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 dinodes. The small cross-section light channels in the high rate tagger microscope that will operate the Hall-D of Jefferson Lab call for a new and more efficient approach. Silicon Photomultipliers (SiPMs) are discussed on the merit 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 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 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. Such devices are also susceptible to spurious, thermally excited pixel breakdowns, each showing up as a single photon hit ("dark count"). High rate of these single-pixel events may create a 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 despite expected fluctuations of these variables is an important requirement.

Another criterion in SiPM selection is its dynamic range. Although this readout device essentially provides digital output - scintillation detected or not - enough of a range is necessary to set a threshold above the noise floor and to account for some pixels being not having required from a previous hit.

= 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 discreet 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. The calibrating this device with the HPD showed a very long decay of its pulse. Several more devices with larger wavelengths were procured and measured settling on a yellow LED (Fairchild MV8304) for its speed. The SiPMs were characterized with respect to one another and the HPD using this device. With a mean wavelength of about 590nm, this LED is near the peak of the SiPM detection spectra.

By the time more detailed studies of the SSPM-06~ were initiated a fast enough device very close the the mean emission wavelength of the BCF-20 was found. This was the Agilent (Avago Technologies) HLMP-CE30-QTC00. Its time width is somewhat larger than the convenient 100ns window that is convenient for data acquisition (explained below), but accurate data can be derived by centering the window at the same spot for every trial.

Data Acquisition
A Tektronix TDS 2024 (2Gsmp/s, 200MHz) is used to acquire the SiPM signal from its preamplifier, the response of which 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. 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 resolved to just collect the first 1000 samples, corresponding to the first 4 divisions on the screen. The waveforms now trickled at 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 can be requested much faster, about 3 per second. This value times the window duration equals the desired integral!

Aside from the convenience of usable results within hours instead of a day, is the issue of avoiding systematic drifts. It was found that while higher statistics smooth out the histogram of integrals, there are also drifts, 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 photon peaks. So, faster data acquisition also meant avoiding 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 (proportional to the SiPM signal (V) integral (Vs) by 1/Gaintrans-impedance (A/V). This allows us to determine the charge collected per activated pixel (per 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 properly belongs at zero [charge collected]
 * 3) calculate the gain and rescale the histogram: the width between adjacent peaks corresponds to the the gain in units of Vs/pixel. (Using the amplifier trans-impedance gain value, this can later be converted to charge/pixel)
 * 4) calculate the mean of this shifted and rescaled set. Since each peak is now pegged to photon count, the mean is in the units of average photons received. Based on this value, corrected by the dark count (described below), the efficiency of the SiPM can be calculated by comparing this average flux to that felt by the HPD.

This procedure is 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 the frequency space weighted by the LED emission spectrum yields the mean detection efficiency of the HPD for that light source. Doing the same with the manufacturer-supplied response function of the SiPM and comparing to the figure for the HPD yields the expected SiPM efficiency relative to the HPD.

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 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. Aside from gains in efficiency and dynamic range of the resulting readout, higher photon detection implies better time resolution because of the scintillation decay time of 2.7ns in the fiber.)

The range of interest for these operating variables were:
 * Vb: from 0.5V below to 0.5V above the operating range, yielding a ranger of interest: 19V-21V
 * T: 0-above room temp., in practice 3&deg;C (to avoid growing snow) to 35&deg;C

However, it was found that the peaks were very indistinct at bias voltages below 20V and temperatures above 20&deg;C. This was probably due to the narrowing of the peaks due to smaller gain or convolution of the additional dark counts detected.

Histogram Fitting Method
The solution to this was to abandon the manual location of pedestals, peak spacing etc. Instead, a model was created by Prof. Richard Jones based on which fitting of the histograms was performed. It has the form:

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

where,

$$\lambda_{(p)}, \lambda_{(s)}, \sigma_0, \sigma_1, g, x_0 \quad$$ 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 best fit to this model and suggested the appropriate gain and other parameters.

Results
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.

= 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)