11institutetext:  Heriot-Watt University, Edinburgh EH14 4AS, UK

# LSTM based IoT Device Identification

Kahraman Kostas

###### Abstract

While the use of the Internet of Things is becoming more and more popular,
many security vulnerabilities are emerging with the large number of devices
being introduced to the market. In this environment, IoT device identification
methods provide a preventive security measure as an important factor in
identifying these devices and detecting the vulnerabilities they suffer from.
In this study, we present a method that identifies devices in the Aalto
dataset using Long short-term memory (LSTM).

While the use of the Internet of Things is becoming more and more popular,
many security vulnerabilities are emerging with the large number of devices
being introduced to the market. In this environment, IoT device identification
methods provide a preventive security measure as an important factor in
identifying these devices and detecting the vulnerabilities they suffer from.
In this study, we present a method that identifies devices in the Aalto
dataset using Long short-term memory (LSTM).

Feed-forward ANN models, such as CNNs, are very good at studying static data.
However, if there is a sequence relationship between the processed data, a
specialized type of ANN has been created to solve it. This model is named RNN
[1, 2, 3].

For example, while ANNs are very successful for images, it is preferred to
apply RNN to videos. Because the video is actually images that are stacked in
a time frame. Examples of sequential / queue dependent data include language
processing, audio, video, stock market, weather and network data.

RNN is a type of artificial neural network used to discover various patterns,
among which are sequential data. While a normal neural network cell is
attached only to the cells in its lower and upper layer, the RNN cell is
connected to and interacts with the previous and next neurons in its layer in
addition to this bond (see Figure 1) [1, 2, 3].

Figure 1: Comparison of ANN, RNN and LSTM architectures.
The figure copied from [4].

However, there are some problems in using RNN. Although RNN cells share data
and interact with each other, the interaction between the two RNN cells
decreases as the distance between them increases. This is called the vanishing
gradients problem. Another problem is that RNN uses some kind of sliding
window method and therefore the data outside the window is ignored. So, RNN is
not successful in long-sequence data due to both lost gradients and limited
window size [1, 2, 3].

Figure 2: Sentence processing scenario.
The figure copied from [1].

In Figure 2, a sentence processing scenario is examined. As can be seen in the
figure, the interaction of the consecutive cells with each other is high,
while the interactions of the cells which is far from each other are low.
Also, interaction with the previous/next sentences (if any) cannot be
established due to the window size. However, the significance levels of any
inputs vary and are often much more complex than a simple order [1, 2].

Various methods have been developed to deal with these negativities. LSTM
(Long Short-Term Memory) and GRU (Gated Recurrent Unit) are the most widely
used solutions. In both methods, the aim is to ensure that important
information is transferred to future cells in a productive way. In other
words, if the information is important, it is transferred to the future/next
neuron regardless of its location and order. If the information is
insignificant, it is forgotten regardless of its location and sequence. The
architecture of these methods is shown below (see Figure 3) [1, 2].

Figure 3: LSTM and GRU architectures.
The figure copied from [2].

RNNs that are actively used in sequential data are also promising in the
analysis of network flow, which is consecutive network packets. There are many
studies in IoT security using this method [5, 6, 7, 8, 9]. For instance, in
Lopez-Martin et al.’s study [9], CNN and RNN methods are used to classify IoT
network traffic. In the 4.2 RNN Implementation section, this study is
described in depth.

RNNs are used extensively in the analysis of sequential data such as video,
audio and text. Network behaviours are also formed by the combination of
sequential packets, and these packets follow a whole set of rules called
”protocols”. Because of this feature of network behaviour, many researchers
have used methods such as RNN and its enhanced versions, LSTM and GRU, in
their work [5, 6, 9, 7, 8].

Among these studies, Lopez-Martin et al.’s study [9] is particularly striking.
In this study, CNN - RNN methods are used to classify IoT network traffic. In
this study, TCP headers are used to obtain input data. For each flow, the
first 20 packets are taken, and the six features of these packets are used
(the source port, destination port, number of bytes in the packet payload, TCP
window size (0 for UDP packets), interarrival time and direction of the
packet). In this way, a 6x20 matrix time series is obtained for each network
flow.

In our application111The script available at: github.com/kahramankostas/LSTM-
based-IoT-Device-Identification, a strategy very similar to this method was
followed. Since RNNs are used in the analysis of time series, we created
consecutive sets of fingerprints to simulate the fingerprints of the devices
into the time series. In the data used, there are 540 sessions in total. These
sessions consist of 27 devices each producing 20 sessions.

By taking the first 12 packets of each session, a series of packets is
created. The reason for choosing the first 12 packets is that this number
creates the lowest limit in the dataset. The device, which produces the least
number of network packets, produces 11 packets per session. Actually, this
lower limit is 11, but instead of using a prime number like 11, the number 12,
which is much more prone to division, was preferred. In this process, a 12th
packet consisting of zeros was added to the session containing less than 12
packs. For session larger than 12, the packets after the 12th packet were
ignored. Since we created the features using the IoTDevIDv1 [10] feature set,
which contains 25 features, 540 matrices of 12X25 size were obtained.

In the learning step, among the many versions of RNN, 4 of them are used,
whose names and brief descriptions are given below (see Figure 4 for the
representation of architectures).

Figure 4: The representation of architectures of LSTM types [11]

Vanilla LSTM: It is the simplest LSTM application. It consists of only one
layer of LSTM [11].

Stacked LSTM:It consists of multiple LSTM layers as hidden layer. It can also
be called as deep LSTM [11].

CNN- LSTM: It consists of merging the CNN layer with the LSTM layer in the
hidden layer. The CNN layer processes mxn size image / pseudo-image data. The
results of this process are used as input in the LSTM layer [11].

Encoder-Decoder LSTM: It is a model consisting of combining two LSTM layers,
one encoding and the other decoding. The Encode layer converts the inputs into
vectors, and the decoding layer converts the vectors to the predicted output
[11].

Figure 5: Distribution of Accuracy Values

| CNN-LSTM | ED-LSTM | Stacked-LSTM | Vanilla-LSTM
---|---|---|---|---
Accuracy | 0.763 | 0.750 | 0.740 | 0.769

Table 1: Comparison of 4 different types of LSTM Results

Table 1 shows the results of the applications of these 4 architectures, and
Figure 5 shows the distribution of these results. The results are the average
of 50 repeats. All applications exceeded more than 0.70 accuracies, achieving
notable success. Among the applications, Vanilla and CNN-LSTM have the highest
accuracy, 0.769 and 0.763, respectively. The lowest value is the Stacked LSTM
method. Statistical test results are available at Table 2 in Appendix G

## References

  * [1] M. Nguyen, “Illustrated guide to recurrent neural networks,” 2018.  Accessed: 2020-03-20.
  * [2] M. Nguyen, “Illustrated guide to lstm’s and gru’s: A step by step explanation,” 2018.  Accessed: 2020-03-20.
  * [3] C. Olah, “Understanding lstm networks,” 2015.  Accessed: 2020-03-20.
  * [4] J. Ma, Y. Ding, V. J. Gan, C. Lin, and Z. Wan, “Spatiotemporal prediction of pm2. 5 concentrations at different time granularities using idw-blstm,” IEEE Access, vol. 7, pp. 107897–107907, 2019.
  * [5] H. HaddadPajouh, A. Dehghantanha, R. Khayami, and K.-K. R. Choo, “A deep recurrent neural network based approach for internet of things malware threat hunting,” Future Generation Computer Systems, vol. 85, pp. 88–96, 2018\.
  * [6] N. Koroniotis, N. Moustafa, E. Sitnikova, and B. Turnbull, “Towards the development of realistic botnet dataset in the internet of things for network forensic analytics: Bot-iot dataset,” Future Generation Computer Systems, vol. 100, pp. 779–796, 2019.
  * [7] N. Moustafa, B. Turnbull, and K.-K. R. Choo, “An ensemble intrusion detection technique based on proposed statistical flow features for protecting network traffic of internet of things,” IEEE Internet of Things Journal, vol. 6, no. 3, pp. 4815–4830, 2018.
  * [8] J. Ortiz, C. Crawford, and F. Le, “Devicemien: network device behavior modeling for identifying unknown iot devices,” in Proceedings of the International Conference on Internet of Things Design and Implementation, pp. 106–117, 2019.
  * [9] M. Lopez-Martin, B. Carro, A. Sanchez-Esguevillas, and J. Lloret, “Network traffic classifier with convolutional and recurrent neural networks for internet of things,” IEEE Access, vol. 5, pp. 18042–18050, 2017.
  * [10] K. Kostas, M. Just, and M. A. Lones, “IoTDevID: A behaviour-based fingerprinting method for device identification in the IoT,” 2021.
  * [11] J. Brownlee, Long Short-term Memory Networks with Python: Develop Sequence Prediction Models with Deep Learning.  Machine Learning Mastery, 2017.

Appendix

Appendix G
4.2 RNN Implementation section Statistical test results

Test | P Value
---|---
ANOVACNN-LSTM,ED-LSTM,Stacked-LSTM,Vanilla-LSTM | 1.32E-21
Utest (CNN-LSTM, ED-LSTM) | 3.42E-05
Utest (CNN-LSTM, Stacked-LSTM) | 8.02E-10
Utest (CNN-LSTM, Vanilla-LSTM) | 0.007966986
Utest (ED-LSTM, Stacked-LSTM) | 0.00066457
Utest (ED-LSTM, Vanilla-LSTM) | 3.07E-11
Utest (Stacked-LSTM, Vanilla-LSTM) | 1.16E-15

Table 2: Result of statistical tests of comparing LSTM architectures,Utest:
Mann Whitney U Test
The significance level is 0.05 for the ANOVA test and it is 0.0083 for the
Mann Whitney U test


# Neutron Irradiation and Electrical Characterisation of the First 8” Silicon
Pad Sensor Prototypes for the CMS Calorimeter Endcap Upgrade

CMS HGCAL Collaboration

###### Abstract

As part of its HL-LHC upgrade program, the CMS collaboration is replacing its
existing endcap calorimeters with a high-granularity calorimeter (CE). The new
calorimeter is a sampling calorimeter with unprecedented transverse and
longitudinal readout for both electromagnetic and hadronic compartments. Due
to its compactness, intrinsic time resolution, and radiation hardness, silicon
has been chosen as active material for the regions exposed to higher radiation
levels. The silicon sensors are fabricated as $20\text{\,}\mathrm{cm}$ (8”)
wide hexagonal wafers and are segmented into several hundred pads which are
read out individually. As part of the sensor qualification strategy, 8” sensor
irradiation with neutrons has been conducted at the Rhode Island Nuclear
Science Center (RINSC) and followed by their electrical characterisation in
2020-21. The completion of this important milestone in the CE’s R$\&$D program
is documented in this paper and it provides detailed account of the associated
infrastructure and procedures. The results on the electrical properties of the
irradiated CE silicon sensors are presented.

##  1 Introduction

In the current decade, the Large Hadron Collider [1] (LHC) at CERN will be
upgraded to the High-Luminosity LHC (HL-LHC) [2]. Its instantaneous luminosity
is designed to reach at least five times the LHC’s design value. The increase
in both the expected number of pile-up interactions and the anticipated damage
due to the enhanced radiation levels will pose significant challenges to the
LHC experiments.
The CMS [3] collaboration has undertaken an extensive R$\&$D program to
upgrade many parts of the detector. One of the planned upgrades consists of
the replacement of the existing endcap calorimeters with a high-granularity
calorimeter (CE) [4]. The new CE will consist of 47 sampling layers
interspersed with absorber plates and will feature close to six million
readout channels. For its compactness, fast signal formation, and acceptable
radiation hardness, silicon has been chosen as one of the active materials.
Approximately $600\text{\,}{\mathrm{m}}^{2}$ of it will be deployed in the
regions where integrated fluences up to $1\times 10^{16}~{}$1-MeV neutron-
equivalents per square centimeter ($\mathrm{n_{eq}}/\mathrm{cm}^{2}$) at the
end of its 10-year operation at the HL-LHC are expected. Prototypes of
silicon-based modules have already been built and were tested with particle
beams [5, 6, 7, 8].
The silicon sensors will be fabricated as multi-pad, DC-coupled, n-on-p
("p-type"), 8” hexagonal wafers with active thicknesses of
$120\text{\,}\mathrm{\SIUnitSymbolMicro m}$,
$200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ or
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$. To assess their anticipated
degradation over the HL-LHC lifetime, irradiation studies are an integral
component to the CE’s R$\&$D efforts. However, the irradiation and electrical
characterisation of full 8” silicon sensors are not trivial due to their large
size and the large number of pads. In fact, previous R$\&$D on the CE silicon
sensors’ bulk degradation in terms of their leakage currents and depletion
voltages was, thus far, limited to testing of small, approximately
$1\text{\,}{\mathrm{cm}}^{2}$-sized, single-diode test structures [9, 10]. As
part of the CE’s prototyping phase in the last few years, the CMS
collaboration has developed the required infrastructure and procedures for the
irradiation and the electrical characterisation of its 8” silicon sensors. The
neutron irradiation was performed at the Rhode Island Nuclear Science Center
(RINSC) which offers the necessary infrastructure to expose such large objects
up to $\sim 10^{16}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$ within a few hours.
Afterwards, the ARRAY system [11] was used for the electrical characterisation
of all $\mathcal{O}(100)$ pads on the silicon sensors. In order to reduce the
fluence-induced leakage current to measurable levels, the tests were conducted
at $-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
This paper is structured as follows: Section 2 deals with the CE silicon pad
sensor prototypes in terms of their design and the production parameters.
Section 3 describes the neutron irradiation of the 8” wafers at RINSC. The
electrical test setup based on the ARRAY system and the measurement procedure
are documented in Section 4. Results on the electrical sensor characteristics
and their limitations are discussed in Section 5. Finally, the conclusions are
given in Section 6.

##  2 Silicon Pad Sensor Prototypes for the CMS Endcap Calorimeter Upgrade

The CMS high granularity calorimeter will be made of more than
$600\text{\,}{\mathrm{m}}^{2}$ of planar DC-coupled silicon pad sensors.
Starting from 8” circular wafers, the sensors are diced into hexagons. P-type
doping of their bulk was chosen due to empirical evidence of superior noise
performance after irradiation with respect to n-type doping [12]. The oxygen
content of those 8” wafers is reduced with respect to the case of the 6”
wafers used for the CMS and ATLAS trackers which, in principle, could impair
the sensor’s radiation hardness.
In this work, the first version prototypes of hexagonal wafer sensors with the
so-called low-density (LD) and high-density (HD) designs were irradiated with
neutrons and electrically characterised. Their design is illustrated in Figure
1. Each CE silicon sensor is segmented into several hundred pads that
constitute the sensitive units. The majority of those pads are shaped as
regular hexagons which are drawn as cyan-colored pads in Figure 1. Special
non-hexagonal structures fill out the sensor periphery. The arrangement of
pads on a sensor is enclosed by a set of three guard rings (grounded,
floating, biased) which protect the sensor from currents drawn from its dicing
edges.

(a)

(b)

Figure 1:  Layout of the tested 8” prototype silicon pad sensors with (a) the
low-density (LD) and (b) the high-density (HD) design. Regular-sized hexagonal
pads are depicted in cyan. Edge and corner pads populate the sensor periphery.
Six (LD), respectively twelve (HD), regular, small hexagonal pads on the
sensor are dedicated for energy calibration with minimum ionising particles up
to the end of life. The colour coding highlights the usage of different pad
geometries. The sensor guard rings are not shown.

The LD sensors were produced from physically thinned p-type float zone silicon
wafers. They are segmented into 198 pads, where full hexagonal pads are about
$1.2\text{\,}{\mathrm{cm}}^{2}$, and $200\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ or $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in active thickness. LD
sensors will be installed in regions of intermediate radiation levels inside
the CE. By contrast, regions with the highest radiation levels will be
populated with HD sensors whose active thickness is
$120\text{\,}\mathrm{\SIUnitSymbolMicro m}$. HD sensors are segmented into 444
pads (full hexagon pad size: $0.5\text{\,}{\mathrm{cm}}^{2}$) and are produced
by epitaxial growth.
As it is foreseen for the final design, p-stop structures were added to all
the tested prototype silicon sensors in this work in order to limit the
accumulation of electrons on the Si/SiO2 interface after exposure to high
radiation levels which otherwise could form a conduction channel, effectively
shorting adjacent pads. Those structures were either bound to the single pads
(individual p-stop) or shared between neighboring ones (common p-stop),
representing two options under consideration for the CE. In addition, the
tested prototype sensors differed in their flatband voltage (pre-irradiation
value of either $-2\text{\,}\mathrm{V}$ or $-5\text{\,}\mathrm{V}$). Unless
explicitly stated otherwise, all other production parameters, such as doping
concentrations and the production process for the oxide material, were
identical for all prototype sensors discussed in this paper.
Prior to irradiation, the sensors had been electrically qualified and proper
functionality could be verified. In particular, full depletion was achieved
around $40\text{\,}\mathrm{V}$ for $120\text{\,}\mathrm{\SIUnitSymbolMicro m}$
sensors, $120\text{\,}\mathrm{V}$ for $200\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ sensors, and $280\text{\,}\mathrm{V}$ for
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sensors. Moreover, per-pad leakage
currents of the non-irradiated sensors did not exceed a few nA, and the total
currents at room temperatures between
20–$24\text{\,}\mathrm{\SIUnitSymbolCelsius}$ over the full sensor remained
well below $100\text{\,}\mathrm{\SIUnitSymbolMicro A}$ for (absolute) bias
voltages up to $850\text{\,}\mathrm{V}$.
In general, exposure of silicon sensors to radiation causes displacement
damage to the silicon lattice which affects both the leakage currents and the
depletion voltages. While the bulk-dominated leakage current density increases
proportionally with the fluence, the expected increase of the depletion
voltage (for p-type sensors) is non-trivial and its quantification, like it is
done e.g. in Refs. [13, 14], is beyond the scope of this work.

##  3 Irradiation at the Rhode Island Nuclear Science Center

###  3.1 Rhode Island Nuclear Reactor

The Rhode Island Nuclear Science Center (RINSC) houses a
$2\text{\,}\mathrm{MW}$, light-water cooled, pool-type reactor in
Narragansett, Rhode Island, USA. Its core consists of fuel assemblies
moderated with a combination of graphite and beryllium. The fuel is plate type
U3Si2, cladded with aluminum, enriched to less than 20$~{}\%$ Uranium-235.
The reactor beam port was used as a sample delivery system because it was the
only reactor access point large enough to fit a full-sized CE sensor. The beam
port in question had not previously been used for experiments, only for
facility-related work. A sketch of the beam port and a photo of its inside are
shown in Figure 2.

Figure 2: (a) Schematic of the beam port sample delivery system at RINSC. (b)
The view into the beam port used for these irradiation studies. (c) The sample
delivery cylinder that contains the sensor-holding hockey pucks and (d) dry
ice for cooling of the silicon sensors in the beam port during and after
irradiation.

It measures about $4\text{\,}\mathrm{m}$ from its opening to the termination
near to the reactor core, and it can accommodate samples with diameters of up
to $20\text{\,}\mathrm{cm}$ and with depths up to $90\text{\,}\mathrm{cm}$. A
shutter assembly is located $3\text{\,}\mathrm{m}$ from the opening of the
beam port, which must be raised to allow for the insertion of the samples and
closed prior to the start of operations. A $85\text{\,}\mathrm{cm}$-long lead
plug serves as a radiation shield that has to be inserted into the opening of
the beam port prior to the start of the irradiation.

###  3.2 Irradiation of CE Silicon Sensor Prototypes

Given the constraints of the beam port system at RINSC, a dedicated sample
delivery method had to be developed for irradiating CE silicon sensors. This
new sample delivery allows for:

  * •

positioning sensors as close to the reactor core as possible;

  * •

protecting them from physical damage during the loading, irradiation, and
unloading;

  * •

keeping the irradiated sensors at low temperatures during and after the
irradiation;

  * •

monitoring the temperature of the samples inside the beam port.

Two compatible pieces of hardware were manufactured: a sensor container,
referred to as a "hockey puck", and a sample delivery cylinder (see Figure 2).
The former is used to protect, orient, and store the sensors during the
irradiation while the latter is used to protect and locate the hockey puck
inside the beam port. The cylinder is made from 6061 aluminum and has an
outer(inner) diameter of
$19.8\text{\,}\mathrm{cm}$($19.1\text{\,}\mathrm{cm}$), allowing for a snug
fit of the cylinder inside the beam port and a smooth insertion and removal of
the hockey pucks. Three different hockey puck materials were considered (see
Figure 3): oak, acrylic, and PEEK. They differ in their mechanical properties
with respect to temperature and humidity fluctuations, in their activation,
radiation hardness and overall cost. As a practical compromise between these
factors, acrylic was found most suitable for irradiation up to fluences of
$5\times 10^{15}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$, and PEEK material
suitable for higher fluences. The usage of oak was eventually discarded
because of its unfavorable tendency to absorb moisture.

Figure 3: (a) Sample containers (’hockey puck’) designed to hold CE silicon
sensors for neutron irradiation at RINSC. Wood (oak), acrylic, and PEEK were
the puck materials that were experimented with. (b) An 8” high-density CE
prototype silicon sensor inside an acrylic puck covered with a Kapton™ foil.

The puck base has an outer diameter of $18.6\text{\,}\mathrm{cm}$ that allows
for a smooth fit inside the cylinder. The interior of the puck is milled out
in the profile of the silicon sensors with an additional clearance of
$1\text{\,}\mathrm{mm}$. With these constraints the thinnest sections of the
wall of the puck are slightly over $1\text{\,}\mathrm{mm}$ thick.
Kapton™ foils were used to separate sensors in a stack such that no sensors
were in direct contact with any metallic surfaces (cf. Figure 3). In addition,
antistatic foam was used for covering the top and bottom of the sensor-Kapton™
stack serving as a cushion against the walls inside the puck. After
preparation of the puck, the latter was inserted into the delivery cylinder.
In general, the silicon sensors should be kept at low temperatures during the
irradiation in order to limit unwanted thermal annealing. For this purpose,
the rest of the delivery cylinder was filled with 15-$18\text{\,}\mathrm{kg}$
of dry ice (Figure 2). In order to monitor the temperature, PT1000 resistance
temperature detectors (RTD) were inserted into the puck, at the front and back
faces, to record the temperature throughout the irradiation for assessment of
the expected sensor annealing during irradiation. Representative temperature
recordings from two irradiation rounds of different duration are shown in
Figure 4.

Figure 4: Representative temperature recordings during two of the RINSC
irradiation rounds of CE prototype silicon sensors. The time when the
irradiation was started and when it ended is indicated. The increase of the
temperature towards its plateau coincides with the sublimation of the dry ice
inside the delivery cylinder.

During irradiation, the temperature rose significantly, eventually reaching
temperatures ranging from a few $10\text{\,}\mathrm{\SIUnitSymbolCelsius}$ to
$100\text{\,}\mathrm{\SIUnitSymbolCelsius}$. In fact, it was found that most
of the dry ice sublimated. Only after shutdown of the reactor, the temperature
decreased again. As a result, the annealing of the silicon sensors inside the
beam port was not negligible. The corresponding annealing time at
$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$, cf. Ref. [13], varied between a
few minutes to a few hundred minutes for all sensors irradiated at RINSC in
2020-21 up to $\sim 10^{16}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$. After
$24\text{\,}\mathrm{h}$ in the beam port after irradiation, the cylinder’s
activation levels had decayed sufficiently, it could be safely extracted, and
transferred into a storage freezer.

###  3.3 Fluence Assessment

In addition to the sensors, mechanical packing material, and temperature
sensors, each puck contained a number of reference samples for measuring the
fluence achieved during an irradiation round. Two different objects were found
appropriate for measuring the fluences during this campaign: silicon diodes,
which were studied for usage in the D0 experiment [15], and ultrapure iron
foils. The diodes were included inside the puck as close to the sensors as
possible by encasing them in small plastic bags and taping them to the inside
faces of the puck. By contrast, the iron foils were attached to the exterior
of the cylinder for ease of removal and gamma spectroscopy measurements. The
latter were performed at RINSC after irradiation for derivation of the
integrated fluence. In addition, CV and IV measurements of the irradiated
diodes were performed at Brown University to assess the depletion voltage, the
associated dark current and ultimately the fluence assuming the literature
value for the current-related leakage current rate of $\left(3.99\pm
0.03\right)\times 10^{-17}~{}$A/cm at
$20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ [13]. The reference silicon diodes
are most useful for the lower to medium range of the targeted fluences, where
their depletion voltage was well within the measurement range
($<$1000\text{\,}\mathrm{V}$$). For higher fluences, full depletion of the
silicon diodes could not be reached, and the gamma ray spectra derived from
the iron foils are considered more reliable. Table 1 in Appendix A shows the
estimated actual fluences from those reference samples. In order to improve
the accuracy of the fluence assessment, future irradiations will include iron
foils inside the puck as well as additional silicon test structures.

##  4 Electrical Characterisation of Neutron-Irradiated Silicon Pad Sensors

The experimental setup and the electrical characterisation procedure of
neutron-irradiated CE silicon pad sensors are presented in this section. The
following paragraphs describe two similar setups installed at CERN and Texas
Tech University, which were used to obtain the results reported in this paper.
Since the majority of the results are based on the CERN setup, its specifics
are elaborated in the following.

###  4.1 ARRAY- and Cold-Chuck Based Setup at CERN

At CERN, the S200FA probe station produced by Wentworth Laboratories Ltd. was
used for the electrical characterisation of neutron-irradiated silicon pad
sensors. Its chuck (Systems att, C200-40 model) is temperature-controlled down
to $-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

Figure 5:  A low-density CE silicon pad sensor right before connecting to the
switch- and probe-card ARRAY system at CERN. The probe station was closed and
continuously flushed with dry air during the testing to prevent the formation
of ice during low-temperature operation.

Apart from a Keithley 2410 power supply, a Keithley 6487 picoammeter, and a
Keysight E4980A LCR-meter, all relevant components were installed inside the
probe station, see Figure 5.
The silicon sensors were first placed on the chuck and then connected to the
probe- and switch-card based ARRAY system that is described in detail in Ref.
[11]. The contact between the probe card and the pads was realised with
spring-loaded pins. Through-holes in the cards and the probe station’s
microscope enable sufficient sensor-to-probe card alignment. Also, the
sensor’s grounded guard ring was accessible via a dedicated contact pad and
could be connected with dedicated pins on the probe card. The high voltage
from the power supply was provided to the chuck and with it to the sensor’s
backside. Two probe cards specific for the LD and HD sensor layouts have been
designed and manufactured. The switch card was operated with a bias resistance
(R${}_{\text{bias}}$) of $1\text{\,}\mathrm{M\SIUnitSymbolOhm}$ and a high
voltage resistance (R${}_{\text{HV}}$) of
$12\text{\,}\mathrm{k\SIUnitSymbolOhm}$, see [11] (Figure 9). In this
configuration, the ARRAY system is designed to safely withstand total leakage
currents up to $2\text{\,}\mathrm{mA}$ and per-pad currents up to
$10\text{\,}\mathrm{\SIUnitSymbolMicro A}$.
Since these limits would have been exceeded by a few orders of magnitude at
room temperature, cooling the neutron-irradiated sensors down to
$-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$ hereby reducing the leakage
current by almost three orders of magnitude with respect to room temperature
was imperative. The spatial variation of the C200-40 chuck temperature profile
at this temperature amounts to
$\pm$0.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$$, cf. Appendix B, whereas
fluctuations with time were found to be negligible. For the purpose of
preventing the formation of ice, the probe station was continuously flushed
with dry air.
With total currents at the order of $\mathcal{O}($1\text{\,}\mathrm{mA}$)$,
the voltage drop at R${}_{\text{HV}}$ for the testing of neutron-irradiated
sensors corresponded to a few volts and was corrected for. Per-pad leakage
currents were measured with the picoammeter, whereas total currents were
measured directly with the power supply. The LCR meter was operated at a
frequency (f${}_{\text{LCR}}$) of $2\text{\,}\mathrm{kHz}$ for the inference
of the per-pad impedance. This particular frequency was chosen to minimise the
error associated to the capacitance that is derived from it [11].

###  4.2 Characterisation Procedure

After connecting the sensor to the probecard, per-pad leakage currents as a
function of the bias voltage for all pads on a given sensor were measured
(IV). This was followed by a per-pad capacitance _vs._ bias voltage assessment
(CV). After each iteration over all pads at a fixed bias voltage, voltages
were incremented in varying steps between 50-$100\text{\,}\mathrm{V}$ up to
$850\text{\,}\mathrm{V}$, whereby the exact choice depended on the measurement
type (IV/CV) and on the thickness of the sensor. Although not applicable for
the results shown in this work, it should be noted that a given measurement
sequence was aborted if the total leakage current exceeded
$2\text{\,}\mathrm{mA}$. Similarly, individual pads whose leakage currents
exceeded $5\text{\,}\mathrm{\SIUnitSymbolMicro A}$ were not measured any
further and in particular were excluded from the subsequent CV. These
compliance limits prohibited large voltage drops inside the test circuitry,
minimising the risk of damage to the ARRAY system.
The entire characterisation sequence was fully automatised as a LabVIEW-based
program (HexDAQ version 1.5.1 [16]). Including voltage ramps and settling
times, the IV(CV) measurements of low-density sensors in this work took about
$1.5\text{\,}\mathrm{h}$($2.5\text{\,}\mathrm{h}$), whereby the duration is
proportional to the number of voltage steps (10-15 here). The duration was
about twice as long for high-density sensors due to the higher number of pads.
In order to quantify the potential performance benefit via annealing, silicon
sensors were warmed up to $60\text{\,}\mathrm{\SIUnitSymbolCelsius}$ inside
the probe station. After a total of $80\text{\,}\min$ at this temperature
111Corresponding to about three years at
$0\text{\,}\mathrm{\SIUnitSymbolCelsius}$., the sensor’s depletion voltage is
expected to be minimal [17] and the studied sensors were cooled again to
$-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$. IV and CV characterisations were
conducted before and after additional annealing.

##  5 Results

The results of the electrical characterisation of the neutron-irradiated CE
silicon pad sensor prototypes are presented in this section. Section 5.1
focuses on the discussion of leakage currents (_IV_) whereas Section 5.2
addresses the capacitance (_CV_) and depletion voltage assessments. Section
5.3 offers a discussion on the drawn conclusion.

###  5.1 Leakage Current

(a)

(b)

Figure 6:  (a) Total leakage currents after irradiation (without additional
thermal annealing) for two representative example sensors. Currents were
measured at $-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$ ($\text{I}_{\text{tot,
$-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$}}$) and at different effective
bias voltages ($\text{U}_{\text{bias}}$). (b) Per-pad leakage currents
normalised to the area of full hexagonal pads as a function of the bias
voltage for different pads with different geometries on one example sensor.

The total leakage current, interpreted as the dark current of a full silicon
sensor, is defined as the current flowing through the high-voltage resistor
R${}_{\text{HV}}$ (cf. Figure 2 in [11]). As it is shown for two prototype
sensors in Figure 6(a), the total leakage current did not break down and
stayed well below the ARRAY system’s compliance of $2\text{\,}\mathrm{mA}$ for
the irradiated sensors discussed in this paper. Irreversible discharges are
undesired but occurred for a handful of sensors where the total leakage
current suddenly increased and exceeded the $2\text{\,}\mathrm{mA}$
limitation. One half of those instances could be traced back to mechanical
damages, e.g. induced during the transport or sensor handling, and the other
half hinted at the presence of a minor flaw in the CE silicon sensor design.
The latter ultimately lead to a design modification with which the risk of
discharges in the future should be minimised222More than 50 prototype sensors
with the improved design have been characterized with voltages up to
$850\text{\,}\mathrm{V}$ in the meantime. None have shown discharges thus
far.. Results of the affected sensors are not discussed further in this paper.
Figure 6(b) shows the per-pad leakage current as a function of the effective
bias voltage for adjacent pads of various sizes on a low density sensor
irradiated up to $\sim 1.9\times 10^{15}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$.
The data demonstrate that, in good approximation, the leakage current of a pad
scales with its volume. The relative increase from $600\text{\,}\mathrm{V}$ to
$800\text{\,}\mathrm{V}$ remains well below $150\text{\,}\mathrm{\char
37\relax}$ meeting the vendor specifications.
The IV curves after different annealing times are shown for a representative
pad in Figure 7(a).

(a)

(b)

Figure 7:  (a) IV-curves of a representative full hexagonal pad for different
annealing durations for a $200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ low-
density prototype sensor irradiated to approximately 2.4$\times
10^{15}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$. (b) Decrease of the per-pad
leakage current ($U_{\text{bias}}=$600\text{\,}\mathrm{V}$$) as a function of
the annealing time ($\text{t}_{\text{annealing}}$) at
$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

For bias voltages beyond full depletion, per-pad leakage currents at
$600\text{\,}\mathrm{V}$ are reduced systematically by
$25\text{\,}\mathrm{\char 37\relax}$ after $80\text{\,}\mathrm{min}$ at
$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$, cf. Figure 7(b). Given the
simultaneous reduction in the depletion voltage, cf. Figure 10(b), leakage
currents around full depletion are even further reduced.
The expected relationship between the per-pad leakage current density and the
fluence was observed. The proportionality for current densities at a bias
voltage of $600\text{\,}\mathrm{V}$, which is well above full depletion for
all investigated sensors (except for the
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sensors irradiated to $13.5\times
10^{14}\mathrm{n_{eq}}/\mathrm{cm}^{2}$), and extrapolated to
$-30\text{\,}\mathrm{\SIUnitSymbolCelsius}$ is displayed in Figure 8.

Figure 8:  Volume-normalised per-pad leakage currents interpolated to an
effective bias voltage of $600\text{\,}\mathrm{V}$ as a function of the
fluence that they were exposed to. The quoted currents were measured after
additional annealing at $60\text{\,}\mathrm{\SIUnitSymbolCelsius}$, and are
scaled to the CE’s planned operation temperature of
$-30\text{\,}\mathrm{\SIUnitSymbolCelsius}$. "0.5x p-stop" denotes HD sensors
with half the p-stop concentration. "TTU" denotes the measurements of
$120\text{\,}\mathrm{\SIUnitSymbolMicro m}$ HD sensors conducted with a
analogous setup to the one described in Section 4.1, at Texas Tech University.
Those exhibit overall consistency with the measurements conducted at CERN.

As expected [18], the current-related damage rate ($\alpha$) is found to be
independent on the tested material properties investigated in this work. The
numerical result for $\alpha$ scaled to room temperature is
$\alpha_{\text{600V}}($20\text{\,}\mathrm{\SIUnitSymbolCelsius}$)=\left(3.2\pm
0.2\pm 0.6\right)\times 10^{-17}~{}$A/cm. The central value is about
$20\text{\,}\mathrm{\char 37\relax}$ less than what is reported in Ref. [13].
A possible explanation could be a systematic overestimation of the fluence at
the RINSC irradiation facility. Follow-up studies in this regard are
anticipated in the mid-term future.
After correction for the chuck temperature non-uniformity, per-pad leakage
current densities across a sensor at a fixed voltage still vary by $\sim
10~{}\%)$. The associated current profiles are present both before (cf.
Figures 9(a), 9(b) and 9(c)) and after additional annealing (cf. Figures 9(d),
9(e) and 9(f)). Furthermore, they are consistent between sensors that had been
irradiated simultaneously in the same puck. Among others, a plausible
explanation for this observation could be the presence of a fluence profile
within the beam port at RINSC that can be approximated as a Gaussian with a
width of $\sigma\sim$10\text{\,}\mathrm{cm}$$.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 9:  Per-pad leakage currents interpolated to an effective bias voltage
of $600\text{\,}\mathrm{V}$ for three representative sensors from different
irradiation rounds before (a-c) and after additional annealing (d-f). Red- or
white-colored edge pads correspond to well-understood measurement effects,
e.g. insufficient contact between the pogo pins and the pads.

###  5.2 Capacitance and Depletion Voltage

The measured per-channel impedance is open-corrected by subtracting the
impedance of the ARRAY system. Subsequently, the sensor pad capacitance is
computed assuming an underlying serial connection to the measurement
circuitry. Due to the finite mobility of the sensor defects, the frequency at
which the impedance is measured may, in principle, have sizeable impact on the
derived capacitance and on the depletion voltages, cf. Ref. [19]. The
impedance measurement was conducted at
$f_{\text{LCR}}=$2\text{\,}\mathrm{kHz}$$. Experimental follow-up indicated an
impact of $2\text{\,}\mathrm{\char 37\relax}$ on the asymptotic capacitance
and a $10\text{\,}\mathrm{\char 37\relax}$ reduction of the depletion voltage
when decreasing $f_{\text{LCR}}$ to $500\text{\,}\mathrm{Hz}$, which have no
implication on the following discussion.
The depletion voltage for each pad is assessed from the saturation of its
squared reciprocal capacitance ($C^{-2}$) of a pad with respect to the bias
voltage ($V$). It is defined as the intersection of a straight-line fitted to
the rising part of the $C^{-2}$ _vs._ $V$ curve with a line fitted to its
plateau. Prior to additional annealing, such a plateau could not always be
reached within the tested bias voltage range, see for example the black line
in Figure 10(a). After additional annealing to $80\text{\,}\min$ at
$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$, the estimated depletion voltage
has been reduced by about a third with respect to the case without annealing,
cf. Figure 10(b).
The per-pad capacitance after irradiation is found to scale well with the area
of the pad, cf. Figure 11(a). Deviations from this scaling amount to less than
$5\text{\,}\mathrm{\char 37\relax}$, suggesting a slight dependence of the
inter-pad capacitances on the pad geometries.
Figure 11(b) illustrates that the estimated depletion voltages depend
primarily on the associated thickness of the depleted zone.

(a)

(b)

Figure 10:  (a) Reciprocal-squared capacitance ($C^{-2}_{\text{pad}}$) as a
function the bias voltage of a representative full hexagonal pad for different
annealing durations for a $200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ low-
density prototype sensor irradiated to approximately 2.4$\times
10^{15}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$. (b) Relative decrease of the
depletion voltage estimate ($U_{\text{dep}}$) as a function of the additional
annealing time ($\text{t}_{\text{annealing}}$) at
$60\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for a subset of full pads.

(a)

(b)

Figure 11:  (a) Area-normalised capacitances as a function of the bias voltage
for different pads with different geometries on a example LD sensor. (b)
Normalised squared-inverse capacitances as a function of the bias voltage to
estimate the sensor depletion voltage of a central pad from different
irradiation rounds. Full depletion was achieved at bias voltages around
$40\text{\,}\mathrm{V}$ for $120\text{\,}\mathrm{\SIUnitSymbolMicro m}$
sensors, $120\text{\,}\mathrm{V}$ for $200\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ sensors, and $280\text{\,}\mathrm{V}$ for the
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sensors before irradiation.

(a)

(b)

Figure 12:  (a) Per-pad depletion voltage estimates for a LD example sensor
irradiated to 1.9$\times 10^{15}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$, and (b)
their correlation to the per-pad leakage current, used as proxy for the
delivered fluence.

The estimated per-pad depletion voltage across the sensor is shown in Figure
12(a). Those estimates exhibit positive correlation with the leakage currents,
taken as proxy for the fluence, cf. Figure 12(b). In fact, the obtained
correlation coefficient from this analysis is positive for all tested sensors
where full depletion could be reached. This can be interpreted as further
evidence for the presence of a fluence profile inside the beam port during
irradiation.

###  5.3 Discussion

The neutron irradiation induced leakage currents are consistent both
qualitatively and quantitatively with previous R$\&$D on irradiated silicon
sensors. They are also found to be independent of the silicon fabrication
process (flatband voltage, p-stop layout). Furthermore, unchanged end-
capacitances and reduced depletion voltages after beneficial annealing are
qualitatively consistent with previous findings.
The findings presented in this paper with the first prototypes of CE silicon
sensors, i.e. hexagonal sensors and fabricated with a new 8” process,
irradiated to fluences corresponding to the end of lifetime of HL-LHC are in
full support of the radiation-hardness of their general design. By
implication, RINSC could be qualified as a valid facility for neutron
irradiation of 8” silicon sensors for the first time. However, more accurate
studies on the electrical sensor properties after neutron-irradiation would
need to incorporate the systematic uncertainty on the effective annealing
during irradiation, that is due to the temperature evolution and its potential
lateral profile inside the reactor’s beam port. Similarly, an accurate
assessment of the actual fluence at each pad would have to address the neutron
flux profile, for whose existence this work provides first evidence.

##  6 Conclusion

An essential component of the silicon sensors’ prototyping for the CMS highly
granular endcap calorimeter upgrade (CE) is the experimental verification of
the radiation hardness in terms of their electrical properties, i.e. leakage
currents, capacitances and depletion voltages. RINSC is one of the few
locations world-wide that offers the infrastructure for the irradiation of
large structures compatible with CE’s 8”-wide silicon pad sensors. Given that
parts of the necessary infrastructure have not been used in this experimental
capacity, the irradiation was non-trivial and specific preparations had to be
made. After irradiation, the probe- and switch card-based ARRAY system [11]
was used for the first time for the electrical characterisation of neutron-
irradiated silicon sensors at CERN and at Texas Tech University. In order to
protect the test system from currents that would exceed its specifications,
the neutron-irradiated sensors were cooled down to
$-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during the tests.
The preparation and execution of the neutron-irradiation at RINSC and the
electrical characterisation of the irradiated sensors at cold temperatures
using the ARRAY system was explained in this paper. Evidence for specific
properties of the RINSC irradiation facility such as a non-uniform flux
profile across the 8” wafer and for non-negligible sensor annealing due to
insufficient cooling during irradiation was reported.
For the planned CMS CE upgrade, the findings in this work are encouraging as
they confirm the overall expected radiation hardness of the prototype silicon
sensors. In particular, their leakage current densities are found to scale
proportionally with the fluence, independent of the properties of the tested
production process variations. It is reconfirmed that annealing the sensors up
to $80\text{\,}\mathrm{min}$ at $60\text{\,}\mathrm{\SIUnitSymbolCelsius}$ has
beneficial impact on the electrical properties by lowering the dark current
and the depletion voltages by $\mathcal{O}\left(10~{}\%\right)$. Despite the
tested sensors being prototypes, the insights from their characterisation can
be considered representative for the final version. Therefore, the results
reported in this work may serve as reference for the expected electrical
performance and degradation of CE’s silicon sensors towards the end of their
lifetime at HL-LHC.

## Acknowledgments

We thank the staff at the Rhode Island Nuclear Science Center for their
support during the preparation and execution of the neutron irradiation of the
CE silicon pad sensor prototypes. The EP-DT and the former EP-LCD group at
CERN have developed essential infrastructure, such as the ARRAY system
including the associated data acquisition software, and have co-financed the
acquisition of the utilised cold-chuck probe station at CERN. Without their
input, this R$\&$D milestone towards the realisation of this novel calorimeter
would not have been possible. We are thankful for the technical and
administrative support at CERN and at other CMS institutes and thank the
staffs for their contributions to the success of the CMS effort. We
acknowledge the enduring support provided by the following funding agencies
and laboratories: BMBWF and FWF (Austria); CERN; CAS, MoST, and NSFC (China);
MSES and CSF (Croatia); CEA, CNRS/IN2P3 and P2IO LabEx (ANR- 10-LABX-0038)
(France); SRNSF (Georgia); BMBF, DFG, and HGF (Germany); GSRT (Greece); DAE
and DST (India); MES (Latvia); MOE and UM (Malaysia); MOS (Montenegro); PAEC
(Pakistan); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS, RFBR, and NRC KI
(Russia); MoST (Taipei); ThEP Center, IPST, STAR, and NSTDA (Thailand);
TUBITAK and TENMAK (Turkey); STFC (United Kingdom); and DOE (USA).

##  Appendix A Irradiation Rounds and Fluences

See Table 1.

Table 1: Irradiation duration and estimated integrated fluences for the neutron-irradiation at RINSC of CE prototype silicon sensors discussed in this work. A comparison to leakage currents of silicon test structures irradiated at the JSI TRIGA reactor [20] indicate an uncertainty on the fluence estimates of about 20$~{}\%$.  Date | No. sensors | Thickness | Duration | Fluence ($10^{14}~{}\mathrm{n_{eq}}/\mathrm{cm}^{2}$) | Reference
---|---|---|---|---|---
26 Aug 20 | 4 | 300$~{}\mu$m | $13\text{\,}\mathrm{min}$ | 7.1 | Si diodes
20 Oct 20 | 4 | 120$~{}\mu$m | $180\text{\,}\mathrm{min}$ | 110.0 | Fe foils
28 Jan 21 | 4 | 200$~{}\mu$m | $38\text{\,}\mathrm{min}$ | 23.5 | Si diodes
11 Feb 21 | 4 | 120$~{}\mu$m | $38\text{\,}\mathrm{min}$ | 16.5 | Si diodes
01 March 21 | 4 | 300$~{}\mu$m | $23\text{\,}\mathrm{min}$ | 13.5 | Si diodes
11 March 21 | 4 | 120$~{}\mu$m | $76\text{\,}\mathrm{min}$ | 50.0 | Fe foils
15 April 21 | 4 | 300$~{}\mu$m | $15\text{\,}\mathrm{min}$ | 8.2 | Si diodes
06 May 21 | 2 | 200$~{}\mu$m | $38\text{\,}\mathrm{min}$ | 19.0 | Si diodes

##  Appendix B Temperature Uniformity of the Systems att C200-40 Cold Chuck

The leakage current in silicon devices dependends on the temperature. For the
investigated sensors in this work, the current is mainly generated in the bulk
for which the temperature ($T$) and current ($I$) are related by Equation B.1
[21], where $E_{\text{eff}}=$1.21\text{\,}\mathrm{eV}$$ is the effective gap
energy and $k_{b}$ denotes the Boltzmann constant.

$\frac{I}{T^{2}}\cdot\exp{\frac{E_{\text{eff}}}{2\cdot k_{b}\cdot
T}}~{}\equiv~{}\text{const.}$ (B.1)

The validity of this temperature scaling law applied for the CE silicon pad
sensors in the relevant temperature range has been verified and is illustrated
in Figure 13.

Figure 13:  Leakage currents as a function of the bias voltage for an example
sensor measured at $-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$,
$-35\text{\,}\mathrm{\SIUnitSymbolCelsius}$,
$-30\text{\,}\mathrm{\SIUnitSymbolCelsius}$, and scaled to
$-35\text{\,}\mathrm{\SIUnitSymbolCelsius}$ using Equation B.1.

Notably, a change by $1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ impacts the
current by more than 10$~{}\%$. Variations of the temperature across the
actively cooled-down chuck, and with it across the sensor, may mimic neutron
fluence profiles as in Figure 9. Thus, they should be identified and corrected
for. In this work, the temperature non-uniformity of the cold chuck at CERN
(C200-40 model produced by Systems att) could be estimated from leakage
current data of neutron-irradiated sensors. By comparing per-pad currents
($I_{i(j,k)}$) at a fixed bias voltage between the symmetry locations $i$,
$j$, $k$, described below, temperature differences $\delta I_{i(j),k}$ can be
calculated according to Equation B.2. For this purpose, one of the neutron-
irradiated low-density sensors was characterised three times at
$0\text{\,}\mathrm{\SIUnitSymbolDegree}$,
$120\text{\,}\mathrm{\SIUnitSymbolDegree}$, and
$240\text{\,}\mathrm{\SIUnitSymbolDegree}$ rotation. The precision in
repeating the sensor placement on the chuck can be neglected with respect to
the size of the pads.

$\frac{\delta I_{i(j),k}}{I_{k}}=\frac{\delta
T_{i(j),k}}{T_{k}}\cdot\left(2+\frac{E_{\text{eff}}}{2\cdot k_{b}\cdot
T_{k}}\right)~{},~{}~{}T_{k}\coloneqq T_{\text{ref}}$ (B.2)

Figure 14(a) shows the hereby computed chuck temperature differences. The
determined variation is consistent with the
$\pm$0.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$$ non-uniformity as specified
by the chuck producer. Assuming a reference temperature of
$T_{\text{ref}}\equiv$-40\text{\,}\mathrm{\SIUnitSymbolCelsius}$$, a two-
dimensional gaussian parameterisation bound to
$[$-0.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$,$0.5\text{\,}\mathrm{\SIUnitSymbolCelsius}$]$
is fitted to reproduce the temperature differences $\delta I_{i(j),k}$. The
result of the fit is shown in Figure 14(b).

(a)

(b)

(c)

Figure 14:  (a) Temperature differences derived from per-pad leakage currents
between symmetric locations of a representative neutron-irradiated CE silicon
sensors on the cold chuck at CERN. (b) Determined profile of temperature
differences, modelled as a two-dimensional gaussian, across the sensor
surface. (c) Closure check: derived temperature differences after accordingly
correcting the measured per-pad leakage currents.

The hereby constructed map of chuck temperature differences is input to
correct the measured per-pad leakage currents using Equation B.1. As a closure
check, the re-application of Equation B.2 on the temperature-corrected dataset
demonstrates the applicability of this particular chuck temperature model as
shown in Figure 14(c).

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