Tektronix MSO58 oscilloscope was used to digitize and save the waveforms of the output signals, and to determine the arrival time of an output signal via the constant-ratio timing (CFD) method in an offline data analysis of the waveform. We obtained a distribution of the time difference between the signals from the two parallel preamplifiers. By fitting the distribution with a Gaussian function, we obtained the standard deviation σ and considered $\sigma /\sqrt{2}$ as the time resolution of one preamplifier. The time resolution versus the amplitude of the input signal is shown in Fig. 5. With ${\tau }_{\text{rise}}=2\text{ns}$ being set for DT5810B, the time resolution of the preamplifier was approximately 20 ps for the input signals with amplitudes larger than 20 mV, or 30-50 ps for the small input signals with amplitudes of 5–10 mV. Figure 5(a) demonstrates that the time resolution worsens when ${\tau }_{\text{rise}}$ is increased. As indicated in Sect. 2.2, PZC can reduce the ${\tau }_{\text{rise}}$, which is significantly useful for increasing the time resolution. We set ${\tau }_{\text{rise}}=7.5\text{ns}$ and compared the preamplifiers with and without The PZC. Figure 5(b) presents their time resolutions versus the amplitude of the input signal. Although the amplitude of the output signal was reduced owing to the PZC, ${\tau }_{\text{rise}}$ improved and a better time resolution was obtained. For example, when testing with input signals having an amplitude of 20 mV, the time resolution increased from 50 ps to 25 ps with the implementation of the PZC.

Fig. 5Full-screen View

The time resolution versus the amplitude of the input signals (a) at different ${\tau }_{\text{rise}}$ values of the input signals, or (b) with and without the PZC, for a comparison. The PZC is not applied for the measurements shown in (a), and the value of ${\tau }_{\text{rise}}$ of the input signals in (b) is 7.5 ns.

We combined our preamplifier and the SiPM to determine the time resolution in photon detection. We used a ps level pulsed laser MDL-PS-450 [26] again as the light source, and the setup for testing and the time resolutions obtained are shown in Fig. 6. We used two SiPMs to detect the photons from the laser; these two SiPMs were connected to two preamplifiers, as shown in Fig. 6(a). We measured the amplitude and arrival time of the signals from the two detecting channels, and then determined the time resolution according to the distribution of their time difference. Typically, the time resolution highly depends on the number of detected photons. According to the amplitude of the measured signal and that of a single photoelectron signal described in Sect. 3.3, we can estimate the number of photons detected in the SiPM (the number of the fired pixels). We studied the time resolution with small SiPMs, such as the EQR10-11-1010 from NDL (Beijing) and the S13360-1350 from Hamamatsu, and found that they have nearly the same performance, as shown in Fig. 6(b). When approximately five photons were detected, their time resolutions were between 40-50 ps. As the number of detected photons increased to >40, the time resolution was approximately 25 ps. We also studied the time resolution with large SiPMs, such as the EQR15-11-6060 from NDL and the S14160-6050 from Hamamatsu [29], both of which have a photosensitive area of 6.0 mm × 6.0 mm. When the number of photons was larger than 60, the performances of the two SiPMs were similar, and their time resolutions were better than 25 ps, as shown in Fig. 6(b). When a small number of photons were detected, S14160-6050 demonstrated a better performance than EQR15-11-6060, which is owing to its advantages of a significantly lower dark count rate and higher gain.

Fig. 6Full-screen View

Measurement of the time resolution of the preamplifier and the SiPM in photon detection. The top presents the diagram of the setup for the measurement, and (a) the bottom presents the image of the setup containing the laser, including the SiPMs and the preamplifiers in a dark box. Plot (b) at the bottom presents the measured time resolution versus the number of detected photons using various SiPMs.

Comparison with some commercial preamplifiers

We compared this preamplifier with other commercial preamplifiers for the SiPM, such as the Hamamatsu C12332-02 [13], NDL AMP-20-2 [14], and Cremat CR-Z-SiPM [15].

1. The commercial preamplifiers are one- or two-channel devices with a size of approximately 5 cm, 10 cm, or 15 cm, whereas the array of the eight preamplifiers shown in Fig. 2(b) only has a length of approximately 10 cm. According to the schematic diagram shown in Fig. 2(a), we can improve the design for significantly higher integration in the implementation of hundreds or thousands of SiPM channels in a large detector.

2. According to the data manuals, C12332-02 has a bandwidth of 200 MHz at a gain of -20 V/ <sidn>V</sidn>, and AMP-20-2 has a bandwidth of 350 MHz at a gain of -10 V/ <sidn>V</sidn>. The testing demonstrates that our preamplifier has a bandwidth of approximately 426 MHz. The CR-Z-SiPM is a charge-sensitive preamplifier, which is not suitable for the amplification of a fast signal.

3. Our preamplifier has an advantage in the noise level. The testing demonstrates that its baseline noise level is approximately 0.6 mV, which is nearly 80% of that of AMP-20-2.

4. Figure 5 presents significantly good time resolutions of our preamplifier.

5. The C12332-02 of Hamamatsu uses OPA846 as the core amplifier. The LMH6629 we used for the preamplifier demonstrates a better performance considering the bandwidth, slew rate, and noise level.

6. The cost of our preamplifier per channel is approximately two orders lower than those of commercial products.

Note, the design of this preamplifer is to enable the implementation of tens of thousands of SiPM channels in a sub-detector of the possible Belle II upgrade project or the CEPC experiment in the future; these detector channels should demonstrate a very good performance. Therefore, we focus on a simple design, high integration, high time resolution, large bandwidth, large dynamic range, low noise level, and low cost.

Summary

Considering the R&D for the upgrade of the KLM in Belle II and the muon detector of CEPC, we designed a compact high-speed and low-noise preamplifier for the SiPM. The preamplifier has a bandwidth of 426 MHz, baseline noise level of 0.6 mV, total noise levels of less than 1 mV for the combination with different SiPMs, a large dynamic range for an input signal of up to 170 mV, and a very fast ${\tau }_{\text{rise}}$ for good time resolution. The PZC was found to be significantly useful for improving both the ${\tau }_{\text{rise}}$ and ${\tau }_{\text{fall}}$ of a SiPM signal, which can significantly improve the time resolution and reduce the pile-up when using a large SiPM or an array of SiPMs. A time resolution of better than 20 ps can be achieved from the preamplifier. The combinations of the preamplifier and different SiPMs demonstrated time resolutions of better than 50 ps; when the number of photons is large, a time resolution of 25 ps can be achieved. The good performance of the preamplifier is helpful for upgrading the KLM in Belle II for a new function of measuring the hit time of a neutral hadron, such as $K_{\text{L}}^0$ or a neutron, according to the hadronic cluster in the detector.