The TimeSPOT sensors (Figure 1), referred also as 3D trench sensors, are silicon 3D pixels with the electrodes shaped in order to maximise the timing performance for MIP detection [5]. The TimeSPOT pixel has a dimension of 55 × 55 μm² with an active thickness of 150 μm. The sensor is characterised by trench shaped electrodes: two external ohmic-wall electrodes, which extend over the entire row of a pixel matrix to provide the bias voltage to each pixel and a collecting electrode 40 × 5 μm² with a thickness of 135 μm [6].

The TimeSPOT sensors have been fully characterised in two beam test campaigns featuring both excellent time resolution, of about 10 ps, and detection efficiency of 99% [5, 7–10].

In general, 3D sensors are expected to have an higher radiation hardness with respect to planar silicon sensors due to the shorter inter-electrodes distance which guarantees a lower trapping probability of charge carriers during their motion towards the electrodes [11]. Radiation tolerance of 3D columnar sensors has been already proved up to 3 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² [12] for what concerns the charge carrier collection efficiency. A similar behaviour is expected also for 3D trench sensors for which however the radiation hardness was never tested. To verify the radiation tolerance of the TimeSPOT sensors an irradiation campaign has been carried out at the TRIGA Mark II Reactor ² at the Jožef Stefan Institute in Ljubljana, Slovenia. Several test structures of the second TimeSPOT batch, produced in 2020 by Fondazione Bruno Kessler (FBK) in Trento, Italy, were irradiated at two different neutron irradiation fluences of 1.0 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² and 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻². After irradiation the test structures were stored in a temperature controlled box at about −20 °C, to prevent radiation damage mitigation due to the reverse annealing. Two types of test structures, the single pixel and the triple-strip (Figure 2), were then wire bonded to the readout boards and stored back at −20 °C. In the single pixel structure the innermost of seven adjacent pixels in a row is readout, while the two adjacent pixels are connected to ground, to guarantee the proper electric field configuration. This structure has been used for the charge collection (amplitude) and timing characterizations. The triple-strip structure consists of 30 pixels placed in three adjacent rows which have the readout electrodes shorted together. This device, having a larger active area, has been used for the efficiency measurements.

The test structures are readout through the TimeSPOT single channel front-end electronic boards detailed in [13]. This circuit features a signal-to-noise ratio (S/N) of about 20 and an electronic jitter below 7 ps at 2 fC input charge. The power consumption is about 70 mW/channel. The board directly hosts the test structures and provides the bias voltage to the sensors by means of a conductive tape placed on the back side of the test structures (Figure 3).

Irradiated TimeSPOT sensors have been tested in May 2022 at the CERN SPS/H8 beamline with a 180 GeV/c positive hadrons beam. The beam, on average, consists of 10⁶ particles which are extracted every 30 s in a 4 seconds-long spill and focused on an approximately circular spot of 8 mm radius measured at the setup location. The setup (Figure 4) consists of a total of four detectors precisely aligned with respect to the beam line: two 3D trench sensors and two microchannel-plate photo-multipliers (MCP-PMTs). The two 3D trench silicon sensors, along with their respective front-end electronics boards, have been securely installed within an electromagnetically shielded light-tight enclosure.

One of the sensors, the irradiated structure, is operated at low temperature. To do that the sensor is placed in a cold, temperature-monitored environment, which is isolated from the other part of the light-tight enclosure by means of a polystyrene box. Dry ice has been regularly filled inside two 3D printed containers positioned inside the polystyrene box. This relatively simple system effectively enables the operation of the irradiated sensors within a temperature range [−40, − 20]°C for about 10 h. The sensor positioned within the polystyrene box is fixed to a stationary mount which only allows to manually rotate the sensor around the vertical direction to measure the sensor response for non-normal beam incidence. The other (non-irradiated) sensor is mounted on a movable holder outside of the thermally isolated box. Such holder is driven by two closed-loop piezoelectric linear stages, allowing movements of up to 16 mm with a position accuracy of 10 nm in the transverse direction relative to the beam line. The second sensor, mounted on the piezoelectric holder, provides a signal for the acquisition trigger allowing unbiased measurements of the device under test (DUT). Two microchannel-plate photo-multipliers are employed for the precise measurement (3–4 ps) of the time of arrival (TOA) of each particle. Both photo-multipliers feature a 18 mm diameter and a 5.5 mm thick quartz input window.

The signals from the silicon sensors and the two MCP-PMTs are processed and recorded by a 8 GHz analog bandwidth 20 GSa/s 4 channels digital oscilloscope. The connection of the sensors and the MCP-PMTs to the oscilloscope is made through low-loss RF cables. The typical trigger requires the coincidence in a time window of 20 ns of two signals, one of the MCP-PMTs and one of the non-irradiated 3D trench sensor, with a minimum amplitude. This trigger condition avoids bias on the DUT measurements, which is not involved in the acquisition requirements. A representative event recorded with the described setup is reported in Figure 5.

The analysis method strictly follows what discussed in previous publications [5, 8]. Each waveform is processed to determine the signal amplitude and time of arrival (TOA).

A signal is identified by looking for a minimum in the waveform in a time window where signals are expected to contribute. The signal amplitude is determined by subtracting the minimum value found from the corresponding extrapolated value of the baseline, which is determined event-by-event by fitting the first samples of the waveform.

Among the different methods already detailed in [5, 8], the reference and the spline are used in this article. The reference method embodies the amplitude and rise time compensation (ARC) method [15]. In this approach, the signal waveform undergoes a delay of approximately half its rise time, followed by subtracting the delayed waveform from the original. Subsequently, the TOA is determined as the time where the resulting waveform exceeds half of its maximum amplitude. On the other hand, the spline method interpolates the waveforms using cubic splines. The TOA is then set to the time at which the signal exceeds a specified fraction (20%) of its maximum amplitude.

While the reference method has shown the best performance in term of time resolution, the spline method has a wider application being a refined, off-line implementation of the constant fraction discriminator.

The analysis method utilised is proved not to bias the results, which is a fundamental requirement for the measurements that are discussed in the following. In particular, it is capable to reconstruct the observables also in case of very low charge deposits, which is important for the characterisation of the performance of the whole detector under test that typically is not part of the triggering logic.

Radiation generates traps in the silicon bulk that block the charge carriers for a time by far larger than the typical sensor charge collection time. As a consequence, irradiated sensors feature a reduction of both the collected charge and the signal amplitude, which can be mitigated by increasing the bias voltage applied to the sensor. To study this effect, the two 3D trench silicon pixel structures, irradiated at 1.0 ⋅ 10¹⁶ and 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻², are operated at different bias voltages (−20 V, − 40 V, − 100 V, − 120 V and −150 V).

Figure 6 shows the resulting amplitude distributions which are compared to the measurements of the non-irradiated pixel from [8]. Both irradiated sensors feature a clear dependency of the most probable amplitude value on the bias voltage. Notice that since the amplifier boards used for the two irradiated sensors have slightly different gains, an exact quantitative comparison between the most probable amplitude values cannot be done. Nevertheless, it is evident that both irradiated sensors recover a pulse height distribution similar to those of the non-irradiated one when a bias voltage slightly lower than −100 V is applied. Moreover, the fact that the sensor irradiated at 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² still shows a regular, Landau-shaped distribution suggests that the radiation hardness limit for such sensors could be even higher.

These measurements clearly prove the radiation hardness of such devices and the unchanged performance with respect to non-irradiated sensors indicate that they can be operated even at fluences higher than 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻².

The detection efficiency of irradiated sensors is studied in different conditions and compared to the published results of the non-irradiated sensors [8]. The measurement is performed using a triple-strip structure as DUT, and by triggering on tracks crossing a 3D trench single pixel precisely centred, projectively along the beam line, in front of the DUT. A particle detected by the triggering pixel will also cross the triple strip producing a signal unless it ends up inside the trenches or gets trapped in the bulk. The two MCP-PMTs are also readout to obtain a precise charged particle time reference.

The efficiency is given by the ratio η = N _ts/N _tr, where N _ts is the number of events detected by the triple-strip sensor and N _tr is the number of triggers. Additional requirements on the TOA of the signal in the DUT with respect to the time reference given by the two MCP-PMTs as well as corrections due to small beam divergence are applied following the same methods reported in [8].

Different measurements are performed using the two irradiated 3D trench triple-strip structures: by varying either the bias voltages or the tilt-angle with respect to the beam line. Figure 7A shows the results for the triple-strip structure irradiated at 1.0 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² as a function of the bias voltage (green points). For V _bias ≤ −60 V the detection efficiency is compatible with the value measured for the non-irradiated sensor (black points). This result is consistent with the recovery of signal amplitude studied in the previous section.

Since the trenches are a non-active volume, 3D trench sensors reach the full detection efficiency only if operated tilted with respect to particle flight directions. Therefore, the detection efficiency of the triple-strip structure irradiated at 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² is evaluated as a function of the tilt angle and compared to the results obtained for the non-irradiated sensor [8]. The results reported in Figure 7B show that the efficiency of the irradiated sensor (red points) is compatible with that of a non-irradiated sensor (black points) reaching about 99% detection efficiency when tilted at angles larger than 10°. The reported measurements are obtained for a bias voltage of −130 V and −100 V for the irradiated and non-irradiated sensors, respectively.

These results show that the irradiated sensors have the same behaviour of non-irradiated ones by providing higher absolute bias voltage, in agreement to what is observed for the amplitude measurements.

Another key aspect to characterise the detection capabilities of the 3D trench silicon sensor in high radiation environment is given by its timing performance after irradiation.

In this section we report the timing performance of the two 3D trench single pixel structures, irradiated at 1.0 ⋅ 10¹⁶ and 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻², operated at different bias voltages ([−150, − 20]V) at two different tilt angles with respect to the beam line (0° and 20°). For these measurements the acquisition was triggered by the coincidence of signals detected on a non-irradiated silicon strip sensor ³ placed upstream the pixel and two MCP-PMTs located downstream. The pixel was carefully aligned in the beam transverse plane with respect to the strip in order to maximise the rate of detected coincidences.

The time of arrival of the tested sensor (t _Si ) is determined by means of the reference and spline methods discussed in Section 2.3. The timing performance of the sensor are measured with respect to the time reference given by the mean of the two MCP-PMTs TOAs (⟨t _MCP-PMTs⟩), which has a precision in the range of 3 ps–4 ps.

Figure 8 shows the distributions of t _Si − ⟨t _MCP-PMTs⟩ for the two irradiated pixels operating at bias voltage of −150 V. Minimal requirements on the amplitudes of the MCP-PMTs and on the triggering sensor are applied to reject badly reconstructed events. The two distributions are very similar to each other and have the same characteristics as the distribution of non-irradiated pixels (see Figure 9 of Ref; [8]), featuring a narrow peak and a small tail due to late signals. The distribution is fit by the sum of two Gaussian functions describing the signal, and a constant modelling the background. The time resolution of the single pixel, σ eff Si is obtained by combining the parameters of the two Gaussian functions and by subtracting the uncorrelated contribution due to the time reference jitter.

Figure 9 shows the resulting values of the time resolution as a function of the sensor bias voltage for the two irradiated pixels and, as a reference, for the non-irradiated one, operated respectively at low (in the range [−40, − 20]°C) and room temperature. Both results obtained with the reference and the spline methods are reported. The irradiated sensors have very similar timing performance to the non-irradiated one. The time resolution obtained with the reference method at a bias voltage of −100 V are 9.8 ± 0.4 ps for the 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² pixel and 11.3 ± 0.7 ps for the 1.0 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² pixel to be compared to the 12.0 ± 0.7 ps of the non-irradiated sensor operated at the same bias voltage. These results clearly show that the time resolution of 3D trench sensor is not affected by the radiation damage up to the considered fluences. The slightly better timing performance of the irradiated sensors with respect to the non-irradiated ones are related to the different performance of the front-end electronic boards used for the different sensors and to the different temperature condition. The measurements also show that the time resolution of both the irradiated and non-irradiated sensors does not improve significantly below a certain value of bias voltage, which is about −25, −60 and −80 V for the non-irradiated, for the 1.0 ⋅ 10¹⁶ and 2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻² sensors, respectively. This effect can be explained by the amplitude decrease of the irradiated sensors when operated at lower absolute bias voltages as discussed in Sec. 3.1.

Given the convenience in operating the 3D trench sensors tilted with respect to the particle flight directions in terms of detection efficiency (Sec. 3.2), the time resolution is also evaluated for a tilt angle of 20°. Table 1 show the results for both the non-irradiated and the irradiated (2.5 ⋅ 10¹⁶ 1 MeV n_eq cm⁻²) pixels. Both pixels feature a similar worsening of the time resolution of maximum +40% when operated at 20°. Such behaviour is due to the larger fraction of tracks that crosses adjacent pixels leading to charge sharing between two pixels and thus in a reduced signal amplitude of the pixel under test (see details in [8–10]). As shown in Ref. [8], in such cases the timing performance recovers that of the single pixel at normal incidence by combining the information of the two hit pixels with a clustering algorithm.