# CommunityFish:
A Poisson-based Document Scaling With Hierarchical Clustering

Sami Diaf
Faculty of Business, Economics and Social Sciences, Department of
Socioeconomics
Universität Hamburg
<EMAIL_ADDRESS>

###### Abstract

Document scaling has been a key component in text-as-data applications for
social scientists and a major field of interest for political researchers, who
aim at uncovering differences between speakers or parties with the help of
different probabilistic and non-probabilistic approaches. Yet, most of these
techniques are either built upon the agnostically bag-of-word hypothesis or
use prior information borrowed from external sources that might embed the
results with a significant bias. If the corpus has long been considered as a
collection of documents, it can also be seen as a dense network of connected
words whose structure could be clustered to differentiate independent groups
of words, based on their co-occurrences in documents, known as communities.
This paper introduces CommunityFish as an augmented version of Wordfish based
on a hierarchical clustering, namely the Louvain algorithm, on the word space
to yield communities as semantic and independent n-grams emerging from the
corpus and use them as an input to Wordfish method, instead of considering the
word space. This strategy emphasizes the interpretability of the results,
since communities have a non-overlapping structure, hence a crucial
informative power in discriminating parties or speakers, in addition to
allowing a faster execution of the Poisson scaling model. Aside from yielding
communities, assumed to be subtopic proxies, the application of this technique
outperforms the classic Wordfish model by highlighting historical developments
in the U.S. State of the Union addresses and was found to replicate the
prevailing political stance in Germany when using the corpus of parties’
legislative manifestos.

_K_ eywords document scaling, hierarchical clustering, Poisson model

##  1 Introduction

Comparative politics has been a privileged domain of application of what is
currently known as text-as-data field, featuring the use of text mining
techniques and machine learning algorithms to identify patterns that
differentiate document contents or track differences at the meta-data level.
Scaling techniques consist mostly of unsupervised methods, whether
probabilistic or non-probabilistic, aiming at extracting one or multiple
dimensions to perform metadata comparisons (Goet, 2019), based on a set of
assumptions concerning the word-level. In other terms, scaling techniques aim
to uncover one or many hidden variables that artificially measure differences
between speakers or parties, mostly based on word counts.

Earlier scaling techniques used statistical learning approaches as for matrix
factorization schemes (Deerwester et al., 1990) or probabilistic model based
on the Poisson distribution as for Wordfish (Slapin and Proksch, 2008), which
ranks documents on a unidimensional scale using word occurrences in each
document of the corpus. Further extensions of Poisson-based inferences
considered a debate structure (Lauderdale and Herzog, 2016), pre-trained
embedding models (Nanni et al., 2019), word variations (Vafa et al., 2020) or
topic variability (Diaf et al., 2022) that provided a sound ranking of
documents depending on assumptions and use cases at the word or document
levels.

As for Wordfish, the inference uses word counts to learn a normally-
distributed hidden dimension, assumed to be a proxy of partisanship among
political parties when scaling manifestos (Slapin and Proksch, 2008). Yet, the
Poisson distribution does not always pertain, as frequent words are likely to
have a normal distribution, while very rare words tend to follow a negative
binomial distribution (Lo et al., 2016). Another noticeable drawback is the
dynamic word usage which needs time-varying parameters for the Poisson ranking
model and further techniques to ensure its stability (Jentsch et al., 2020),
or to consider the structure document-topic-word to get polarization at the
topic level (Diaf and Fritsche, 2022).

Although the choice of scaling techniques is abundant, it does not necessarily
meets the expectation of practitioners because the inference is done at the
word-level, while the analysis often target documents’ content in terms of
groups of words that translate the interest of researchers, either as specific
keywords or as topics. The word contributions to the built scale in Wordfish
is static and cannot be fully interpretable if the corpus’ word usage
underwent several changes between parties/speakers over time (Jentsch et al.,
2020) and the sign of specific words could be different from the position of
documents they mostly represent, thus not in-line with experts’ assessments
(Hjorth et al., 2015). These shortcomings are imputable to the bag-of-word
assumption and the underlying agnostic hypothesis of word independence that
prevents a sound scaling of documents (Nanni et al., 2019).

Advances in social network analysis demonstrated the efficiency of
hierarchical clustering to uncover latent groups of users, or communities,
that are homogeneous and distinguishable from other neighbors, based on their
interactions. This concept could be easily extended to a corpus of documents
to identify independent, semantic groups of words, in form of n-grams, that
differentiate documents based on their occurrence while delivering informative
signals that outperform analyses based on single-word usage. Louvain algorithm
(Blondel et al., 2008) remains a popular clustering approach and was applied
to the study social networks but also to get word groups that better represent
the rhetoric used in the corpus (Bail, 2016) or to study the lexical shift in
the State Of The Union addresses (Rule et al., 2015). Similar clustering
schemes were proposed as for Infomap (Rosvall and Bergstrom, 2008) which uses
random walk map-equation instead of optimizing the modularity as for Louvain,
although the functioning of both methods was found to be similar
(Lancichinetti and Fortunato, 2009). Traag et al. (2019) proposed a faster and
enhanced clustering algorithm known as Leiden that was found to outperform
Louvain when applied to big networks.

This paper prolongs the idea of lexical shift (Rule et al., 2015) by
identifying communities as representative groups of words with a high density,
able to achieve a fast and interpretable scaling of documents upon which a
Poisson ranking model could be easily built, instead of considering a plain
word-count model relying on the bag-of-word hypothesis. I argue that
communities offer a better polarization level when differentiating documents
and metadata than a standard word-level model, in addition of efficiently
speeding up the learning process by reducing the size of the document-term-
matrix, whose sparsity may hinder the convergence of Poisson models. Regular
words used by all parties/speakers are likely to form communities featuring a
high number of words but less likely polarized compared to communities whose
usage is exclusive, denoting the focus of a given party/author to a specific
subject of item that could be uncovered without the need to run topic models.

Hence, the proposed two-step scaling technique, CommunityFish, brings two
major novelties in the document scaling field. First, it successfully
identifies communities as powerful word representations without the need to
use agnostic topic models, neither running transfer learning, in terms of word
embedding (Mikolov et al., 2013) nor adopting priors as for keywords
identification (Eshima et al., 2020), but by simply running a hierarchical
clustering, whether with Louvain or Leiden algorithms. Second, it yields a
fast and interpretable scaling where communities could be easily associated
with metadata without requiring much efforts as for classic word-based
techniques.

Two historical corpora, in English and German, were chosen to test this novel
approach. Application on the U.S. State Of The Union (SOTU) addresses
(1854-2019) shows a clear dominance of historical developments as for economic
issues, local affairs and foreign policy that ranked addresses on a two-regime
scale whose transition could be identified during the great depression. On the
manifestos of German political parties (2013-2022), CommunityFish uncovered
granular themes at the center of election debates that were found to replicate
the ideological spectrum of political parties with AFD and Linke parties being
the ideological bounds of the learned scale, while other parties seem to share
many featured themes, hence reinforcing their centric positions.

The paper expands the concepts used by CommunityFish from a network analysis
perspective (Section 2) and from statistical learning (Section 3), then
applies the proposed algorithm to two corpora (Section 4) and compares to the
standard Wordfish used by practitioners.

##  2 Network Analysis

Analysis of social media, especially the interactions between users, drove the
attention of scientists on the necessity to adopt advanced clustering methods
able to extract information that describe hidden relationships between
speakers via the types of messages or ideas they produce (White, 2008),
instead of simple link structures between individuals (Bail, 2016).

Network analysis witnessed important contributions on identifying distinct
subgroups in social networks and several optimization schemes were developed
to offer intuitive clustering (Lancichinetti and Fortunato, 2009) and
meaningful ranking of users.

For such tasks, researchers need to pay attention to the selected clustering
methods for community detection as well as considering centrality scores
(Mester et al., 2021). For large networks, Louvain algorithm (Blondel et al.,
2008) is usually preferred to FastGreedy algorithm (Clauset et al., 2004) due
to its relative low complexity, as it achieves a local optimization of the
modularity $Q$ at the node-level, defined as :

$Q={\frac{1}{2m}}\sum\limits_{ij}{\bigg{[}}A_{ij}-{\frac{k_{i}k_{j}}{2m}}{\bigg{]}}\delta(c_{i},c_{j})$

with $A_{ij}$ representing the edge weight between nodes $i$ and $j$, $k_{i}$
and $k_{j}$ are the sum of the weights of the edges attached to nodes $i$ and
$j$, respectively; $m$ is the sum of all of the edge weights in the graph;
$c_{i}$ and $c_{j}$ are the communities of the nodes; and $\delta$ is
Kronecker delta function $\delta(x,y)=1$ if x=y, 0 otherwise.

Louvain algorithm iteratively optimizes the modularity $Q$ by starting with
different node being its own community, and the concept is to place a node
$n_{i}$ to one of its neighboring nodes community, in a way to maximize the
modularity change (Mester et al., 2021). Similar to users in social networks,
Louvain algorithm could be applied to cluster words in a given corpus, so to
extract groups of words, in a form of n-grams of different lengths, having an
independent, non-overlapping structure stemming from the specific word usage
found in documents.

Traag et al. (2019) proposed Leiden clustering as a reliable alternative,
outperforming Louvain when it comes to discern small connected communities in
large network structures. Altough Leiden was found to be faster, in terms of
execution, then Louvain, both do not differ when the network structure is
relatively small, as for collection of documents with limited vocabulary,
meaning the community structures of both algorithms share many similarities.

##  3 Poisson ranking model

To apply CommunityFish, the corpus is decomposed into bigrams and a minimum
threshold $\pi$ is set before running Louvain algorithm that yields $K$
communities used as features of the Document-Term-Matrix (DTM), instead of
considering all words in the corpus, hence communities serve as features to
the Wordfish scaling algorithm. This scheme could be seen as a semantic
clustering of the DTM that identifies correlated pairs of words in local
contexts thanks to hierarchical clustering on bigrams, which differs from a
simple bigram grouping of the initial DTM features.

The resulting DTM is given as an input to Wordfish (Slapin and Proksch, 2008)
to learn document positions, or ideal points, that scale documents based on
the occurrence of communities. As a scaling technique, Wordfish uncovers a
latent scale $\theta$, assumed to be a proxy of partisanship or ideological
differences between parties or speakers, depending on the used context.

While the use of the Poisson distribution is justified by the occurrence of
words in the corpus, assumed to be rare events, it does not always pertain to
cases where the word usage concerns few documents, meaning the Poisson’s
expectation departs significantly from the variance, as demonstrated by Lo et
al. (2016) who suggested the use of the Negative Binomial distribution with
resampling inference.

I argue that the use of communities frees the DTM from potential biases raised
by rare words and allows a fast convergence of Wordfish algorithm when applied
to big corpora. CommunityFish could be seen as a double dimensionality
reduction technique: first to uncover communities, as the primary unit of
analysis, and second to learn a scale of ideal points using Wordfish.

Algorithm : CommunityFish

1\. Community detection Run the Louvain algorithm over the bigram features of
the corpus and extract $K$ groups of words or communities.

2\. Wordfish The $K$ communities are used as features for the Document-Term-
Matrix, to be given as input to a Poisson Scaling Model (Slapin and Proksch,
2008) to uncover the scale $\theta_{i}$ from the specification:

$log(\lambda_{ij})=\alpha_{i}+\psi_{j}+\theta_{i}\beta_{j}$, where:

$\lambda_{ij}$: frequency of the community j in document i

$\alpha_{i}$: document fixed effect

$\psi_{j}$: community fixed effect

$\theta_{i}$: the position of document i

$\beta_{j}$: the effect of community j to the document position

The hierarchical clustering applied to the corpus (Louvain algorithm) could be
interpreted as an implicit factorization of the traditional unigram Document-
Term-Matrix (DTM) to a more interpretable feature matrix stemming from the
learned communities. Aside from lowering the DTM dimension, it permits to
intuitively concentrate the scaling on meaningful groups of words
(communities) that discriminate the ideal points based on their occurrences in
the documents, offering a more balanced basis to discern documents of the
corpus based on similarities in the communities’ probabilistic distributions.

##  4 Application

Two popular datasets, with different specifications, are chosen to perform
CommunityFish, one featuring dynamic word usage as documents span over 163
years (State Of The Union) targeting several aspects of American politics, and
another gathering political manifestos of main German political parties during
the last three legislative elections that help identify similarities and
differences in the used rhetoric in the pre-election political debates. For
both corpora, the hierarchical clustering was applied on lemmatized bigrams
who occur more than 30 times in the corpus, to concentrate the information on
a reasonable number of communities.

###  4.1 State Of The Union

State Of The Union (SOTU) addresses consist of speeches given during the
period (1854-2019), so to highlight the duality democratic-republican in the
scaling (Diaf et al., 2022). The corpus was lemmatized using udpipe model
(Straka et al., 2016) to reduce the size of the Document-Term-Matrix and learn
robust communities, in comparison with the raw corpus. The application of the
Louvain algorithm yielded 52 different communities111Leiden clustering yielded
a similar community structure to Louvain, with minor differences concerning
two communities, out of 52. The same results was found using the German
political manifesto corpus. (Table 1) with a historical context that spans
over one and half century, with different episodes of modern American history.
Noticeable is that 22, out of 52, communities are constituted of bigrams and
the remaining are n-grams of different lengths.

Communities, whose contributions to the scale $\beta_{j}$ are different from
zero, polarize the overall scale $\theta$ via their respective signs. From
Figure 1, communities 45, 40, 11 and 8 contribute to documents whose positions
in the overall scale (Figure 2) are positive, consisting of earlier addresses
from the second half of the Ninetieth century targeting neighboring countries
and local administration, while modern addresses have negative positions
(Figure 2) and demonstrate a strong influence of foreign policy and defense
interests (communities 38 and 49) as well as business/economic environment
(communities 43 and 2). Figure 2 shows a two-regime scale, whose transition
could be identified during the great depression (Hoover addresses during the
period 1929-1933, coinciding with the position $\hat{\theta}=0$), indicating a
potential shift in the rhetoric, or transition into modern addresses, used by
US presidents and captured via communities that represent proxies of most
tackled interests during the addresses. The classic Wordfish (Figure 5) yields
more clustered document positions that cannot not be differentiated in small
periods, even if given by different speakers.

Table1: Communities in SOTU corpus | Table 2: Communities in German Manifesto corpus
---|---
| Community | Words
---|---
com_1 | agricultural, product
com_2 | american , billion , business , enlist , every , fellow , million , silver , small
young , citizen , family , people , republics, dollar , man , day , americans
com_3 | annual , special, message
com_4 | armed , military, naval , force
com_5 | ask , come , current , end , fiscal , five , four , last , many , next , past precede ,
previous, recent , ten , three , two , year , congress, june , session , ago ,
ahead
com_6 | attorney , british , can , federal , general , government, local , make , must
national , postmaster, self , social , spanish , supreme , help , court , sure
also , continue , bank , defense , security
com_7 | balanced, budget
com_8 | base , call , confer , depend , enter , impose , urge , upon , attention
com_9 | careful , favorable , consideration
com_10 | central, latin , south , america
com_11 | civil , hard , human , interest , postal , public , right , tax , work , service , rate
debt , building , land , opinion , now , credit , cut , reduction, together
com_12 | commerce , interstate, commission
com_13 | earnestly, recommend
com_14 | economic , development, growth
com_15 | executive, branch , order
com_16 | exist , international, law , present , tariff , enforcement , condition , system
com_17 | far , thus , reach
com_18 | first, time
com_19 | foreign , free , great , nation , office , post , take , treasury , war , world
country com_ , power , trade , britain , department, place , ii
com_20 | full , employment
com_21 | go , look , move , forward
com_22 | god , bless
com_23 | good , faith
com_24 | health , medical , care , insurance
com_25 | high , level , priority, school
com_26 | internal, revenue
com_27 | large , number, part
com_28 | let, us
com_29 | long, run , term
com_30 | low , income
com_31 | may , well
com_32 | merchant, marine
com_33 | middle, class , east
com_34 | minimum, wage , worker
com_35 | mr , speaker
com_36 | natural , resource
com_37 | new , job , program, york
com_38 | nuclear, weapon
com_39 | one , half , hundred, third
com_40 | panama, canal
com_41 | per , annum, cent
com_42 | philippine, islands
com_43 | private , enterprise, sector
com_44 | progress, step , toward
com_45 | puerto, rico
com_46 | set , forth
com_47 | several, united , states , nations
com_48 | sink, fund
com_49 | soviet, union
com_50 | vice , president
com_51 | welfare, reform
com_52 | white, house

| Community | Words
---|---
com_1 | abkomme , abkommen
com_2 | afd , demokrat, deshalb , fordern , frei , linke , stehen , setzen
com_3 | alt , brauchen , immer , jung , mehr , mensch
, million , gerechen , stark , geld , personal , transparenz, zeit
com_4 | arbeit , beruflich , gut , kulturell , selbstbestimmt , arbeiten
, bildung , arbeitsbedingung, leben , zukunft
com_5 | arbeitgeber , arbeitnehmer, patient , verbraucher , innen
com_6 | arbeitsplatz , dass , deutschland , einsetzen , ganz , gestalten
, jed , neu , schaffen , sicherstellen, sorgen verhindern
| , zeigen , einzeln , form , kind , technologie
com_7 | beitrag , bund , dabei , etwa , gelten , gerade , gesellschaftlich,
insbesondere , land , mittel , projekt , regelung
| , sollen , sowie , teilhabe , wichtig , zugang , leisten , na , mitteln ,
rolle
com_8 | bezahlbar, wohnraum
com_9 | biologisch, vielfalt
com_10 | cdu, csu
com_11 | corona, krise
com_12 | demokratisch, kontrolle
com_13 | deutsch , bundestag, sprache
com_14 | digital , it , sozial , infrastruktur , welt , sicherheit , absicherung
, gerechtigkeit , marktwirtschaft , netzwerk , sicherungssystem
| , wohnungsbau , zusammenhalt
com_15 | drei , euro , letzt , milliarde, mrd , pro , seit , vergangen, vier , zehn , jahr
com_16 | erhalten, bleiben
com_17 | erneuerbare , erneuerbaren, energie , energien
com_18 | erst , schritt
com_19 | eu , ebene , kommission , mitgliedstaat, staat
com_20 | fair , wettbewerb
com_21 | gering , hoch , mittler , einkommen , unternehmen
com_22 | gesetzlich , mindestlohn , rent , rentenversicherung
com_23 | gleich, recht , chance, lohn , rechte
com_24 | hartz, iv
com_25 | lage , versetzen
com_26 | medizinisch, versorgung
com_27 | nachhaltig , wirtschaftlich, entwicklung
com_28 | offen , gesellschaft
com_29 | qualitativ, hochwertig
com_30 | rechnung, tragen
com_31 | rechtlich, rundfunk
com_32 | regel , regeln
com_33 | schnell , internet
com_34 | schon, heute
com_35 | schwarz, gelb
com_36 | sexuell , orientierung
com_37 | start, ups
com_38 | stelle , stellen
com_39 | strukturschwach, region
com_40 | stunde , stunden
com_41 | teil , teilen
com_42 | treffen, triefen
com_43 | verein , vereinen
com_44 | vereint, nation
com_45 | vgl , kapitel

Figure 1: Communities’ contributions to the scale ($\beta$) vs communities’
positions $\psi$ (SOTU corpus) Figure 2: Learned CommunityFish ideal points
with 95% confidence intervals (SOTU Corpus).

###  4.2 German Manifesto

The corpus of Manifesto Project (Volkens et al., 2021) was used to get the
manifestos of the six main German political parties, during the period
2013-2021 (Diaf and Fritsche, 2022), then lemmatized using a German language
model (Straka et al., 2016) to reduce the vocabulary length of the corpus. It
resulted 45 communities (Table 2) reproducing most of the debated themes in
social life, politics and economic development which constitute the basis of
the learned scale (Figure 4), found to replicate the prevailing political
partisanship in Germany. AFD and Linke parties are the two bounds of the
learned scale, while other parties have central positions, with noticeable
firm positions (small standard deviations of their ideal points) of the Linke
and Gruene parties throughout the studies period, while AFD and CDU positions
seem to have the highest variability (wide standard errors). The blue line in
Figure 4 is the Loess curve used to separate parties into two distinct classes
(left-right) based on learned scale from the established communities (Table
2), resulting into a bi-partisanship AFD-CDU-FDP and SPD-Gruene-Linke. As a
comparison to Wordfish (Figure 6), CommunityFish highlights the polarization
AFD-Linke better than Wordfish, whose scale does not demonstrate a clear
partisanship.

From Figure 2, communities 40 and 45 support the position of the Linke party,
as their contribution to the scale is strongly positive, in comparison to
communities 5, 11 and 12 whose $\beta_{j}$ are still positive but rather close
to the origin. Most of the learned communities have a low contribution to the
scale ($\beta_{j}$ $\rightarrow$ 0) and denote shared interests of political
parties.

Figure 3: Communities’ contributions to the scale ($\beta$) vs communities’
positions $\psi$ (German Manifesto corpus) Figure 4: Learned CommunityFish
ideal points with 95% confidence intervals (German Manifesto Corpus). Blue
line is the Loess curve. Figure 5: Learned Wordfish ideal points with 95%
confidence intervals (SOTU Corpus). Blue line is the Loess curve. Figure 6:
Learned Wordfish ideal points with 95% confidence intervals (German Manifesto
Corpus). Blue line is the Loess curve.

##  5 Conclusion

Scaling techniques remain useful application tools used by political
scientists to investigate partisanship among parties and to study the
ideological spectrum of speakers, but still suffering from the limitation of
considering words as the sole unit of analysis. While many solutions were
devised to enhance scaling results using external information from borrowed
corpora, the use of hierarchical clustering, as a pre-processing step, permits
to identify communities, as robust groups of associated words, that proved
semantically efficient in delivering substantial and interpretable results,
coupled with a faster execution time. CommunityFish is a summarization scaling
technique that translates the unit of analysis from words to communities, also
regarded as an implicit factorization of the document-feature-matrix,
unveiling informative sub-topic structures for an in-depth scaling of
historical corpora as well as political manifestos. Optimal use of
CommunityFish requires selecting most informative communities in an already-
lemmatized corpus by mean of a clustering technique (could it be Louvain or
Leiden algorithms). This ensures an independent community structure when
aggregating the document-feature-matrix, helping the spread of the ideological
stance learned via Poisson rank model, so to outperform classic Wordfish
algorithm without the need to adopt advanced, and usually expensive, NLP
solutions that may bring extra biases from other corpora or tasks. Applied to
two different corpora, it showed a great ability in extracting communities
from a language-variable corpus (SOTU) and identifying common items in debate-
based documents (German manifesto) for an efficient and meaningful scaling of
documents.

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 LHCb-PUB-2016-002

Characterisation of Medipix3

Silicon Detectors in a Charged-Particle Beam

K. Akiba1, J. Alozy2, R. Aoude3, M. van Beuzekom4, J. Buytaert2, P. Collins2,
A. Dosil Suárez5, R. Dumps2, A. Gallas5, C. Hombach6, D. Hynds7, M. John8, A.
Leflat9, Y. Li10, E. Pérez Trigo5, R. Plackett11, M. M. Reid12, P. Rodríguez
Pérez6, H. Schindler2†††Corresponding author., P. Tsopelas4, C. Vázquez
Sierra5‡‡‡Corresponding author., J. J. Velthuis13, M. Wysokiński14

1 Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
2 European Organization for Nuclear Research (CERN), Geneva, Switzerland
3 Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil
4 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
5 Universidade de Santiago de Compostela, Santiago de Compostela, Spain
6 School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
7 School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
8 Department of Physics, University of Oxford, Oxford, United Kingdom
9 Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
10 Center for High Energy Physics, Tsinghua University, Beijing, China
11 Diamond Light Source Ltd., Didcot, United Kingdom
12 Department of Physics, University of Warwick, Coventry, United Kingdom
13 H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
14 AGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland

While designed primarily for X-ray imaging applications, the Medipix3 ASIC can
also be used for charged-particle tracking. In this work, results from a beam
test at the CERN SPS with irradiated and non-irradiated sensors are presented
and shown to be in agreement with simulation, demonstrating the suitability of
the Medipix3 ASIC as a tool for characterising pixel sensors.

Published in JINST

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

##  1 Introduction

As part of the upgrade of the LHCb experiment, scheduled for the second long
shutdown of the LHC in 2018/19, the present microstrip-based Vertex Locator
(VELO) is foreseen to be replaced by a silicon hybrid pixel detector [1] with
an ASIC dubbed “VeloPix” which will be derived from the Medipix family of
ASICs. Like its predecessors Medipix2, Timepix, Medipix3, and Timepix3, the
VeloPix chip will feature a matrix of $256\times 256$ square pixels with a
pitch of 55 ${\,\upmu}$m. Prior to the arrival of the Timepix3 ASIC, Timepix
and Medipix3 were the most suitable devices for the qualification of prototype
sensors for the VELO upgrade. Until the end of lifetime of the upgraded
experiment, the pixels closest to the beam line ($r=5.1$ mm) accumulate a
fluence of up to $8\times 10^{15}$ 1 MeV n${}_{\text{eq}}$ cm-2. Qualifying
silicon sensors in terms of radiation hardness is therefore a key element of
the VELO upgrade R&D programme.

Timepix silicon detectors have been characterised extensively in terms of
charged-particle tracking performance [2]. Since the ASIC has per-pixel
information on the collected charge in terms of a time-over-threshold (ToT)
value, a direct measurement of the charge deposition spectrum is possible.

Medipix3 [3, 4] on the other hand is a pure counting chip which was designed
primarily for photon imaging applications. In order to measure the deposited
charge in the sensor one therefore has to resort to indirect methods (Section
3). Among the large-scale ASICs in the high-energy physics community, Medipix3
has been the first to be based on IBM 130 nm CMOS technology. Compared to the
Timepix (which was fabricated in 250 nm technology), it is expected to be more
radiation tolerant [5] and thus lends itself for testing irradiated sensors.

In this work, we report on measurements with irradiated and non-irradiated
Medipix3 assemblies carried out in 2012 at the H8 beamline of the CERN North
Area facility, using positively charged hadrons with a momentum of 180
GeV/$c$. These measurements are intended to provide a validation of the chip
functionality and performance complementary to characterisation measurements
using photon sources. In addition, they also represent a first step towards a
comprehensive evaluation of the radiation hardness of silicon pixel sensors
with the “Medipix footprint” of $55\times 55$ ${\,\upmu}$m2 pixels.

##  2 Setup

Figure 1: DUT mount and cooling setup. A Peltier cooler (not visible in the
photograph) is clamped between the cooling block and the TPG sheet onto which
the chip is glued.

The Timepix telescope, described in Ref. [6], was used for reconstructing the
tracks of particles crossing the Medipix3 device under test (DUT). In order to
minimise the pointing error, the DUT was placed in the centre of the
telescope. For reading out the Medipix3 chip, the “Merlin” data acquisition
system [7] developed at the Diamond Light Source facility was used. The
synchronisation of Timepix and Medipix3 is straightforward, as both ASICs work
in a “camera-style” frame-based readout mode. An external circuit implemented
using NIM modules was used for sending shutter opening and closing signals to
the telescope and the device under test. The coincident firing of two
scintillators located upstream and downstream of the telescope was used for
counting the number of beam particles traversing the telescope and the
duration of a shutter was adjusted such that 50 scintillator triggers were
accumulated in one frame. During one spill (9.6 s) typically about 500 frames
were recorded.

The temperature of the irradiated samples was controlled using a combination
of thermoelectric and CO2 cooling, the latter being provided by a portable
cooling plant [8]. As can be seen on the photograph in figure 1, the chip was
glued onto a tape of Thermal Pyrolytic Graphite (TPG) the other end of which
was attached to the cold side of a Peltier cooler. The hot side of the Peltier
cooler was put in contact with an aluminium cooling block through which CO2
was circulating. With the chip switched off, a temperature of approximately
$-20^{\circ}$ C was reached, rising to $-15^{\circ}$ C with the chip in
operation. The setup was placed in a light-tight aluminium case which was
flushed with nitrogen. The non-irradiated assemblies were measured at room
temperature.

In all measurements discussed below, the DUTs were $n$-on-$p$ silicon sensors
bump-bonded to Medipix3.1 ASICs. The ASICs were operated in single-pixel high-
gain mode and only one threshold (DAC THL) was used. Before taking data, a
threshold equalisation was performed using the front-end noise as reference.
The equalisation procedure consists of optimising the DAC values of two global
current sources (ThresholdN and DACpixel) and the threshold adjustment bits of
each pixel, such that the THL value corresponding to the noise floor lies
within a certain window for all pixels. For the non-irradiated assemblies a
target window of $5<\text{THL}<25$ was used.

Prior to the beam test, calibration measurements using testpulses were
performed to determine the relation between THL DAC and injected charge. To
verify the viability of the testpulse method, data were taken with a 241Am
source for the two non-irradiated assemblies discussed below, and – after
applying the calibrations obtained from the testpulse scan – the signal peaks
were found to match within 2% between the two assemblies. These measurements
were however made with a different readout system [9] and equalisation mask
than used in the testbeam (at that time the testpulse functionality was not
yet implemented in Merlin).

Where possible111One of the assemblies (W20_B6) was accidentally damaged after
the beam test., calibration measurements using test pulses were later (after
the beam test) made also using the Merlin system. These calibration curves are
used in the following for a relative comparison of the signals measured with
different sensors.

##  3 Measurements

For each track reconstructed in the telescope, the intercept with the DUT
plane is calculated. In order to suppress fake tracks a requirement on the
track quality is applied and the tracks are required to include hits on all
telescope planes. If an unused cluster with a centre of gravity within a
radius $r_{w}=110$ ${\,\upmu}$m around the track intercept is found, it is
associated to the track and tagged as used. In case of multiple candidate
clusters, the closest one is selected. The hit efficiency (or cluster finding
efficiency) $\varepsilon$ is then given by the fraction of tracks with an
associated cluster on the DUT. The pointing resolution of the telescope ($\sim
1.5$ ${\,\upmu}$m in the present configuration) allows one to probe the hit
efficiency as function of the track intercept within a pixel cell. In the
analysis we divide the pixel cell in $9\times 9$ bins and calculate separate
efficiencies for each bin.

The most probable value (MPV) of the deposited charge can be estimated by
scanning the hit efficiency as function of threshold. Assuming that the
distribution of the collected charge can be described by a Landau distribution
$f_{L}$ convoluted with a Gaussian distribution $f_{G}$, the hit efficiency as
a function of the threshold $Q$ is given by

$\varepsilon\left(Q\right)=\int\limits_{Q}^{\infty}\text{d}xf_{L}\otimes
f_{G}\left(x\right).$ (1)

By fitting the measured efficiency with Eq. (1), the MPV and width of the
Landau distribution and the $\sigma$ of the Gaussian can be determined (the
mean of the Gaussian is fixed to zero). This method requires that the entire
charge deposited by a track is collected by a single pixel. We therefore use
the hit efficiency in the central bin of the $9\times 9$ matrix for this
measurement.

To determine the spatial resolution, the distributions of the residuals
between the $x,y$ coordinates of the track intercepts and the associated
clusters are calculated. The standard deviation of the residual distribution
is used as a resolution metric (the pointing error of the telescope represents
only a small correction when subtracted in quadrature).

##  4 Results

###  4.1 Non-irradiated assemblies

Figure 2: Hit efficiency (for tracks crossing the centre of a pixel cell) in
non-irradiated Medipix3 assemblies with 100 ${\,\upmu}$m thick $n$-on-$p$
sensors as function of threshold, for (left) assembly W20_B6 and (right)
assembly W20_J9. The insets show the distribution of the charge deposition in
units of THL. The error bars represent the statistical uncertainty of the
measurements. For several points the error bars are smaller than the symbols.

The measurements before irradiation were carried out using $n$-on-$p$ active-
edge sensors with a nominal thickness of 100 ${\,\upmu}$m manufactured by
VTT222VTT Technical Research Centre of Finland, Espoo, Finland. The MPV of the
charge deposition spectrum is thus expected to be around $7000-7500$
electrons.

Two assemblies, W20_B6 and W20_J9, were tested with beam. After the beam test,
part of the backside metallisation was removed from the sensor on W20_B6, and
by injecting laser pulses the depletion voltage $V_{\text{dep}}$ was
determined to be approximately $-15$ V. In the beam test, both sensors were
operated at a bias voltage of $-60$ V, and were oriented perpendicularly to
the beam. For each point in the threshold scan, a data set comprising
typically $1-2\times 10^{5}$ reconstructed telescope tracks was recorded.

From the hit efficiency in the centre of the pixel cell as function of
threshold (figure 2), the most probable value of the charge deposition
spectrum is determined to correspond to THL $\sim 111.2$ for assembly W20_B6
and THL $\sim 71.6$ for assembly W20_J9. The statistical errors of the fit
values are given in figure 2. Uncertainties due to tracking cuts, alignment,
non-linearity of the THL DAC give rise to a systematic error on the MPV of
$\sim\pm 2.5\%$. The MPVs in terms of THL DAC values differ significantly
between the two devices. This can be attributed to non-optimised settings of
the DAC “Vcas” (for voltage cascode), which sets the reference voltage for
some transistors in the pixel circuit and, if not tuned properly, can have an
impact on the operating point of the circuit.

As discussed in section 2, testpulse calibration measurements using the Merlin
readout system could only be made for assembly W20_J9. To facilitate the
comparison between the devices, the results discussed below are therefore
presented as function of the threshold-to-signal ratio, i. e. the applied THL
DAC normalised to the respective MPV.

Figure 3: Hit efficiency in non-irradiated Medipix3 assemblies with 100
${\,\upmu}$m thick sensors as function of the track intercept within a pixel
cell, for (left) assembly W20_B6 at THL/MPV$\sim 0.45$ and (right) assembly
W20_J9 at THL/MPV$\sim 0.56$.

Figure 3 (left) shows the hit efficiency as function of the track intercept
within a pixel cell for the lowest threshold-to-signal ratio (THL/MPV$\sim
0.45$) covered by the threshold scan. At this threshold – which is high
compared to a typical operational threshold of 1000 electrons – the detector
can be seen to be fully efficient ($\varepsilon>0.99$), except at the corners.
With increasing threshold – as illustrated in figure 3 (right) – a drop in
efficiency becomes noticeable at the borders of the pixel cell. This is a
consequence of charge sharing due to diffusion, as can be seen from figure 4
which shows the average cluster size as function of the track intercept within
the pixel cell.

Figure 4: Average cluster size as function of the track intercept within a
pixel cell for assembly W20_B6 (100 ${\,\upmu}$m thick sensor) at THL/MPV$\sim
0.45$. Multi-pixel clusters are found predominantly at the edges and corners
of the pixel cell.

Figure 5: Average cluster size (left) and standard deviation of the
$x$-residual distribution (right) at perpendicular track incidence as function
of threshold-to-signal ratio for assemblies W20_B6 (empty circles) and W20_J9
(full circles). Results for a Timepix assembly with the same type of sensor
are shown with full squares. The error bars represent the statistical
uncertainty of the measurements. For most points the error bars are smaller
than the symbols.

Figure 6: Residual distribution for (left) one-pixel and (right) two-pixel
clusters extending over two columns in a non-irradiated 100 ${\,\upmu}$m thick
sensor (assembly W20_B6, at THL/MPV$\sim$0.45).

Figure 5 (left) shows the average cluster size as function THL/MPV. At the
lowest threshold, an average cluster size of $1.103\pm 0.001$ is found, with
single-pixel clusters constituting $\sim 91.3\%$ and two-pixel clusters $\sim
7.7\%$ of all associated clusters. The cluster size as function of
threshold/signal follows the same shape for both sensors, exhibiting a minimum
around THL/MPV$\sim 0.9$ and a subsequent maximum around THL/MPV$\sim 1.6$.
With increasing threshold, an increasing fraction of the observed clusters is
produced by primary particles which suffer collisions with large energy loss.
These collisions give rise to energetic electrons which further ionise along
their path and produce electron-hole pairs away from the trajectory of the
primary particle.

The residual distributions (in the $x$ direction) at low threshold for one-
pixel and two-pixel clusters are shown in figure 6. Averaged over all cluster
sizes, the standard deviation of the residual distribution is found to be
$\sim 15.7$ ${\,\upmu}$m in both $x$ and $y$. As expected from the dominance
of one-pixel clusters, this value is close to the binary limit ($55$
${\,\upmu}$m$/\sqrt{12}\sim 15.9$ ${\,\upmu}$m). Figure 5 (right) shows the
$\sigma$ of the residual distribution in $x$ as function of threshold/signal.
The resolution can be seen to deteriorate significantly after the threshold
crosses the MPV.

Figure 5 also includes results obtained with a Timepix ASIC bump-bonded to a
100 ${\,\upmu}$m thick $n$-on-$p$ sensor from the same batch. The Timepix
assembly was measured in the same beam test campaign and was operated at a
threshold of 1000 electrons and a bias voltage of $-60$ V. The data were taken
in ToT mode, but the values shown in figure 5 were calculated with the ToT
values set to one to mimic the Medipix3 behaviour. The results for the Timepix
assembly are in agreement with the extrapolated results from the Medipix3
assemblies.

Figure 7: Simulated average cluster size (left) and standard deviation of the
$x$-residual distribution (right) at perpendicular track incidence as function
of threshold-to-signal ratio. Full (empty) symbols show the results with
(without) the spatial extent of the ionisation pattern being included in the
simulation.

To understand better the observed shapes of resolution and cluster size as
function of threshold, a simple simulation using the Garfield++ toolkit [10]
was used. The primary ionisation process is calculated using the Heed program
[11], which in addition to the energy loss by the traversing charged particle
also simulates the ionisation cascade from high-energy (“delta”) electrons
produced in the interactions of the charged particle with the silicon medium
as well as the spatial distribution of the resulting electron-hole pairs. Each
electron is subsequently transported through the sensor, based on the drift
velocity and diffusion coefficient as function of the electric field. A one-
dimensional approximation for the electric field is used333The electric field
is assumed to vary linearly between $E=\left(V-V_{\text{dep}}\right)/d$ at the
sensor backside and $E=\left(V+V_{\text{dep}}\right)/d$ at the implants, where
$d$ is the sensor thickness..

As can be seen from figure 7, the features in the measured cluster size and
resolution as function of threshold-to-signal ratio are reproduced by the
simulation, provided that the spatial extent of the ionisation pattern is
taken into account. This corroborates the conclusion that these features are
due to “delta” electrons.

###  4.2 Irradiated assemblies

Figure 8: Leakage current as function of reverse bias voltage at
$T=-13^{\circ}$ C after irradiation to $0.5\times 10^{15}$ 1 MeV
n${}_{\text{eq}}$ cm-2 (100 ${\,\upmu}$m thick $n$-on-$p$ active-edge sensor
with 100 ${\,\upmu}$m pixel-to-edge distance). Figure 9: Hit efficiency in
Medipix3 assembly W20_H5 with 100 ${\,\upmu}$m thick $n$-on-$p$ sensor as
function of threshold, after irradiation to $0.5\times 10^{15}$ 1 MeV
n${}_{\text{eq}}$ cm-2. The inset shows the distribution of the charge
deposition in units of THL (Landau distribution convoluted with a Gaussian).

Figure 10: Average cluster size (left) and standard deviation of the
$x$-residual distribution (right) at perpendicular track incidence as function
of threshold-to-signal ratio for irradiated assembly W20_H5.

A set of Medipix3.1 assemblies, with VTT $n$-on-$p$ active-edge sensors from
the same batch as the non-irradiated sensors discussed above, were irradiated
at the Ljubljana TRIGA reactor [12] to a 1 MeV neutron equivalent fluence of
$5\times 10^{14}$ cm-2 and subsequently annealed for 80 minutes at
$60^{\circ}$ C. From lab measurements with a laser, the effective depletion
voltage $V_{\text{dep}}$ of these sensors after irradiation was measured to be
between $-85$ and $-105$ V. One of the assemblies, W20_H5, was characterised
in the beam test. The sensor, which has a pixel-to-edge distance of 100
${\,\upmu}$m, was operated at a bias voltage of $-100$ V as operation at
higher bias was inhibited by the onset of electrical breakdown (figure 8).

In general, the irradiated assemblies exhibited a higher dark count rate
compared to the non-irradiated ones, which was attributed to electrons from
the $\beta$-decay of 182Ta produced by neutron activation during the
irradiation of the ASIC444 The presence of 182Ta in the irradiated assemblies
was confirmed by gamma spectroscopy measurements performed by the CERN
radioprotection group.. This – presumably in combination with other radiation
effects – resulted in problems during the equalisation procedure for some
assemblies, as well as a larger threshold dispersion. The optimised values of
the DACs which control the global currents (ThresholdN and DACpixel) were
larger (by a factor 2 – 3) compared to the non-irradiated assemblies.

As can be seen from figure 9, the MPV of the charge deposition spectrum
corresponds to a THL DAC of $\sim 53.9$. After correcting for the differences
in gain and offset using testpulse calibration curves, this value is found to
be approximately 8.5% lower than the MPV of the non-irradiated sensors.

As in the non-irradiated case, the cluster size spectrum is dominated by
single-pixel clusters. Cluster size and $\sigma$ of the $x$-residual
distribution as function of threshold-to-signal ratio (figure 10) follow
closely the corresponding curves for the non-irradiated assemblies (figure 5).

Figure 11: Hit efficiency in Medipix3 assembly W20_H5 with 100 ${\,\upmu}$m
thick $n$-on-$p$ sensor as function of the track intercept within a pixel cell
at THL = 40 (threshold/signal $\sim 0.74$), after irradiation to $0.5\times
10^{15}$ 1 MeV n${}_{\text{eq}}$ cm-2. The drop in efficiency at the edges of
the pixel cell is more pronounced than in figure 3 mainly because of the
higher threshold-to-signal ratio.

Figure 11 shows the hit efficiency as function of the track intercept within a
pixel cell at the lowest measured threshold ($\text{THL}=40$). In the centre
of the pixel cell, an efficiency of $0.93\pm 0.01$ is found, compared to
$0.97\pm 0.01$ for the non-irradiated assemblies at the same threshold-to-
signal ratio ($\sim 0.74$).

Figure 12: Hit efficiency in Medipix3 assembly W20_D6 with 200 ${\,\upmu}$m
thick $n$-on-$p$ sensor (diced at 400 ${\,\upmu}$m from the last pixel) as
function of the track intercept within a pixel cell at THL = 50 and 300 V bias
voltage, after irradiation to $2.5\times 10^{15}$ 1 MeV n${}_{\text{eq}}$
cm-2. The asymmetry of the efficiency profile is attributed to a small
inclination of the assembly with respect to the beam.

A further beam test measurement was performed with a Medipix3.1 ASIC bump-
bonded to a 200 ${\,\upmu}$m thick $n$-on-$p$ sensor manufactured by
CNM555Centro Nacional de Microelectrónica, Barcelona, Spain. The sensor
featured two guard rings and was diced at a distance of 400 ${\,\upmu}$m from
the border of the pixel matrix. The assembly (W20_D6) was also irradiated at
Ljubljana, but to a higher fluence, $2.5\times 10^{15}$ 1 MeV
n${}_{\text{eq}}$ cm-2. During the equalisation procedure, a large threshold
dispersion was observed, such that the upper limit of the equalisation target
window needed to be increased to $\text{THL}=40$. In addition, a significant
fraction ($\sim 10\%$) of the pixels needed to be masked. Tracks crossing a
masked pixel were thus excluded from the efficiency measurements for this
device.

Because of time constraints, data were taken only at three THL values with
this device, such that determining the MPV of the charge deposit spectrum was
not possible.

Figure 12 shows the efficiency as function of the track intercept. The
dependency of the efficiency on the applied threshold and bias voltage is
shown in figure 13.

Figure 13: Overall hit efficiency in irradiated assembly W20_D6 with 200
${\,\upmu}$m thick $n$-on-$p$ sensor as function of the THL value for
different bias voltages (stars: $-100$ V, triangles: $-200$ V, circles: $-300$
V). The assembly was irradiated to a fluence of $2.5\times 10^{15}$ 1 MeV
n${}_{\text{eq}}$ cm-2. The lines are drawn to guide the eye.

##  5 Conclusions

First results on the performance of hadron-irradiated pixel detectors with the
“footprint” of the upgraded LHCb VELO ($55\times 55$ ${\,\upmu}$m2 pixels)
have been obtained from a beam test at the CERN SPS, using Medipix3.1 ASICs
bump-bonded to thin $n$-on-$p$ silicon sensors. As the Medipix3 ASICs do not
provide a direct measurement of the collected charge, threshold scans were
used for characterising the sensor.

Reference measurements with non-irradiated Medipix3.1 assemblies were made in
the same testbeam campaign. The threshold DAC value (THL) corresponding to the
most probable value of the charge deposition spectrum was determined from the
hit efficiency as function of threshold. The measured cluster size and
resolution as function of the THL/MPV ratio are consistent between the
assemblies and in good agreement with simulations.

After irradiation with reactor neutrons to a fluence of $0.5\times 10^{15}$ 1
MeV n${}_{\text{eq}}$ cm-2, a larger threshold dispersion and an increased
power consumption of the ASIC were observed. A direct comparison between the
performance of irradiated and non-irradiated sensors is complicated due to the
fact that the non-irradiated sensors were operated at overdepletion while the
irradiated sensor (due to early electrical breakdown) needed to be operated
close to depletion. The difference in operating conditions may explain the
small drop in efficiency and MPV measured with the irradiated sensor. The
shapes of average cluster size and resolution versus threshold are not changed
significantly compared to the non-irradiated sensors.

The studies presented in this paper are being continued using the Timepix3
ASIC, which has recently become available.

## Acknowledgements

We gratefully acknowledge strong support from the CERN Medipix Group. in
particular Rafael Ballabriga. We would also like to thank Juha Kalliopuska and
Sami Vähänen from VTT/Advacam and Giuglio Pellegrini from the IMB-CNM
Radiation Detectors Group. The research leading to these results has received
partial funding from the European Commission under the FP7 Research
Infrastructures project AIDA, grant agreement no. 262025. We gratefully
acknowledge the expert wire bonding support provided by Ian McGill of the CERN
DSF bonding lab. We extend warm thanks to Igor Mandić and Vladimir Cindro for
irradiating the Medipix3 assemblies.

## References

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