Slawomir Piatek, PhD, Hamamatsu Corporation & New Jersey Institute of Technology
January 3, 2017
The silicon photomultiplier (SiPM) is a photodetector sensitive to individual photons due to its very high 105 − 107 internal gain. The source of this gain is Geiger mode operation of avalanche photodiodes (APDs), which, in numbers ranging from 100s to 10,000s, are the main constituent of a SiPM. When a charge carrier (an electron or a hole) enters the high-field section of an APD's depletion region, it may trigger Geiger discharge — an avalanche — which is rapidly put out by the quenching resistor in series with the APD. The output is a current pulse. The charge carrier that triggered the avalanche may have originated from either absorption of a photon or from thermal generation. Although the resulting output pulse is identical in each case, the former process yields potentially useful "signal," whereas the latter results in "noise" referred to as "dark count." This note discusses how changing temperature affects the rate of dark counts in a SiPM.
A dark count is primarily due to a free charge carrier, generated in the APD's depletion layer, that has diffused into the high-field region and triggered Geiger discharge. There are two processes responsible for the generation of a free charge carrier. The first is a trap-assisted generation (Shockley-Read-Hall process) in which an electron transfers from the valence to the conduction band via a state (or trap) within the band gap. The rate of this process is sensitive to temperature and the density and relative energy of the traps. Impurities and lattice defects create the traps. The second process responsible for the generation is a combination of direct and trap-assisted band-to-band tunneling. Here the rate is sensitive to the strength of the electric field and is only weakly dependent on temperature. The two aforementioned processes have comparable contributions at some "corner" temperature; above this temperature, the first process has a greater weight, whereas below, the second does. The corner temperature depends on the architecture of a SiPM and quality of silicon; its value, though, is generally below 0 °C. Given the nature of the two free-carrier generation processes, one expects that the dark count rate (DCR) is a function of both temperature and the bias voltage.
Measuring DCR as a function of temperature and bias voltage is a part of the basic characterization of a SiPM. In a normal operation, the bias voltage VBIAS on a SiPM is larger than the APD's breakdown voltage VBD by a few volts; the difference ΔV = VBIAS − VBD is known as "overvoltage." Overvoltage is a key parameter affecting a number of opto-electronic characteristics of a SiPM, including the gain. The gain is linearly proportional to ΔV.
The left panel of Figure 1 shows plots of DCR (in Hz) versus T for several values of ΔV. The SiPM (manufactured by Hamamatsu) has 667 microcells yielding a total photosensitive area of 1.3 × 1.3 mm2. The right panel shows plots of DCR versus ΔV for several values of T. For the temperature range of the experiment, there is an exponential-like dependence of the DCR on T and, for a given T, a linear dependence on ΔV. For ΔV = 1 V and T = 20 °C, the plots imply DCR density of about 150 kHz per mm2. The DCR density for newer SiPMs is a factor of 3 − 4 lower.
Figure 1. (Left panel) Plots of dark count rate versus temperature for several values of overvoltage. (Right panel) Plots of dark count rate versus overvoltage at several temperatures. Both figures are from Vacheret et al. (2011) for Hamamatsu S10362-11-050C.
If VBIAS is held constant, changing temperature affects the gain of a SiPM because VBD, and, thus, ΔV, is a function of T. To prevent the gain from changing, either the SiPM operates in a temperature-controlled environment or it operates at the ambient temperature but VBIAS is adjusted in response to changing T so that ΔV remains constant. The latter approach may be preferable to users; however, its undesirable aspect is that DCR changes with T and Figure 2 illustrates the rate of change.
Figure 2. (Left panel) Dark count rate density versus relative overvoltage (ΔV/VBD) for several temperatures. The arrow on the X-axis points to the recommended setting of relative overvoltage. (Right panel) Dark count rate relative to that at 40 °C as a function of temperature at fixed relative overvoltage for Hamamatsu S13360-3050CS SiPM. Source: Otte et al. (2016).
The left panel in Figure 2 shows plots of DCR density as a function of relative overvoltage (ratio of overvoltage and breakdown voltage) for several temperatures. The SiPM is Hamamatsu S13360-3050CS. The right panel shows a plot of DCR relative to that at 40 °C as a function of T at fixed ΔV (note the logarithmic scale on the Y axis). The figure implies that the DCR doubles for every 5.3 °C increase in T.
Dark counts have adverse effects on the performance of a SiPM. In a photon counting regime, DCR imposes a lower limit on a measurable photon rate and contributes to the upper limit too. In an analog (or continuous wave) operation, DCR is represented by the magnitude of dark current. Although the mean dark current can be subtracted, the shot noise associated with it cannot. It is therefore desirable that DCR is the smallest possible.
Reduction of DCR for a given SiPM can be achieved in two ways: lower temperature of operation and/or lowest permissible (by application) overvoltage. If both gain stability and constancy of DCR are required in an application, then stable-temperature operation is the most suitable option.
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