EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-PUB-2015-015 Oct 9, 2015

Testbeam studies of pre-prototype silicon strip sensors for the LHCb UT
upgrade project

A. Abba1, M. Artuso2, S. Blusk2,6, T. Britton2, A. Davis3, A. Dendek4, B.
Dey5, S. Ely2, T. Evans7, J. Fu1, P. Gandini2, F. Lionetto5, P. Manning2, B.
Meadows3, R. Mountain2, N. Neri1, M. Petruzzo1, M. Pikies4, T. Skwarnicki2, T.
Szumlak4, J. C. Wang2

1Instituto Nazionale di Fisica Nucleare - Sezione di Milano, Italy
2Syracuse University, Syracuse, NY USA
3University of Cincinnati, Cincinnati, OH USA
4AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
5Physik-Institut, Universität Zürich, Zürich, Switzerland
6European Organization for Nuclear Research (CERN), Geneva, Switzerland
7Department of Physics, University of Oxford, Oxford, United Kingdom

The LHCb experiment is preparing for a major upgrade in 2018-2019. One of the
key components in the upgrade is a new silicon tracker situated upstream of
the analysis magnet of the experiment. The Upstream Tracker (UT) will consist
of four planes of silicon strip detectors, with each plane covering an area of
about 2 m2. An important consideration of these detectors is their performance
after they have been exposed to a large radiation dose. In this article we
present test beam results of pre-prototype n-in-p and p-in-n sensors that have
been irradiated with fluences up to $4.0\times 10^{14}~{}n_{\rm eq}$/cm2.

Published in Nucl. Instrum. Meth. A.

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

The Upstream Tracker (UT) detector is a key part of the LHCb Upgrade,
replacing the current TT tracking stations [1, 2]. The UT improves over the
current TT in that it (i) eliminates all gaps within the detector acceptance,
(ii) has largely improved granularity to cope with the higher instantaneous
luminosity expected in the LHCb upgrade, and (iii) improves the coverage close
to the beam pipe by employing a circular cutout to match the beam pipe
profile. The UT, like the TT, is situated just in front of LHCb’s dipole
analysis magnet. In this position, it provides a crucial link between segments
reconstructed in the upgraded vertex detector [3] and the tracking chambers
downstream [4] of the LHCb magnet. It provides a factor of 3 improvement in
speed for the tracking in the the fully-software-based trigger [5], reduces
the rate of fake tracks being formed by a factor of 2-3, and improves the
momentum resolution by about 25% relative to tracks not using UT hits. The
factor of 3 in speed is enabled by enabling a very fast estimate of the
momentum of charged particles, which can then be used to reduce the size of
the hit search windows in the downstream tracking stations. Due to the
increased speed of the trigger and the higher purity of tracks considered,
larger data sets with better signal-to-background can be acquired.

Figure 1: Cartoon showing the layout and dimensions of the four UT planes.

The UT detector consists of four silicon planes, each about 1.53 m in width
and 1.34 m in height. Each plane is composed of 1.5 m long staves that are
tiled with $\sim$10 cm $\times$ 10 cm silicon wafers. Consecutive wafers are
mounted on opposite sides of the stave to ensure no gaps along the height, and
adjacent staves are also overlapped to ensure no gaps in the horizontal
direction. The majority of the detector area utilizes sensors with an
approximate pitch of $190~{}\mu$m, however the inner region features sensors
with half the pitch ($95~{}\mu$m) to cope with higher occupancy. Both n-in-p
and p-in-n type sensors are being considered for the outer region, but for the
inner region, only n-in-p are being considered due to better radiation
hardness. For the innermost region of the UT, the largest fluence expected,
with a safety factor of about two, is about $5\times 10^{14}~{}n_{\rm
eq}$/cm2. Outside this region, the fluence is not expected to exceed about
$2\times 10^{13}~{}n_{\rm eq}$/cm2.

The primary goals of this test beam were to quantify the performance of
several pre-prototype n-in-p mini-sensors from Micron Semiconductor, Ltd [6],
after a high radiation fluence, and compare to corresponding results from
similar unirradiated detectors. The properties investigated include, but are
not limited to:

  * •

Landau distributions as a function of bias voltage;

  * •

Cluster size versus bias voltage and angle of incidence;

  * •

Charge collected versus interstrip position;

  * •

Resolution versus angle;

  * •

Characteristics of sensors near the quarter-circle region (these emulate the
sensors surrounding the beam pipe).

One p-in-n mini-sensor irradiated to the maximum level expected in the outer
region of the UT was also tested, but its study was not a primary focus of the
test beam results presented here.

##  2 Experimental setup

The test beam discussed in this article was conducted in October 2014 at the
SPS at CERN. The beam consisted of positively charged hadrons with momentum of
180 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. The beam was delivered in spills
at rate of about 4 spills/minute, with each spill lasting about 4 seconds. For
most of the data taking, the beam size was collimated down to about 0.5 cm in
diameter and each spill provided a particle rate of order 1 MHz.

###  2.1 Telescope description

The pre-prototype UT sensors, or detectors under test (DUT), were studied
using the TimePix3 (TP3)-based telescope [7], composed of 8 pixel planes. Each
pixel plane is about $1.4~{}\mathrm{cm}\times 1.4~{}\mathrm{cm}$ and has a
pixel size of $55~{}\mu\mathrm{m}\times 55~{}\mu\mathrm{m}$. The planes are
tilted in order to provide more charge sharing, and thus better position
resolution. A cartoon of the telescope layout is shown in Fig. 2.

Figure 2: Cartoon showing the TimePix3 telescope [7] used to study the UT
sensors.

With the high momentum beam of 180${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, the
reconstructed tracks provide excellent pointing resolution of about 2 $\mu$m
at the DUT. The telescope readout does not require an external trigger: hits
are recorded continuously once a run is started. For each pixel hit, both
position and a time-stamp with 1.56 ns precision is recorded. Tracks are then
formed (offline) by combining hits that have compatible time values.

###  2.2 Detectors under test

The mini-sensor pre-prototypes tested in the October 2014 test beam were
obtained from Micron Semiconductor, Ltd [6]. One of the sensors tested was a
p-in-n, and six were n-in-p. The resistivities of the sensors, as determined
from capacitance versus voltage measurements, were about 0.9 $k\Omega$ cm for
the p-in-n sensor and about 2.8 $k\Omega$ cm for the n-in-p. Each sensor was
1.115 cm x 1.125 cm in size with a nominal thickness of 250 $\mu$m, and had
128 strips with a strip pitch of 80 $\mu$m and a strip (implant) width of 30
$\mu$m. Prior to irradiation, all the of sensors had a depletion voltage of
about 180 V. A schematic of the mini-sensors is shown in Fig. 3. In this
schematic, the strips run horizontally.

Figure 3: Schematic of the mini-sensors tested during the October 2014 test
beam. The two sensors in the middle are full mini-sensors, while the ones on
the left and right have a quarter-circle cut out. The difference between the
left-most (MBP1) and right-most sensors (MBP2) is in the guard-ring structure,
as shown just below them.

Of the six n-in-p sensors tested, three had the strips terminated such that
they form a quarter-circle inactive region of the sensor. Two different guard-
ring structures were implemented, as shown in Fig. 3. More details of the
sensors under test are shown in Table 1. The MBP1 and MBP2 sensors are
differentiated by the guard ring structures, and are shown on the left and
right side of Fig. 3, respectively. The MBP1 (leftmost sensor in figure)
differs from the MBP2 sensor (rightmost) in that it implements a stepped
structure along the innermost guard ring to maintain an equal separation
between the edge of the strip and the innermost guard ring, more like a
conventional rectangular-shaped detector.

ix of the seven sensors were irradiated at the Massachusetts General Hospital
(MGH) proton irradiation facility [8] in June 2014, using protons of kinetic
energy equal to 226 $\mathrm{\,Me\kern-1.00006ptV}$ and fluences ranging from
$0.27\times 10^{14}~{}n_{\rm eq}$/cm2 to $4.0\times 10^{14}~{}n_{\rm eq}$/cm2.

Table 1: Specific details of the senors tested in the October 2014 test beam. Here, $\rho$ refers to the resistivity of the silicon and $N_{e,h}$ indicates either the electron or hole concentration. For sensor 3091-10-MBP2, CV measurements were not available. Sensor | Type | Fluence | $N_{e,h}$ | $\rho$ | Other
---|---|---|---|---|---
ID |  | ($10^{14}~{}n_{\rm eq}$/cm2) | ($10^{12}$ cm-3) | ($k\Omega$ cm) | spec.
3092-1-MS2 | p-in-n | 0.27 | 5.1 | 0.87 | 250 $\mu$m
3091-8-MS1 | n-in-p | 1.0 | 5.0 | 2.79 | 242 $\mu$m, p-spray
3091-10-MBP2 | n-in-p | 0.0 | n/a | n/a | 238 $\mu$m, p-spray
3091-7-MS2 | n-in-p | 4.0 | 5.0 | 2.76 | 254 $\mu$m, p-spray
3091-7-MS1 | n-in-p | 1.8 | 4.9 | 2.85 | 254 $\mu$m, p-spray
3091-8-MBP2 | n-in-p | 4.0 | 5.2 | 2.69 | 242 $\mu$m, p-spray
3091-8-MBP1 | n-in-p | 4.0 | 5.0 | 2.79 | 242 $\mu$m, p-spray

Between the time of the irradiation in June 2014, and the test beam in October
2014, the sensors were kept in a freezer, at a temperature below -10 ∘C. The
sensors were warmed up to room temperature for no more than 7 days to
transport the sensors and for wirebonding.

The DUT readout for this testbeam was based on the Alibava DAQ system [9, 10,
11, 12], which uses Beetle chips [13, 14] as the front end ASIC. The main
components of the Alibava system are a detector board to which sensors are
mounted, a daughterboard that includes two Beetle chips (128 channels each),
and a motherboard that manages the data flow to/from the Beetle chips and
to/from the data acquisition PC.

The DUT was housed in an Aluminum box to provide both shielding and a light-
tight environment. A Peltier device was used to cool the sensor to about -13
oC, and a continuous nitrogen flow maintained the relative humidity close to
zero. The entire box was mounted on a stage that allowed for horizontal and
vertical translations, as well as rotations about the vertical axis to allow
for studies of the detector performance versus particle incident angle. The
system was equipped with both temperature and relative humidity monitoring. A
photograph of the telescope with the UT DUT being installed is shown in Fig.
4. Various components are indicated.

Figure 4: Photograph of the TimePix3 telescope and the DUT during installation
at the SPS, together with a description of the different components.

###  2.3 Trigger and synchronization

The trigger was formed from the coincidence of two scintillators, one just
upstream and a second just downstream of the TimePix3 telescope (see Fig. 2)
and a not-busy signal from the Alibava motherboard. This trigger signal was
fanned out to both the TimePix3 telescope and the Alibava motherboard. Because
the data acquisition systems of the TimePix3 telescope and the DUT were
independent of one another, the common trigger signal was used to synchronize
the two systems. The signal sent to the Alibava system initiated a readout of
the DUT, while the signal sent to the TimePix3 system produced a timestamp in
the TimePix3 event record. This timestamp used the same clock used to time
stamp the pixel hits, and in this way, pixel hits could be associated with a
specific trigger. Since the number of time stamps in the TimePix3 event record
was identical to the number of triggers sent to the Alibava system, the
synchronization only required matching the first event in the Alibava system
with the pixel hits/tracks associated to the first trigger time stamp, and
then the second event matched to the second trigger time stamp, and so on. In
this way, the beam tracks reconstructed in the TimePix3 system were properly
matched to the corresponding hits produced in the DUT.

##  3 Corrections and calibrations

Before being able to quantify the performance of the sensors, various
calibrations and corrections were applied. These corrections included pedestal
and common-mode noise suppression, a cross-talk correction, an out-of-time
correction, and are detailed below.

###  3.1 Calibration scans

Calibration scans, which were taken periodically during the test beam, showed
that 1 ADC was equivalent to about 275 $e^{-}$. The exact value varied by a
few percent, depending on the sensor/readout board. Since the calibration
circuit has its own inherent parasitic capacitances, we estimate that there is
an inherent uncertainty in the overall calibration not larger than about 5%.
Charges presented throughout this article are given in terms of ADC counts,
and must be multiplied by 275 to obtain the corresponding charge in number of
electrons.

###  3.2 Pedestal and common mode noise suppression

Pedestals are calculated from datasets of $10^{4}-10^{5}$ events recorded
during beam stops and are then subtracted from the beam-on runs recorded under
the same conditions. (The events are self-triggered through the Alibava
motherboard). Dead or noisy strips are excluded from all parts of the
analysis. The pedestal of a given Beetle channel is evaluated as the mean of
the raw ADC counts of that channel over the whole pedestal run, after
excluding anomalously large or small ADC values. After subtracting the
pedestals, the common mode noise is computed (event-by-event) as the average
ADC value in a given chip, and is then subtracted from each channel. After the
pedestal and common mode noise suppression, the noise level is about 3.5 ADC
counts, or about 1000 electrons.

###  3.3 Cross-talk correction

From analysis of the data, it was found that there was cross-talk between the
Nth and the (N$+1)^{\rm th}$ channel. The effect was easily seen by studying
the charge asymmetry between the (N-1)th and (N$+1)^{\rm th}$ channel about
the peak strip ($N$) in a cluster with tracks at normal incidence. Due to
capacitative coupling some charge sharing is expected, but it should not be
asymmetric. The asymmetry is studied for even and odd-numbered peak strips
separately. The resulting asymmetries are shown in Fig. 5 (top) before the
correction and (bottom) after the linear correction for one of the DUTs. The
even channels show a larger cross-talk than the odd channels. An empirical
correction based on the linear fit shown is applied, and the asymmetry after
the correction is shown. This is believed to be due to a sub-optimal timing of
the ADC sampling phase, which was a fixed setting in the firmware of the
motherboard. The Beetle chip itself is known to have a small amount of cross-
talk [14], but the level is below 2%; thus most of the effect is attributable
to the readout. All DUTs have similar odd-even cross-talk corrections.

Figure 5: Mean of the difference in charge detected,
$\langle$ADC(N+1)-ADC(N-1)$\rangle$ between the (N+1)th and (N-1)th strips, as
a function of the charge seen in the Nth strip, for sensor 3092-1-MS2. The top
pair of plots show the values for even and odd channels before the correction,
the bottom pair after the correction. Plots with an even peak strip numbers
are shown on the left, while plots with an odd peak strip number are shown on
the right. The red lines are linear fits to the data.

The even/odd cross-talk correction was similar for all of the DUTs, but not
identical. Therefore, each sensor had a unique cross-talk correction to remove
this bias.

###  3.4 Out-of-time correction

The Alibava system provides a 40 MHz clock to sample the signals from DUT in
the front end of the Beetle chip. However, beam particles arrive
asynchronously with respect to this clock. The Alibava system stores the TDC
time between the signals from the scintillators and the edge of the 40 MHz
clock. In the offine analysis, the sampled pulse heights are sorted with the
TDC values. When timing in the system, we adjusted the latency such that the
signal from a beam particle arrives at about 10 ns. That is, the maximum
charge is collected from the Beetle when the TDC time is 10 ns. To make use of
the data not precisely at the peak, we include and correct the measured charge
for signals within $\pm$3.5 ns of the peak. The correction is obtained by
fitting the average ADC value for signal clusters as a function of the TDC
time to a Gaussian function. In this limited range, the correction is no more
than about $5-6\%$. Figure 6 (left) shows the raw time spectrum of all
triggered events, overlaid with the average ADC for signal clusters as a
function of the TDC time. The right panel shows the average ADC versus time
before and after the correction, where only the region used in the fit is
shown.

Figure 6: (Left) Raw TDC time spectrum, overlaid with the average ADC versus
TDC time for DUT signal clusters. (Right) Average ADC versus TDC time for DUT
signal clusters before (black points) and after (blue points) the time
correction.

###  3.5 Alignment

The coordinate system is defined such that $X$ is horizontal, $Y$ is vertical,
and $Z$ is parallel to the beam axis. Sensors are aligned with respect to
tracks using the residual distribution, which is defined as the difference
between the reconstructed $X$ position of the hit and the $X$ position of the
track extrapolated to the position of the sensor. The degrees of freedom
considered are: (i) offsets in the $X$ direction, (ii) offsets along the $Z$
axis, (iii) rotations around the $Z$ axis, and (iv) rotations around the $Y$
axis. A typical set of alignment plots are shown in Fig. 7, after the
alignment is done. The profile plots are close to flat at zero. Small
deviations are seen in the edges of the bottom pair of distributions, but is
likely an artifact of limited numbers of tracks and a possible bias due to the
steep dropoff of the beam profile near the edges.

Figure 7: Alignment plots for sensor 3092-1-MS2, after alignment, showing (top
left) $X$ residual, (top right) average $X$ residual vs $Y$ position, (bottom
left) average $X$ residual vs $X$ slope, and (bottom right) average $X$
residual vs $X$ position, after the alignment is performed. The $X$ and $Y$
positions and $X$ slope are obtained from the matching TimePix3 track.
Superimposed on the bottom left plot (red line) is the slope distribution of
the tracks.

##  4 Results

The results of the test beam are presented below, starting with the results
obtained from particles striking the detector at normal incidence, and
continuing with the dependence on the incidence angle.

###  4.1 Cluster finding in the DUT

Clusters in the DUT are built up by searching for a seed strip that has a
collected charge more than 20 ADC counts. Moving away from the seed strip, we
add adjacent side strips having at least 11 ADC counts (about
3$\times\sigma_{\rm noise}$). The cluster is terminated when a side strip
charge is below 11 ADC threshold. Thus, by definition, a cluster has between 1
and 5 strips included; each strip has charge of at least 11 ADC counts, and
there is at least one strip with at least 20 ADC counts. Therefore the minimum
charge of any cluster is 20 ADC counts. When there are multiple strips in the
cluster, the position is computed using linear charge weighting, namely
$\bar{x}=\sum{x_{i}q_{i}}/\sum{q_{i}}$, where $x_{i}$ and $q_{i}$ are the
positions and charges of the strips in the cluster. Better resolution can be
achieved with a non-linear correction, but optimizing the resolution on these
pre-prototype sensors is not a central goal of this test beam study.

###  4.2 Tracking information

Tracks were reconstructed using the TimePix3 telescope. About 95% of tracks
had 8-pixel hits; the remainder was 7-hit tracks. Only tracks with good fit
quality were used, by requiring that the $\chi^{2}$/ndf$<$4, where ndf is the
number of degrees of freedom. Figure 8 shows the beam profile ($Y$ vs $X$) for
tracks that have a DUT hit within 100 $\mu$m from the track. The quarter-
circle regions in board 2 chip 1, and board 4 chips 0 and 1 are evident. The
sharp vertical edges are due to the collimators in the beamline, and the
boundaries along $Y$ are fiducial cuts used in the analysis.

Figure 8: Profile of the beam ($Y$ vs $X$) at the DUT for each of the 7
sensors for a typical set of runs. The 3 DUTs with the quarter-circle edge are
evident in these distributions.

The beam intensity was tuned so that most of the triggered events had a single
beam track, although about 10% of events had more than one track. Multi-track
events are excluded from the analysis, to ensure that the reconstructed track
is the one which produced the trigger.

###  4.3 Single event displays

A few typical events, after all corrections are applied, are shown in Fig. 9.
Here, no requirement is made on the number of tracks. Strips with large ADC
counts are indicative of the passage of a beam particle through the detector.
The other channels show roughly Gaussian fluctuations about zero, typical of
incoherent detector noise. Signals generally stand out significantly above the
noise.

Figure 9: A few examples of single events for sensor 3092-1-MS2 (p-in-n), with
a bias voltage of 250 V.

###  4.4 Noise

To investigate the noise more quantitatively, the distribution of ADC counts
on all strips for a typical run of each sensor is shown in Fig. 10. The runs
are chosen to be in a range where each detector is fully depleted. While these
are beam-on data, the signal contribution to the shown distributions is
negligible, since clusters typically have charge $\sim$70-80 ADC counts on
average, and are therefore off the plot. In addition, most events have only
one cluster among the 255 channels. For each distribution, the core of the
distribution is fit to a Gaussian function and show the width, which is found
to be in the range of about 3.3$-$3.5 ADC counts. Since the charge
calibrtation is about 275 $e^{-}$/ADC, this corresponds to a noise level of
about 1000 $e^{-}$. Pedestal data with the beam off give compatible results.

Figure 10: Noise distributions (in ADC counts) for the DUTs after all
corrections during beam-on runs. The red curves show a Gaussian fit to the
core of the distribution.

###  4.5 Landau distributions versus bias voltage

The most important aspect of these test beam studies is to validate that the
sensors still have a high signal-to-noise ratio (S/N) at the highest expected
radiation fluence. For each sensor, data was recorded at bias voltages ranging
from $50$ V (well below full depletion) to $500$ V (well above it). A few of
the resulting distributions of cluster charge for sensor 3091-8-MBP2 (n-in-p,
$4.0\times 10^{14}~{}n_{\rm eq}$/cm2) are shown in Fig. 11

Figure 11: Signal distributions (in ADC counts) for sensor 3091-8-MBP2, which
is an n-in-p type sensor, irradiated to $4.0\times 10^{14}~{}n_{\rm eq}$/cm2,
for several bias voltages. Each distribution is fitted to a Landau convoluted
with a Gaussian resolution function and is overlaid.

The cluster charge distributions are each fit to a Landau convoluted with a
Gaussian function, and the fit parameters are indicated. For bias voltages
smaller than 75 V, the fits are biased because of the 20 ADC threshold
requirement on the seed strip in the cluster. As the bias voltage increases,
so does the collected charge.

The results for all DUTs tested are summarized in Fig. 12, which shows the
most probable value (MPV) of the Landau fit as a function of the bias voltage,
for each of the sensors. The p-in-n sensor is shown with a dashed curve and
the n-in-p sensors are represented by solid curves. All of the curves exhibit
a plateau in the $300-400$ V range, although there is a clear trend that the
sensors with the higher accumulated fluence exhibit a lower MPV in the plateau
region. The loss is about 10% at a fluence of $4\times 10^{14}~{}n_{\rm
eq}$/cm-2, compared to no irradiation. Similar loss of collected charge in
highly irradiated detectors has been seen previously (see for example Refs.
[15, 16, 17, 18, 19]). The three highest fluence ($4.0\times 10^{14}~{}n_{\rm
eq}$/cm2) sensors show a similar behavior. A small difference in the MPV in
the plateau is seen for one of the sensors, and this is most likely indicative
of small differences in its charge calibration relative to the other two.
Since the noise is $\sim$3.5 ADC per channel, the S/N is still quite high,
about 18 for $V>400$ V, even in the most irradiated detectors. The S/N depends
on the detector capacitance, and hence we would expect smaller S/N in full
size sensors.

Figure 12: The most probable value of the collected charge for all cluster
sizes from the Landau fit as a function of bias voltage for each of the DUT.
Tracks are at normal incidence to the sensor.

###  4.6 Cluster size

Figure 13 shows the distribution of cluster sizes for the DUTs after all
corrections are applied, all at normal incidence, and at bias voltages in the
plateau region of Fig. 12. In the p-in-n sensor, about 85% of the clusters are
single hit clusters. On the zero fluence n-in-p sensor, the single hit cluster
fraction is a bit lower, about 82%. The irradiated n-in-p sensors show a
substantially larger fraction of 2-strip clusters, of about 40%. While there
is a loss of total charge collected in the highly irradiated detectors, a
larger amount of charge sharing is observed.

Figure 13: Distributions of the cluster size for the DUTs, after all
corrections for tracks at normal incidence. The runs are taken from the
plateau region of each DUT.

###  4.7 Cluster charge versus cluster size and interstrip position

In this section, we investigate the dependence of the collected charge on the
cluster size. With zero thresholds, and no radiation effects, one would expect
that the collected charge to be independent of the cluster size. However,
radiation effects and non-zero thresholds can lead to a difference. Figure 14
shows the Landau distributions in the plateau region of the sensors, and
overlaid are the separate contributions from 1 and 2-strip clusters. The
1-strip and 2-strip clusters have similar MPVs, although not identical. Due to
the threshold bias mentioned above, the $0.27\times 10^{14}~{}n_{\rm eq}$/cm2
p-in-n and the zero fluence n-in-p sensors have larger cluster charge for
2-strip clusters compared to the 1-strip clusters. However, for the irradiated
sensors, the opposite is seen, that is, 2-strip clusters have a lower charge
collected than 1-strip clusters.

Figure 14: Distributions of charge collected in each DUT in the plateau region
for tracks at normal incidence. The black points show all clusters matched
within 100 $\mu$m of a track, and the colored histograms show 1-strip and
2-strip cluster contributions. The data are fit to a Landau convoluted with a
Gaussian resolution function, and the fit is shown.

From these observations, we conclude that the n-in-p sensors that received the
radiation fluence (i) have reduced total charge, (ii) have a larger fraction
of two-strip clusters, and (iii) have less charge collected in two-strip
clusters compared to 1-strip clusters.

Additional information can be gained by investigating the charge collection as
a function of the relative position between two strips. For each track, the
interstrip position is defined to be the position at the DUT mapped onto the
range from [0, 1], where 0 is the center of the $N^{th}$ strip and 1 is the
center of the $(N+1)^{th}$ strip. The distributions of the average cluster
charge as a function of the interstrip position are shown in Fig. 15 for each
of the DUTs. It is seen that the heavily irradiated n-in-p sensors exhibit a
steady decrease in charge collection as the track approaches the middle region
between two strips. At the center, a loss of approximately 15% in collected
charge is observed. The p-in-n and unirradiated n-in-p show a small loss in
the middle between two strips, but the effect is not more than a few percent.
Similar loss of collected charge in the mid-region between two strips in
irradiated detectors has been reported in test beams of the ATLAS SCT [20].

From this, it is evident that a sizeable part of the drop in collected charge
of the irradiated sensors is due to loss of charge when the track has an
interstrip position between 0.2 and 0.8, where a 10-15% loss in charge is
seen. When the track has an interstrip position less than 0.2 or greater than
0.8, the loss in collected charge is not as pronounced. Nevertheless, it is
the average over the strip which is relevant for the detector performance.

Figure 15: Distributions of the average cluster charge as a function of the
relative position within a strip, for tracks at normal incidence. A second
order polynomial fit is overlaid just to guide the eye.

The efficiency versus the interstrip position has also been investigated, and
in all cases, it is at least 99%. Despite the loss in collected charge, there
is no indication of any loss of efficiency.

###  4.8 Cluster size and resolution versus angle

Studies of the detector performance were also carried out at angles ranging
from normal incidence to 30o (with respect to the normal to the sensor). The
fraction of 1, 2 and 3-strip clusters as a function of the angle for (left)
the p-in-n sensor and (right) one of the $4.0\times 10^{14}~{}n_{\rm eq}$/cm2
n-in-p sensors, is shown in Fig. 16. There is a clear increase in the fraction
of 2-strip clusters in both cases, which reaches a maximum at about 22.5o,
beyond which the 3-strip clusters start to become sizeable. The main
difference between the two sensors is the cluster size at zero angle. For the
heavily irradiated detectors, at normal incidence, the 2-strip cluster
fraction is significantly larger (see cluster size distributions for normal
incidence in Fig. 13).

Figure 16: Fraction of 1-strip, 2-strip, and 3-strip clusters as a function of
angle for (left) 3092-1-MS2 ($0.27\times 10^{14}~{}n_{\rm eq}$/cm2 p-in-n) at
$V_{\rm bias}=250$ V, and (right) 3091-8-MBP2 ($4.0\times 10^{14}~{}n_{\rm
eq}$/cm2 n-in-p) at $V_{\rm bias}=350$ V,.

The residual distributions between the UT hit and the track are shown in Fig.
17 for the $0.27\times 10^{14}~{}n_{\rm eq}$/cm2 p-in-n sensor. The angles
range from 0o to 30o in 5o steps. The contributions from 1, 2, and 3-strip
clusters are also shown. The 3-strip clusters make up only a very small
fraction, except at the two largest angles. As the angle increases the
resolution improves, as indicated by the RMS of the distributions. The best
resolution should be achieved when $\tan^{-1}$(pitch/thickness)$\sim 18^{\rm
o}$. The RMS is minimum for the $20^{\rm o}$ angle (RMS $=10.6~{}\mu$m.) The
2-strip residual distribution is fit to a Gaussian function, and the width
returned by the fit, $\sigma_{2}$, is shown. Two-strip clusters provide a
resolution of about $7~{}\mu$m for tracks with angles in the 15-20o range,
which is about 3 times better than binary resolution (80${\,\upmu\rm
m}$/$\sqrt{12}$). At small angles, most of the clusters are single strips, and
the residual distribution is roughly flat, as one would expect. At very large
angles, the 2-strip resolution worsens. This is likely due to a third strip
that should have been included in the cluster but was below the minimum ADC
side strip threshold to be included. Improved resolution, primarily for tracks
at low incidence angle, was demonstrated by applying a non-linear charge
weighting to two-strip clusters, but it is not presented here.

Figure 17: Residual distributions for angles ranging from $0^{\rm o}$ to
$-30^{\rm o}$ for DUT 3092-1-MS2 ($0.27\times 10^{14}~{}n_{\rm eq}$/cm2
p-in-n) at $V_{\rm bias}=250$ V. The contributions from 1-strip, 2-strip, and
3-strip clusters are also shown. The 2-strip cluster distributions are each
fit to a single Gaussian function, and the widths, $\sigma_{2}$, are also
indicated.

Figure 18 shows the corresponding residual distributions for one of the
$4.0\times 10^{14}~{}n_{\rm eq}$/cm2 n-in-p sensors. A similar resolution is
obtained in the 15-20o angular range, as for the p-in-n sensor. However, the
notable difference (with respect to the p-in-n sensor) is that at low angles,
the 2-strip contribution is sizeable, and shows the improved resolution that
is generally accompanied by a 2-strip cluster. This clearly illustrates that
the larger cluster sizes associated with the irradiated n-in-p sensors are not
an anomaly, since they are also accompanied by better position resolution.

Figure 18: Residual distributions for angles ranging from $0^{\rm o}$ to
$-30^{\rm o}$ for DUT 3091-8-MBP2 ($4.0\times 10^{14}~{}n_{\rm eq}$/cm2 n-in-p
at $V_{\rm bias}=-350$ V). The contributions from 1, 2, and 3-strip clusters
are also shown. The 2-strip cluster distributions are each fit to a single
Gaussian function, and the widths, $\sigma_{2}$, are also indicated.

The position resolution as a function of the angle is presented for 3 of the
sensors in Fig. 19, the $0.27\times 10^{14}~{}n_{\rm eq}$/cm2 p-in-n, the
$1.0\times 10^{14}~{}n_{\rm eq}$/cm2 n-in-p and one of the $4.0\times
10^{14}~{}n_{\rm eq}$/cm2 n-in-p sensors. The resolution of the p-in-n sensor
increases as one approaches normal incidence, reaching a maximum of about
$23~{}\mu$m, which is approximately binary, e.g. $80~{}\mu$m/$\sqrt{12}$. For
the n-in-p sensors at normal incidence, the position resolution is much
better, about $13~{}\mu$m, owing to the larger amount of charge sharing
between the strips (see Fig. 16). The $4.0\times 10^{14}~{}n_{\rm eq}$/cm2
irradiated n-in-p sensor shows slightly worse position resolution than the
$1.0\times 10^{14}~{}n_{\rm eq}$/cm2 sensor, but it is only at the $2~{}\mu$m
level in the worst case. This difference is not of great concern for the UT
detector.

Figure 19: RMS of the residual distribution as a function of angle (with
respect to the normal to the sensor) for 3 different sensors. The bias
voltages for the 3 sensors are 250 V for the

###  4.9 Charge collection near the quarter-circle region

Three of the sensors studied during the test beam have a quarter-circle region
where there are no strips (see Fig. 3). One of the sensors with this quarter-
circle is the unirradiated n-in-p sensor, and the other two are board 4
sensors 0 and 1. The latter two have different guard-ring structures, as shown
in Fig. 3. We investigate whether there is any drop in charge collected as one
approaches the quarter-circle radially. Using the data, the center of the
circle is determined using the 3D information from the TP3 tracks that have
matched DUT clusters. The average ADC value as a function of the radial
distance from the center of the circle is then analyzed. The results for the 3
sensors are shown in Fig. 20, where each row shows the results for a single
sensor. The left column shows the XY profile of tracks that have matched DUT
hits, along with an arc that shows the estimated circle to match the quarter-
circle region void of strips. The right hand plots show an overlay of the
radial distribution of tracks with matched DUT hits, with the average ADC
value of clusters as a function of the radius. In this figure, several runs
with bias voltage above $350$ V are combined, and the average ADC is the raw
value with no TDC time requirement. This is done to increase the sample size,
as the main interest is to uncover a trend, while the absolute value is of
less concern.

Figure 20: (Top row) XY distributions of tracks matched to clusters for each
of the 3 mini beam-pipe sensors for a bias voltage of -350 V. (Bottom row)
Overlay of average ADC value vs radial coordinate (red with error bars) and
the radial distribution of tracks at the DUT (blue histogram). The radius is
computed using the center of the red circles shown in the left column.

There is no clear indication of large loss of charge collection near the
quarter-circle edge. A small loss in average charge in the final 50 $\mu$m or
so from the edge cannot be ruled out, but the drop is most likely just the
precision on which the center of the circle is determined, which is about 50
$\mu$m. No significant difference between the two guard-ring structure designs
(MBP1 versus MPB2 in bottom set of plots) is observed. Moreover, no
significant differences between the unirradiated and irradiated detectors is
seen.

##  5 Summary

Results from a test beam at the CERN SPS of 7 pre-prototype UT sensors, one
p-in-n and 6 n-in-p, have been presented. The n-in-p sensors were irradiated
at fluences of $1.0\times 10^{14}~{}n_{\rm eq}$/cm2, $1.8\times
10^{14}~{}n_{\rm eq}$/cm2 and $4.0\times 10^{14}~{}n_{\rm eq}$/cm2, and showed
a gradual loss in total charge collected with increased fluence. The maximum
charge loss is about 10% for the detectors with the largest accumulated
fluence. All detectors plateaued in the 300-400 V region, yielding a S/N of at
least 15. With the full size UT sensors (10 cm x 10 cm, or 10 cm x 5 cm),
there will be a larger input capacitance, and hence it is likely that the S/N
will be lower. However, the studies presented indicate that the anticipated
500 V maximum will be sufficient for operation of these detectors for the full
50 fb-1 data set expected to be collected in Run III of LHCb.

We also find that the irradiated n-in-p DUTs have substantially larger cluster
sizes at normal incidence, compared to either the unirradiated n-in-p DUT, or
the $0.27\times 10^{14}~{}n_{\rm eq}$/cm2 p-in-n DUT. These larger clusters
sizes at normal incidence are accompanied by improved position resolution, as
one expects when there is charge sharing between strips.

The dependence of the charge collection on the interstrip position has also
been studied. For the irradiated n-in-p DUTs, it is found that about 15% less
charge is collected when a track goes through the middle of two strips,
relative to the amount collected when it passes through the center of a given
strip. This is consistent with findings from other experiments. The efficiency
as function of interstrip position has also been studied, and in all cases it
is found to exceed about 99%.

The position resolution in the various sensors has also been investigated. At
normal incidence, the irradiated detectors show substantially better position
resolution than the unirradiated detector. This stems from the larger fraction
of 2-strip clusters in the irradiated detectors. This goes against the
conventional thinking that in irradiated detectors, less charge is collected,
resulting in a reduction of the fraction of multi-strip clusters. At large
angles, all detectors studied show improved spatial resolution, and the best
resolution achieved is about 8 $\mu$m at an incidence angle in the $15-20^{\rm
o}$ range. A resolution of about 6.5 $\mu$m is found for the subset of 2-strip
clusters.

The charge collection close to the circular portion of the DUTs was studied,
and there is no indication of any significant degradation of charge collection
in the region close to this region.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the SPS. INFN (Italy); MNiSW and NCN
(Poland); SNSF and SER (Switzerland); and NSF (USA). We also acknowledge the
efforts of the VELO TimePix3 group, most notably Heinrich Schindler, Martin
van Beuzekom, Hella Snoek, Paula Collins, Raphael Dumps, Kazu Akiba, Xabier
Cid Vidal, Alvaro Dosil, Bas van der Heijden Sophie Richards, Dan Saunders,
Panos Tsopelas, Jaap Velthuis and Mark Williams, for providing a high
precision telescope to enable many of the studies presented in this paper. We
also thank Ethan Cascio of the MGH proton irradiation facility for his support
in carrying out the sensor irradiations.

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