**2.3 Performance and measurement techniques**

In this section and in next, the attention will focus on SPADs with integrate quenching resistor. In contrast to APDs, to establish the performances are necessary a new set of parameters and measurement techniques.

A primary "static" characterization is made on-wafer by using temperature-controlled probe stations and semiconductor parameter analysers. By working in dark condition the SPAD reverse/forward I-V characteristics can be determined, with and without quenching resistor and as a function of the temperature. In this way we get information about leakage current, breakdown voltage, quenching resistor and hence on the overall device performance. For example the leakage current is linked to the generation of electrical carriers both in the bulk as well as on the surface depleted region around the junction. Then, low values of leakage current can be interpreted as the first evidence of the low defectivity of the diode and then of the low dark counting rate. The figure 4 reports the I-V characteristics of ST-Microelectronics SPAD (Mazzillo et al. 2008).

The operation of a SPAD with integrated quenching resistor can be easily investigated by measuring the current across a low resistivity path RS ("dynamic" characterization). In figure 5a is reported the pulse of a single dark count event observed on a FBK SPAD.

The fast leading edge (rise time) is governed by the time that avalanche takes to spread all over the diode active area. The slower exponential decay (discharge time) as previous mentioned is instead determined by a constant time given by the product of the diode internal resistance (few k) and the sum of parasitic and internal diode capacitances. After the breakdown current has been quenched, the diode will slowly recharge through the quenching resistor (see fig.5b).

Time Resolved Camera: The New Frontier of Imaging Devices 313

The distribution of the *Afterpulsing* events, as a function of the temperature and EBV, can be obtained by building the histogram of the time delay between two consecutive pulses within a time window of some hundreds of ns, being the probability of two independent dark counts events in such a time window negligible (the average time scale between two uncorrelated dark events is of the of the order of ms). The distribution is then normalized to the total number of collected events. The histogram is bell-shaped (Mazzillo et al. 2008) as a convolution of the exponentially decreasing probability of releasing a carrier from a trap and the exponentially increasing EBV due to the recharging phase of the depletion layer. The probability that a released carrier can trigger an avalanche event increases with time because during the recharging phase the voltage at the depletion layer approaches exponentially to the bias voltage. On the other hand the probability of release of the captured carriers decreases very quickly with time since this phenomenon is mainly due to traps that are located near the conduction and valence band edges. The afterpulsing

The *Photon Detection Efficiency* (PDE) of SPAD detector is given by the product of two parameters: the quantum efficiency (QE) and the avalanche triggering probability (PT).

The QE represents the probability for a photon to generate an *e*–*h* pair in the active thickness of the device. It is given by the product of two factors: the transmittance of the dielectric layer on top of the silicon surface and the internal QE. Both are wavelength dependent. The former can be maximized, by implementing an anti-reflective coating. The second term represents the probability for a photon that has passed the dielectric layer to generate an *e*–*h* pair in the active thickness. In a conventional *n*+/*p*/*p*+ diode, the active layer is roughly limited on top by the undepleted *n*+ layer, whereas on the bottom by the *p*+ layer used for the ohmic contact or by the highly doped substrate in case of epitaxial substrates. Indeed, when a pair is generated in those regions, there is a high probability for the electron and hole to recombine due to Auger or Shockley–Read–Hall processes (Tyagi 1991). For short wavelengths, the problem is focused in the top layer. As an example, a 420nm light is almost totally absorbed in the first 500 nm of silicon, which, for non-optimized fabrication

There is a finite probability for a carrier to initiate an avalanche when passing through a high-field region. In case of a photogeneration event, two carriers are created travelling in opposite directions. Both contribute to the *PT* that can be evaluated from the following expression: *PT* = *Pe* + *Ph* – *PePh*. Where *Pe* and *Ph* are the electron and hole breakdown initiation probabilities. These terms can be calculated as a function of the generation position by solving two differential equations involving the carrier ionization rates. *Pe* and *Ph* depend on the impact ionization rates of electrons (n) and holes (p), respectively. These parameters are not well determined yet, and large discrepancies exist among the values extracted from the various models (Grant et al. 1973). Anyway, despite the differences in absolute values, some features are well established: (i) both coefficients increase with the electric field, (ii) the electron has an ionization rate higher than the hole (is about twice p),

This behaviour is reflected in the probabilities *Pe* and *Ph*. Thus, to maximize the triggering probability: (*i*) the photogeneration should happen in the p side of the junction in order for the electrons to pass the whole high field zone, and (*ii*) the bias voltage should be as high as

probability is commonly a few percent.

processes, is usually well inside the undepleted layer.

and (iii) their difference decreases with increasing fields.

possible.

Fig. 4. I-V characteristics for a square shaped (30 m side) ST-Microelectronics SPAD; *a)* reverse; *b)* forward.

Total charge and device gain can be extracted by integrating the pulse, converted into a current signal. The junction capacitance can be evaluated estimating the slope of the charge-EVB characteristic.

The *Dark Noise* is a function of EBV, temperature and detector area. Commonly it may vary from a minimum of tens of hertz to a few kilohertz and is a superposition of dark count and afterpulsing rate. In figure 5b the oscilloscope was triggered on a SPAD Geiger pulse (either dark count or afterpulsing event), while the device was kept in dark condition. The time delay between the leading edges of the reference pulse and a consecutive pulse, which can be due to dark count or afterpulsing, was measured. Then the average delay between two consecutive pulses was obtained. The inverse of this value represents the dark noise rate of the device.

Fig. 5. Dynamic characterization of a circular FBK-IRST SPAD (30 m diameter). The signals in *a*) and *b*) correspond to dark events when the device is respectively biased at 10 and 20 % of EBV. In *a*) is displayed the structure of a single pulse; *b)* reports the afterpulses distribution through a persistence image.

Fig. 4. I-V characteristics for a square shaped (30 m side) ST-Microelectronics SPAD; *a)*

Total charge and device gain can be extracted by integrating the pulse, converted into a current signal. The junction capacitance can be evaluated estimating the slope of the charge-

The *Dark Noise* is a function of EBV, temperature and detector area. Commonly it may vary from a minimum of tens of hertz to a few kilohertz and is a superposition of dark count and afterpulsing rate. In figure 5b the oscilloscope was triggered on a SPAD Geiger pulse (either dark count or afterpulsing event), while the device was kept in dark condition. The time delay between the leading edges of the reference pulse and a consecutive pulse, which can be due to dark count or afterpulsing, was measured. Then the average delay between two consecutive pulses was obtained. The inverse of this value represents the dark noise rate of the device.

Fig. 5. Dynamic characterization of a circular FBK-IRST SPAD (30 m diameter). The signals in *a*) and *b*) correspond to dark events when the device is respectively biased at 10 and 20 %

of EBV. In *a*) is displayed the structure of a single pulse; *b)* reports the afterpulses

distribution through a persistence image.

reverse; *b)* forward.

EVB characteristic.

The distribution of the *Afterpulsing* events, as a function of the temperature and EBV, can be obtained by building the histogram of the time delay between two consecutive pulses within a time window of some hundreds of ns, being the probability of two independent dark counts events in such a time window negligible (the average time scale between two uncorrelated dark events is of the of the order of ms). The distribution is then normalized to the total number of collected events. The histogram is bell-shaped (Mazzillo et al. 2008) as a convolution of the exponentially decreasing probability of releasing a carrier from a trap and the exponentially increasing EBV due to the recharging phase of the depletion layer. The probability that a released carrier can trigger an avalanche event increases with time because during the recharging phase the voltage at the depletion layer approaches exponentially to the bias voltage. On the other hand the probability of release of the captured carriers decreases very quickly with time since this phenomenon is mainly due to traps that are located near the conduction and valence band edges. The afterpulsing probability is commonly a few percent.

The *Photon Detection Efficiency* (PDE) of SPAD detector is given by the product of two parameters: the quantum efficiency (QE) and the avalanche triggering probability (PT).

The QE represents the probability for a photon to generate an *e*–*h* pair in the active thickness of the device. It is given by the product of two factors: the transmittance of the dielectric layer on top of the silicon surface and the internal QE. Both are wavelength dependent. The former can be maximized, by implementing an anti-reflective coating. The second term represents the probability for a photon that has passed the dielectric layer to generate an *e*–*h* pair in the active thickness. In a conventional *n*+/*p*/*p*+ diode, the active layer is roughly limited on top by the undepleted *n*+ layer, whereas on the bottom by the *p*+ layer used for the ohmic contact or by the highly doped substrate in case of epitaxial substrates. Indeed, when a pair is generated in those regions, there is a high probability for the electron and hole to recombine due to Auger or Shockley–Read–Hall processes (Tyagi 1991). For short wavelengths, the problem is focused in the top layer. As an example, a 420nm light is almost totally absorbed in the first 500 nm of silicon, which, for non-optimized fabrication processes, is usually well inside the undepleted layer.

There is a finite probability for a carrier to initiate an avalanche when passing through a high-field region. In case of a photogeneration event, two carriers are created travelling in opposite directions. Both contribute to the *PT* that can be evaluated from the following expression: *PT* = *Pe* + *Ph* – *PePh*. Where *Pe* and *Ph* are the electron and hole breakdown initiation probabilities. These terms can be calculated as a function of the generation position by solving two differential equations involving the carrier ionization rates. *Pe* and *Ph* depend on the impact ionization rates of electrons (n) and holes (p), respectively. These parameters are not well determined yet, and large discrepancies exist among the values extracted from the various models (Grant et al. 1973). Anyway, despite the differences in absolute values, some features are well established: (i) both coefficients increase with the electric field, (ii) the electron has an ionization rate higher than the hole (is about twice p), and (iii) their difference decreases with increasing fields.

This behaviour is reflected in the probabilities *Pe* and *Ph*. Thus, to maximize the triggering probability: (*i*) the photogeneration should happen in the p side of the junction in order for the electrons to pass the whole high field zone, and (*ii*) the bias voltage should be as high as possible.

Time Resolved Camera: The New Frontier of Imaging Devices 315

A typical way to achieve electrical isolation in silicon planar technology is to employ isolation diffusion, i.e. a thus electrically isolating the epitaxial layer, of the opposite doping sufficiently deep diffusion that reaches the substrate of the same doping type, type, as shown in Figure 7. However, the hardest problem to solve in SPAD array design is optical

Fig. 7. Optical cross-talk representation between two neighbouring devices. The avalanche current in one pixel can trigger the process in surrounding pixels, due to photons emitted by

During the avalanche process each ionization impact causes high deceleration in electron drift, so the Bremsstrahlung process enables a secondary photons production inside the junction (the emission probability is estimated in 10-5 photons per carrier crossing the

The optical cross talk is then activated by the emission of secondary photons, that can travel along the silicon bulk, transparent to the optical wavelength, and cross another diode that is triggering a correlated avalanche (Fig. 7). The time delay between the two produced signals is less than the measurable one and induced signals cannot be distinguished from the generated one. A further contribute to the optical cross talk was found in the indirect optical

In order to avoid the optical cross-talk, it is possible design and fabricate arrays that are optically and electrically isolated by deep thin trench technology. The trench process starts with a vertical etch (about 10 μm deep and 1μm large), a subsequent oxide deposition for complete electrical isolation. The process continues with tungsten fill to avoid optical

Nevertheless, all the cross-talk contributions previous mentioned, become important when the density of implemented elements is higher and the distances between neighbouring devices are smaller as required by imaging applications or by silicon PhotoMultiplier

A photomultiplier based on the silicon technology represents the new frontier of photodetection. SPADs integrated on the same substrate, with a common read-out, could satisfy such expectations. The main limitation of a single diode working in Gaiger mode is

pat enabled by the optical reflection by the back part of the device.

technology. They influence the total Dark counting rate of the device.

crosstalk and ends with planarisation.

**3.1 Silicon photomultiplier concept** 

hot carriers.

junction).

coupling. This effect is peculiar to the above-breakdown operation of SPADs.

Fig. 6. *a)* PDE of ST-Microelectronics SPAD at 5 and 10% of EBV; *b*) Photon timing of passively quenched ST-Microelectronics SPAD.

The measurement principle adopted for the evaluation SPAD PDE is a direct comparison with a calibrated photodiode that receives the same photon flux of SPAD. An example of experimental set-up where, with high level of accuracy, are possible PDE measurements is discussed by Bonanno et al. 2005. In figure 6a is reported the typical PDE measured for the ST-Microelectronic devices.

The SPAD performance in *Photon Timing* is characterized by its time resolution curve, which is the statistical distribution of the delay between the true arrival time of the photon and the measured time, marked by the onset of the avalanche current pulse. These can be obtained by means of a time-correlated photon counting apparatus (Privitera at al. 2008), where optical pulses with short time duration (less than 30 - 40 ps) are used to illuminate the devices. After a careful check that the contribution of the laser pulse and the eventual electronic jitter to the SPAD response are negligible, by using a digital oscilloscope it is possible to build the histogram of the time delay between the laser reference pulse and the SPAD pulse.

 In figure 5b is reported the time resolution curve obtained by using laser pulses of 408 nm wavelengths, 35 ps FWHM and 1 kHz repetition rate, on an ST-Microelectronic SPAD. It is consistent with the typical values reported in the literature for other devices.
