Noise

SiPMs suffer from erroneous counting due to dark noise effects that can deteriorate their performance. The noise effects can be mainly grouped in three categories:

• dark count: electron-hole pairs created in the depletion layer by random thermal ionization;

• optical crosstalk: parasitic avalanche triggering by photons created during a pri- mary avalanche migrating to a neighbouring cell;

• afterpulsing: time-delayed release of a “hot” carrier by a trap level due to imper- fections in the lattice, leading to a time-delayed second avalanche.

Optical cross-talk has been reported to be significantly reduced for SiPMs featuring optical trenches (strips of material with different refractive index placed between neigh- boring cells, which deflect photons away from the active area [136]). Dark noise levels and SiPM performance in general are heavily dependent on manufacturing quality and techniques, and on features such as the number of SPADs in the array; nevertheless, the user can tailor a given device to a particular end by modifying either or both the operating temperature and the bias voltage. In general, though, SiPMs are operated at room temperature for simplicity and because the lower dark count obtained by cooling the device comes at a price of highly increased after-pulsing, due to the longer trapping time at lower temperatures [137]. Bias voltage, on the other hand, is a more useful parameter to vary, as quantum detection efficiency, detector response and dark count rate significantly increase for increasing bias. Increasing the bias voltage increases the electric field across the depletion layer, hence the carriers acquire the energy needed for impact ionization in a shorter path, leading to more secondary carriers being lib- erated; it is therefore more likely that a free carrier (created by an impinging photon, or by thermal ionization) will result in an avalanche event. From a user’s perspective, it is important to be able to assess the manufacturing quality of available SiPMs and exploit the advantages of varying the bias voltage. SiPMs feature characteristics pe- culiar to the collective behavior of the array. While increasing the number of SPADs

in the array linearly increases the dynamic range, as more photons can be detected (provided the photon beam is large enough to cover the whole active area, which is usually not a problem), it also equally increases the rate of dark count events: high dynamic range comes at the price of sacrificing single photon detection. To assess the contribution of all these phenomena on the Cherenkov signal a novel procedure to characterize SiPMs in terms of their manufacturing quality is described at the end of this section together with comparative measurements of optical cross-talk [138]. The chacterization procedure involves monitoring dark count signal and device response for varying bias voltage.

Dark noise The main source of noise limiting the SiPM performance is the dark noise rate, which mainly originates from the carriers created thermally in the depletion layer. In Fig. 4.13 a typical dark noise signal with an overvoltage of 1.5 V is shown. Each

Figure 4.13: SiPM dark noise signal recorded during laboratory tests with an overvoltage of 1.5 V in the absence of light. The small peaks corresponds to a single cell firing, the larger one to a double cell.

electron-hole recombination mechanism can be reversed leading to a carrier generation. When there is a large excess of charge carriers, recombination leads to a decay in the number of carriers. However, if the number of carriers is small, generation events can lead to an increase in the number.

We can distinguish 3 ways of recombination [139–141]:

1. Band to band recombination or radiative recombination: electron-hole pairs re- combine directly from band to band with the energy carried away by photons. An electron falls from its state in the conduction band into the empty state in the valence band which is associated with the hole. Its counterpart is the optical electron-hole pair generation.

2. Trap assisted recombination, also called Shockley-Read-Hall effect: electron-hole pairs recombine through deep-level impurities. An electron falls into a “trap”, an energy level within the bandgap caused by the presence of a foreign atom or a structural defect. The electron occupying the trap can, in a second step, fall into an empty state in the valence band, thereby completing the recombination process. It is possible to envision this process either as a two-step transition of an electron from the conduction band to the valence band or also as the annihilation of an electron and the hole which can meet each other in the trap. The energy liberated during the recombination event is dissipated by lattice vibrations or phonons. Its counterpart is thermal electron-hole pairs generation.

3. Auger recombination: an electron and a hole recombine in a band to band tran- sition, but the resulting energy is absorbed by a third carrier (another electron or hole). Its counterpart is the impact ionization.

Usually a recombination event needs a third partner to allow conservation of energy and momentum. This third partner is often a lattice defect, most commonly an impurity atom, with an energy state deep in the band gap, not close to the band edge. Re- combination is then determined by these states or deep levels [141]. When an electron is thermally generated in a pixel of the SiPM array, it triggers an avalanche exactly as if the pixel would have been fired. Increasing the bias voltage the dark count rate increases mainly because the dark count is primarily generated by thermal generation of electron/hole pairs in the depletion region and secondly by thermal bulk diffusion of electrons to the depletion region.

Afterpulsing Traps may result from the damage caused by an implantation during the fabrication process of the SiPM. These centers appear as deep levels in the energy gap of the semiconductor. They trap some avalanche carriers and release them with a statistical delay. If the delay is greater than the dead time after the previous avalanche pulse, a released carrier can re-trigger an avalanche and cause a statistically correlated pulse named anafterpulse. The probability that an afterpulse occurs increases with the amount of charge that flows through the diode during a Geiger discharge. Thus, the

afterpulsing probability increases with the increase of the bias voltage. For high over- voltages the afterpulsing considerably increases the dark noise leading to a distortion of the distribution of the photons arrival time.

Cross-talk Hot carriers in an avalanche p-n junction can emit photons even in the visible range, which then fall in the detection range of other pixels. There are 3 different ways that cross talk can occur, differing in the way the created photon reaches the

neighboring pixel: direct, inside the depletion layer and through reflection. These

mechanisms are shown in Fig. 4.14. A solution to avoid the first cross-talk mechanism

Figure 4.14: Three ways of cross-talk between SiPM pixels: 1) direct, 2) inside the depletion layer, 3) through reflection.

is to isolate pixels optically by trenches filled with an opaque material as shown in Fig. 4.15, whilst the others can be reduced by improving the purity of the material used and especially the quality of the manufacturing process, where it is essential to avoid defects. All of this depends on the manufacturer, and influences the choice of the supplier.