Threshold Determination

Once the chip’s performance is validated, the T-thresholds are determined. This procedure applies only to the operation with disabledE-threshold validation. Due to the low number of photons, this is the case for the Mu3e scintillating fibre detector but not for the scintillating tile detector or the operation with Lutetium-Yttrium Oxyorthosilicate (Lu_2(1−x)Y_2xSiO₅) (LYSO) crystals in aPETapplication.

Sensor Biasing: Voltage and Currents

TheSIPMDAC, which is available for each channel, allows adjusting the voltage at theASIC’s positive input terminal to which the sensors cathodes are connected (see subsection C.1.1).

The potential at the input terminal is typically in a range 100 mV to 900 mV and it is not linear in theDAC value. Figure C.4 shows typical input voltages as a function ofSIPM DAC

values. This feature allows homogenizing the overvoltage of the differentSiPMcolumns. The

DCR, measured as the event rate at a specific threshold or as the current through one column, provides a suited handle for this task.

Table C.10 summarizes the measured currents through the biased sensors at different oper-ation voltages in the absence and the presence of a beta source.

11.2. MEASUREMENT AND ANALYSIS PROCEDURE: A USER’S GUIDE

0 5 10 15 20 25

30 T­threshold [DAC]

0 25 50 75 100 125 150 175 200

rate [k event/s]

10V54.2V 55.2V 56.2V 57.2V 58.2V 59.2V

Figure 11.8:Measured event rate at differentSiPMsensor bias voltages atTTHRESHOLDDACscale 0as a function ofT-threshold of a randomly chosen channel (26). The step functions are fitted with sigmoid functions to determine the position of the step.

CHAPTER 11. MUTRIG

T-Threshold Scans

The thresholds are determined through threshold scans with attached and biased sensors. Due to the sensorsDCR behaviour, the measured rate as a function of the threshold yields a step function as shown in Figure 11.8 in section 5.2. The simplest method to determine the rate of each channel at a given threshold utilizes theCEC. This prevents huge amounts of data. Per threshold step the meanCECvalue over 1 s is determined and plotted as a function of threshold

DACvalue. TheT-threshold consists of 64DACvalues in 8 different scales and covers both signal polarities. Only the positive range is probed. Table C.8 lists the channelDACsettings used for the threshold scans. One scan is performed with a sensor bias below breakdown to determine the systems’ noise, respectively theASIC’s baseline level.

Figure 11.8 shows aT-threshold scan of a randomly chosen channel (26) atscale 0at different

SiPMbias voltages. Below breakdown, the baseline is determined, and potential system noise is measured. With increased bias voltage, theDCRincreases which manifests in the increased level of the plateau. At the same time the gain increases, hence the larger signals shift the step function edge to larger amplitude, corresponding to smallerDAC values. Note that the stated voltages are applied with respect to ground. The potential at the positive MuTRiG input terminal can be adjusted and showsO(0.5 V) positive offset to ground. TheDCRscans are fitted with a sigmoid function to determine the position of the edge.

T-Threshold Range

Based on theT-threshold scans, as shown in Figure 11.8, the possible dynamic range of MuTRiG in combination with the utilised sensor can be determined. Figure 11.9 shows in the top the edge positions of theDCRsteps at different bias voltages in combination with the baseline level.

The amplitude of one single photoelectron inDACsteps is given by the distance of the edges to the baseline. This is shown in the middle part. The dynamic range is approximately given by the availableDACsettings above baseline divided by the above-stated amplitude. This is summarized in the bottom of Figure 11.9. Note the significant deviations between channels and that the linearity of theDACvalues is only approximated.

T-Threshold Scale The dynamic range of theT-threshold can in principle be adjusted with theDAC’s scale. Figure 11.10 shows threshold scans of a randomly chosen channel (26) of a sensor biased with 56.2 V at all availableDACscales. In two scales, 3 and 7, no single photon step is present at all. It turns out that the dynamic range in the default baseline scale 0is maximized.

Input Bias A second handle on the dynamic range is given by the constant current of the input stage controlled by the INPUTBIAS DAC which affects the gain. Figure 11.11 shows threshold scans of a randomly chosen channel (26) of a sensor biased with 56.2 V for different values of thisDAC. The effect at small signals, as in case of the Mu3e scintillating fibre detector, is minor.

11.2. MEASUREMENT AND ANALYSIS PROCEDURE: A USER’S GUIDE

0 10 20

edge position [DAC] 30

0 10 20 30 40

photo electron amplitude [DAC]

0 5 10 15 20 25 30

channel 0

2 4

dynamic range [photo electron]

10V57.2V 57.2V

Figure 11.9:The position of the sub-breakdown 10 V ( ), 57.2 V ( ) and 59 V ( ) edges (top).

The amplitude of single photoelectrons inDACsteps is derived from the edge position differences (middle). The resulting dynamic range ofMuTRiGwith the utilized sensors (bottom). Channels 8 through 16 are missing in this measurement.

CHAPTER 11. MUTRIG

Figure 11.10:Measured event rate at a sensor bias of 56.2 V for all availableDACscales as a function of theT-threshold of a randomly chosen channel (26).Scale 0is used as the default baseline scale.

11.2. MEASUREMENT AND ANALYSIS PROCEDURE: A USER’S GUIDE

Figure 11.11:Measured event rate at a sensor bias of 56.2 V for different values of theINPUTBIAS

DACas a function ofT-threshold of a randomly chosen channel (26). Input bias setting of 4 is the default baseline.

CHAPTER 11. MUTRIG

0 2000 4000 6000 8000 10000

period [ns]

counts

threshold 28: noise threshold 10: DCR exponential fit f =^122 kHz

dead time = 40ns

0 100 200 300 400

Figure 11.12:Period spectrum of a single channel connected to aSiPMarray biased with 58.2 V at two different thresholdDACsettings: a threshold of28( ) is in the noise whereas a threshold of 10( ) corresponds to 0.5 photoelectron trigger level. An exponential fit of the distributions tail ( ) allows the extraction of theDCR. Furthermore, theTDCdead time manifests in the spectrum’s lower edge cutoff at 40 ns.

Summary The presented consideration to the possible dynamic range of MuTRiG in com-bination with the employed SiPMcolumn arrays yield the conclusion that at reasonable bias voltages (above 56.2 V) it is feasible to operate up to≈2 photoelectron thresholds in all chan-nels. The dynamic range of most channels is larger than this. But, the possible uniform threshold levels of all channels is dominated by the one with the minimal range. For high bias voltages (≈60.2 V) the possible dynamic range is below 2 photoelectrons in the worst channels. This has to be considered especially in the scope of irradiated sensors which show significantDCRincrease and potential raised pixel to pixel crosstalk.

Threshold Validation

Based on theT-threshold scans the desired operation point is chosen. Typically, thresholds at 0.5 or 1.5 photoelectrons are chosen. These thresholds are validated by the period spectrum of each channel. Figure 11.12 shows an example of one channel with two different threshold settings with a SiPMarray biased at 58.2 V. The threshold at aDACvalue of 28 is below the ampitude of noise, respectively theASIC’s baseline. A few discrete frequencies dominate the spectrum. The noise in the presented example consists of two main contributions at frequen-cies of≈2.99 MHz and≈766 kHz. The period spectrum outside of the baseline at approxim-ately 0.5 photoelectron at aDACvalue of 10 is expected to be smooth. The presence of peaks is a strong indication of pick up of noise. An exponential fit of the distribution’s tail yields the

DCRat this threshold level. Furthermore, theTDC’s dead time manifests itself the lower cut off of the period spectrum at 40 ns.

11.2. MEASUREMENT AND ANALYSIS PROCEDURE: A USER’S GUIDE

0 5 10 15 20 25 30

fine counter bin [no]

counts per fine counter bin [50ps]

0.0 0.2 0.4 0.6 time [ns]0.8 1.0 1.2 1.4 1.6

Figure 11.13:The fine counter bin distribution ( ) caused by the non-uniform delays of theVCO

delay stages. TheDNLeffects can be corrected for as shown in the time distribution ( ) binned into the mean fine counter width of 50 ps.