Test-beam results of a silicon pixel detector with Time-over-Threshold read-out having ultra-precise time resolution

A time-tagging hybrid silicon pixel detector developed for beam tracking in the NA62 experiment has been tested in a dedicated test-beam at CERN with 10 GeV/c hadrons. Measurements include time resolution, detection efficiency and charge sharing between pixels, as well as effects due to bias voltage variations. A time resolution of less than 150 ps has been measured with a 200 μm thick silicon sensor, using an on-pixel amplifier-discriminator and an end-of-column DLL-based time-to-digital converter.


The Gigatracker detector
A hybrid silicon pixel detector, named GigaTracKer (GTK), was developed for beam tracking in NA62, the experiment designed to detect about 100 events of the ultra-rare decay K + → π + νν with a signal-to-background ratio of 10 in about two years of data taking at the CERN Super Proton Synchrotron [1,2].
The NA62 beam tracker is composed of three GTK stations, installed upstream of the fiducial decay region, that provide precise momentum, angle and time measurements of the beam particles [3]. A station is composed of a 60 × 27 mm 2 single silicon sensor bump-bonded to ten read-out chips, each featuring 1800 300 × 300 µm 2 pixels.
The total beam rate is close to 1 GHz, therefore measurements of kaon rare decays with high statistics and low background demand a time-tagging resolution better than 200 ps to associate the correct parent kaon track with the decay products. Single track efficiency must be higher than 99% per single GTK station. In addition, operation in vacuum and a total material budget of less than 0.5% X 0 per station is required in order to reduce multiple scattering and hadronic interactions to acceptable levels. To cope with these stringent requirements we opted for a solution which combined a 200 µm thick silicon sensor bump bonded to 100 µm thick read-out chips thermally coupled to an ultra-thin cooling plate based on micro-channel cooling technology [4].
In addition each GTK station will have to withstand high and non-uniform hadron fluences, with a maximum in the center of about 2 × 10 14 1 MeV n eq /cm 2 expected in one year of data taking in the NA62 environment. This paper presents the characterisation of non-irradiated detectors only.

JINST 10 P12016 2 Prototype read-out chip with time-over-threshold readout
The most challenging requirement for the GTK detector is the time resolution with such a high channel density, which can be achieved by reducing the jitter of the signal and by carefully compensating for the signal time-walk. For this purpose, a read-out architecture based on an on-pixel Time-over-Threshold (ToT) circuit followed by a time-to-digital converter (TDC) shared by a group of pixels has been designed and produced as small-scale prototype in 130 nm IBM CMOS technology [5].
Signal amplification and discrimination are performed in each pixel, and the discriminated signals are propagated to the chip periphery through dedicated transmission lines using the preemphasis technique in order to maintain timing precision. Processing inside the pixel cell is thus minimised to reduce noise to a minimum: hit arrival times are measured using a delay-locked loop based TDC with 98 ps bins at the end of the pixel columns. Two time measurements are performed for each hit (leading and trailing edges) and the time-over-threshold of the signal is used for offline time-walk correction. The architecture of the chip is such that these time measurements are sent out every time a hit is registered without the need of a trigger signal.
The prototype chip contains a main array of 45 pixels (a folded full column) with nine end-ofcolumn TDC blocks each one serving five pixels through an arbiter block. In addition it includes a small array with nine pixels and a test array of six test pixels with analog output, for a total of 60 pixels. For the purpose of the test-beam, only the folded full column was read out: in this paper we focus only on the performance of the corresponding 9 × 5 pixel matrix (2.7 × 1.5 mm 2 active area).
Five pixels are multiplexed to a single TDC channel: 9 TDCs for the leading edge time and 9 TDCs for the trailing edge time are used for each pixel column. A digital arbiter circuitry has been designed to send hit pulses to the TDC banks and block signals from the same group of 5 pixels in case they would overlap in time. These overlaps are flagged and the information is added to the output data stream.
Based on the successful prototype tests, a full scale version of the chip named TDCpix has been developed [6] and is currently being commissioned in the NA62 experiment.

Test-beam setup
This paper reports the results of a dedicated test-beam performed at the CERN T9 beamline (PS East Hall). A secondary hadron beam (mainly π + and p) with 10 GeV/c momentum, typical divergence of about 2 mrad and spot size of 1 cm, traversed four consecutive GTK detectors. The instantaneous beam intensity was kept intentionally to about 4 × 10 4 particles/cm 2 ·s, a much lower value than the one expected during NA62 operations but instrumental to reduce pile-up effects and measure detector properties in the best possible conditions. Beam particle extraction lasted 400 ms out of an overall period of several seconds.
Given the small dimensions of the active detector area, an accurate alignment with respect to the beam was needed in order to maximise the number of tracks passing through the active parts of four consecutive detectors under test (DUTs). For that reason the DUTs were installed on the precisely aligned mechanical supports shown in figure 1. Pre-alignment was achieved by installing one DUT after the other, and aligning the reference marks on the silicon sensor back-side to a precision of about 150 µm with the help of theodolites. The sensors were then protected from -2 - illumination by a black cover. The DUTs were connected to custom printed circuit boards (PCBs), installed on linear translational stages with 10 µm resolution for fine adjustment of the detector position perpendicularly to the beam. The distance between consecutive DUTs was 10 cm, while the detector PCBs and read-out boards were separated by 40 cm in the direction perpendicular to the beam to avoid any beam interactions with the external digital read-out electronics. A set of finger scintillators (about 3 × 6 mm 2 ) were used for alignment and monitoring and were mounted on the same optical breadboard used for the DUTs. Signals from two scintillators bars read out by four photo-multiplier tubes were combined to provide the precise time reference of a beam particle crossing with a resolution of about 50 ps (later referred to as "fast scintillators").

Detectors under test
The sensor is a planar p-in-n silicon produced by Fondazione Bruno Kessler from 200 µm thick float zone wafers. Approximately 15×10 3 e-h pairs are generated by a minimum ionising particle crossing the sensor (most probable value), corresponding to 2.4 fC. The electrical signal is propagated from the pixel through the bonding bump to the amplifier, with average gain of 65 mV/fC and a r.m.s. spread smaller than 2%.
Few tens of Volt were sufficient to completely deplete the sensor, that was operated at high over-depletion (300 V) for a large fraction of the test-beam. Bias voltages were also set to 100, 200 and 400 V on selected DUTs in order to test the system performance. DUTs were not actively cooled and were exposed to ambient temperature and humidity. No sensor breakdown was observed up to voltages slightly above 400 V.
-3 -For the prototype read-out chip, the threshold value of the on-pixel discriminators was set by a unique digital-to-analog converter for all pixels. The thresholds during the test were set to an average value of 0.7 fC and showed a r.m.s. spread of 0.17 fC. With these thresholds, a very low level of noise was measured during the whole test-beam, as no pixel hits were recorded in the out-of-spill period.

Data acquisition system
The data acquisition (DAQ) system was formed by two independent components: one for the four DUTs and the other for the scintillators.
The first of these comprised a custom designed PCB to which the DUTs were glued and wire bonded, providing locally regulated power supplies and the necessary references. This card was designed to interface to a commercially produced FPGA evaluation board for which firmware was written to buffer and packetise the data sent from the DUTs. The data were then transmitted over Ethernet to PC for logging. The DUTs operate in a triggerless (or self-triggered) fashion, time stamping and sending all discriminator activity off-chip serially, and the readout was implemented in the same manner, packetising and sending all packets to the PC without any on-line data suppression.
The scintillators read-out was based on the CAEN V1290N TDC operated in "trigger matching mode": the TDC records all the hits in a time window which is opened each time it receives an external trigger signal. The CAEN TDC clock was provided by an external 40 MHz frequency generator, while the DUT read-out used a 320 MHz external clock, phase-locked to the previous one. To ensure synchronisation between the two read-out systems, the DUT and scintillators DAQs were correlated on a spill-by-spill basis: a common reset was issued at the start of spill after delivery of a "spill warning" signal. This signal was also connected to one CAEN TDC channel, and the pulse trailing edge gave the global time reference.
In order to cover the whole PS spill length (400 ms) without interruptions we exploited the "Extended Trigger Time Tag" feature of the V1290N. When enabled the trigger signals are time tagged, therefore we could time-stamp each hit without ambiguity by measuring the hit arrival time inside a window. For our application a window length of 51 µs was set and trigger signals were generated by a pulse generator at 20 kHz in order to have a small overlap between the windows.

Data analysis
Data from the two DAQ streams were logged on independent files: at the analysis stage they were reprocessed, filtered and merged to a single file format.
DUTs and scintillators data were time-aligned on a spill by spill basis. During the test beam, a slow drift of the time offsets between the scintillators and DUT DAQs was observed and corrected for prior to the analysis. This effect, of the order of nanoseconds, is mainly caused by the change of ambient temperature during the data taking period. To ease the analysis we defined an "event" by requiring scintillators coincidence together with at least one hit in one or more DUTs within a 10 ns window. Given the beam intensity and size of the active detector area, the probability of having more than one particle crossing the DUT in the event time window was negligible. For a precise time determination it is mandatory to apply to each pixel the correction due to time-walk and that related to the different path length of the discriminator signal from the pixel to the TDC. With our setup both corrections can be determined by comparing the DUT hit time to the fast scintillators combined time (T FASTS ).
For each pixel, the time difference between DUT leading time and the fast scintillators combined time was plotted as a function of the DUT time-over-threshold, which is the difference between trailing and leading times. In figure 2 we show a plot of DUT leading time as a function of ToT for a typical pixel. For each pixel a linear fit was performed and the line parameters were combined to correct both for time-walk and offsets. An alternative correction method was applied by slicing the two-dimensional plot using 100 ps wide bins in ToT and determining the mean of T DUT − T FASTS for each bin. These values were stored in look-up tables and time-walk corrections were applied for each pixel, obtaining similar time resolutions as the previous method.
In the prototype TDCpix chip used in this test-beam, when a pixel of a 5-pixel hit arbiter group is hit consecutively, the absolute delay of the second hit will be shifted in time by a constant, deterministic, time delay. In order to simplify the analysis for time resolution measurement, consecutive pixel hits belonging to the same 5-pixel hit arbiter group are rejected, resulting in a 20% loss of the available data statistics.

Clustering and tracking
An algorithm was implemented to cluster hits in adjacent pixels when they fall in a 10 ns time window. For each cluster, position and leading time are defined as the mean of the individual pixels values weighted by their respective time-over-threshold.
The DUT misalignment in the plane perpendicular to the beam was corrected by measuring residual position distributions. Tracking for the purpose of efficiency calculation was performed using three stations out of four: a line is fitted using three clusters and the extrapolated track impact point is calculated for the fourth station.

Detector performance
After applying the proper data quality cuts, alignments and corrections, the GTK prototype performance is evaluated in the following sections.

Time resolution
GTK time resolution was computed using two independent methods, the first relying on the time difference between two consecutive DUTs and the second computing the time difference between one DUT and the combined fast scintillator detectors.   Timing resolution computed using the fast scintillators is slightly worse due to large tails in the combined scintillators resolution and due to the non-perfect timing alignment. Large deviations from the average value are observed for few pixels and are mainly due to pixels with very low threshold (smaller than 0.45 fC). This effect becomes clear when looking at figure 5, which shows the hit time resolution as a function of the individual pixel threshold: for very low threshold values the time resolution is worse since the signal slope is smaller. It should be noted that the time-walk and offset correction depends on the pixel threshold value, therefore a new correction had to be applied to each pixel when changing the threshold value.
Time resolution dependence on the silicon sensor bias voltage is shown in figure 6, measured with data from the DUTs only and with the fast scintillators as reference, too. As expected, charge carrier velocity increases with the applied electric field up to the saturation value, which is not yet reached at 400 V. It is worth noting that the NA62 requirement on timing resolution is met at 200 V already, with a resolution better than 200 ps on single hits.

Charge sharing between pixels
While charge carriers drift through the sensor under the action of the electrical field, they diffuse laterally. For a particle impinging on the pixel at small distance from the edge, a fraction of the released charge will be collected by the adjacent pixel. To reject as much as possible clusters caused by knock-on electrons, we selected only those with two pixels and rejected events with very high energy deposition (with time-over-threshold higher than 20 ns).
The fraction of two pixels clusters over single pixels is plotted in figure 7 for different sensor bias voltages, showing a strong dependence as expected. This fraction depends also on the pixel thresholds, and given the large number of adjacent pixel threshold combinations only the average value across all pixels is shown for a given bias (corresponding to an average threshold of 0.7 fC). For 300 V bias the charge sharing probability is 3.6% and is compatible with the value computed with a simple analytical model considering drift velocities and lateral diffusion (neglecting signal induction into adjacent pixel and capacitive coupling). This model allowed to estimate a probability of about 3% for a minimum ionising particle, impinging orthogonally and uniformly distributed over the sensor surface, to fire two adjacent pixels operated at 300 V with 0.7 fC thresholds.

Particle detection efficiency
A sub-sample of the selected events has been defined by requiring exactly one hit in each of three DUTs: the fourth target DUT is left free of constraints. A track fit is performed in both horizontal and vertical directions, and the extrapolated track impact position to the target DUT is calculated.
The plot of residual positions shows a r.m.s. of about 110 µm for both views of the target DUT.
Given the relatively poor extrapolated track position resolution (due to the 300 µm wide pixels plus multiple scattering, and the absence of an external tracker with finer position resolution) the detection efficiency must necessarily be calculated by looking for hits not only at the extrapolated pixel position, but also in the 8 neighbouring ones. If a matching pixel exists in the 3 × 3 matrix around the extrapolated pixel, we assign an "efficiency tag" to the pixel hit; conversely if no matching exists we assign an "inefficiency tag" to the extrapolated pixel. With this method we measure a detection inefficiency smaller than 1% for the central region of a DUT as can be seen in figure 8: external and dead pixels have been excluded from the efficiency calculation.

Conclusions
The performance of the NA62 Gigatracker prototype detector has been evaluated in a dedicated test-beam using 10 GeV/c charged hadrons beam. The requirements of the experiment in terms of time resolution and efficiency are completely fulfilled; the detector shows a time resolution better than 200 ps at 200 V and a detection efficiency higher that 99%. When operating the silicon sensor at 400 V bias we measured an unprecedented resolution of less than 150 ps for a hybrid pixel detector. The clear time resolution trend with bias voltage suggests that even smaller values can be reached provided the bias voltage could be increased to reach charge carriers saturation speed.