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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 19 — Sep. 14, 2009
  • pp: 16885–16897
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Multipixel silicon avalanche photodiode with ultralow dark count rate at liquid nitrogen temperature

M. Akiba, K. Tsujino, K. Sato, and M. Sasaki  »View Author Affiliations


Optics Express, Vol. 17, Issue 19, pp. 16885-16897 (2009)
http://dx.doi.org/10.1364/OE.17.016885


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Abstract

Multipixel silicon avalanche photodiodes (Si APDs) are novel photodetectors used as silicon photomultipliers (SiPMs), or multipixel photon counter (MPPC), because they have fast response, photon-number resolution, and a high count rate; one drawback, however, is the high dark count rate. We developed a system for cooling an MPPC to liquid nitrogen temperature and thus reduce the dark count rate. Our system achieved dark count rates of <0.2 cps. Here we present the afterpulse probability, counting capability, timing jitter, and photon-number resolution of our system at 78.5 K and 295 K.

© 2009 OSA

1. Introduction

Single-photon detection technology is used in various fields such as quantum information, medicine, and high-energy physics. However, further improvements in single-photon detectors are required for some applications. For example, quantum information and communications technology requires high photon detection efficiencies (optical quantum computation [1

1. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]

], quantum optimal receiver [2

2. M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers,” Phys. Rev. A 78(2), 022320 (2008). [CrossRef]

]), high count rates (quantum key distribution [3

3. E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14(26), 13073–13082 (2006). [CrossRef] [PubMed]

], quantum random number generators [4

4. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008). [CrossRef]

]), and photon-number resolution (nonclassical photon statistics [5

5. E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92(11), 113602 (2004). [CrossRef] [PubMed]

], quantum key distribution [6

6. T. Moroder, M. Curty, and N. Lutkenhaus, “Detector decoy quantum key distribution,” arXiv:0811.0027v1 [quant-ph] (2008).

]). The detection of low-intensity light from scintillation (in high-energy physics and positron emission tomography (PET), for instance) requires large detection areas [7

7. M. Moszynski, T. Ludziejewski, D. Wolski, W. Klamra, M. Szawlowski, and M. Kapusta, “Subnanosecond timing with large area avalanche photodiodes and LSO scintillator,” IEEE Trans. Nucl. Sci. 43(3), 1298–1302 (1996). [CrossRef]

,8

8. V. N. Solovov, F. Neves, V. Chepel, M. I. Lopes, R. F. Marques, and A. J. P. L. Policarpo, “Low temperature performance of a large area avalanche photodiode,” J. Mod. Opt. 51, 1351–1357 (2004).

].

Single-photon detectors based on avalanche photodiodes (APDs) are widely used for visible and near-infrared wavelengths because they are commercially available and convenient to operate. Si APDs have high detection efficiencies (>50%), low afterpulse probability (<1%) at a dead time of 70 ns, and low dark count rates (<100 cps); but they have low count rates (up to about 20 MHz at detection efficiencies below 35%) because of the large dead time and lack photon-number resolution. However, InGaAs APDs have a high count rate of 100 MHz [9

9. Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007). [CrossRef]

] and photon-number resolution [10

10. B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008). [CrossRef]

]. However, the resolution is still poor and the detection area of InGaAs APDs is so small (usually 30 μm in diameter) that they can only be used in communications experiments with single-mode optical fibers.

Much effort has been devoted so far toward improving the performance of APDs. Problems such as the low count rate and lack of photon-number resolution for Si APDs can be solved by using multiplexed detectors. For example, the dead time can be effectively reduced by 1/N by employing N detectors and a 1-by-N optical switch [11

11. S. Castelletto, I. P. Degiovanni, V. Schettini, and A. Migdall, “Reduced deadtime and higher rate photon-counting detection using multiplexed detector array,” J. Mod. Opt. 54(2), 337–352 (2007). [CrossRef]

]. Time-multiplexed detectors can correctly measure the number of simultaneously incident photons by using conventional photon counters. The basic idea behind time-multiplexed detectors is that an incident light pulse is divided into several pulses that are separated by a time interval, allowing each pulse to be measured subsequently by the photon counters [12

12. K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003). [CrossRef] [PubMed]

14

14. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003). [CrossRef]

]. However, to obtain a fine photon-number resolution and fast counting capability, several APDs or measurement loops will be required.

Multipixel Si APDs are novel photon counting devices that comprise several Geiger-mode APDs in parallel [15

15. G. Bondarenko, P. Buzhan, B. Dolgoshein, V. Golovin, E. Guschin, A. Ilyin, V. Kaplin, A. Karakash, R. Klanner, V. Pokachalov, E. Popova, and K. Smirnov, “Limited Geiger-mode microcell silicon photodiode: new results,” Nucl. Instrum. Methods 442(1-3), 187–192 (2000). [CrossRef]

18

18. B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, and I. Tikhomirov, “Calice/SiPM Collaboration, “Status report on silicon photomultiplier development and its applications,” Nucl. Instrum. Methods 563(2), 368–376 (2006). [CrossRef]

]. This design overcomes the drawbacks of Si APDs [19

19. A. N. Otte, J. Barral, B. Dolgoshein, J. Hose, S. Klemin, E. Lorenz, R. Mirzoyan, E. Popova, and M. Teshima, “A test of silicon photomultipliers as readout for PET,” Nucl. Instrum. Methods 545(3), 705–715 (2005). [CrossRef]

21

21. N. Dinu, R. Battiston, M. Boscardin, G. Collazuol, F. Corsi, G. F. Dalla Betta, A. Del Guerra, G. Llosa, M. Ionica, G. Levi, S. Marcatili, C. Marzocca, C. Piemonte, G. Pignatel, A. Pozza, L. Quadrani, C. Sbarra, and N. Zorzi, “Development of the first prototypes of silicon photomultiplier (SiPM) at ITC-irst,” Nucl. Instrum. Methods 572(1), 422–426 (2007). [CrossRef]

]. Each Geiger-mode APD produces a pulse of almost the same level regardless of the number of incident photons, and the pulses generated in different pixels can be superposed. Therefore, when all the photons are injected into different pixels, the output pulse height is proportional to the number of incident photons. The distribution of photons over multiple pixels is effective in reducing the dead time, because even when some pixels are not active, others are [11

11. S. Castelletto, I. P. Degiovanni, V. Schettini, and A. Migdall, “Reduced deadtime and higher rate photon-counting detection using multiplexed detector array,” J. Mod. Opt. 54(2), 337–352 (2007). [CrossRef]

,20

20. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]

]. Another advantage of multipixel Si APDs is that they have a large area because of the parallel combination of several Si APDs.

The dark count rates of multipixel Si APDs, however, are much higher than those of single APDs due to the parallel combination [21

21. N. Dinu, R. Battiston, M. Boscardin, G. Collazuol, F. Corsi, G. F. Dalla Betta, A. Del Guerra, G. Llosa, M. Ionica, G. Levi, S. Marcatili, C. Marzocca, C. Piemonte, G. Pignatel, A. Pozza, L. Quadrani, C. Sbarra, and N. Zorzi, “Development of the first prototypes of silicon photomultiplier (SiPM) at ITC-irst,” Nucl. Instrum. Methods 572(1), 422–426 (2007). [CrossRef]

23

23. M. Petasecca, B. Alpat, G. Ambrosi, P. Azzarello, R. Battiston, M. Ionica, A. Papi, G. U. Pignatel, and S. Haino, “Thermal and electrical characterization of silicon photomultiplier,” IEEE Trans. Nucl. Sci. 55(3), 1686–1690 (2008). [CrossRef]

]. The dark count rates are generally reduced at low temperatures [23

23. M. Petasecca, B. Alpat, G. Ambrosi, P. Azzarello, R. Battiston, M. Ionica, A. Papi, G. U. Pignatel, and S. Haino, “Thermal and electrical characterization of silicon photomultiplier,” IEEE Trans. Nucl. Sci. 55(3), 1686–1690 (2008). [CrossRef]

25

25. K. Tsujino, M. Akiba, and M. Sasaki, “Experimental determination of the gain distribution of an avalanche phtodiode at low gain,” IEEE Electron Device Lett. 30(1), 24–26 (2009). [CrossRef]

]. We thus measured the dark count rates of a multipixel Si APD cooled to liquid nitrogen temperature. On the other hand, at low temperatures, the afterpulse probabilities of APDs generally increase [26

26. J. J. Fox, N. Woodard, and G. P. Lafyatis, “Characterization of cooled large-area silicon avalanche photodiodes,” Rev. Sci. Instrum. 70(4), 1951–1956 (1999). [CrossRef]

]. Hence, we also measured the afterpulse probabilities at liquid nitrogen temperature and room temperature. Furthermore, we investigated other characteristics of multipixel APDs at these temperatures by using electrical circuits optimized for each measurement.

2. Experimental setup and time response

The multipixel APD used in this experiment was a multipixel photon counter (MPPC S10362-11-100U) supplied by Hamamatsu Photonics. The specifications of this product are listed in Table 1

Table 1. Parameters of the MPPC

table-icon
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. The experimental setup is shown in Fig. 1
Fig. 1 Schematic diagram of apparatus used to measure the MPPC characteristics. The blue parts in the diagram are at 78.5 K. The high-pass filter is not used in the measurement of the time response of the MPPC. A preamplifier is placed just behind the MPPC output in the cryostat for several measurements (not seen in the figure).
. The detector was placed in a liquid nitrogen cryostat and was electrically connected to a room-temperature circuit through aCuNi SMA cable, which was used for thermal isolation. The temperature of the detector was 78.5 K.

We measured the height distributions of the afterpulses, the fast count rates, and the photon-number resolutions using a UV pulsed laser diode (LD; Hamamatsu Photonics, PLP 10-040C) emitting at a wavelength of 407 nm with pulse width of 75 ps. A light-emitting diode (LED) emitting at a wavelength of 450 nm was used for determining the photodetection efficiency and afterpulse probability because the intensity of the LED was more stable compared with that of the LD. The light from the LD or LED was passed through neutral density filters and then focused on a single-mode fiber by focus lenses. The light signal from the single-mode fiber was collimated through a collimator lens and injected into the detector through a 5-mmφ aperture. The position of the detector was slightly changed after cooling because of the shrinking of the liquid nitrogen tank (<1 mm). The intensity of the collimated beam was nearly uniform over the aperture diameter of 5 mm and was varied by 2% in order to reduce the effect of the displacement of the detector on the intensity of light injected into the detector. The absolute optical power injected into the detector was calculated from the intensity of the light from the aperture and effective area of the detector.

To measure the dark count rate, the height distributions of the afterpulse, the afterpulse probability, and the photon-number resolution, we needed a low-noise amplifier. For that purpose, a preamplifier was placed just behind the MPPC output in the cryostat. The preamplifier comprised a common source circuit with a GaAs high electron mobility transistor. The amplifier gain was 3.9 and 3.6 at 78.5 K and 295 K, respectively. The preamplifier had a disadvantage of deteriorated time response due to ringing in the preamplifier circuit.

The signal from the detector was acquired by using a high-speed oscilloscope (Lecroy SDA3000A). All the following results were obtained after signal analysis. We first measured the time response of the detector without the high-pass filter (Fig. 2a
Fig. 2 (a) Output signals from the MPPC when no high-pass filter is used, and (b) output signals from the high-pass filter when two pulses were generated successively.
). The slopes of the exponential tails of the response were found to increase from 25 ns at 295 K to 210 ns at 78.5 K. The tail could act as an obstacle to the detection of photons. A threshold level is also required to discriminate between signals created by photons and electrical noise. The electrical noise level would exceed the threshold level at high signal rates due to superposition of the tails. This problem is solved by using a high-pass filter [20

20. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]

]. Tails also exist for common single-pixel Si-APDs operated in the Geiger mode, and the length of the tail can be decreased by using an active quenching circuit [27

27. H. Dautet, P. Deschamps, B. Dion, A. D. MacGregor, D. MacSween, R. J. McIntyre, C. Trottier, and P. P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993). [PubMed]

]. However, to the best of our knowledge, the active quenching circuit has not been used in mulitpixel APDs so far.

Although the exponential tail at 78.5 K was longer than that at 295 K, it is found that the cooled APD had a rapid fall time around the peak. Therefore, using the RC high-pass filter having a cut-off frequency of 300 MHz, we could obtain a fast time response at 78.5 K (see Fig. 2b). Figure 2b shows two pulses that were generated successively at 78.5 K and 295 K when the detector was irradiated by the LED. As can be seen, the two pulses (separated by 2 ns) can be distinguished at 78.5 K. All the following measurements were carried out with the high-pass filter.

3. Measurements of dark count rate, afterpulse probability, and photon detection efficiency

3.1 Dark count rate

The dark count rates were measured while the optical input window (the lens in Fig. 1) of the cryostat was closed. To determine the intrinsic dark count rate when carriers are generated by processes other than photoexcitation, the dark count rate due to electrical noise must be much lesser than the intrinsic dark count rate. For the determination of intrinsic dark count rates less than 0.01 cps, an adequate threshold level must be set so as to distinguish between the intrinsic dark counts and the dark counts from electrical noise. The threshold level was set to more than 7.2 times the standard deviation of the noise, considering the value of the error function. Since the pulse heights of the intrinsic dark counts are determined by the bias voltage applied to the detector, the electrical noise level must be reduced to realize a high signal-to-noise ratio. Therefore, we used the preamplifier mentioned earlier in this paper.

Before measuring the dark count rate of the MPPC, we confirmed that dark counts due to noise were not observed, lowering the bias voltage sufficiently below the breakdown voltage at 78.5 K.

Figure 3
Fig. 3 Dark count rate as a function of overvoltage. The statistical error in the measurements is almost within the size of symbols.
shows the dark count rates as a function of overvoltage, that is, the difference between the breakdown voltage and the bias voltage. The dark count rates include afterpulses. On cooling, the dark count rate of the MPPC dramatically decreases. The dark count rate was much lower than that of silicon photomultipliers at liquid nitrogen temperature (a few kcps) as described in [16

16. P. Buzhan, B. Dolgoshein, L. Filatov, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, E. Popova, and S. Smirnov, “Silicon photomultiplier and its possible application,” Nucl. Instrum. Methods 504(1-3), 48–52 (2003). [CrossRef]

]. The dark count rates increased rapidly when the overvoltage exceeded 1.2 V at both temperatures due to an increase in the number of afterpulses. Therefore, we decided to limit the overvoltage to 1.2 V for the following measurements.

3.2 Afterpulse probability

In this subsection, we first discuss the difference between the pulse height distributions of photon detection events and afterpulse events and then describe the method used to obtain the distributions. The threshold voltage used to discriminate between photon detection events and    electrical noise was set on the basis of this difference. Subsequently, we discuss the afterpulse probability as a function of the overvoltage and the number of incident photons at 78.5 K and 295 K.

Afterpulses are spurious pulses that follow shortly after a primary output pulse. These primary pulses include not only photon-induced events but also the dark count, or even other afterpulses. At 78.5 K, a large number of afterpulses are possibly created during the course of the long-tailed primary pulse. The height distribution of the afterpulses created on the tail may be different from that of the primary pulses. The reason is as follows: In the Geiger mode, an output pulse is produced due to avalanche breakdown at a single APD. The breakdown current flows through the p-n junction of the APD while consuming the charge on the junction capacitor (see Fig. 4
Fig. 4 Schematic of MPPC. Junction capacitors of the single APDs are explicitly indicated.
). The breakdown stops when the voltage at the junction drops below the breakdown voltage because of the charge reduction. The tail is produced due to the compensation current supplied through the resistor connected in series with the APD. Since the voltage at the junction is below the original level while the compensation current continues to flow, the heights of the afterpulses may be small on the tail.

The measurement of small pulse heights requires a low-noise preamplifier. As mentioned in section 2, the time response of the preamplifier deteriorated due to the ringing of the circuit. Hence, we set the dead time to 10 ns by software when analyzing the data. Furthermore, to obtain the height distribution of the afterpulses, we used a method that we call direct measurement. In this method, very weak light pulses from the UV pulsed LD were used. When an output pulse created by a photon from the weak UV pulse was detected, the heightsof the pulses that followed the signal pulse were measured (see Fig. 5
Fig. 5 Schematic diagram of the method used for the direct measurement of the afterpulses at 78.5 K. The intensity of light pulses was set such that there was negligible probability of two or more photons being detected simultaneously. The time interval of the light pulses was set to 10 μs, and after this interval, the afterpulses probability were completely negligible. The pulse height distributions were determined at an overvoltage of 0.7 V.
). A repetition rate of 100 kcps was set to ensure that there was sufficient time for the afterpulses to be subdued. The intensity of the light pulses was set such that there was negligible probability of two photons or more being detected simultaneously (0.01 detections per light pulse). At 78.5 K, since the dark count rate of the MPPC was negligibly small, pulse counts besides those originating from the LD were attributed to the afterpulses. By this method, the pulse height distribution of the afterpulses was obtained. Note, however, that the direct measurement method cannot be used to count afterpulses when the number of incident photons is large or when the dark count rate is high.

The pulse height distributions for signal pulses generated by single photons and afterpulses at an overvoltage of 0.7 V (bias voltage of 59.5 V) at 78.5 K are shown in Fig. 5. The distributions of the signal pulses and afterpulses are quite different. The afterpulses have a very broad height distribution with a considerable number of small-height pulses. Since the voltage at the p-n junction increases with the time delay from the primary pulse, as discussed above, a smaller height pulse is expected at a shorter delay time. To clarify the mechanism, we investigated the dependence of the pulse height on the delay time. Figure 6
Fig. 6 Two-dimensional frequency distribution with respect to the delay time and the pulse height.
shows the two-dimensional frequency distribution of the delay time versus the pulse height. Afterpulses began to be generated at a delay time of around 100 ns; they had a small pulse-height. The pulse height increased with the delay time, while the number of counts reduced. The afterpulses finally reached the level of the signal pulses at a delay time of around 350 ns. These values of the delay time are consistent with the discussion of the tail, which has a length of 210 ns. However, afterpulses that are comparable in height to the primary pulses are also created shortly after the primary pulse. The number of such afterpulses is about 10% of the total number of afterpulses counted. At present, we do not know the mechanism behind the generation of such afterpulses.

The direct measurement method was employed to count the number of afterpulses. The afterpulse probability was obtained as the average of the number of afterpulses per primary pulse. The afterpulse probability at 78.5 K depends on the threshold level because the pulse height distribution of the afterpulses differs from that of signal pulses. In the measurements discussed in the subsequent sections, we set each threshold value at a level where the signal pulse count was sufficiently low (see Fig. 5). Since the direct measurement method was not applicable to the measurements at 295 K for the reasons mentioned above, we used the autocorrelation function method, which is the method generally employed [28

28. J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, “Single-photon counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes,” Appl. Opt. 39(36), 6746–6753 (2000). [CrossRef]

]; the low-noise preamplifier was also used, and the dead time was set to 10 ns. Furthermore, since the autocorrelation function method requires a continuous-wave light, the 450 nm LED was used as the light source. Figure 7a
Fig. 7 (a) Afterpulse probability as a function of overvoltage. Open circles denote data obtained using the direct measurement method. Filled circles represent data obtained using the autocorrelation function method at an incident photon number of 30 M photons/s. The error in the measurements obtained using the direct measurement method is almost within the size of the symbols. At 295 K, the direct measurement method could not be used due to the high dark count rate. (b) Afterpulse probability as a function of the number of incident photons. The overvoltage for all the measurements was 0.7 V and 0.8 V at 78.5 K and 295 K, respectively. The open circle datum (direct measurement method) is the same as the datum corresponding to 0.7 V in panel (a). On the other hand, the filled circle data (autocorrelation function method) at 30 M photons/s and the data in panel (a) were measured individually.
shows the afterpulse probability as a function of the overvoltage. The afterpulse probabilities determined with the two methods at 78.5 K were different. The most notable difference was in the number of incident photons—the incident photon number was 30 M photons/s when the autocorrelation function was used, but only 4 k photons/s when the direct measurement was used. To investigate the cause of this difference, the dependence of the afterpulse probability on the number of incident photons was examined by the autocorrelation function method (Fig. 7b). Consequently, we observed that the afterpulseprobability varied with the number of incident photons when the incident photon number was high at 78.5 K. Moreover, the afterpulse probabilities obtained by the direct measurement method were consistent with those obtained by the autocorrelation function method at low photon numbers. However, at 295 K, a variation with the incident photon number was not clearly observed.

3.3 Photon detection efficiency

To measure the photon detection efficiency, the absolute intensity of incident light is needed. The output signals of MPPCs become saturated under strong incident light [20

20. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]

]. However, the high-precision photodetector used in this study cannot accurately measure light of less than 0.1 nW. However, the power of the light from the 5-mmφ aperture could be measured with the high-precision photodetector. And since the light from the aperture was collimated and its intensity (W/cm2) was almost uniform, the intensity of the light incident on the MPPC was calculated from the intensity and the effective area of the MPPC. As a result, the number of incident photons per second was found to be 30 × 106. The error in the measurement of the incident power was mainly due to the noise from the high-precision photodiode. The photon detection efficiencies shown in Fig. 8
Fig. 8 Photon detection efficiency as a function of overvoltage at 78.5 K and 295 K.
are net values excluding the afterpulses. The photon detection efficiencies at 78.5 K are comparable with those at 295 K, within a 10% error.

4. Measurements of timing jitter and counting capability

4.1 Timing jitter

To measure the parameters discussed in section 4, we used the UV pulsed LD. The timing signal from the LD controller had a timing jitter that could be measured between the timing signal and the laser pulses (electronic timing jitter). The jitter (75 ps) was measured by measuring the timings of the output signals from the high-speed photodetector when irradiated by the laser pulses and comparing this with the timing signal. Figure 9
Fig. 9 Timing jitters for single-photon detection at an overvoltage of 1 V
plots the timing jitter for single-photon detection, including the laser pulse width (75 ps) and the electronic timing jitter. The timing jitter of the MPPC was found to be 158 ps at 78.5 K and 181 ps at 295 K, after subtracting the laser and electronics contributions. The jitter showed a slight improvement at 78.5 K.

4.2 Counting capability

To investigate the counting capability of the detector, the responses to high-repetition-rate light pulses were determined. To measure the counting capability at the single-photon detection level, the average number of photon detections per light pulse must be adjusted adequately. When the average number is high, the counting capability is not at the single-photon detection level. When the average is small, the effective repetition rate is reduced. We adjusted the average number of photon detections to 1.6 per light pulse, which is the net value excluding the number attributed to cross-talk. The probability of photon detection per light pulse was measured to be 0.8, which is consistent to the value calculated assuming a Poissonian distribution for the light pulse having an average number of photon detections of 1.6. The average number was obtained by analyzing the pulse heights acquired by the oscilloscope at the repetition rates below 10 MHz. The pulse height was defined as the maximum value within a 2-ns time window that was set at the light-pulse arrival time measured in advance. Therefore, the afterpulse counts are not included in the average photon number, even if an afterpulse was created in the time window.

Figure 10
Fig. 10 Detection rate plotted against high-repetition-rate light pulses. The overvoltage values were 0.7 and 0.8 V at 78.5 K and 295 K, respectively. The average number of photon detections, which were determined from the data collected below 10 MHz, was 1.6 per incident light pulse. The slope value of 0.8 represents the photon detection probability per incident light pulse at repetition rates below 10 MHz.
shows the response of the detector. While the detection rate at 78.5 K decreases at a high repetition rate of 100 MHz, the detection rate at 295 K decreases slightly. This is because the number of active pixels at 78.5 K decreases with the dead time. The ratio of the detection rate to the effective repetition rate, which is defined as the product of the repetition rate and the probability of photon detection per light pulse, is proportional to the ratio of the number of the active pixels to the total number of pixels (R). R is derived from the following differential equation as a function of time t:
dRdt=rn0NR+1td(1R),
(1)
where r, no, td, and N are the repetition rate of light pulses, average number of output pulses per light pulse at R = 1, dead time, and number of pixels of the MPPC, respectively. The afterpulses and pulses generated by cross-talk are also included in no, The first and second terms of the equation represent a decrease in the number of active pixels due to output pulse generation and an increase in the number due to reactivation of the dead pixels after the dead time, respectively. The solution to Eq. (1) is

R=F1+Fexp(1+Ftdt)+11+FF=rn0tdN.
(2)

The measured ratio of the detection rate to the effective repetition rate can be calculated from the second term of Eq. (2) when the variables are known. Since the heights of photon-induced pulses or pulses due to cross-talk are also affected by the amount of charge on the junction capacitor in the same manner as the afterpulses, the dead time for all output pulses can be inferred from the relation between the delay time and the heights of afterpulses. The threshold level of 0.015 V, at which the data in Fig. 10 are obtained, is observed to correspond to 0.06 V in Fig. 6 when the gain of the preamplifier is considered. When the threshold level to discriminate between signals and afterpulses is set at 0.06 V in Fig. 6, most of the afterpulses occurring after a time delay less than 300 ns from the primary pulses are eliminated, which indicates that the detector is dead for 300 ns. Assuming that the ratio of the dead time to the time scale of the tail at 295 K is the same as that at 78.5 K, the dead time at 295 K is estimated to be 36 ns. Since the afterpulse probabilities at a repetition rate of 100 MHz are inferred to be small from Fig. 7b, the probabilities were neglected in this calculation. The ratio of the detection rate to the effective repetition rate at a repetition rate of 100 MHz was calculated to be 0.64 and 0.93 at 78.5 K and 295 K, respectively. These values are consistent with the measured values of 0.62 at 78.5 K and 0.96 at 295 K.

5. Photon-number resolution and cross-talk probability

By combining several single APDs in parallel, multipixel APDs acquire photon-number resolution, while the peculiar problem of cross-talk is encountered [29

29. E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk Characterization in Geiger-Mode Avalanche Photodiode Arrays,” IEEE Electron Device Lett. 29(3), 218–220 (2008). [CrossRef]

]. The photon-number resolution and cross-talk probability were determined from the output pulse height distributions obtained when several photons were simultaneously incident on the MPPC. In order to measure the deviation of the pulse height distribution precisely, the circuit noise should be less than the deviation. Therefore, the preamplifier was used for this measurement. The method used to measure the pulse height distributions was the same as that mentioned in subsection 4.2.

The repetition rate of the light pulse from the UV pulsed LD was 100 kHz. The output pulse height distributions measured at 78.5 and 295 K and the theoretical distribution curves are shown in Fig. 11
Fig. 11 Pulse height distributions for short light pulses at 78.5 K (a) and 295 K (b). The parameters used for determining the distribution are listed in Table 2.
. The theoretical curve D(V) as a function of the output voltage V was calculated using the following expressions:
D(V)=Anps(n)12πσexp((VVn)22σ2)σ2=σc2+nσp2,
where A is the total number of measured data; Vn, the output voltage corresponding to the number of detections n; σc, the circuit noise; and σp, the standard deviation of the pulse height distribution when a single photon is detected. The probability that n photons are simultaneously detected, ps(n), is expressed as follows:
ps(n)=pth(n,m)+(n1)pth(n1,m)pct1+mpctps(0)=pth(0,m),
(3)
where pth(n,m) is a Poissonian distribution with a mean value m, and pct is the cross-talk probability. The expression for ps(n) is the same as p(n) in [20

20. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]

] except that ps(n) must be replaced by pth(n,m) in the second term of the numerator and the value n in the second term of the denominator is replaced with m. This means that a pulse generated by cross-talk is assumed to not generate another pulse. When Eq. (3) is used, the theoretical distributions fit the experimental ones better as compared to the case where the expression for p(n) is used. All the parameters obtained by fitting the theoretical distributions to the experimental ones are listed in Table 2

Table 2. Parameter Values Used for Calculation of Pulse Height Distributions

table-icon
View This Table
| View All Tables
. The resolution for a single photon Vn/(2σp) is also listed in the table. At 78.5 K, the resolution was slightly lower while the cross-talk probability was considerably improved.

7. Conclusion

By cooling the MPPC to 78.5 K, we successfully reduced the dark count rate to less than 0.2 cps. To investigate the merits and demerits of the MPPC at 78.5 K, we measured various performance characteristics at 78.5 K and 295 K.

The timing jitter and temporal resolution at 78.5 K showed slight improvement: they were recorded as 158 ps and 2 ns, respectively. The count rate decreased from more than 100 MHz at 295 K to 50 MHz at 78.5 K.

To obtain the photon-number resolution and cross-talk probability, pulse height distributions for simultaneously incident photons were measured and fitted to the theoretical distributions, assuming that output pulses generated by cross-talk did not generate further output pulses. The parameter values determined by fitting indicated that the photon-number resolution deteriorated somewhat and that the cross-talk probability improved considerably at 78.5 K.

The drawbacks of the MPPC at 78.5 K are the decrease in the count rate and the increase in the afterpulse probability. We can improve the count rate to more than 100 MHz using a MPPC with a larger number of pixels and/or smaller-sized pixels. The use of a suitable threshold level for discriminating between photon-induced pulses and afterpulses is effective in decreasing the afterpulse probability, albeit at the cost of the photon detection efficiency. The mechanism behind the increase in the afterpulse probability at low temperature needs further study.

Acknowledgements

This work was supported by the National Institute of Information and Communication Technology (NICT) under the Ministry of Internal Affairs and Communications of Japan. We also would like to thank anonymous referees for many valuable comments and suggestions.

References and links

1.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]

2.

M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers,” Phys. Rev. A 78(2), 022320 (2008). [CrossRef]

3.

E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14(26), 13073–13082 (2006). [CrossRef] [PubMed]

4.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008). [CrossRef]

5.

E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92(11), 113602 (2004). [CrossRef] [PubMed]

6.

T. Moroder, M. Curty, and N. Lutkenhaus, “Detector decoy quantum key distribution,” arXiv:0811.0027v1 [quant-ph] (2008).

7.

M. Moszynski, T. Ludziejewski, D. Wolski, W. Klamra, M. Szawlowski, and M. Kapusta, “Subnanosecond timing with large area avalanche photodiodes and LSO scintillator,” IEEE Trans. Nucl. Sci. 43(3), 1298–1302 (1996). [CrossRef]

8.

V. N. Solovov, F. Neves, V. Chepel, M. I. Lopes, R. F. Marques, and A. J. P. L. Policarpo, “Low temperature performance of a large area avalanche photodiode,” J. Mod. Opt. 51, 1351–1357 (2004).

9.

Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007). [CrossRef]

10.

B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008). [CrossRef]

11.

S. Castelletto, I. P. Degiovanni, V. Schettini, and A. Migdall, “Reduced deadtime and higher rate photon-counting detection using multiplexed detector array,” J. Mod. Opt. 54(2), 337–352 (2007). [CrossRef]

12.

K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003). [CrossRef] [PubMed]

13.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387–2389 (2003). [CrossRef] [PubMed]

14.

M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003). [CrossRef]

15.

G. Bondarenko, P. Buzhan, B. Dolgoshein, V. Golovin, E. Guschin, A. Ilyin, V. Kaplin, A. Karakash, R. Klanner, V. Pokachalov, E. Popova, and K. Smirnov, “Limited Geiger-mode microcell silicon photodiode: new results,” Nucl. Instrum. Methods 442(1-3), 187–192 (2000). [CrossRef]

16.

P. Buzhan, B. Dolgoshein, L. Filatov, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, E. Popova, and S. Smirnov, “Silicon photomultiplier and its possible application,” Nucl. Instrum. Methods 504(1-3), 48–52 (2003). [CrossRef]

17.

V. Golovin and V. Saveliev, “Novel type of avalanche photodetector with Geiger mode operation,” Nucl. Instrum. Methods 518(1-2), 560–564 (2004). [CrossRef]

18.

B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, and I. Tikhomirov, “Calice/SiPM Collaboration, “Status report on silicon photomultiplier development and its applications,” Nucl. Instrum. Methods 563(2), 368–376 (2006). [CrossRef]

19.

A. N. Otte, J. Barral, B. Dolgoshein, J. Hose, S. Klemin, E. Lorenz, R. Mirzoyan, E. Popova, and M. Teshima, “A test of silicon photomultipliers as readout for PET,” Nucl. Instrum. Methods 545(3), 705–715 (2005). [CrossRef]

20.

P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]

21.

N. Dinu, R. Battiston, M. Boscardin, G. Collazuol, F. Corsi, G. F. Dalla Betta, A. Del Guerra, G. Llosa, M. Ionica, G. Levi, S. Marcatili, C. Marzocca, C. Piemonte, G. Pignatel, A. Pozza, L. Quadrani, C. Sbarra, and N. Zorzi, “Development of the first prototypes of silicon photomultiplier (SiPM) at ITC-irst,” Nucl. Instrum. Methods 572(1), 422–426 (2007). [CrossRef]

22.

E. Grigoriev, A. Akindinov, M. Breitenmoser, S. Buono, E. Charbon, C. Niclass, I. Desforges, and R. Rocca, “Silicon photomultipliers and their bio-medical applications,” Nucl. Instrum. Methods 571(1-2), 130–133 (2007). [CrossRef]

23.

M. Petasecca, B. Alpat, G. Ambrosi, P. Azzarello, R. Battiston, M. Ionica, A. Papi, G. U. Pignatel, and S. Haino, “Thermal and electrical characterization of silicon photomultiplier,” IEEE Trans. Nucl. Sci. 55(3), 1686–1690 (2008). [CrossRef]

24.

D. L. Robinson and B. D. Metscher, “Photon detection with cooled avalanche photodiodes,” Appl. Phys. Lett. 51(19), 1493–1494 (1987). [CrossRef]

25.

K. Tsujino, M. Akiba, and M. Sasaki, “Experimental determination of the gain distribution of an avalanche phtodiode at low gain,” IEEE Electron Device Lett. 30(1), 24–26 (2009). [CrossRef]

26.

J. J. Fox, N. Woodard, and G. P. Lafyatis, “Characterization of cooled large-area silicon avalanche photodiodes,” Rev. Sci. Instrum. 70(4), 1951–1956 (1999). [CrossRef]

27.

H. Dautet, P. Deschamps, B. Dion, A. D. MacGregor, D. MacSween, R. J. McIntyre, C. Trottier, and P. P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993). [PubMed]

28.

J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, “Single-photon counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes,” Appl. Opt. 39(36), 6746–6753 (2000). [CrossRef]

29.

E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk Characterization in Geiger-Mode Avalanche Photodiode Arrays,” IEEE Electron Device Lett. 29(3), 218–220 (2008). [CrossRef]

OCIS Codes
(040.0040) Detectors : Detectors
(040.1240) Detectors : Arrays
(040.5160) Detectors : Photodetectors
(040.5570) Detectors : Quantum detectors
(040.1345) Detectors : Avalanche photodiodes (APDs)

ToC Category:
Detectors

History
Original Manuscript: June 22, 2009
Revised Manuscript: August 13, 2009
Manuscript Accepted: August 31, 2009
Published: September 8, 2009

Citation
M. Akiba, K. Tsujino, K. Sato, and M. Sasaki, "Multipixel silicon avalanche photodiode with ultralow dark count rate at liquid nitrogen temperature," Opt. Express 17, 16885-16897 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16885


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References

  1. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]
  2. M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers,” Phys. Rev. A 78(2), 022320 (2008). [CrossRef]
  3. E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14(26), 13073–13082 (2006). [CrossRef] [PubMed]
  4. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, postprocessing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008). [CrossRef]
  5. E. Waks, E. Diamanti, B. C. Sanders, S. D. Bartlett, and Y. Yamamoto, “Direct observation of nonclassical photon statistics in parametric down-conversion,” Phys. Rev. Lett. 92(11), 113602 (2004). [CrossRef] [PubMed]
  6. T. Moroder, M. Curty, and N. Lutkenhaus, “Detector decoy quantum key distribution,” arXiv:0811.0027v1 [quant-ph] (2008).
  7. M. Moszynski, T. Ludziejewski, D. Wolski, W. Klamra, M. Szawlowski, and M. Kapusta, “Subnanosecond timing with large area avalanche photodiodes and LSO scintillator,” IEEE Trans. Nucl. Sci. 43(3), 1298–1302 (1996). [CrossRef]
  8. V. N. Solovov, F. Neves, V. Chepel, M. I. Lopes, R. F. Marques, and A. J. P. L. Policarpo, “Low temperature performance of a large area avalanche photodiode,” J. Mod. Opt. 51, 1351–1357 (2004).
  9. Z. L. Yuan, B. E. Kardynal, A. W. Sharpe, and A. J. Shields, “High speed single photon detection in the near infrared,” Appl. Phys. Lett. 91(4), 041114 (2007). [CrossRef]
  10. B. E. Kardynał, Z. L. Yuan, and A. J. Shields, “An avalanche-photodiode-based photon-number-resolving detector,” Nat. Photonics 2(7), 425–428 (2008). [CrossRef]
  11. S. Castelletto, I. P. Degiovanni, V. Schettini, and A. Migdall, “Reduced deadtime and higher rate photon-counting detection using multiplexed detector array,” J. Mod. Opt. 54(2), 337–352 (2007). [CrossRef]
  12. K. Banaszek and I. A. Walmsley, “Photon counting with a loop detector,” Opt. Lett. 28(1), 52–54 (2003). [CrossRef] [PubMed]
  13. D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett. 28(23), 2387–2389 (2003). [CrossRef] [PubMed]
  14. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A 68(4), 043814 (2003). [CrossRef]
  15. G. Bondarenko, P. Buzhan, B. Dolgoshein, V. Golovin, E. Guschin, A. Ilyin, V. Kaplin, A. Karakash, R. Klanner, V. Pokachalov, E. Popova, and K. Smirnov, “Limited Geiger-mode microcell silicon photodiode: new results,” Nucl. Instrum. Methods 442(1-3), 187–192 (2000). [CrossRef]
  16. P. Buzhan, B. Dolgoshein, L. Filatov, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, E. Popova, and S. Smirnov, “Silicon photomultiplier and its possible application,” Nucl. Instrum. Methods 504(1-3), 48–52 (2003). [CrossRef]
  17. V. Golovin and V. Saveliev, “Novel type of avalanche photodetector with Geiger mode operation,” Nucl. Instrum. Methods 518(1-2), 560–564 (2004). [CrossRef]
  18. B. Dolgoshein, V. Balagura, P. Buzhan, M. Danilov, L. Filatov, E. Garutti, M. Groll, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, F. Kayumov, S. Klemin, V. Korbel, H. Meyer, R. Mizuk, V. Morgunov, E. Novikov, P. Pakhlov, E. Popova, V. Rusinov, F. Sefkow, E. Tarkovsky, and I. Tikhomirov, “Calice/SiPM Collaboration, “Status report on silicon photomultiplier development and its applications,” Nucl. Instrum. Methods 563(2), 368–376 (2006). [CrossRef]
  19. A. N. Otte, J. Barral, B. Dolgoshein, J. Hose, S. Klemin, E. Lorenz, R. Mirzoyan, E. Popova, and M. Teshima, “A test of silicon photomultipliers as readout for PET,” Nucl. Instrum. Methods 545(3), 705–715 (2005). [CrossRef]
  20. P. Eraerds, M. Legré, A. Rochas, H. Zbinden, and N. Gisin, “SiPM for fast photon-counting and multiphoton detection,” Opt. Express 15(22), 14539–14549 (2007). [CrossRef] [PubMed]
  21. N. Dinu, R. Battiston, M. Boscardin, G. Collazuol, F. Corsi, G. F. Dalla Betta, A. Del Guerra, G. Llosa, M. Ionica, G. Levi, S. Marcatili, C. Marzocca, C. Piemonte, G. Pignatel, A. Pozza, L. Quadrani, C. Sbarra, and N. Zorzi, “Development of the first prototypes of silicon photomultiplier (SiPM) at ITC-irst,” Nucl. Instrum. Methods 572(1), 422–426 (2007). [CrossRef]
  22. E. Grigoriev, A. Akindinov, M. Breitenmoser, S. Buono, E. Charbon, C. Niclass, I. Desforges, and R. Rocca, “Silicon photomultipliers and their bio-medical applications,” Nucl. Instrum. Methods 571(1-2), 130–133 (2007). [CrossRef]
  23. M. Petasecca, B. Alpat, G. Ambrosi, P. Azzarello, R. Battiston, M. Ionica, A. Papi, G. U. Pignatel, and S. Haino, “Thermal and electrical characterization of silicon photomultiplier,” IEEE Trans. Nucl. Sci. 55(3), 1686–1690 (2008). [CrossRef]
  24. D. L. Robinson and B. D. Metscher, “Photon detection with cooled avalanche photodiodes,” Appl. Phys. Lett. 51(19), 1493–1494 (1987). [CrossRef]
  25. K. Tsujino, M. Akiba, and M. Sasaki, “Experimental determination of the gain distribution of an avalanche phtodiode at low gain,” IEEE Electron Device Lett. 30(1), 24–26 (2009). [CrossRef]
  26. J. J. Fox, N. Woodard, and G. P. Lafyatis, “Characterization of cooled large-area silicon avalanche photodiodes,” Rev. Sci. Instrum. 70(4), 1951–1956 (1999). [CrossRef]
  27. H. Dautet, P. Deschamps, B. Dion, A. D. MacGregor, D. MacSween, R. J. McIntyre, C. Trottier, and P. P. Webb, “Photon counting techniques with silicon avalanche photodiodes,” Appl. Opt. 32, 3894–3900 (1993). [PubMed]
  28. J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, “Single-photon counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes,” Appl. Opt. 39(36), 6746–6753 (2000). [CrossRef]
  29. E. Sciacca, G. Condorelli, S. Aurite, S. Lombardo, M. Mazzillo, D. Sanfilippo, G. Fallica, and E. Rimini, “Crosstalk Characterization in Geiger-Mode Avalanche Photodiode Arrays,” IEEE Electron Device Lett. 29(3), 218–220 (2008). [CrossRef]

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