MPV = (1.776 +- 0.008) fC
Geant4 Simulation
Counts
Charge deposition [fC]
Figure 6.10: Charge deposition from a90Sr source in Geant4 simulation. Most probable value (MPV) of the distribution is 1.776±0.008 fC.
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performed with pions with momentum of 180 GeV/c at the CERN SPS to study the efficiency and time resolution of the un-thinned chip. The sensor was operated at a voltage of 160 V for the pixels and 120 V for the innermost guard ring. The electric field in the un-thinned analog prototype chip is not uniform in depth and is not large enough to saturate the carrier drift velocity, as shown in figure 6.11.
These effects are expected to degrade the timing performance of the the un-thinned sensor.
Figure 6.12 shows the setup of the testbeam experiment. The two un-thinned chips were under test and the chips were aligned on the beam line. The discrim-inator threshold was set individually for each readout. A 50µm-thick Low Gain Avalanche Detector (LGAD) sensor produced by CNM [53] was placed downstream of the chips under test as a reference for the timing measurement. The LGAD sensor was operated at 230 V and is expected to have 30 ps time resolution with the hadron beam. The three sensors were placed downstream of the Geneva FE-I4 telescope [54], which provides the trigger and the tracking information of the beam.
Efficiency
The tracks of the pions were reconstructed by hit informations from the telescope planes. The reconstructed tracks were required to pass through the region of the pixels on the chips under test and efficiency was obtained by calculating the fraction of the number of selected tracks detected by the sensor. Figure 6.13 shows the efficiency map of the chips under test. The areas contoured in black correspond to the region of the pixels to select the reconstructed tracks. The efficiency is (99.79±0.01)% for the upstream chip and (99.09±0.04)% for the small pixel of the downstream chip. The red dashed rectangle represents the LGAD active area on the sensors. The efficiency of the downstream chip increased to(99.88±0.04)%
after requiring hit on the LGAD sensor. This is because multiple scattering events on the upstream chip degraded the tracking performance of the telescope, hence the efficiency for the downstream chip was underestimated.
Time Resolution
The area contoured in red solid line in figure 6.13 represents the region of interest for the timing study. ToT distribution of the small sensor of the upstream chip and time difference between the sensor and the LGAD sensor are shown in figure 6.14. A polynomial function was fitted to the time walk distribution (figure 6.14b) and the parameters of the fitted function were used to correct the time walk effect.
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Figure 3. Results of the TCAD simulation: cross section of the sensor showing the depletion region and the electric field intensity underneath the small pixel, large pixel and guard ring. The white line represents the limit of the depletion region. The fact that the thick substrate was not thinned to 100µm and the absence of the backplane metallization cause an electric field gradient as a function of the sensor depth and prevent the saturation of the drift velocity of the charge carriers.
The capacitance of the small and large pixels have been measured at the same operating point of 160 V to be 0.8 pF and 1.2 pF, respectively. For these capacitance values, the expected preamplifier noise (E NC) from Cadence4simulation is less than 600 e RMS for the small pixel and 750 e RMS for the large one. The pulse rise time at the output of the preamplifier is equivalent to the charge collection time. The working voltage is adjustable and has been optimized using Cadence in terms of the contribution to the time jitter and the power consumption (figure4). The breakdown voltage was measured to be approximately 165 V.
Figure 4. Results of the Cadence simulation: the front-end electronics contribution to the time jitter for a 1.6 fC input signal as a function of the preamplifier power supply, for the capacitance values of the two pixels under study. This is expected to be the dominating contribution to the time jitter in the parallel-plate approximation with saturated drift velocity of the charge carriers.
4https://www.cadence.com— Software: Virtuoso ADL.
Figure 6.11: Simulation result of electric field distribution on the cross section of the un-thinned chip for a positive bias voltage of 160 V applied to the pixels.
White line (∼130µm) shows the edge of the depletion region of the sensor.
Beam Our sensors
(un-thinned) Telescopes
Reference:
LGAD
Figure 6.12: Setup of a test beam measurement
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Development of Annihilation Photon Detection with Fast Timing Monolithic Silicon Pixel Sensors
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uniform efficiency. The areas contoured in black in figure 6 correspond to the region of the pixels selected to study the efficiency. The dashed rectangle is the projection of the LGAD active area on the sensors. The region of interest on which the time resolution has been studied is represented by the red rectangles.
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Efficiency Map - Upstream Sensor
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Efficiency Map - Downstream Sensor 1
Figure 6 . Efficiency map of the upstream chip (left) and the downstream small pixel (right). The areas contoured in black represent the regions of the monolithic pixels selected to measure the efficiency; the dashed rectangles represent the projection of the LGAD active area on the monolithic chips. The red rectangles are the regions of interest used for the time resolution measurement. In the downstream sensor, only the small pixel was read out.
The measured efficiency for MIP detection is ( 99 . 79 ± 0 . 01 ) % for the upstream sensor and ( 99.09 ± 0.04 ) % for the small pixel of the downstream sensor. The smaller value obtained for the downstream pixel is probably due to the multiple scattering produced by the upstream board, which is reducing the tracking precision of the telescope. In order to reduce this effect, the efficiency of the downstream pixel has been measured in the same region selecting only the events from the telescope that were detected also by the LGAD. The downstream small pixel efficiency with this selection was measured to be ( 99.88 ± 0.04 ) %.
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Figure 7 . Map of the most probable time-over-threshold values for the upstream small pixel. For small signals, the time-over-threshold at the output of the amplifier is proportional to the charge deposited in the pixel.
The uniformity of response over the pixel area was also studied. The most probable time-over-threshold (ToT) of the signal was used to estimate the charge deposited in the different regions of
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(a)
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and calculating the fraction of events detected by the sensor. The three pixels show a high and uniform efficiency. The areas contoured in black in figure 6 correspond to the region of the pixels selected to study the efficiency. The dashed rectangle is the projection of the LGAD active area on the sensors. The region of interest on which the time resolution has been studied is represented by the red rectangles.
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Efficiency Map - Upstream Sensor
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Efficiency Map - Downstream Sensor 1
Figure 6. Efficiency map of the upstream chip (left) and the downstream small pixel (right). The areas contoured in black represent the regions of the monolithic pixels selected to measure the efficiency; the dashed rectangles represent the projection of the LGAD active area on the monolithic chips. The red rectangles are the regions of interest used for the time resolution measurement. In the downstream sensor, only the small pixel was read out.
The measured efficiency for MIP detection is ( 99.79 ± 0.01 ) % for the upstream sensor and ( 99.09 ± 0.04 ) % for the small pixel of the downstream sensor. The smaller value obtained for the downstream pixel is probably due to the multiple scattering produced by the upstream board, which is reducing the tracking precision of the telescope. In order to reduce this effect, the efficiency of the downstream pixel has been measured in the same region selecting only the events from the telescope that were detected also by the LGAD. The downstream small pixel efficiency with this selection was measured to be ( 99 . 88 ± 0 . 04 ) %.
4800 4900 5000 5100 5200 5300 5400 5500 5600 µm]
Figure 7. Map of the most probable time-over-threshold values for the upstream small pixel. For small signals, the time-over-threshold at the output of the amplifier is proportional to the charge deposited in the pixel.
The uniformity of response over the pixel area was also studied. The most probable time-over-threshold (ToT) of the signal was used to estimate the charge deposited in the different regions of
(b)
Figure 6.13: Efficiency map of the upstream sensor (a) and the downstream sensor (b).
The area contoured in black represents the event selection of reconstructed tracks. The red dashed rectangle represent the projection of the LGAD active area on the monolithic chips. The rectangles in red solid line corre-spond to the region of interest for the timing study. Only small pixel was readout for the downstream sensor.
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Figure 9. a) Time-over-threshold distribution (a) and average time walk of the signal as a function of the time-over-threshold (b) for the small pixel of the upstream sensor. The vertical offset is arbitrary. The time walk correction is done by fitting the data with a polynomial function.
The time resolution after the time walk correction of the small pixel from the upstream sensor is shown in figure10(a). This result is degraded by the non-uniformity of the response of the sensor due to the lack of backplane metallization. This effect can be partly corrected by measuring the variation of the average time-of-flight as a function of the particle hit position on the sensor surface.
Figure10(b) shows the time resolution obtained for the same pixel after this correction. Following the same analysis procedure, the time resolution measured for the three pixels under study, before and after the correction for the particle hit position, is reported in table2.
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Time difference upstream small pixel - LGAD [ps]
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Time difference upstream small pixel - LGAD [ps]
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Figure 10. Measurement of the jitter on the time difference between the small pixel of the upstream monolithic sensor and the LGAD without correcting for the particle hit position (a) and correcting for it (b).
The mean value of the time difference distributions is set to zero by the time walk correction. The data are fitted with a Gaussian distribution to measure the standard deviation.
The large pixel shows⇠ 20% worse time resolution with respect to the small pixels. Since the E NC is proportional to the pixel capacitance, the difference is the detector capacitance of a factor 1.5 between the large and the small pixels under study, should lead to an increase of the time resolution by the same factor. The smaller difference measured implies that the time resolution is affected, for both pixels, by an additional term, which is not proportional to the amplifierE NC.
This term could be attributed to the non-uniformity of the electric field, the thick substrate and the absence of the sensor backplane metallization.
(a)
Figure 9. a) Time-over-threshold distribution (a) and average time walk of the signal as a function of the time-over-threshold (b) for the small pixel of the upstream sensor. The vertical offset is arbitrary. The time walk correction is done by fitting the data with a polynomial function.
The time resolution after the time walk correction of the small pixel from the upstream sensor is shown in figure10(a). This result is degraded by the non-uniformity of the response of the sensor due to the lack of backplane metallization. This effect can be partly corrected by measuring the variation of the average time-of-flight as a function of the particle hit position on the sensor surface.
Figure10(b) shows the time resolution obtained for the same pixel after this correction. Following the same analysis procedure, the time resolution measured for the three pixels under study, before and after the correction for the particle hit position, is reported in table2.
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Time difference upstream small pixel - LGAD [ps]
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Time difference upstream small pixel - LGAD [ps]
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Figure 10. Measurement of the jitter on the time difference between the small pixel of the upstream monolithic sensor and the LGAD without correcting for the particle hit position (a) and correcting for it (b).
The mean value of the time difference distributions is set to zero by the time walk correction. The data are fitted with a Gaussian distribution to measure the standard deviation.
The large pixel shows ⇠20% worse time resolution with respect to the small pixels. Since theE NC is proportional to the pixel capacitance, the difference is the detector capacitance of a factor 1.5 between the large and the small pixels under study, should lead to an increase of the time resolution by the same factor. The smaller difference measured implies that the time resolution is affected, for both pixels, by an additional term, which is not proportional to the amplifier E NC.
This term could be attributed to the non-uniformity of the electric field, the thick substrate and the absence of the sensor backplane metallization.
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(b)
Figure 6.14: ToT distribution of the small pixel of the upstream sensor (a) and the time difference distribution between the small pixel and the LGAD as a function of ToT, fitting with a polynomial function (b).
Figure 6.15 shows the time difference between the small pixel from the upstream sensor and the LGAD sensor after the time walk correction. Approximately220 ps time resolution of the small sensor of the upstream chip was measured. Measured time resolution is summarized in table 6.1. Approximately 20% worse time res-olution for large sensor was observed with respect to small pixels, while the two small pixel sensors showed similar time resolution. This is probably caused by larger ENC, which depends on the pixel capacitance of the sensor. In addition, non-uniformity of the electric field due to the absence of the wafer thinning and the backside processing may further degrade the timing performance.
Table 6.1: Measured time resolution for the analog prototype chip Pixel Time resolution (ps) Capacitance (pF)
Downstream small 202.3±0.8 0.8
Upstream small 219.0±0.7 0.8
Upstream large 265±1 1.2
6.3 Discussion
The achievements of the measurements of the analog prototype are summarized as follows:
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