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G. Lutz and R. Klanner
5.11.3 Solid-State Photo Multipliers: SiPMs
In the last decade a new type of avalanche photon detector has reached maturity and
is now commercially available, the Solid State Photo Multiplier, also referred to as
SiPM (Silicon Photo Multiplier), G-APD (Geiger Mode Avalanche Photo Diode)
or MPPC (Multi Pixel Photon Counter) [47]. It consists of two dimensional arrays
of 100–10,000 single photon avalanche diodes (SPADs), called pixels, with typical
dimension between (10 μm) 2 and (100 μm) 2 . The pixels are operated in limiting
Geiger mode and every pixel gives approximately the same signal, independent
of the number of photons which have produced simultaneously electron-hole pairs
in the amplification region of the pixel. The sum of the pixel signals is equal to
the number of pixels with Geiger discharges, from which the number of incident
photons can be determined. As the output charge for a single Geiger discharge is
typically larger than 10 5 elementary charges, 0, 1, 2, and more Geiger discharges
can be easily distinguished, enabling the detection of single optical photons with
high efficiency and sub-nanosecond timing. The quenching of the Geiger discharge
is either achieved by a resistor in series with each pixel or an active feedback.
Two types of SiPMs have been developed: Analogue and Digital. In Analogue
SiPMs [47] the individual pixels are connected to a common readout and the SiPM
delivers the summed analogue signal. In Digital SiPMs [48] each pixel has its own
digital switch to a multi-channel readout system and the output is the digitized pulse
height and precise time information for the pixels with Geiger discharges. Digital
SiPMs also allow disabling pixels with high dark-count rates.
The pulse shape and the gain of SiPMs are explained with the help of Figs. 5.53
and 5.54: A schematic cross section of a single pixel is shown in Fig. 5.53, and an
electrical model of a pixel with resistor quenching, in Fig. 5.54. The bias voltage is
denoted V bias , the single pixel capacitance C pix , and the quenching resistance R q .
Frequently, in particular for SiPMs with larger pixel sizes, a capacitance C q parallel
to R q is implemented. In the quiescent state the voltage over C pix is V bias . When an
electron-hole pair in the amplification region starts a Geiger discharge, in the model
the switch is closed and C pix is discharged through the current source until the turnoff voltage V off is reached, at which the Geiger discharge stops and the switch opens.
The assumption of a constant current source is certainly oversimplified. However the
sub-nanosecond discharge time is so short, that details of the time dependence of the
discharge current hardly affect the results of the simulation. If a finite capacitance C q
is present, a fast pulse with charge C q ·(V bias – V off ) appears. After the switch opens,
C pix is charged up to V bias with the time constant τ ≈ R q ·C pix and the total signal
charge is approximately (C pix + C q )·(V bias – V off ). Figures 5.55 and 5.56 show
two examples of pulse shapes: (a) For a KETEK SiPM with (15 μm) 2 pixels and
negligible C q , and (b) for a KETEK SiPM with similar doping profiles however with
(50 μm) 2 pixels and a finite C q . The value of R q has to be sufficiently high to quench
the Geiger discharge. As C pix increases with increasing pixel area, τ = R q ·C pix also
increases, and a finite C q has to be introduced to achieve a good timing performance
and an increased pulse height if fast pulse shaping is used.
G. Lutz and R. Klanner
5.11.3 Solid-State Photo Multipliers: SiPMs
In the last decade a new type of avalanche photon detector has reached maturity and
is now commercially available, the Solid State Photo Multiplier, also referred to as
SiPM (Silicon Photo Multiplier), G-APD (Geiger Mode Avalanche Photo Diode)
or MPPC (Multi Pixel Photon Counter) [47]. It consists of two dimensional arrays
of 100–10,000 single photon avalanche diodes (SPADs), called pixels, with typical
dimension between (10 μm) 2 and (100 μm) 2 . The pixels are operated in limiting
Geiger mode and every pixel gives approximately the same signal, independent
of the number of photons which have produced simultaneously electron-hole pairs
in the amplification region of the pixel. The sum of the pixel signals is equal to
the number of pixels with Geiger discharges, from which the number of incident
photons can be determined. As the output charge for a single Geiger discharge is
typically larger than 10 5 elementary charges, 0, 1, 2, and more Geiger discharges
can be easily distinguished, enabling the detection of single optical photons with
high efficiency and sub-nanosecond timing. The quenching of the Geiger discharge
is either achieved by a resistor in series with each pixel or an active feedback.
Two types of SiPMs have been developed: Analogue and Digital. In Analogue
SiPMs [47] the individual pixels are connected to a common readout and the SiPM
delivers the summed analogue signal. In Digital SiPMs [48] each pixel has its own
digital switch to a multi-channel readout system and the output is the digitized pulse
height and precise time information for the pixels with Geiger discharges. Digital
SiPMs also allow disabling pixels with high dark-count rates.
The pulse shape and the gain of SiPMs are explained with the help of Figs. 5.53
and 5.54: A schematic cross section of a single pixel is shown in Fig. 5.53, and an
electrical model of a pixel with resistor quenching, in Fig. 5.54. The bias voltage is
denoted V bias , the single pixel capacitance C pix , and the quenching resistance R q .
Frequently, in particular for SiPMs with larger pixel sizes, a capacitance C q parallel
to R q is implemented. In the quiescent state the voltage over C pix is V bias . When an
electron-hole pair in the amplification region starts a Geiger discharge, in the model
the switch is closed and C pix is discharged through the current source until the turnoff voltage V off is reached, at which the Geiger discharge stops and the switch opens.
The assumption of a constant current source is certainly oversimplified. However the
sub-nanosecond discharge time is so short, that details of the time dependence of the
discharge current hardly affect the results of the simulation. If a finite capacitance C q
is present, a fast pulse with charge C q ·(V bias – V off ) appears. After the switch opens,
C pix is charged up to V bias with the time constant τ ≈ R q ·C pix and the total signal
charge is approximately (C pix + C q )·(V bias – V off ). Figures 5.55 and 5.56 show
two examples of pulse shapes: (a) For a KETEK SiPM with (15 μm) 2 pixels and
negligible C q , and (b) for a KETEK SiPM with similar doping profiles however with
(50 μm) 2 pixels and a finite C q . The value of R q has to be sufficiently high to quench
the Geiger discharge. As C pix increases with increasing pixel area, τ = R q ·C pix also
increases, and a finite C q has to be introduced to achieve a good timing performance
and an increased pulse height if fast pulse shaping is used.