What is an SiPM and how does it work?

A silicon photomultiplier (SiPM) is a solid-state photodetector that in response to absorption of a photon can produce a current pulse several tens nanoseconds long containing 10⁵ to 106 electrons. Therefore, a SiPM has a gain. This gain is comparable to that of a photomultiplier tube (PMT).

A SiPM is a pixelated device where each pixel, or a microcell, is a series combination of an avalanche photodiode (APD) and a quenching resistor (RQ). All of the microcells are connected in parallel; thus, a SiPM has two prongs: an anode and a cathode. The three panels in the figure below show, from left to right, a cross section of three microcells in a possible architecture, top view — the side of impinging light — of the device, and an equivalent electrical circuit.

In practical SiPMs, the microcells of identical size are arranged in a rectangular pattern. Depending on the device, the size of a microcell varies from 10 μm to 100 μm and the number of microcells per device ranges from several hundreds to several tens of thousands. SiPMs have active areas ranging from 1 mm² to 6 mm² and spectral sensitivities from UV to IR, peaking in the visible (400 nm - 500 nm).

A SiPM is externally biased so that the voltage on each APD is above its breakdown voltage. Thus each APD operates in Geiger mode. The difference between the biasing voltage and the breakdown voltage is known as overvoltage — the main adjustable parameter controlling operation of the device. If a SiPM absorbs a photon, the resulting charge carrier (an electron or hole depending on the structure) can trigger an avalanche in the gain region (shown as the gray oval in the figure) within the p⁺ - n⁺ structure. The avalanche can produce 105 - 10⁶ carriers; this constitutes the gain. The role of the quenching resistor is to restore the APD back to the Geiger mode. The gain of a SiPM depends linearly on the overvoltage and the value of junction capacitance. Even though a SiPM is a pixelated device, it is not an image sensor. It does not store charge like a CCD does. It is an analog device producing a time-varying output signal that is measured in real time.

There are several key parameters characterizing a SiPM. These are breakdown voltage, gain versus overvoltage relation, photon detection efficiency, crosstalk probability, afterpulsing probability, and dark count rate.

A SiPM most resembles a PMT in its operation and characteristics. Compared to a PMT, a SiPM requires a lower operating voltage; has immunity to magnetic fields; is sturdier and more rugged; and is smaller in size. For these and other reasons, the SiPM has begun to replace PMTs in low-light applications such as positron emission tomography (PET), light detection and ranging (LIDAR), or radiation detection in high-energy physics.

A silicon photomultiplier (SiPM), though pixelated, is a photodetector that produces an analog output signal in real time. The output is a time sequence of waveforms (or current pulses), which have a discrete distribution of amplitudes: A, 2A, 3A, etc. The histogram of the amplitudes depends on the intensity and time-characteristics of the incident light. This note is a closer look into how a single microcell of a SiPM generates a waveform in response to light.

All of the microcells in Figure 2 are in parallel. A microcell is a series combination of an avalanche photodiode (APD) and a quenching resistor R_Q. The circuit modeling the APD is a parallel combination of a capacitor C_J (representing the junction capacitance) with a series combination of a switch S, voltage source V_BD (equal to the breakdown voltage), and a resistor R_S (representing the resistance of the entire APD during a discharge).

In the absence of light and ignoring dark counts, S is open and the voltage on C_J is V_BIAS (V_BIAS > V_BD) — the microcell is in a light-sensitive state and the APD is in Geiger mode. When the microcell absorbs a photon, an electron-hole pair forms; one of the charge carriers drifts to the avalanche region, where it can initiate an avalanche. At the instant the avalanche begins, S closes causing C_J to be discharging through R_S (R_S ≪ R_Q) with the time constant R_SC_J. The voltage on C_J decreases, lowering the probability of impact ionization. For optimal R_Q, the probability eventually becomes so small that the avalanche quenches. At this moment, S opens and V_BIAS recharges C_J with the time constant R_QC_J.

An avalanche photodiode in a SiPM operates in Geiger mode. If a charge carrier triggers a discharge in a microcell, the consequence is a current pulse with the total amount of charge Q flowing through the terminals of the SiPM. The gain μ is defined as a ratio of Q and the fundamental charge e = 1.6 x 10^‐19 C. Typical values of μ are in the range of 10⁵ ‐ 10⁷. This note is a closer look at the gain.

Figure 4 shows a simplified electrical equivalent circuit of a microcell that is externally biased with V_BIAS. In the absence of light and dark counts, the microcell is in Geiger mode: the switch S is open, the voltage on the junction capacitance C_J is V_BIAS, and no current flows through the quenching resistor R_Q or the series resistance R_S. At the instant a charge carrier triggers a discharge (avalanche), the switch S closes and C_J begins to discharge through R_S (shown in the figure with the red swirl) causing a voltage drop on R_Q and, thus, a current through the terminals of the SiPM.

Learn more about how temperature affects SiPM performance.

Photon detection efficiency (ξ) is a probability that a silicon photomultiplier (SiPM) produces an output signal in response to an incident photon. It is a function of overvoltage ΔV and wavelength λ of the incident light, and can be expressed as a product ξ(ΔV,λ) = ƒ · η · P_G. In the equation, ƒ is a geometrical fill factor, η quantum efficiency, and P_G probability of Geiger discharge. Photon detection efficiency is a key characteristic of a SiPM; below is its more detailed discussion.

A SiPM is a pixelated device. In a given SiPM, all of the pixels, or microcells, are square, of the same size, and arranged in a rectangular (tiled) pattern. The total area occupied by the microcells is known as an active area. Depending on the design of a SiPM, the active areas range from 1 x 1 mm² to 6 x 6 mm². Because certain regions of a microcell have no photosensitivity, only some fraction of the active area is sensitive to light. This fraction is known as the geometrical fill factor. The values of ƒ range from ∼30% to ∼80%, with the larger value for the larger size of a microcell.

This parameter is the probability that an incident photon produces a charge carrier (electron or hole) capable of triggering Geiger discharge in the avalanche section of the depletion region. The layered structure of a SiPM can be optimized through the Beers-Lambert law so that the absorption of light occurs in the depletion layer for the desired range of wavelengths. An electric field in the depletion region separates the photo-generated electron-hole pair and injects one of the charge carriers into the avalanche region. Outside of the depletion region, the electric field is weak and the photo-generated electron-hole pair is likely to recombine. The above discussion implies that η is a function of wavelength.

Once in the avalanche region, the injected charge carrier gains kinetic energy from the electric field and if the kinetic energy exceeds the ionization threshold, may be able to impact-ionize silicon atoms, thus triggering an avalanche. The likelihood of this scenario depends on three factors: 1) the strength of the electric field, which is controlled by ΔV; 2) the width of the avalanche region, which also depends on ΔV and 3) collisional cross section of charge carriers with phonons and the specific history of these interactions. If ΔV < 0, the likelihood of Geiger discharge is exceedingly small. As ΔV increases above 0, the kinetic energy of a charge carrier can be above the ionization threshold energy and, moreover, the width of the avalanche region widens, making the likelihood increasingly higher. Inelastic scattering of charge carriers with phonons increases with ΔV, which limits steeply the likelihood of Geiger discharge rising with ΔV. The figures are samples of plots showing how ξ depends on ΔV and λ.

The construction of a silicon photomultiplier (SiPM) consists of microcells (pixels) connected in parallel. Each microcell is a series combination of an avalanche photodiode (APD) and a quenching resistor. In a normal application, an external voltage source V_BIAS biases the SiPM so that each APD operates in Geiger mode: the voltage on the APD, equal to V_BIAS, is larger than its breakdown voltage, V_BD. The difference V_BIAS − V_BD is known as overvoltage ΔV, which is one of the most important parameters affecting the operation of a SiPM. Thus, knowing the value of V_BD is crucial because it determines the required value of V_BIAS for the desired ΔV. V_BD is the key characteristic of a SiPM.

Several techniques of measuring V_BD exist. This note describes one that relies on the reverse-bias I-V characteristic. Figure 8 shows the experimental setup. The SiPM is in darkness, inside of a temperature-controlled "black box." It is reverse-biased with a voltage source V_S and the picoammeter A measures the current.

Figure 9 shows a possible I-V characteristic around V_BD.¹ For V_S << V_BD (not shown), the (dark) current I monotonically increases with V_S. The dark current has two contributions: 1) the bulk current due to thermally generated charge carriers, primarily in the depletion region, and 2) the surface current due to defects at the Si-SiO₂ interface. Both contributions increase with V_S. As V_S approaches V_BD, the carriers generated in the bulk begin to have enough energy to impact ionize Si atoms in the avalanche section of the depletion region — an APD has a gain larger than 1. The current now increases more rapidly with each voltage step, reaching the highest rate of increase when V_S = V_BD. For V_S > V_BD, the APDs operate in Geiger mode, with the gain linearly proportional to ΔV. In addition, crosstalk and afterpulsing contribute to the net current. The current increases with the voltage but at the smaller rate than when V_S was approaching V_BD. However, as V_S increases further, another region develops on the I-V characteristic where the current sharply increases with V_S. Here, the density of charge carriers is so high that the quenching resistors cannot restore the APDs back to Geiger mode and the SiPM becomes an Ohmic device. Plotting d(log I)/dV_S versus V_S reveals the voltages at which the maximum rate of the current increase with voltage occurs; these voltages correspond to the peaks on this plot.

Figure 10 shows such a plot for the I-V characteristics listed in this scenario. The first peak (at the lower voltage) exists at V_BD. This is how V_BD can be measured. The precision of the measurement depends on the voltage step used while performing the sweep. A smaller step yields more accurate determination of V_BD. In practice, one would first determine the approximate value of V_BD with coarse voltage steps. A finer sweep around V_BD would follow. Repeating the finer sweeps and averaging the results would further improve the accuracy of the measured V_BD.

Analogously to a photomultiplier tube, a SiPM can operate in two distinct modes: continuous wave and photon counting. In the former, the output pulses are neither detected nor counted individually; instead, an analog output current is measured. In the latter, the individual pulses are either counted (digital photon counting) or integrated to yield the charge released in Geiger discharge (analog photon counting). The choice of the detection technique depends, among other factors, on the frequency and duration of the output pulses. If the pulses are crowded and overlapping, the continuous wave mode is appropriate. If the pulses are distinguishable, then photon counting — analog or digital — is preferable.

The excess noise figure F must be known for the above equation for S/N to be useful. The theoretical understanding of F is still lacking because numerous factors may contribute to F in a complex way. It is likely that F is a function of overvoltage, input light level, crosstalk probability, afterpulsing probability, microcell-to-microcell gain variations, and stochastic nature of the gain mechanism in a single microcell.

Optical crosstalk occurs when a primary discharge (avalanche) in a microcell triggers secondary discharges in one or more adjacent microcells. The secondary discharge may be nearly simultaneous with the primary (direct or prompt crosstalk) or delayed by several 10's of ns (delayed crosstalk). Optical crosstalk is an example of a correlated noise: it can be present only if a primary discharge is present. The primary discharge can be due to 1) absorption of a photon, 2) thermal generation of a charge carrier in the multiplication region, 3) injection of a charge carrier, thermally generated outside of the avalanche region, into the avalanche region, or 4) crosstalk-induced secondary discharge becoming the primary discharge for subsequent crosstalk events. If not corrected for, crosstalk makes the output signal higher than that implied by the amount of the incident light.

The figure below depicts the mechanism for the prompt (P-CT), delayed (D-CT), and no (No-CT) crosstalk. The primary avalanche in the middle pixel creates three representative photons. One of them moves directly to the avalanche region of the microcell on the right and triggers a simultaneous secondary avalanche there. This is a direct or prompt crosstalk (P-CT). The other photon creates a charge carrier in the vicinity of the avalanche region of the microcell on the left. The charge carrier diffuses to the avalanche region, triggering a secondary avalanche that is delayed with respect to the primary. This is a delayed crosstalk (D-CT). The third photon leaves the SiPM; no crosstalk occurs (No-CT). The majority of photons produced by the primary discharge does not produce crosstalk.

The probability of optical crosstalk depends on several factors: 1) the size of a microcell, 2) the layered architecture of a SiPM, and 3) the difference between the bias voltage and the breakdown voltage, or the overvoltage. For a given SiPM, the first two factors are fixed; therefore, the overvoltage is the parameter that primarily controls the probability. The probability increases with increasing overvoltage.

1. If a SiPM is used to measure the incident photon flux, whether it is by photon counting or continuous wave operation, crosstalk causes an appearance of a higher incident flux.
2. Crosstalk is the main contributor to the excess noise figure.
3. Crosstalk effectively limits the practical setting for the gain.

A Geiger discharge in a microcell of a SiPM emits isotropically about a few tens of photons that have enough energy to create an electron-hole pair. Most of these photons either escape the SiPM or create pairs far from the avalanche region. However, there is a finite probability that a photon creates a pair in, or close to, an avalanche region of a nearby microcell. One of the charge carriers from the pair may trigger a secondary avalanche — this avalanche is known as crosstalk. It is also possible that not only one but two, or more, photons emitted by the primary discharge trigger secondary discharges. The probability of crosstalk for a given SiPM is a function of overvoltage ΔV. This note describes a method of measuring crosstalk probability P_CT.

In the absence of crosstalk, the output waveform resembles the one labeled 1 p.e. in the figure above. If the primary avalanche is accompanied by one secondary crosstalk discharge, the resulting waveform, labeled 2 p.e. in the figure, is a superposition of two 1 p.e. waveforms. If it is accompanied by two, a 3 p.e. waveform results, and so on. The figure is an oscilloscope trace with the display set to persistence mode. The SiPM is in darkness; the 1 p.e. waveforms are due to dark counts. The color gradient, from warmer (red) to cooler (blue), is proportional to the "density" of waveforms, that is, the frequency of occurrence. The most common events are 1 p.e., followed by 2 p.e., 3 p.e., etc. All of the waveforms that are different from 1 p.e. are due to crosstalk.

The primary waveforms (1 p.e.) are due to dark counts; whereas, 2 p.e., 3 p.e., etc. are due to crosstalk. Let N_1p.e., N_2p.e., N_3p.e. be the number of 1 p.e., 2 p.e., 3 p.e., etc. waveforms counted within some observation time τ. Therefore, the dark count rate is (N_1p.e. + N_2p.e. + N_3p.e. +... )/τ, whereas the probability of crosstalk is P_CT = (N_2p.e. + N_3p.e. + N_4p.e. + ...)/(N_1p.e. + N_2p.e. + N_3p.e. + ...).

A relatively simple procedure to measure this probability is to count the number of waveforms with the setup shown in Figure 13.

The SiPM operates in the dark. The wide-bandwidth amplifier G converts the output current signal to a voltage signal and amplifies the signal's strength. The output of the amplifier is an input to a digital counter such as Tektronix FCA3100. The counter counts a signal if its amplitude exceeds a certain user-set level (lower discrimination threshold). The experimental data consist of the number of counts per unit time as a function of threshold level. Plotting this data produces the characteristic "staircase" shown in Figure 14.

The vertical axis plots the count rate (frequency) and the horizontal axis the threshold level. The frequency corresponding to the top red line is due to all detectable waveforms, whereas that for the red line below the top is due to crosstalk waveforms. Referring to the first frequency as ν_0.5p.e. and the other as ν_1.5p.e., the probability of crosstalk is P_CT = ν_1.5p.e./ν_0.5p.e..

1 Adopted from "Study of the Silicon Photomultipliers and Their Applications in Positron Emission Tomography," PhD Dissertation by Chen Xu.

Slawomir S. Piatek, PhD, is a senior university lecturer of physics at New Jersey Institute of Technology. In his role as scientific consultant at Hamamatsu Corporation, he has developed a photonics training program for engineers and is involved in popularizing SiPM as a novel photodetector by writing and lecturing about the device.