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We report a new and improved photon counting method for the precision PDE measurement of SiPM detectors, utilizing two integrating spheres connected serially and calibrated reference detectors. First, using a ray tracing simulation and irradiance measurement results with a reference photodiode, we investigated irradiance characteristics of the measurement instrument, and analyzed dominating systematic uncertainties in PDE measurement. Two SiPM detectors were then used for PDE measurements between wavelengths of 368 and 850 nm and for bias voltages varying from around 70V. The resulting PDEs of the SiPMs show good agreement with those from other studies, yet with an improved accuracy of 1.57% (1σ). This was achieved by the simultaneous measurement with the NIST calibrated reference detectors, which suppressed the time dependent variation of source light. The technical details of the instrumentation, measurement results and uncertainty analysis are reported together with their implications.
©2014 Optical Society of America
1. Introduction
The silicon photo-multiplier (hereafter SiPM) is a semiconductor photodiode containing many micropixels operating in Geiger mode. Connecting all the micropixels in parallel permits the SiPM to act as an analogue device, which provides a linear superposition of signals from activated photodiodes [1,2]. Over the past decade, SiPMs have been developed as photo sensors that achieve an ultimate sensitivity of single photon detection for a wide range of applications, including minimally-invasive imaging technologies, photometry, spectroscopy and calorimetry in the field of medical science, biology, astronomy and high energy instrumentations.
Photon detection efficiency (hereafter PDE) is one of the important measures of SiPM performance. The precision measurement of PDE requires not only precise measurements of SiPM response, but a well calibrated light source with a high degree of uniformity as well as a high accuracy of irradiance. The best equipment providing these irradiance characteristics is an integrating sphere with a light source and it has been widely used in photometry [3,4]. The internal surface of the sphere provides ideally diffused light with a reflectance close to Lambertian [5] even to the infrared wavelength [6].
A number of interesting techniques, with or without integrating spheres, have been studied concerning the PDE measurement of high sensitivity photo sensors [7–12]. Yamamoto et al. [7] applied a photocurrent method to measure the PDE values of 100, 400, and 1600 micropixel SiPMs, called Multi-Pixel Photon Counters (hereafter MPPCs) over the 280 nm to 900 nm wavelength range. The PDE determined for a 100 micropixel MPPC, for example, reaches about 66% at 400 nm. However, the authors acknowledged that their method tends to overestimate the PDE as a result of contributions by crosstalk and after pulses.
Otte et al. [8] attempted a photon counting method in the PDE measurement of a 1024 micropixel SiPM over the wavelengths coverage from 395 nm to 650 nm. An example of the resulting PDE is 3.32 ± 0.18% at 590 nm. In their study, they attempted to reduce the differences in sensitivity between the SiPM and the reference detector. However, the irradiance ratio measurement between the reference detector and the SiPM suffers from a relatively large error, and this limitation was further confirmed when they discovered that their PDE values, measured with a commercially available avalanche photodiode (APD), differed by about 15% from the manufacturer’s measurement.
On the other hand, Eraerds et al. [9] used a photon counting method to measure the PDE of a 132 micropixel SiPM by focusing 532 nm wavelength light onto the detector via a set of lenses. The resulting PDE shows 14 ± 1.2% for 31V. An avalanche photodiode used as the reference detector and the target SiPM were placed at the focal position alternately, for each PDE measurement. This led to different timings for measurements by the reference and target detectors, which may have resulted in unmeasured fluctuations of the irradiance arriving at either detector for any given measurement.
Bonanno et al. [10] used both photocurrent and photon counting methods to measure the PDE of a 100 micropixel SiPM and two MPPCs of 100 and 400 micropixels. Their PDE measurement instrument has an integrating sphere and a monochromator as the light source. The example results for the 100 micropixel MPPC include PDE of 44% (photocurrent method) and of 20% (photon counting method), showing a large difference in the measured PDE for the same detector at a wavelength of 500 nm. They claimed that the photon counting method tends to produce more accurate measurement results through the reduction of afterpulse and crosstalk effects. The different sensitivity in different detectors may introduce additional systematic uncertainty in the measurement of PDE.
Eckert et al. [11] used both photocurrent and photon counting methods to measure PDEs of thee MPPC detectors of 100, 400 and 1600 micropixels. Specially, two pin holes (i.e. 0.6 mm wide for the photon counting method and 0.8 mm wide for the photocurrent method) were used to compensate the difference between the two methods. An example result for the 100 micropixel MPPC is a PDE of 36.8 ± 2.4% at 440 nm (peak wavelength). Even with the use of the reference detector calibrated to 1% accuracy, they noticed that the flux measurement error after implementing the pin holes still played a major role in increasing the PDE measurement error.
Using two integrating spheres, Lefeuvre et al. [12] obtained 17.8 ± 0.4% in the quantum efficiency of a photomultiplier tube (PMT) at the 377nm wavelength, where the geometrical uncertainty 1.5% was not added. Specifically, the integrating spheres were used to compensate the difference in sensitivity between the reference detector and the sample PMT and the irradiance uniformity of the integrating sphere exit port was taken into account in the measurement.
In general, whilst researchers have been successful in measuring PDE, their results tend to exhibit large variations, depending on their choice of measurement method and instrument, and these results are often limited to PDE measurements at either a few selected wavelengths or bias voltages. These limitations are further aggravated by a relatively large measurement uncertainty, with a relative uncertainty ranging from 2.7% to 10%. In this study, we developed a new instrument capable of achieving high accuracy PDE measurements over a range of wavelengths and bias voltages. Our method benefits from the utilization of two integrating spheres and calibrated reference detectors. This approach is further strengthened by the inclusion of a ray tracing simulation study to confirm the irradiance level incident upon the detector surface.
Particularly, we emphasize that, as we see it from Eraerds et.al [9], the amount of light from the light source varies with time. We improved the measurement technique and overcame this fundamental limitation by making simultaneous measurements with reference photodiodes so that the measurement accuracy depends mostly on a NIST certification to 1.5%. Section 2 describes the theoretical basis and its characteristics, and the design and construction of the PDE measurement instrument are illustrated in Section 3. Section 4 provides an estimation of the flux incident on the SiPM surface, and experimental measurements of the flux and PDE. Uncertainty estimates in our experiment and discussion are given in Section 5, before the concluding remarks in Section 6.
2. Characteristics of photon detection efficiency measurement
Integrating spheres are often combined with calibrated photodiodes and used as uniform radiation sources for testing optoelectronic devices such as SiPMs. The PDEs of the SiPMs are then determined by the ratio of the number of detected photons (NDetected) to the number of incident photons (NIncident), as shown in the following equations
where NSiPM is the number of photons captured by a SiPM and NDark specifies the signal, representing the number of photons detected by the SiPM in total darkness. PPD is the power received by the reference detector, PDark, the power read by the reference detector in total darkness, λ, the wavelength utilized in the measurement, T, the duration of measurement, APD, the area of the reference detector, ASiPM, the SiPM area, and R, the ratio of the flux measured at the reference detector to that measured at the SiPM. In practice, computing the above Eq. (3), and hence estimating a PDE, is achieved from measurements of NDetected and NIncident.As noted earlier, the determination of NIncident in Eq. (2) involves a fair amount of systematics, particularly from R. Both the output irradiance and the uniformity of its light source are important factors in the precise determination of R. A large size of integrating sphere relative to the port size or the utilization of multiple spheres can enhance the uniformity of the light output. However, very few photons would arrive on the SiPM surface for the case of multiple spheres, even though the light source initially provides many photons. For this reason, the Poisson equation is applied as described in Section 4.3.
Ray tracing Monte Carlo simulations of incident flux could be made by taking into account the instrument geometry which will be discussed in Section 4.1.
3. Instrument setup for PDE measurement
Figure 1 shows a schematic diagram of the PDE measurement instrument, including two integrating spheres (i.e. IS-1 and IS-2). An LED light source capable of emitting light of 20 nm FWHM at 14 wavelengths is placed in one of IS-1 input ports. The light pulses have durations of 20 ns. The emitted light is incident on IS-1, and portions of the scattered light arrive at the reference photodiode detectors 1 (PD1) and 2 (PD2). The remaining light enters into IS-2 and is scattered once again, before a portion of the scattered light reaches the SiPM surface at 100 mm distant from the IS-2 exit port. The scattering characteristics of IS-1 and IS-2 are Lambertian. Two photodiodes are used as the reference detectors calibrated to the NIST standard with 1.5% of 1σ in uncertainty.
Fig. 1 The schematic diagram of the PDE measurement instrument including two integrating spheres, multi-wavelength LEDs, reference photodiodes of Ophir PD300R-UV and Thorlabs S150C, and the SiPM with its readout electronics.
The light pulses arrive at the Hamamatsu SiPMs: MPPC S10362-11-100C (micro pixel: 100, 1 mm2, VBreakdown = 69.4V), and S10362-11-025C (micro pixel: 1600, 1 mm2, VBreakdown = 70.6V). These two SiPMs were used for the PDE measurement over the range of wavelengths between 368 and 850 nm. The over voltages for S10362-11-100C and S10362-11-025C varied from 0.8 to 1.8V, and from 2.3 to 4.3V, respectively, as determined by measurements of the breakdown voltages. The temperature of the dark box for the PDE measurement was maintained at 25 ± 1°C. Once registered, the corresponding electrical signal was amplified before being converted by a 12 bit ADC. Figure 2 shows a photograph of the measurement instrument we constructed.
Fig. 2 PDE measurement instrument as built (right): (1) reference photodiode 1, (2) reference photodiode 2, (3) LED light source, (4) integrating sphere 1, (5) integrating sphere 2, (6) integrating sphere 2 exit port, (7) SiPM(MPPC), (8) amplifier & high voltage power supply. The left figure illustrates the 3D cross-sectional diagram of integrating sphere 1 and 2 along the line (9) in the right figure, where the divergence angle of LED is shown.
4. PDE measurement
4.1. Number of incident photons to the SiPM
We performed a ray tracing simulation model to make estimation of the flux incident on the SiPM. Using an ASAPTM environment, the light source was modeled as an emitting source with a 10 degree divergence angle, emitting 20 million light rays. IS-1 and IS-2 appear as two Lambertian spheres with 99% in reflectance and the interfacing pupil between IS-1 and IS-2 was assumed to have a 0.5% reflectance. The supporting structure for reference detector 2 has a measured reflectance that varies with wavelength. All the dimensional characteristics of the parts and components were defined by reference to the suppliers’ technical sheets. The result from ray tracing simulation appears in Fig. 3.
Fig. 3 The number of photons arriving at the SiPM versus wavelength of LED pulse. Blue squares and red triangles indicate the measurement at the SiPM location and the result of simulation, respectively.
We measured the photon flux arriving at the SiPM location with reference photodiode 1,which is designed to measure incoming light of about 20 pW and thus, for the 465 nm wavelength, 4.7x108 photons per second. For each LED pulse of 20 ns width, the number of photons arriving at the SiPM location is plotted against wavelength in Fig. 3, and their data are listed in Table 1. The measurement results indicated by the blue squares were derived by using the reference photodiode 1 inside IS-1 and the relationship shown in Fig. 4, while the simulation was performed at the SiPM location.
Table 1. Number of incident photons per pulse at the SiPM location (MPPC S10362-11-100C)
Fig. 4 Irradiance ratio variation between PD1 and SiPM locations, as defined as R in Eq. (2), plotted against wavelength. Vertical errors are too small to be seen.
As shown in Fig. 3, the number of detected photons increases with wavelength. The ray tracing simulation predicts the measured number of photons well as measured by the experiment. These results prove the validity of the estimated number of photons arriving at the SiPM location.
4.2. Measurement of R: Irradiance (W/m2) ratio between the IS-1 PD1 location and the SiPM location
PD2 was mounted to one of the 3 exit ports of IS-1 at a fixed location and used to measure the irradiance inside IS-1. On the other hand, the location of PD1 was alternated back and forth between the IS-1 exit port and the SiPM location, so that the wavelength dependent irradiance at the two locations could be measured. The resulting ratio of the irradiance values at the two locations are plotted against wavelength in Fig. 4, which shows that the ratio decreases somewhat sharply near the 400 nm and 700 nm wavelengths, but much less markedly at other wavelengths. This data quantifies the inherent characteristics of the instrument and is very useful for deducing the irradiance at the SiPM location, using the measurement at the IS-1 PD1 location.
4.3. PDE measurement results
The determinations of NSiPM and NDark in Eq. (1) are made from the distribution of the SiPM output signal, typically in terms of an ADC value. The distribution of the photon count can be represented by a Poisson distribution function [13].
The pedestal area indicates the probability of n = 0 in Poisson Eq. (4). Therefore, by fitting a Gaussian function to the associated ADC value range, the pedestal number can be derived and subsequently applied to Eq. (5) for an estimation of µ. Once obtained, µ can be used in Eq. (6) for determination of the photon number counted where nped is the pedestal number and ntot is the total number of counted events.Figure 5 shows an example of the number of events plotted against the ADC value measured by our SiPM. The signal histogram is a Poisson distribution of a photon count. The pedestal area in Fig. 5 indicates the probability of n = 0 in Poisson Eq. (4).
Fig. 5 The histogram of SiPM signal in unit of ADC values. It follows a Poisson distribution. The pedestal value is determined by Gaussian fitting to the count data.
By fitting a Gaussian function to the ADC value range of the 50-250, the pedestal number can be obtained and subsequently applied in Eq. (5) for an estimation of µ. Here nped is the pedestal number and ntot is the total number of events counted. Once obtained, µ can be used in Eq. (6) for a determination of the photon count.
We made the PDE measurement over the wavelength range between 368 nm and 850 nm at over voltages in each case, as noted in Section 3. Figure 6 shows the results of the PDE measurement for four wavelengths and six overvoltage points, which indicates the clear dependences of PDE on the wavelength. We note that the 100 micropixel MPPC shows relatively higher PDE slopes than that of 1600 micropixel MPPC as the over voltage increases.
Fig. 6 The PDE measurement versus “over voltage” for MPPC 100 micropixel (S10362-11-100C; left) and MPPC 1600 micropixel (S10362-11-25C; right) for different wavelengths.
Figures 7 and 8 show, respectively, PDE measurements for S10362-11-100C and S10362-11-25C across wavelengths ranging from 368 to 850 nm at six different over voltage levels. The measured PDEs increase to their highest levels at around 450 nm and decrease gradually for longer wavelengths. The results also show that the measured PDE increases with the over voltage.
Fig. 7 Measured PDE of S10362-11-100C plotted against wavelength. Symbols represent the measurement data from different over voltages.
Fig. 8 Measured PDE of S10362-11-25C plotted against wavelength. Symbols represent the measurement data from different over voltages.
5. Measurement uncertainty and discussion
5.1. Test of irradiance (W/m2) uniformity from integrating spheres
We tested the irradiance uniformity of our double integrating sphere instrument by taking into account the parameters of sphere diameter, exit port diameter, port fraction, and radiance uniformity. The reference photodiode detector is 10 mm in diameter, while SiPM has a sensitive area of 1 mm by 1 mm. For this difference to be taken into account, the incident irradiance ratio needs to be corrected by the application of a constant equivalent to the ratio of the surface areas of the two sensors. Using the estimation method suggested in another study [14], the output irradiance uniformities at the IS-1 PD1 location were computed. PD1 is located 6.99 mm from an exit port of IS-1. A pinhole of 1 mm in diameter is positioned 0.7 mm away from the PD1 surface. The PD1 and pinhole assembly was placed 100 mm from the IS-2 exit port, mounted on the XYZ stage, and moved +/−5 mm from the port center, to measure the irradiance across the IS-1 exit port diameter. Both theoretical computation and measurement results are shown in Fig. 9 to be well above 99.5%. We also note that vertical errors are in the range from 0.09% to 0.25%, which contributes to the systematic error in R by 0.13%.
5.2. Systematic uncertainties in PDE measurement
Using the error estimation methods [13,15], we analyzed the uncertainty factors and estimated their contributions to the PDE measurement. In general, the uncertainty varies with wavelength and with bias voltage. An example of uncertainty estimation is provided in Table 2. First, we note that for S10362-11-025 the relative measurement uncertainty was estimated to be about 1.57% (1σ) for 4.3V over voltage at a wavelength of 465 nm, leading to a PDE value of 19.65 ± 0.31%. We understand that the primary contributor to the uncertainty of 1.57% (1σ) mentioned above is the reference diode calibrated only to about 1.5%. Nevertheless this value is much better than the 6.8% of the photo-current method used elsewhere [11]. Second, the errors in the table fall into two categories. The first is the statistical uncertainty from including two Poisson counts and repeatability and the second corresponds to the systematic uncertainties associated both with instruments and also with the evaluation of R. Specially, we note that the method we developed in this study successfully reduced R, which is a dominant error factor in PDE measurement.
Table 2. Example of PDE measurement uncertainty budget (S10362-11-025C, over voltage: 4.8V, λ: 465nm)
6. Concluding remarks
Overcoming the limitations of earlier studies, this work reports the construction of a new and improved instrument for PDE measurement utilizing the photon counting technique. Our device consists of a light source diode, two reference photo diodes calibrated to the NIST standard, two integrating spheres connected serially, and two target SiPM detectors. This instrument was constructed in house, and its characteristics were investigated both analytically and with a ray tracing simulation.
The PDE was then measured over wavelengths ranging from 368 nm to 850 nm and for over voltages ranging between 0.8 V and 1.8 V for MPPC S10362-11-100C, and between 2.3 V and 4.8 V for MPPC S10362-11-25C. Our measurements of the PDEs agree with those of other studies, while our results have an uncertainty of 1.57% (1σ), which is a significant improvement over previous results. The systematic uncertainty in R is significantly lowered to 0.13% in our study, which implies that the overall uncertainty in PDE measurement can be improved through the utilization of reference photodiodes that have been calibrated to a better accuracy. The instrument reported in this study can be applied widely for precision measurements of photon detection efficiency for a wide range of light sensitive detectors.
Acknowledgments
The work is supported by the Defense Acquisition Program Administration (DAPA) and the Agency for Defense Development (ADD) in Korea (ADDR-117), Creative Research Initiatives of NRF (RCMST), and NRF SRC 2010 0027910.
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