KETEK

Device Parameters

Photon Detection Efficiency

The photon detection efficiency (PDE) is defined as the quantity of photon-discharged cells divided by the quantity of incident photons.

For a given device the PDE value depends on the applied overvoltage (Figure 2) and the wavelength of the incoming light (Figure 3). First one is due to the fact that the Geiger efficiency is increasing with increasing overvoltage until it reaches its maximum. Second one is due to the very different interaction- and absorption behavior of light with different wavelength in silicon. The KETEK SiPM has been optimized for blue light. This is suitable for many scintillator materials like LSO, NaI:Tl, CsI, GSO, Anthracen, etc.

Figure 2: Increase of PDE with rising overvoltage: For small overvoltage the PDE is still increasing with increasing overvoltage until the Geiger efficiency gets maximal. This saturation regime starts at approximately 15% relative overvoltage.

Noise effects like dark pulses, crosstalk and afterpulses are causing an excess signal which has to be subtracted to achieve the real PDE value. This can be done by a Poisson statistic based evaluation of single photon spectra.

Figure 3: Relative PDE versus wavelength of incoming light. Peak sensitivity of KETEK SiPMs is at 420 nm.
Figure 4: Absolute PDE of KETEK SiPMs versus geometrical efficiency for blue and green light.


Gain

The Geiger discharge of a micro pixel is determined by the pixel capacitance and the applied overvoltage ΔV = VBias - VBreakdown. Without any excess noise this single pixel discharge is equivalent to the gain of the SiPM. Therefore in a first approximation the gain of a SiPM is scaling linear with the applied overvoltage.

The excess noise is causing a slight reduction of the real gain compared to the single pixel discharge. This effect is increasing with increasing overvoltage, but quite small under normal operation conditions.

Figure 5: Single pixel discharge for different micropixel types. The single pixel discharge is strongly influenced by the micropixel size and the geometrical fill factor.


Avalanche diodes have a positive temperature coefficient of the break down voltage. This temperature coefficient is directly affecting the applied overvoltage DV and with it the gain according to the following formular:

Therefore the temperature coefficient of the gain is decreasing drastically with increasing overvoltage.

Figure 6: Temperature coefficient of the gain versus relative overvoltage.

Noise Effects

Dark Count Rate

Pulses not being excited by incoming light are termed as dark pulses. They are triggered by thermally generated electrons. Its frequency is termed as dark count rate. Figure 7 shows the dark count rate versus the wavelength for KETEK Silicon Photomultipliers with (green) and without (blue) trench technology at room temperature.
For KETEK devices the dark rate is below 500 kHz/mm2 at the working point of 20% relative overvoltage.

Figure 7: Dark count rate versus relative overvoltage for KETEK Silicon Photomultipliers with (green) and without (blue) trench technology at 20°C.

The dark count rate is scaling with the carrier density in silicon. Therefore the dark count rate shows a strong dependency on the temperature. Roughly every 10°C the dark rate is reduced by a factor of 2 (Figure 8).

Figure 8: Dark count rate versus Temperature.


Optical Cross Talk

Depending on the quantity of hot electrons in the Geiger discharge of a microcell something like three to fifty secondary photons (in average three photons per 105 avalanche electrons) with a wavelength range from 450 nm to 1600 nm are emitted from the excited cell in all directions. These secondary photons are just like the incoming light able to cause a further Geiger discharge in case they are able to reach any other charged microcell within the SiPM device. To this end several light pathes are possible (Figure 9):

Figure 9: Schematic of optical cross talk mechanism.

(1) Most obviously the secondary photons can travel directly to a neighboring cell (direct optical crosstalk),

(2) A secondary photon is able to generate an electron-hole-pair close to a neighboring cell. The carriers can diffuse to the microcell and cause their discharge (delayed optical crosstalk),

(3a, b) Secondary photons, being reflected at one of the various interfaces like e.g. package, scintillator and device backside, can reach a neighboring cell via an indirect path (indirect optical cross talk).

The optical crosstalk mechanism according to (1) can be suppressed by a deep optical trench isolation between the individual microcells. In case the trench is deep enough, it helps also to suppress the crosstalk according to mechanism (2).

Figure 10 shows the reduction of the optical cross talk probability by introducing the KETEK trench technology. At 20% relative overvoltage the optical crosstalk probability is reduced by a factor of two.

Figure 10: Optical crosstalk probability versus relative overvoltage for a PM1150 with and without trench technology. At 20% relative overvoltage the optical crosstalk probability is reduced by a factor of two by the KETEK trench technology.

IV Characteristics and Breakdown Voltage

In contrast to APDs SiPM devices are operated above breakdown voltage. In this regime the current density is in the range of 10 µA/cm2 up to 1 mA/cm2. This dark current is caused by thermally generated electrons, which trigger the discharge of micropixels.

Below breakdown the current density is dominated by carrier diffusion and generation. The current level is typically 1 nA/cm2.

Figure 11: Current density of a KETEK PM3350 SiPM below and above break down voltage.

Avalanche diodes have a positive temperature coefficient of the break down voltage. The value of this temperature coefficient depends in a first approximation on the depth of the avalanche zone. For KETEK SiPMs this value is 22 mV/K.

Due to this temperature coefficient of the breakdown voltage the applied overvoltage DV to the SiPM and with it the gain are influenced by temperature variations. (see also "GAIN").

Figure 12: Breakdown Voltage versus Temperature.

Pulse Shape

The single photoelectron (phe) pulse shape of a KETEK SIPM device is asymmetric due to the fact that the dis- and recharging procedure of a fired SiPM microcell is determined by different RC values.
This behavior can be followed by an electrical model (Figure 13) which has been proposed by F. Corsia et. al. in e.g. “Modeling a silicon photomultiplier (SiPM) as a signal source for optimum front-end design” [NIM A 572 (2007) 416–418].

 

Figure 13: Electrical model of a SiPM as a signal source according to F. Corsia et. al.

The SiPM device is modeled here with the following single components:

  • CD:         Capacitance of the micro-Avalanche diode
  • IPulse:      Internal current source representing the Geiger discharge
  • RQ:         Quenching resistor
  • CQ:         Parasitic quenching capacitance
  • CG:         Stray capacitance of all electrical traces
  •  RS:         Series resistance

The time constant of the leading signal edge is determined by the fired micro APD capacitance and the series resistance according to τD =  RS CD. It is below 1 nsec as long as the series resistance is small enough (< 1 kΩ).


The signal tail has two different time constants:

  1. A slow one which is determined by the quenching resistor and the micro cell capacitances according to τD =  RS (CD + CQ).
  2. A fast one which is determined by the series resistance, the parasitic quenching capacitance and the parasitic grid capacitance. It is only visible as long as the series resistance is small enough.

Figure 14 shows a single phe pulse of a KETEK PM3350 device measured with a 17 Ω series resistance as well as the fitting results for the fast and the slow component. The signal rise time is clearly below 1 nsec.

Figure 14: Single photo electron pulse shape of a KETEK PM3350 SiPM device.

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