Characterizing SiPMs

= SiPM Performance Requirements =



A novel method of low light readout is evaluated here. Traditionally, signals of tens to hundreds of photons are read out by photomultiplier tubes (PMTs), which provide gain of $$10^6$$ via a cascade of electrons multiplied on collision at each of the device's sequential dynodes. The small cross-section scintillating fibers in the high rate tagger microscope that will operate in Hall-D of Jefferson Lab call for a new and more compact readout. Silicon Photomultipliers (SiPMs) are discussed on the merits of their gain, detection efficiency, speed and noise level.

The tagger microscope consists of many identical and well isolated readout channels, each consisting of a several cm long scintillating fiber connected to a clear acrylic fiber light guide. A tagging electron travels axially down the length of a scintillating fiber depositing an average of 4 MeV of energy in the fiber, resulting in ~1600 scintillation photons within the forward capture cone of the fiber. Assuming that 80% of these are delivered to the SiPM active surface and a conservative estimate of 15% for the efficiency of the SiPM leads to an estimate of 190 for the average SiPM pixel count per event. Monte Carlo simulations have shown that an efficient detection threshold corresponds to 40% of the average pulse height, or 80 SiPM pixels. This implies a requirement for the dark rate that spontaneous pulses never exceed 80 pixels.

The large photon yield expected at the end of the light guide does not demand unusual detection efficiency on the part of the SiPM. For example, 10% efficiency with the above number of photons still yields a signal of 130 photons. However, given that the scintillator (BCF-20) has a finite decay time (2.7ns) the more photons are produced the more clearly resolved is the leading-edge time of the pulse.

The device is expected to have a high enough gain (measured in electrons per photon detected) - around 106 in order for such a small light signal to be recorded by conventional electronics. SiPM devices are also susceptible to spurious, thermally excited pixel breakdowns, each showing up as a single photon hit ("dark count"). Very high rates of these single-pixel events may create pileup above the signal threshold. All of the above parameters (detection efficiency, gain and dark rate) depend on applied bias voltage and temperature. Stability of performance within the expected fluctuations of these environmental variables is an important requirement.

Another criterion in SiPM selection is its dynamic range. Although the tagger essentially provides digital information - scintillation detected or not in each energy channel within each beam bucket - sufficient range is necessary to set a threshold above the noise floor and to allow for some degree of gain variation at high rates arising from the finite pixel recovery time.

= Bench Test Setup =

Hardware
A fast light source operating in an environment with little background is necessary for the tests described here. The challenge is in preventing light leaks in this chamber despite the need for access ports, patching wires through walls and installing sensor and temperature control modules that must interface with the outside.

It is also preferred that the light source is fast and close in wavelength to the light from scintillating fibers, which are in the blue-green.

Dark Box Construction
Running this setup with a hybrid photodiode (HPD) module DEP PP0350 of known characteristics allows us to calibrate the light intensity. The SiPM detection efficiency can then be characterized relative to the HPD. The signal from the SiPM was clean enough to distinguish peaks corresponding to discrete photon (pixel) counts in the histogram signal integrals. Therefore, the gain of the SiPM was found independently of the HPD - the SiPMs were self-calibrating! The measurements section below describes this feature further.

Below are the diagrams of the dark box with the HPD and SiPM assemblies installed. A temperature controller system (TE Tech. TC-24-12) was procured, which operates by driving a Peltier junction based on feedback from a thermistor compared to voltage-specified reference temperature. It was calibrated and installed into the wall of the dark box via a custom-designed light-tight frame.

Light Pulser


A pulser circuit was designed with a pulse height controlled by the amplitude of a step function from a function generator. The pulser differentiates the step function signal and therefore can create pulses as narrow as the rising edge of the step function. Above a saturation point, the pulse broadens to a maximum of 6 ns. The adjacent figure shows the pulser circuit that drives the LED. The LED has some finite rise time and sometimes a very long decay tail. This response function convolves the pulser signal so the speed of the combined system has to be analyzed for each LED type and evaluated for the use of photon detector characterization.

Choice of Light Source
The original LED available to the group was the blue QT Optoelectronics MV5B60. Analyzing the pulses from the HPD illuminated with this device showed an initial spike in its light output followed by a tail with a very long decay constant. Several more devices with longer wavelengths were procured and measured. We settled on a yellow LED (Fairchild MV8304) for subsequent measurements because it had no long tail in its light pulses. The SiPMs were characterized with respect to one another and the HPD using this LED. Its mean wavelength is about 590nm, near the peak of the SiPM photon detection efficiency curve.

By the time more detailed studies of the SSPM-06 were initiated, a fast LED very close the the mean emission wavelength of the BCF-20 was found. This was the Agilent (Avago Technologies) HLMP-CE30-QTC00. Its pulse shows a small tail in the light output that lasts for about 100ns, but this is fast enough to be contained in the 100ns integration gate used for these tests.

Data Acquisition
A Tektronix TDS 2024 (2Gsamp/s, 200MHz) was used to acquire the SiPM signal from its preamplifier. The response of the SiPM preamplier is well understood based on detailed analysis and simulation. Since tens of thousands of waveforms are necessary to construct a clean histogram of collected charge, a fast PC based data collection system was necessary. The data export module installed on this oscilloscope allows RS-232 interface over which commands can be issued and data transfer requested. Unfortunately going above the baud rate of 9600 always resulted in lost bytes. At 9600 the 2500-sample waveform collected by the oscilloscope takes about 2-3 seconds to transfer over the serial link to the host PC. Since we are dealing with time windows of 1&mu;s in which the unit is too slow to collect all 2500 samples (it was found to copy or interpolate between actual samples) it was decided to just collect the first 1000 samples, corresponding to the first 4 divisions on the screen. Under these conditions, the waveforms were collected at a rate of one per second.

For the purposes of collecting integrals of waveforms (proportional to total charge collected per received flash) it was later found that the averages of the functions could be automatically computed by the oscilloscope and then the results transferred much faster than the entire waveform, about 3 per second. This value times the window duration equals the desired integral!

Aside from the convenience of being able to collect usable results within hours instead of a day, this speedup also minimized the problem of systematic drifts that occur during long runs. It was found that the higher statistics obtained during extended runs would sometimes be offset by the blurring of peaks due to slow drifts in the gain and pedestal. Whether due to environmental variations over the course of a day or electronic effects, these drifts smeared the histograms, most of which already had a very faint sign of resolved photon peaks. So, faster data acquisition also meant reducing the effects of these drifts.

= SiPM Measurements =

Analysis Approach


The first remarkable feature of the the SiPM statistics is the presence of discrete peaks in the histogram of charge collected in the SiPM. The SiPM pulse charge is computed as the SiPM signal integral (Vs) divided by the Gaintrans-impedance (V/A) of the preamplifier. This allows us to determine the charge collected per activated pixel (per detected photon) and therefore gives the gain of the device. This is the "self-calibration" referred to above.

The general analysis procedure was to
 * 1) histogram the collected set of function integrals;
 * 2) get the pedestal: the first peak corresponds to events with no photon hits, so it defines zero charge collected;
 * 3) calculate the gain and rescale the histogram to units of detected photons

Since each peak in the histogram shown in the figure at the right is expressed in units of photon count, the mean is the average number of detected photons per pulse. After subtracting away the contribution from the dark counts (described below), the efficiency of the SiPM can be calculated by comparing this average yield to that found by the HPD.

This procedure was repeated with the LED and/or SiPM covered to measure the dark rate. Depending on which distribution showed the photon peaks more distinctly, either the illuminated or dark datasets were used for the gain calculation and pedestal calculation. Either way, a mean was extracted from the dark distribution to calculate the dark rate and to subtract the average dark pixel count measured from the average pixel count measured while illuminated.

Efficiency calculated in the manner described is compared to the expected efficiency. Integrating the HPD response function in frequency space weighted by the LED emission spectrum yields the mean detection efficiency of the HPD for that light source. The same exercise was carried out using the photon detection efficiency function supplied by the SiPM manufacturer, and compared with the measured efficiency as a check that we had obtained the expected SiPM performance.

Summary of Basic Characteristics and Comparison of SiPMs
Below is the summary of results obtained from these measurements performed on the two SiPMs acquired from Photonique.

Detailed Characterization
Since the SiPM performance is sensitive to the bias voltage applied and the ambient temperature, a measurement of SiPM properties as functions of bias voltage (Vb) and temperature (T) was performed on the SSPM-06. By this point, the SSPM-06 was judged to be a better sensor for the tagger microscope, owing to higher sensitivity in the blue-green range and better active area match to the fiber cross-section. Higher photon detection efficiency is not required for the sake of pulse-height resolution, but it is important in that it improves the time resolution because of the intrinsic scintillation decay time of 2.7 ns in the fiber.

The range of interest for these operating variables were:
 * Vb: from 0.5 V below to 0.5 V above the operating range, yielding a range of interest: 19-21 V
 * T: 3&deg;C (to avoid accumulating frost) up to 35&deg;C

Histogram Fitting Method
It was found that the individual photon peaks were very indistinct at bias voltages below 20 V and also at temperatures above 20&deg;C. This merging of the peaks is explained by the reduction in pixel gain that occurs for lower bias voltages and higher temperatures, while the electronic noise from the preamplifier remains relatively constant. The solution to this was to abandon the manual location of pedestals, peak spacing etc. Instead, a parametrized model was created by Prof. Richard Jones based on which fitting of the histograms was performed. It has the form:

$$ f(q) = \sum_{p,s} \left(\frac{e^{-\lambda} \lambda^p}{p!}\right)\left(\frac{e^{-p \mu}(p \mu)^s}{s!}\right) \left(\frac{\exp \left(-\frac{1}{2}\; \frac{\left[q-(p+s)\right]^2}{\sigma_0^2+(p+s)\sigma_1^2}\right) } {\sqrt{2\pi}\left[\sigma_0^2+(p+s)\sigma_1^2\right]^{\frac{1}{2}} }\right) $$

where,

$$\lambda, \mu, \sigma_0, \sigma_1, g, x_0 \quad$$ are the fit parameters. Note the absence of a vertical scale parameter. The vertical scale depends on the number of samples collected, whereas the equation in this model is normalized. Rescaling works as follows:

If $$f(x)=T\,f(q)$$, where $$T$$ is a vertical scaling parameter and since $$dq = dx/g$$,

$$\int_{-\infty}^{\infty} f(x)\, dx = Tg \int_{-\infty}^{\infty} f(q)\, dq = Tg $$ implies that Tg is the number of events collected times the bin width (in Vs).

Now, with this powerful instrument at hand used with a fitter in Paw, the histograms collected as function of T and Vb were analyzed. It turned out that even histograms with nearly indistinguishable peaks yielded a reasonable fit to this model.

Results for SSPM06
Below is the analyzed data on dark rate, gain and photon detection efficiency (PDE) as function of T and Vb. An attempt was also made at mapping the rate of secondaries (multi-Poisson parameter) as a function of these variables but the small trends perceived in the data were within the parameter's error bars.

Results for Hamamatsu 400 pixel MPPC
Data were collected with the 1mm x 1mm Hamamatsu MPPC using a similar procedure as was used for the Photonique SiPM studies reported above. The integration window was 250 ns wide, and contained all of the positive side of the signal and about 15% of the negative undershoot tail from the differential-coupled output. The data below were taken with a pulse amplitude giving approximately 1pe per pulse, and with the pulser covered to measure the dark rate (last figure). Each run contains about 15000 samples.

The black histograms in the plots are the data and the red curves are the best fit to the data using the multi-Poisson model described in a preceeding section, with two modifications.
 * The Gaussian smearing of the individual pixel pulse-height distribution was replaced with the following function that has an asymmetric tail.
 * This function is normalized to unity and is described by parameters:
 * $$\alpha$$ = inverse length of left-side tail
 * $$\beta$$ = fraction of peak integral in left-side tail
 * $$\sigma$$ = sigma of Gaussian right-side tail = $$ (\sigma_0^2+(p+s)\sigma_1^2)^{1/2}$$


 * The mean cross-talk parameter, formerly p&mu; in the treatment described above, has been replaced with p2&mu;.

Without the second change above, the fit to the data is significantly worse. It might be explained by the tendency of cross-talk to bunch up because of self-coupling feedback. A simpler explanation might be that it takes into account a natural variation in the light output of the pulser from pulse to pulse. This remains to be investigated. The parameters of the fit function listed in the above plots are listed below.


 * 1) Integral of fit function, in rescaled (pe) x-axis units.
 * 2) Centroid of zero pe peak, in V-s.
 * 3) Gain of readout, in V-s/pe.
 * 4) Mean detected photon count (&lambda;p)
 * 5) Mean cross-talk pixels per detected photon (&lambda;s)
 * 6) Excess noise per pixel (&sigma;1), in pe
 * 7) &alpha; parameter of peak shape function, see above
 * 8) &sigma;0 parameter of peak shape function, see above
 * 9) &beta; parameter of peak shape function, see above

The Fortran source code where the fit function is implemented can be found here.

= Links =


 * SiPM Vendors
 * BCF-20 Scintillating Fiber (catalog)
 * Detection spectrum of the HPD photocathode.
 * Temperature Controller (vendor page)
 * Callibration of the temperature controller: a lookup table for the control and monitor voltage.
 * Brandan Krueger's pages on the SiPM Amplifier and MATLAB amplifier in detail
 * Photonique SA SiPM Specification Sheets: SSPM-05~ and SSPM-06~

= References =


 * 1) I. Senderovich and R.T. Jones, "Suitability of Silicon Photomultiplier Devices for Readout of a Scintillating Fiber Tagger Hodoscope", GlueX-doc-760 (2007)
 * 2) Z. Sadygov (Dubna), Three advanced designs of avalanche micro-pixel photodiodes: their history of development, present status, maximum possibilities and limitations.
 * 3) P.Pakhlov (ITEP), SiPM: Development and Applications

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Written and last edited by Igor Senderovich 18:30, 13 August 2007 (EDT)