Performance of almost edgeless silicon detectors in CTS and 3D-planar technologies

The physics programme of the TOTEM experiment requires the detection of very forward protons scattered by only a few microradians out of the LHC beams. For this purpose, stacks of planar Silicon detectors have been mounted in moveable near-beam telescopes (Roman Pots) located along the beamline on both sides of the interaction point. In order to maximise the proton acceptance close to the beams, the dead space at the detector edge had to be minimised. During the detector prototyping phase, different sensor technologies and designs have been explored. A reduction of the dead space to less than 50 μm has been accomplished with two novel silicon detector technologies: one with the Current Terminating Structure (CTS) design and one based on the 3D edge manufacturing. This paper describes performance studies on prototypes of these detectors, carried out in 2004 in a fixed-target muon beam at CERN's SPS accelerator. In particular, the efficiency and accuracy in the vicinity of the beam-facing edges are discussed.


Introduction
In general, planar silicon detectors have a wide (typically 1 mm) insensitive border around the active area, occupied by a sequence of guard rings that control the potential distribution between the detector's sensitive area and the die cut. Such a large insensitive near-edge area was unacceptable for the TOTEM experiment [1,2] at the interaction point 5 of the LHC. TOTEM's primary goal, the precise measurement of the total pp cross-section, requires the measurement of elastically or diffractively produced very forward protons, scattered by merely a few microradians out of the high-intensity beams. The trajectories of these particles, determined mainly by their scattering angles and momentum losses in conjunction with the LHC lattice configuration [3], are measured by silicon detectors placed between 5 and 10 times the transverse (1-sigma) beam size from the beam centre. The influence of the near-edge insensitive volume on the proton acceptance can be quantified by the lowest detectable scattering angle, given in table 1.
The running scenarios presented in table 1 are characterised by the betatron function β * at the interaction point, which -for a given transverse emittance -determines the beam size and hence defines the smallest tolerable Roman Pot distance to the beam centre. The width of the insensitive edge area becomes particularly crucial for the β * = 1535 m optics, foreseen in the ultimate TOTEM -1 - Table 1. Smallest detected scattering angle Θ min in the vertical RPs installed at 220 m from IP5 in case of fully sensitive detectors (d = 0) and in case of standard planar silicon detectors with an insensitive nearedge zone of d = 1 mm width. The values are given for three typical running scenarios [2] characterised by the betatron function β * in the vertex and by the normalised transverse emittance ε n . In all cases, a centre-of-mass energy √ s = 14 TeV and a detector distance of 10 σ from the beam centre are assumed. running scenario for the most precise total pp cross-section measurement at √ s = 14 TeV. For this lattice configuration, the horizontal and vertical beam sizes at 220 m from the interaction region are only 30 µm and 81 µm, respectively. In case of a typical 1 mm-wide insensitive edge volume and a 10 beam standard deviation detector approach, the smallest detected angle is 6.6 µrad compared to 3 µrad for a 50 µm dead space, corresponding to a minimum observable four-momentum transfer |t| min = Θ 2 min p 2 = 19 × 10 −4 GeV 2 instead of 4 × 10 −4 GeV 2 . The TOTEM collaboration has therefore investigated two novel techniques for microstrip sensors: the Current Terminating Structure (CTS) [4,5] and the 3D-planar detector with active edges [6].

Current terminating structure (CTS)
The CTS [1,2,4,5] and its biassing scheme are shown in figure 1. The basic idea of the CTS approach is to reduce the insensitive border below 100 µm by applying a large fraction of the detector bias across the detector chip cut through an outer current terminating ring (CTR) that collects the major part of the resulting surface-generated current I CTR . A ring placed between the CTR and the strips, called clean-up ring (CR), is biased at the same potential as the CTR. The leakage current ICR collected at the CR consists mainly of a small fraction of the current generated at the cut surface due to diffusion. This structure decouples the high leakage current generated at the detector cut edge from the sensitive volume. The strips are biased by punch-through between the biasing electrode and the strips.
First samples of silicon detectors with CTS have been developed in a joint effort between the TOTEM group at CERN and Megaimpulse, a spin-off company from the Ioffe PT Institute in St. Petersburg (Russia). The 350 µm thick prototypes covering an area of 1.2 × 1.2 mm 2 were successfully tested in September 2003 with a muon beam in the SPS fixed target beam line X5 at CERN [4,5]. The detectors exhibited an insensitive margin of at most 60 µm width. Based on this experience, final-size detectors (300 µm thick, with an area of 3.5 × 3.5 cm 2 ) were developed -2 -  and extensively studied in X5 [3]. In particular, the tracking capabilities and the efficiency in the near-edge area (see figure 2) were analysed in detail with a ∼100 GeV muon beam and are reported in the following sections.

3D-planar detector technology
In the 3D-planar silicon devices the central part is also, as in the case of the CTS sensors, a planar microstrip detector, while the edge is fabricated using 3D processing [7][8][9]. In this configuration, the free edges of the planar sensor are deep etched and n + dopant is diffused in. Then the sensor is removed from the wafer, again by etching, thus avoiding the typical surface defects produced by saw cuts. In this way the edges become an extension of the back-side n + electrode [6], as shown schematically in figure 3. The enclosing n + electrode -the "active edge" -completely defines the electric field distribution when a reverse bias voltage is applied. The potential difference is not applied along the cut edge from the back plane to the front plane, but across the 33 µm-wide gap between the n + doped active edge (5 µm thick) and the strip end. The gap between the edge electrode and the strips is passivated by phosphorus to further reduce the leakage current and to increase the breakdown voltage.
As a result of 3D edge manufacturing, the surface leakage current, usually present after a device has been saw-cut, is suppressed. Moreover, the sensor is now active up to a few microns from the edge.   Prototypes of 3D-planar sensors (220 µm thick, covering an area of 3.4×3.4 cm 2 ) were studied in the same beam tests as the CTS devices discussed in section 2.1. The layout of the near-edge region is shown in figure 4.

Detector test setup
The CTS and 3D-planar silicon detectors under test were sized and shaped according to the TOTEM specifications [2]. They were segmented in 512 strips of 66 µm pitch. Each detector was glued to a PCB ("hybrid board", see figure 5) and bonded to four read-out chips.
-4 -  The sensors were assembled in four packages (figure 6), each consisting of four pairs of hybrids. The two hybrids of each pair were mounted back-to-back, thus having orthogonal strip directions, called u and v. The majority (24 detectors) was read out with CMS's analogue APV25 chips [12,13], while a few were equipped with prototypes of TOTEM's own newly developed digital front-end chip VFAT [14].
The four packages formed a telescope placed inside a vacuum tube, as drawn in figure 7. Two packages acted as reference detectors to define the muon tracks while the other two packages in the centre contained the detectors to be studied. The tracking information was calculated on the basis of the strip hits acquired through the APV25 chips and the associated analogue readout electronics [15]. The CTS and 3D-planar detectors were operated at a bias voltage of 40 V and 30 V, respectively, and at a temperature of −10 • C.

Alignment
The positions of all the detectors had to be determined to a precision better than the detector resolution. Since the theoretical resolution σ x,y of a 66 µm pitched strip detector without charge sharing is 66 µm/ √ 12 = 19.1 µm, the optimal achievable interpolation resolution in the centre between the reference packages was about 9 µm.
The alignment of the detectors was accomplished with metrology measurements and with a software algorithm based on reconstructed muon tracks.

Metrology measurements
The metrology measurements using optical and mechanical instruments allowed for a determination of the sensor positions to an accuracy of only a few tens of microns. This is illustrated by a residual distribution of reconstructed tracks in one typical detector (figure 8). The histogram reveals a detector shift of 32 µm. The rms value of 19.1 µm -consistent with the pure one-strip resolution -indicates that the rotation misalignment is small. As expected, the observed distribution is not gaussian but a smeared box distribution.

Software alignment
The muon tracks in the SPS test beam were perpendicular to the detector planes, with a beam divergence of less than 1 mrad. Due to negligible multiple scattering of about 0.1 µrad per silicon detector, the particle trajectories are fitted with straight lines in the coordinate system of the telescope. Its x and y coordinates were defined transverse to the beam running in the positive z direction. The objective of the alignment procedure was to find the displacements (∆x i , ∆y i ) and the rotations ∆γ i about the z-axis of the individual sensors relative to their nominal positions and orientations. Since the detector packages were composed of pairs of hybrids with orthogonal strips, the full three-dimensional track reconstruction was possible. The impact points used in the analysis were reconstructed on the basis of the analogue information from the APV25 chips after a signal-to-noise cut S/N > 4. The impact position was reconstructed with a centre-of-gravity algorithm [16] acting on clusters of adjacent strip hits weighted with their signal amplitudes. The tracks were reconstructed by minimisation of χ 2 , defined as where V is the covariance matrix of the measurements and ε is a vector of residuals, defined as the difference between the impact position and the reconstructed track intersection with the detector plane.
In the alignment procedure only tracks traversing all the available detectors were used. The precision of the detector alignment obtained with "Grand χ 2 " minimisation, i.e. fitting misalignment and track parameters simultaneously, was considerably better than the detector resolution, as can be seen in figure 9. In contrast to figure 8, the mean value is now close to 0, which indicates that the displacements were correctly determined, allowing an optimal interpolation precision in the efficiency and resolution studies.
The y-position of each detector's critical edge was determined by a combination of mechanical measurements and tracking information with a precision of 7-14 µm.

Detector performance
Four CTS detectors (listed in table 2) and one 3D-planar detector were used for the performance tests.
All CTS devices were operated at a reverse bias of 40 V and exhibited similar behaviour. In the following sections detector 11 will be discussed in more detail, whereas summary results are presented for all the detectors.
The 3D-planar prototype detector was operated slightly under-depleted at a reverse bias voltage of 30 V. This choice was made because of a large leakage current injected by a noisy strip and possible break-down at higher bias voltages. Figure 10 shows the signal-to-noise distribution of the CTS detector 11 without applying any reconstruction cuts. The signal peak with a most probable value of 17 is well separated from the noise pedestal, resulting in a high detector efficiency. When the same detector was operated at a higher reverse bias of 100 V, this value increased to 27. The signal-to-noise dependence upon the bias voltage is discussed in more detail in [17].

Signal-to-noise ratio
The signal-to-noise distribution of the 3D-planar detector is shown in figure 11. Due to the limited allowable bias range and the sensor thickness of only 220 µm, the most probable value of the signal-to-noise ratio was 10.5, leading to a slightly reduced efficiency for this early prototype detector.  ciency close to the cut edge was determined as a function of the y-coordinate that is parallel to the detector plane and perpendicular to the critical detector edge. The edge efficiency profile of the CTS detector 11 is shown in figure 12. The profile was fitted with

Edge efficiency
where Erf is the Gaussian error function, η 0 is the plateau efficiency, y 0 is the 50 % efficiency position, and σ y represents the width of the efficiency rise interval (with a contribution from the track interpolation error). The details of the fits for all the tested CTS detectors are summarised in table 2.
The efficiency was observed to rise from 10 to 90 % of its plateau value within 34 µm on average, with an rms spread of 7 µm between the individual sensors. As described in the previous chapter, the track interpolation uncertainty is about 9 µm, which would by itself lead to a (10 − 90)% rise interval of 23 µm. Deconvolution of this smearing yields a pure efficiency rise interval of 23 µm average width. The distance between the cut edge -known with a precision between 7 and  µm -and the 90 % efficiency point was found to be on average 51 µm with a spread of 7 µm. After correction for the interpolation smearing, this distance amounts to 47 µm. The efficiency plateau for all the detectors has a level of about 95 %, where the missing 5 % were caused mainly by 4 unbonded and typically 2 noisy strips out of the 208 strips covering the critical edge.
The efficiency profile of the 3D-planar detector's active edge is shown in figure 13. The efficiency rises from 10 to 90 % within 24 µm. Given the extrapolation accuracy of 9 µm as discussed for the CTS detectors, the (10 − 90)% interval of the test device alone is only 7 µm wide. This steep efficiency increase is likely to start directly at the cut edge, but the metrology uncertainty of this particular detector setup was about ±20 µm. The edge-to-90 %-efficiency interval with and without extrapolation smearing can only be crudely estimated to be (37 ± 20) µm and (28 ± 20) µm, respectively.

Charge sharing
Depending on the particle impact point on the detector, the charge generated may be distributed over several adjacent strips, creating multi-strip signal clusters. This charge sharing can be quantified by the fraction ρ of the cluster charge collected by the main strip, i.e. the one having the highest signal: ρ = Q Mainstrip /Q Cluster . The charge sharing profile maps in figures 14 (CTS detector) and 15 (3D-planar detector) show the mean value of ρ as a function of the impact point (x, y) given by the reference detectors. To reduce statistical fluctuations, the data of all parallel strips have been superimposed. Generally, the amount of charge sharing is low, which corresponds to ρ values close to 1. For the CTS detector, significant charge sharing is only visible in a ∼ 10 µm-wide area located in the middle between adjacent strips. The width of the strip charge collection area is slightly enlarged due to the reference detectors' interpolation smearing of ∼ 10 µm. From the charge sharing profile the direction of charge collection can be inferred by calculating the gradient of ρ. In the regions far from the edge, the charge is collected, as expected, in directions perpendicular to the strips. However, in the edge area, the direction of strip charge collection is observed to be orthogonal to the edge, which indicates that the charge is collected from areas not geometrically covered by the strips.
-10 - The 3D-planar detector exhibits two regions with increased charge sharing: (a) the narrow bands in the middle between adjacent strips, like in the CTS case; (b) the region between the active edge and the strip ends. Since the 3D implant at the cut edge is at the same potential as the backplane electrode, the reverse bias voltage is directly applied to the 33 µm wide volume between the strips and the 5 µm thick active edge. Such a high potential difference over a small distance creates a high electric field orthogonal to the edge (and at 45 • with respect to the strips -see figure 4), which is responsible for the observed charge collection direction. The long charge collection path following the curved field lines from the active edge to the strips on the detector surface enhances diffusion and thus charge sharing with neighbouring strips.

Cluster size
The hit cluster size, i.e. the number of adjacent strips with a signal above threshold, is a direct consequence of the charge sharing discussed in the previous section. Figures 16 and 17 give the observed fractions of single-, double-and triple-strip clusters as a function of the distance from the edge for the CTS and the 3D-planar detectors, respectively.
At distances above 0.2 mm, single-strip clusters represent 70 to 80 % for CTS detectors and about 65 % for 3D-planar detectors. The slightly bigger average cluster size in the 3D-planar detector under test was caused by the lower bias leading to a longer charge collection time and more diffusion.
In the vicinity of the edge (< 0.2 mm) the ratio of single to multi-strip clusters differs substantially for the CTS and the 3D-planar detectors, which can be explained by the charge collection. The mean signal-to-noise ratio, proportional to the collected charge, is given in figures 18  than for the 3D-planar design. In the CTS detector the bias voltage is applied by the punch-through mechanism putting the guard rings and the strips to about the same potential. Thus the charge generated in the vicinity of the cut edge is distributed between the current terminating ring, the clean-up ring and the detector strips. For impacts close to the edge, only a small portion of the charge is collected by the strips. Consequently, the mean signal-to-noise decreases from 20 in the detector bulk to only 6 at the edge. Due to this reduced cluster charge at the edge, the signals in the neighbours of the main strip tend to be below threshold. Hence single strip clusters are favoured and dominate at 90 %. The situation is different for the 3D-planar detector ( figure 19). Far from the edge, at y > 300 µm, about 65 % of clusters consist of one strip. From y ∼ 300 µm to the strip ends at y = 38 µm the field lines are more and more bent by the vicinity of the active edge, favouring dispersion during charge collection and hence increasing the charge sharing among adjacent strips (section 5.3). For y < 160 µm the double-strip clusters constitute the majority (up to 80 %). In contrast to the CTS detectors, the charge generated near the end of the strips is not shared with any non-read-out ring electrodes but collected entirely by the strips, avoiding any major signal losses. For y < 38 µm, from the strip ends to the active edge, the number of single-strip clusters increases again, although charge sharing still keeps the double-strip clusters in the majority. This trend towards single-strip clusters despite high diffusion is related to a slight reduction in collected charge, also visible in the signal-to-noise ratio, that keeps the signals of neighbour strips in a cluster below threshold. The incomplete charge collection is hypothesised to be caused by under-depletion in the low-field corner volume between the back plane and the active edge.

Impact point reconstruction performance
As discussed in section 5.3, the charge drift in the region between the strip ends and the detector edge has a component perpendicular to the edge, i.e. tilted by 45 • with respect to the strips. This leads to a bias on the reconstructed impact point. In figures 20 and 21, the track residual profile is given as a function of the distance from the edge for both detector designs. the bars indicate the rms of the residual distribution (about 18 µm). The shift of the reconstructed points towards the detector bulk is most pronounced for impact points between the cut edge and the area covered by strips. It could be fully corrected in software procedures based on beam tests or calibration runs.
For the CTS detectors, the bias amounts to about 40 µm at the edge, decreases approximately linearly with the distance from the edge and vanishes after about 80 µm. The observed phenomenon is in agreement with the cut-edge electric field measurements reported in [18,19].
In the case of the 3D planar sensor (figure 21), the field towards the edge is even larger than for the CTS sensor, leading to a more pronounced shift of the coordinate towards the edge. The 3Dplanar sensor shows a reconstruction offset of up to 100 µm. The effect extends to about 300 µm from the active edge.
The reconstruction resolution, represented by the error bars in figures 20 and 21, depends on the cluster size. For both detector types, the resolution far away from the sensitive edge is determined by the dominant single-strip clusters and hence amounts to about 18 µm ∼ 66 µm/ √ 12. In the 3D-planar detectors, the strong position dependence of the cluster size leads to an improved resolution in the region between 40 and 160 µm from the edge, whereas in the CTS detectors the resolution variation is much less pronounced.

Conclusions
The final size prototypes of the TOTEM CTS-planar microstrip silicon detectors (66 µm pitched and 300 µm thick) were tested in a ∼100 GeV muon beam, in the SPS X5 area at CERN. The test telescope was aligned with a precision of ∼ 1 µm and had an interpolation resolution of ∼ 9 µm. The insensitive area of the CTS planar silicon detectors, quantified by the distance between the detector edge and the point where 90 % of the plateau efficiency is reached, was measured to be 47 µm on average. The results of the beam tests are in good agreement with the CTS edge simulations and measurements reported in [17][18][19]. The measured resolution of the CTS planar devices -about 18 µm -is compatible with the expected value. The observed detection efficiency was about 95 %. The 5 % inefficiency was mainly caused by some dead and noisy strips due to bonding problems. During the edge efficiency studies, the prototype CTS detectors were biased with only 40 V, giving on average a most probable signal-to-noise value of 18. Subsequent tests of the same sensors with higher bias voltage revealed that a value of 27 is reached at 100 V. The charge collection mechanism below the CTS structure and the strips tilted by 45 • result in an impact point reconstruction bias of up to 40 µm in the region adjacent to the edge. This small shift does not pose any problem for the proton track reconstruction. If needed, it could be fully corrected for.
In addition to the CTS-planar detectors, the collaboration has also studied prototype 3D-planar microstrip silicon detectors. The efficiency at the edge was observed to rise from 10 to 90 % within 7 µm. The impact point reconstruction bias at the edge was measured to reach 100 µm. In the bulk area the detectors show the expected resolution of 17 µm determined by the strip pitch. The first 3D-planar prototypes were manufactured in only 220 µm thick wafers which results in a lower signal-to-noise ratio than achievable with standard, 300 µm thick, wafers.
The tests have demonstrated that the planar detectors with two new and innovative designs of the detector edge were fully operational and reliable. In the final design, the TOTEM Roman Pots have been equipped with the CTS sensors read out via digital VFAT chips. They are successfully operating in the LHC.