Charge collection properties of prototype sensors for the LHCb VELO upgrade

An extensive sensor testing campaign is presented, dedicated to measuring the charge collection properties of prototype candidates for the Vertex Locator (VELO) detector for the upgraded LHCb experiment. The charge collection is measured with sensors exposed to fluences of up to $8 \times 10^{15}~1~\mathrm{\,Me\kern -0.1em V}~ \mathrm{ \,n_{eq}}~{\mathrm{ \,cm}}^{-2}$, as well as with nonirradiated prototypes. The results are discussed, including the influence of different levels of irradiation and bias voltage on the charge collection properties. Charge multiplication is observed on some sensors that were nonuniformly irradiated with 24 GeV protons, to the highest fluence levels. An analysis of the charge collection near the guard ring region is also presented, revealing significant differences between the sensor prototypes. All tested sensor variants succeed in collecting the minimum required charge of 6000 electrons after the exposure to the maximum fluence.


Introduction
The Vertex Locator (VELO) [1] is the silicon vertex detector surrounding the interaction region of the LHCb experiment [2]. Throughout LHC Runs 1 and 2, the VELO was based on silicon strip sensors. The VELO will be upgraded to a hybrid pixel system for Runs 3 and 4. The detector is designed to withstand a maximum fluence of 8 × 10 15 1 MeV n eq cm −2 , corresponding to the amount expected after an integrated luminosity of 50 fb −1 [3] over the 8-year lifetime of the upgraded experiment. The charge collection properties of the prototype sensors prior to, and after irradiation up to maximum fluence are reported in this paper.
An extensive R&D programme was launched to obtain sensors able to meet the challenging requirements for radiation hardness of the VELO upgrade. One of the crucial sensor requirements is that the amount of charge collected for a high energy charged particle is more than 6000 e − after the detector is exposed to the maximum fluence. This ensures that the signal is sufficiently above the expected highest threshold of 1000 e − , even if the charge is shared amongst several pixels. Furthermore, it was essential to evaluate the performance at the edge of the sensor, since this is the region closest to the interaction point and hence with the highest occupancy during the operations of the detector.
The prototype sensors have been characterised using readily available Timepix3 ASICs [4]. The Timepix3 ASIC has a data-driven readout which provides a 10 bit Time-over-Threshold (ToT) measurement, and a timestamp with ∼ 1.56 ns precision.
In this paper, the performance of several different prototypes is discussed, comparing results of irradiated and nonirradiated samples. The different sensor designs are described in Section 2. The experimental setup is outlined in Section 3, with a detailed description of the charge calibration method in Section 3.2. The irradiation programme is detailed in Section 4. The charge collection results for different bias voltages are discussed in Section 5.1. During the evaluation programme, radiation induced charge multiplication was observed and results are described in Section 5.2. The edge performance is presented in Section 5.3, followed by the conclusion in Section 6.

Sensor prototype designs
A VELO upgrade assembly consists of a single sensor bump-bonded to three ASICs, and is referred to as a triple-chip assembly. However, for the charge collection studies, single ASIC assemblies have also been used, since it makes the irradiation and testing in the lab or in the beam more affordable. The size of the sensors for the VELO upgrade is approximately 42.5 × 14.1 mm 2 , consisting of three groups of 256 × 256 pixels. The pixels have a 55 μm pitch, except for those in the interchip region, which are elongated in order to have complete coverage between the ASICs. The elongated pixels are either 110 or 137.5 μm depending on the round of production.
For the first round of prototyping, sensors have been produced by two vendors, Hamamatsu Photonics K. K. (HPK) and Micron Semiconductor Ltd . The HPK sensors have been produced with n-type implants separated by p-stop implants on a 200 ± 20 μm thick float-zone p-doped silicon substrate (resistivity of 3-8 kΩ cm). Two different guard ring designs with distances of 450 and 600 μm from the edge of the sensor to the edge of pixel matrix have been evaluated. This distance is often referred to as Pixel-To-Edge (PTE). The pixel implants are either 35 or 39 μm squares with rounded corners. The Micron prototypes have been produced with 36 μm wide n-type implants with rounded corners and p-spray isolation. Two different types of substrates have been used: 200 μm p-type (> 5 kΩ cm) and 150 μm n-type (> 1.5 kΩ cm). The latter is double sided processed with guard rings on the backside of the sensor partially implanted underneath the edge pixels (see Figure 1). There are two PTE variants with corresponding distances of 250 μm and 450 μm.
The highest operational voltage needed to yield a signal of at least 6000 e − after the highest fluence is expected to be 1000 V [3]. For n-on-p sensors the operation above a certain voltage can generate an electrical discharge between the sensor and the ASIC if the assembly is placed in a gaseous environment. The n-on-n sensor design does not suffer from electrical discharge at voltages below 1000 V since these sensors are processed on both sides allowing for guard rings on each side of the sensor. This lowers the potential on the side closer to the ASIC. In order to prevent discharges Hamamatsu Photonics K. K., 325-6, Sunayama-cho, Naka-ku, Hamamatsu City, Shizuoka, 430-8587, Japan Micron Semiconductor Ltd, 1 Royal Buildings, Marlborough Road, Lancing BN158UN, United Kingdom µ µ Figure 1. A cross section of the sensor connected to the ASIC. The different implants are indicated with different colors. Both the design of the n-on-p and n-on-n sensors are shown in this diagram, since the only difference is the guard rings on the back of the sensor. in n-on-p sensors, these sensors either received a C-type parylene coating prior to irradiation or are operated in vacuum.

The Timepix3 telescope at CERN SPS
An extensive testbeam programme has been carried out at the SPS H8 beamline at CERN to characterise the sensors at high rate. The beam is a mixed charged hadron beam (∼ 67% protons, ∼ 30% pions) at 180 GeV/ . The Timepix3 telescope [5] is a high rate, data-driven beam telescope, composed of two arms of four planes each. Each plane is equipped with a 300 μm p-on-n silicon sensor that is bump bonded to a Timepix3 ASIC. The centre of the telescope is reserved for the Device Under Test (DUT). The DUT area is equipped with remotely controlled motion stages able to translate in and directions (orthogonal to the beam axis) and rotate about the axis. A vacuum box can also be installed on the central stage to facilitate testing of irradiated devices at high voltage. The cooling block connected to the ASIC can be cooled down to temperatures of −35°C, which keeps the sensors below −20°C . The pointing resolution at the DUT position is about 1.6 μm, enabling intrapixel studies of the DUT. The typical temporal resolution on a track using only the Timepix3 timestamps is about 350 ps.

Front-end calibration
The recorded Time-over-Threshold (ToT) values are converted to a corresponding number of electrons via a charge calibration procedure. The measured ToT for a given injected charge varies from pixel to pixel due to variations in the discharge current across the pixel matrix. The relation between ToT and charge for each pixel can be determined by injecting testpulses with known charge into the preamplifier. The injected charge depends on the voltage difference of two internal voltage DACs whose value can be measured externally, and on the capacitance of the test capacitor which varies only slightly across the ASIC.
Comelec SA, La Chaux-de-Fonds, Switzerland A calibration curve is determined separately for each pixel [6]. The test pulse calibration method was validated for one of the assemblies by comparing it to the characteristic lines from an 241 Am source and agreed to within 4% [7], and was also cross-checked using X-rays with several energies from the LNLS synchrotron in Brazil.

Irradiation programme
The fluence that the VELO upgrade will receive is estimated using simulations of proton collisions at 14 TeV [3]. The hadronic collisions produce a nonuniform fluence exposure over each sensor. The maximum integrated fluence expected at the most irradiated sensor position is 8 × 10 15 1 MeV n eq cm −2 . The difference in fluence over a single sensor due to this nonuniform irradiation can be as large as a factor 120.
Three different types of irradiation are used in the studies presented in this paper. Sensors received uniform neutron irradiation at the TRIGGA MARK II reactor at JSI [8] in Ljubliana, Slovenia, of half, and of maximum fluence. The IRRAD facility at CERN [9] provides a 24 GeV proton beam that is approximately normally distributed, hence yielding a nonuniform fluence profile. Forschungszentrum Karlsruhe Cyclotron at Karlsruhe (KIT) can provide a MeV proton beam with a small cross section which can be scanned over the sensor in order to approximate the nonuniform radiation profile of the upgraded VELO. The fluences provided by JSI, IRRAD, and KIT are known with an accuracy of ±10%, ±10%, and ±20%, respectively. Table 1 shows a summary of the properties of the three facilities.

IRRAD profile
After irradiation, the residual activation of the assemblies is used to determine the radiation profile, modelled using a two-dimensional Gaussian distribution. The activation profile is then normalised to match the fluence measured by an aluminium foil that was placed alongside the assemblies during irradiation. The foil was later subdivided in six regions, examined for activation through -ray spectroscopy. The reconstructed fluence profile of a single-chip assembly is shown in Figure 2. The corresponding fluence measured with the aluminium foil is overlaid for each region, where the measured proton fluence has been converted in neutron equivalent unit using a hardness factor of 0.62 ± 0.04) [10]. The reconstructed fluence profile is found to be consistent with the measured charge collection profile.

Results with beam
The prototype sensors were characterised using the Timepix3 telescope in beam tests using the SPS at CERN. Only DUT clusters associated to a telescope track are selected in order to mitigate background hits from internal radioactivity and noise. Clusters are matched to a track if they are within a space (time) region of 110×110 μm 2 (100 ns) from the value predicted by the telescope. The cluster size is limited to four pixels since larger clusters are usually due to nuclear interactions (with a much larger energy deposition) or -rays. A fit is performed to the cluster charge distribution, which can be described by a convolution of Landau and Gaussian distributions, in order to determine the Most Probable Value (MPV) of the Landau. The standard deviation of the MPV distribution over the chip is quoted as the uncertainty on the MPV, and is determined for this assembly to be around 350 e − , which is much larger than the statistical estimate from the fit. The standard deviation on the MPV is determined with a single nonirradiated 200 μm n-on-p assembly measured also using the hadron beam, for which the MPV is determined for each pixel. This uncertainty is a combination of effects from the ASIC and the statistical uncertainty. The uncertainty on the absolute calibration is determined to be 4%, as discussed in Section 3.2.
This section is organised as follows. In Section 5.1 the charge distribution is studied for both nonirradiated and uniformly irradiated sensors operated at different bias voltages and placed perpendicular to the beam. It is followed by Section 5.2 in which the charge distribution as a function of fluence for nonuniformly irradiated sensors also placed perpendicular to the beam is discussed. Finally, the performance at the edge of the sensors is discussed in Section 5.3, in which different angles of the sensor with respect to the beam are used. For figures in which devices of different types are shown together, a colour code is used: green for HPK n-on-p, blue for Micron n-on-p, and purple for Micron n-on-n. An overview of the assemblies is given in Appendix A.

Nonirradiated assemblies
Assemblies were tested in the SPS beam at the same time as the irradiation campaign, thus not all of the assemblies could be studied prior to being irradiated; therefore, a representative subset of assemblies was tested prior to being irradiated in order to make comparisons with the results post irradiation. Figure 3 shows the MPV as a function of bias voltage for several nonirradiated assemblies. For the HPK sensors, indicated by the green curves, the MPV of the collected charge saturates between 100 and 110 V and shows no dependence on the implant size. The MPV of the Micron sensors, indicated by the blue curves (n-on-p) and purple curves (n-on-n), reaches a plateau at less than 40 V. The difference in MPV for the Micron sensors is due the different thicknesses of the two types, 200 μm and 150 μm for n-on-p and n-on-n sensors, respectively. The small differences in MPV between sensors of the same type are due to wafer-to-wafer variations in thickness up to 10%, and variation in the testpulse capacitance due to process variations of about 5% (1 sigma).
The main difference other than the area between the single-chip and triple-chip assemblies is the presence of elongated pixels located in the region in between the chips. It is important that the response of the inter-chip region is similar to the rest of the sensor. This region is investigated for the HPK n-on-p triple-chip assembly T23 before irradiation. The MPV of the interchip region of HPK triple-chip assembly T23 is show in Figure 4, where the middle between chips is defined as zero. Three characteristics can be observed: the dips between columns; the variation from column-to-column (the narrow flat regions); and the slightly lower MPV of the interchip region (wider flat regions). The dips between columns are due to threshold effects, and the variation from column-to-column is due to the charge calibration. The MPV is slightly lower for the two elongated columns compared to the other columns in the figure. However, this difference still falls within the total variation of 350 e − . Therefore, it is concluded that the interchip region collects all charge.

Irradiated assemblies
The MPV as a function of bias voltage after irradiation to full fluence at JSI is shown in Figure 5. All of the assemblies follow the same trend, with the MPV increasing linearly from about 2500 e − at 200 V to about 8000 e − at 1000 V. The leakage current at bias voltages higher than 600 V for S24 was larger than the leakage current compensation in the ASIC, resulting in changes in the charge calibration per pixel. Hence these points are excluded from this figure.
The measurements shown in Figure 5 were performed before any controlled annealing. A subset of the assemblies were tested again with beam after having been annealed for 80 minutes at 60 • C. As can be seen in Figure 6, the results before and after annealing are in agreement. The leakage current at bias voltage of 900 V for S17 after annealing was larger than the leakage current compensation in the ASIC, resulting in changes in the charge calibration per pixel.
Several assemblies have been irradiated with either reactor neutrons or protons. As described in reference [12], the damage to silicon from neutron irradiation is different to the damage from proton irradiation. Figure 7 shows the MPV as a function of bias voltage for two HPK single-chip assemblies after uniform irradiation to a fluence of 4×10 15 1 MeV n eq cm −2 at KIT (assembly S4proton irradiation) and JSI (assembly S15 -neutron irradiation). The curve for S15 does not extend up to 1000 V because the assembly sparked, as it was not parylene coated and thus measurements were performed only up to 675 V in a CO 2 atmosphere.

Charge multiplication
As reported in several previous studies [13][14][15], charge multiplication in planar silicon sensors is expected at fluences above 5 × 10 15 1 MeV n eq cm −2 but typically in considerably larger pitches than presented here. Figure 8 shows the MPV as a function of the fluence at different bias voltages after irradiation at IRRAD. Charge multiplication is observed in all sensors where the bias voltage can reach 1000 V, except for the Micron n-on-n assembly. This effect emerges at a fluence of about 6.5×10 15 1 MeV n eq cm −2 and increases with bias voltage. The difference in the n-on-p and n-on-n sensors that leads to the presence (absence) in charge multiplication is not known.
Charge multiplication is expected to occur in regions with a high electric field. These positions are close to the pixel implant, and thus the amount of charge multiplication could depend on the intrapixel position.  Figure 9. The MPV of the cluster charge distribution within a pixel for S8 at 1000 V after irradiation at IRRAD. Only clusters in the region of the sensor exposed to fluences in the range 7.3 to 7.9×10 15 1 MeV n eq cm −2 are selected. are selected in the regions of the sensor that were exposed to fluences in the range of 7.3 to 7.9×10 15 1 MeV n eq cm −2 . As a comparison, the intrapixel MPV for S8 before irradiation is shown in Figure 10. Diagonal bands can be seen near the corners of the pixel; here the MPV is lower than in the corner itself. This is due to charge sharing with neighbouring pixels. A detailed explanation is given in Appendix B.
For the IRRAD assemblies, the intrapixel MPV study is performed for different fluence values up to maximum fluence. By comparing a slice of 5.5 μm along the middle of the pixel ( = 27.5 μm) of the intrapixel cluster charge distribution at different fluence levels, the position within the pixel where charge multiplication occurs can be determined, as is shown in Figure 11. The MPV decreases with fluence up to 7 × 10 15 1 MeV n eq cm −2 . At this point the MPV begins to increase with fluence, which is a clear indication that charge multiplication is occurring. The small drop from the middle to the edge of the pixel is due to charge sharing effects. The charge collected relative to that of the lowest fluence bin is shown in Figure 12 in order to demonstrate where in the pixel the charge multiplication occurs. It can be concluded that charge multiplication occurs uniformly over the centre of the pixel, while towards the edge of the pixels charge multiplication seems to be lower.

Edge performance
The performance of the sensors at the edge, near the guard ring region, is investigated by illuminating these areas with the beam. Results are shown for one corner of the sensor, but it has been verified that the other corners behave the same. The sensors are operated at a bias where they are above the depletion voltage estimated from charge saturation measurements. The results are shown for single chip sensors, but all prototypes tested exhibit consistent behaviour at the edge between single and triple sensors as well as between different types of irradiation.
The performance at the edge of the pixel matrix is quantified by measuring the cluster charge as a function of the track intercept position. The expected behaviour is to collect charge from tracks traversing the pixel matrix, but not from tracks passing through the guard ring area apart from a small amount of diffused charge. The MPV as a function of the track distance from the edge  in the direction (corresponding to increasing column numbers) can be seen in Figure 13 for all the tested nonirradiated assemblies. The uncertainty assigned to the MPV is statistical only. The solid line represents the edge of the pixel matrix and the dashed lines the borders between pixels. Two prototype variants exhibit an undesired behavior. All of the 200 μm Micron n-on-p sensors accumulate charge in the last pixel from tracks traversing the sensor beyond the edge of the pixel matrix, while the 150 μm Micron n-on-n (250 μm PTE backside guard rings) sensor does not collect the full charge in the last pixel. None of the HPK sensors show this behaviour apart from some expected charge diffusion at the boundary between the guard ring and the edge pixel. The simplest geometrical model that can explain the observed edge effect for Micron n-on-p and Micron n-on-n sensors is a tilted border between the charge collection region of the guard rings and that of the pixels. This is illustrated in Figure 14 for Micron n-on-p sensors, where the charge distribution as a function of the track intercept position, , is studied at three different angles: -12 • , 0 • and +12 • . In the schemes, the black arrow represents the particle trajectory nearest to the physical edge where the deposited charge is fully collected, with the red cross showing the corresponding measured position of the intercept between the track and the sensor, and the shaded area indicating the charge collection region of the guard rings. At -12 • the slope of the charge deposit is present and extends far beyond the edge of the matrix. The charge is fully collected by the pixel implants up to the point indicated by the red cross. Beyond that point the first pixel starts to pick up charge from the guard ring region (represented in grey). At +12 • the slope in the charge deposit almost disappears. The charge is either fully collected by the pixel implant or fully collected by the guard rings. This model explains why in the case of Micron n-on-p sensors charge is collected from the guard ring region at the pixel side. Analogously, angled measurements with Micron n-on-n sensors show that the border is tilted in the opposite direction, such that charge from the outermost pixel is lost to the guard rings at the backplane side [16]. The tilted border hypothesis could be verified by a TCAD simulation, but this was not pursued because the details of the guard ring design is proprietary information. For Micron n-on-p sensors, the observed edge effect leads to an approximately 30% excess of hits in the first column of the pixel matrix with the sensor biased above depletion voltage and Technology Computer Aided Design traversing tracks at normal incidence. The second column of the pixel matrix also shows an excess of hits, leading to the conclusion that the distortion of the electric field is such that the second to last column collects charge from tracks going through the last column. A similar effect has been observed for active-edge silicon sensors in ref. [17]. The excess of hits decreases with increasing operation voltage due to the stronger electric field, and it is also observed to decrease when tracks are at an angle with respect to the sensor. An excess of hits in the first column and row of the pixel matrix is also observed in a lab experiment using a 90 Sr source, verifying the beam test findings. Data have been collected operating the sensor at different voltages and the observed hit excess dependence has the same trend as the one obtained from testbeam data.
The MPV profiles for irradiated sensors are shown in Figure 15 as a function of the distance to the edge in the direction. After irradiation by either protons or neutrons with fluences ranging from 2 to 8×10 15 1 MeV n eq cm −2 , the behaviour at the edge is comparable among the different prototype variants. The linear charge deposit extending beyond the edge observed in nonirradiated Micron n-on-p sensors is strongly reduced after irradiation. This can be explained by the fact that the sensors are not fully depleted even at the highest operational voltage used in the tests.

Conclusions and outlook
An extensive testing campaign has been performed for the VELO upgrade, investigating several planar silicon sensor designs from two different vendors: HPK and Micron. In this paper, a study of the charge collection before and after irradiation up to 8 × 10 15 1 MeV n eq cm −2 of these sensors is presented. Irradiation of the sensors was performed at JSI with neutrons and at IRRAD and KIT with protons. The MPV as a function of bias voltage is determined before irradiation, and shows saturation at 16 ke − , 17 ke − , and 12 ke − for HPK n-on-p, Micron n-on-p, and Micron n-on-n, respectively. After irradiation, the MPV decreases significantly and shows a linear dependence on the bias voltage. At a bias voltage of 1000 V, the MPV is around 8 ke − , indicating that the sensor achieves the requirement of collecting 6 ke − after irradiation to the maximum expected fluence for the VELO upgrade.
During the campaign charge multiplication was observed for both the HPK and Micron n-on-p sensors, while no charge multiplication is observed for the Micron n-on-n sensors. Charge multiplication is observed uniformly over the centre of the pixel, while it seems less near the edge.
Two classes of tested prototypes exhibited unexpected behaviour at the edge prior to irradiation. In the case of Micron n-on-p sensors, charge is gained from the guard ring region at the pixel implant side, while in the case of the Micron n-on-n sensors with 250 μm PTE, charge from the outermost pixels is lost to the guard ring area. In view of the VELO upgrade the observed edge effect is critical, since it would increase the occupancy in the part of the sensor where it is already the highest. Moreover, it leads to a loss of spatial resolution for the first measured point.
The studies presented in this paper were decisive in the choice to adopt the 200 μm thick HPK n-on-p sensors with 39 μm implant width and 450 μm guard ring size for the VELO upgrade.

A List of assemblies
The details of the assemblies that are tested during this analysis are summarised here. Two different types of substrates (n-on-p and n-on-n) are used from two different vendors. Further differences between individual assemblies are indicated in the table below.

B Shape of the intrapixel cluster charge distribution
The MPV distribution within a single pixel shows an peculiar feature: a diagonal region near the corner is observed to have a lower MPV than both the centre and the corners of the pixel, as is shown in Figure 16. For this figure, the four corners of pixel have been 'folded' into one in order to maximise the effective size of data sample. The MPV distribution as a function of the intrapixel position is split by the size of the cluster in order to study the origin of this structure, as is shown in Figure 17, where the fraction of clusters of each size is also indicated. From the intrapixel position of the different cluster sizes it can be seen that the contribution to the band is mainly from clusters of size two or three, while the contribution to the corner is mainly from four-hit clusters. Because for four hit clusters all three neighbouring pixels must also measure a hit, there is no possibility to have undetected charge due to the signal in the neighbouring pixels being below the detection threshold. Conversely, for the other cluster sizes, there is the possibility that a neighbouring pixel collected some of the charge, but that it did not pass the detection threshold. If this occurs, the measured cluster charge is incomplete. For a single pixel cluster up to three contributions could be missing. This inefficiency is unlikely to occur for hits in the middle of the pixel due to the limited size of the charge cloud, while it is more likely to happen to hits near the corners.