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\chapter{Abstract}
\label{ch:Abstract}
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\chapter{Performance analysis of Timepix3}
\label{ch:Performance analysis of Timepix3}
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\chapter{Test beam analysis: supplemental material}
\label{ch:Test beam analysis: supplemental material}
\section{Test beam analysis: supplemental material}
\label{sec:Test beam analysis: supplemental material}
This section provides additional material related to the test beam analysis presented in \cref{ch:Test Beam at the DESY-II synchrotron}
\section{Cluster size distribution of MIMOSA26 pixel sensors}
\label{sec:Cluster Size Distribution Of MIMOSA26 Pixel Sensors}
\cref{fig:clustersize_allplanes} illustrates the cluster size distribution of all the MIMOSA26 pixel sensors of the AZALEA beam telescope. The distribution corresponds to Run6275. % with a threshold of $1340$ LSB and an applied reverse bias voltage of \SI{-20}{\volt}.
\begin{figure}[H]
\centering
\includegraphics[width =1\linewidth]{files/pictures/clustersize_allplanes.png}
\caption[Cluster size distribution of all the M26 senor planes]{The cluster size distribution of all the M26 sensor planes of the AZALEA beam telescope.}
\label{fig:clustersize_allplanes}
\end{figure}
\section{Correlations}
\label{sec:correlations}
The spatial correlations along the x- and y-directions before and after performing the pre-alignment routine are illustrated for all the telescope planes in \cref{fig:correlationsX} and \cref{fig:correlationY}, respectively. The spatial correlations are calculated between the cluster position on each detector plane and the fourth telescope plane (plane 3) which is assigned as the reference plane in this analysis. Peaks are visible in the spatial correlation plots in both X and Y for all detectors. The peaks are superimposed with a "triangular" background, which comes from non-correlated clusters, either from different tracks or noise. The correlations are shifted towards zero during the pre-alignment, thereby compensating for the translational misalignment. The widths of the distribution remain unchanged as the pre-alignment algorithm only corrects for shifts along x- and y-directions. Furthermore, the self-correlation of the reference plane can be understood from the very sharp distribution at $0$, as seen in figures MIMOSA26\_3:correlation X and MIMOSA26\_3:correlation Y.
\begin{figure}[H]
\centering
\includegraphics[width =1\linewidth]{files/pictures/correlationsX.png}
\caption[Spatial correlations of M26 sensors along x-direction]{Spatial correlations of M26 sensors along x-direction. The fourth telescope plane (plane 3) is assigned as the reference plane in this analysis }
\label{fig:correlationsX}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width =1\linewidth]{files/pictures/correlationsY.png}
\caption[Spatial correlations of M26 sensors along y-direction]{Spatial correlations of M26 sensors along y-direction. The fourth telescope plane (plane 3) is assigned as the reference plane in this analysis }
\label{fig:correlationY}
\end{figure}
\section{Telescope alignment}
\label{sec:telescope alignment}
The spatial residuals along the x- and y-directions after performing the coarse pre-alignment and precise track-based telescope alignment are illustrated for all the telescope planes in \cref{fig:spatialresX} and \cref{fig:spatialresY}, respectively. The distribution obtained after the pre-alignment routine is well centered at zero (blue histogram), correcting the telescope planes' translational misalignment. Furthermore, the precise track-based telescope alignment rectifies the global misalignments such as the rotations of the telescope planes with respect to the beam, consequently resulting in a narrow distribution (red histogram).
\vspace{0.5cm}
In the biased residual distributions illustrated in \cref{fig:spatialresX} and \cref{fig:spatialresY}, the first and the last telescope plane features an improved track pointing resolution (narrow histogram) than other planes. The direction of the track coming into and out of the beam telescope is mostly defined by the hit in the first and last plane. The absence of an additional hit outside the telescope results in a better track prediction at the first and the last planes compared to others, thereby systematically narrowing down the biased residual distribution, resulting in the observed trend.
\begin{figure}[H]
\centering
\includegraphics[width =0.8\linewidth]{files/pictures/spatialresidualXM26.png}
\caption[x-residuals of M26 sensors]{Spatial residuals of M26 sensors along x-direction. The illustrated figures are the biased track residuals as obtained from the GBL trajectory fit.}
\label{fig:spatialresX}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width =0.8\linewidth]{files/pictures/spatialresidualYM26.png}
\caption[Spatial correlations of M26 sensors along y-direction]{Spatial residuals of M26 sensors along x-direction. The illustrated figures are the biased track residuals as obtained from the GBL trajectory fit.}
\label{fig:spatialresY}
\end{figure}
\chapter{General characterization studies of the Timpix3 ASIC}
\label{ch:General characterisation studies of the Timpix3 ASIC}
\section{Threshold dispersion and equalization}
\label{sec:Threshold dispersion and equalization}
3D plots clearly illustrating the effects of the equalization procedure are shown in \cref{fig:3d_thr_eq} The x- and y-axis represent the pixel row and column numbers, respectively, while the z-axis represents the position of noise edge in units of the global threshold DAC.
\begin{figure}[h]
\centering
\includegraphics[width =1\linewidth]{files/pictures/3d_thr_eq.png}
\caption[3D Illustration of the threshold equalization]{Illustration of the threshold equalization. The noise edge distributions for minimum (0X0), maximum (0XF), and equalized trim DACs are shown.}
\label{fig:3d_thr_eq}
\end{figure}
\section{Threshold gain measurement}
\label{sec:Threshold gain measurement}
Fitting the Modified Error Function in \cref{eq:modified_erf} to the S-curve distribution obtained after test pulse injection of varying amplitudes yields the mean values in units of LSB. These extracted mean values and plotted against the injection voltage and a linear fit performed to determine the gain in the units of \si{LSB\per}\si{\milli\volt} for all the 256 pixels is illustrated below.
\begin{figure}[h]
\centering
\includegraphics[width =1\linewidth]{files/pictures/THR_VOLTAGE_all.png}
\caption[Mean values Vs. injection voltage]{Mean values Vs. injection voltage for all the 256 pixels. A linear fit is performed on the plots of each pixel to determine the gain per threshold step of each pixel. }
\label{fig:linear_fit}
\end{figure}
\subsection{Cluster size distribution}
\label{ssec:Cluster size distribution}
An unbiased analysis requires the DUT to be excluded from the tracking procedure. Consequently, clusters on the DUT are associated with the reference tracks based on spatial and time cuts (time\_cut\_abs $=$ \SI{200}{\micro\second} and spatial\_cut\_abs $=$ \SI{200}{\micro\second},\SI{200}{\micro\second} ) in a separate step of the reconstruction done by the DUTAssociation module. Thus, the cluster size distribution of the associated clusters as a function of threshold and the applied reverse bias voltages are shown in \cref{fig:meanclustersizeAssoc_thr} and \cref{fig:associated_clustersize_v_bias}, respectively. Single-pixel noise clusters are no longer seen in \cref{fig:meanclustersizeAssoc_thr} as opposed to \cref{fig:meanclustersize_thr} due to the spatial and time cuts imposed.
\begin{figure}[h]
\centering
\includegraphics[width =0.7\linewidth]{files/pictures/meanclustersizeAssoc_thr.png}
\caption[The mean cluster size Vs. threshold]{The mean cluster size Vs. threshold for the associated clusters.}
\label{fig:meanclustersizeAssoc_thr}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width =0.7\linewidth]{files/pictures/associated_clustersize_v_bias.png}
\caption[The mean cluster size Vs. bias voltage]{The mean cluster size Vs. applied reverse bias voltage for the associated clusters.}
\label{fig:associated_clustersize_v_bias}
\end{figure}
\subsection{Detection efficiency}
\label{ssec:detection_efficiency}
The detection efficiencies focusing between $95$-$100$ \% as a function of the applied bias voltage is illustrated in \cref{fig:EffVsVoltage_zoom}
\begin{figure}[H]
\centering
\includegraphics[width =0.8\linewidth]{files/pictures/EffVsVoltage_zoom.png}
\caption[The mean cluster size Vs. bias voltage]{The detection efficiency as a function of the applied bias voltage focusing between $95$-$100$ \% }
\label{fig:EffVsVoltage_zoom}
\end{figure}
\chapter{Summary}
\label{ch:Summary}
The EUDET-type beam telescopes based on M26 sensors have been a workhorse for detector R\&D, providing unparalleled tracking resolution of $(3.24 \pm 0.09)$ \hspace{0.1cm} $\si{\micro\meter}$ for test beam users over the last decade. With the last available MIMOSA26 pixel sensors reaching their end-of-life and the demanding requirements of the future detectors in terms of timing resolution($\mathcal{O}(\si{\pico\second}$)) and capability to process higher particle rates, both short and long term upgrade activities of the current pixel beam telescope at the DESY-II test beam facility is foreseen. This thesis explores the possibility of integrating a Timepix3 tracking plane with the existing pixel beam telescope to perform track time-stamping at the nanosecond scale. Timepix3, a 65K channel multipurpose readout ASIC employs time-of-arrival and time-over threshold techniques to measure the arrival time and energy deposited by the incident particle. Both the methods are severely affected by the timewalk phenomenon, thus requiring pixel-by-pixel calibration to achieve the best possible energy and time resolution. The results of the studies undertaken in the laboratory and the DESY-II test beam facility to understand the general characteristics of the Timepix3 ASIC in regards to timing performance are presented in \textcolor{red}{Chapter: Results} and briefly summarized below.
\vspace{0.5cm}
The assembly used in this study (W5\_E2) consists of a \SI{100}{\micro\meter} thick n-in-p silicon sensor bump bonded to a Timepix3 ASIC. A threshold equalization study (see \textcolor{red}{Threshold variation and equalization}) is first performed on the assembly to compensate for the per-pixel variations in the thresholds induced by the process variations during the wafer production process. The equalization procedure reduces the per-pixel variations by a factor of 6 (see \textcolor{red}{Fig: threshold equalization}), determines the baseline ($1120.24$ LSB), and recommends the nominal operational threshold ( 6 sigmas away from the baseline, 1207 LSB) used in the test beam. Threshold gain measurement (\textcolor{red}{ssec: Gain measurement}) is performed to establish the mean gain per threshold LSB of the chip as $1.88$ LSB/\si{\milli\volt}. The baseline and noise distribution of the pixel matrix after equalization is also determined and is illustrated in \textcolor{red}{Fig: Baseline and noise distribution)}. In the presented work, a C-V scan is not performed in the lab to determine the nominal operating voltage. However, the value for the Timepix3 assembly under investigation is known from the studies performed in \cite{Pitters2018TimeAE}.
\vspace{0.5cm}
After performing the lab measurements to determine the chip's nominal operating threshold and voltage, the assembly is studied in the test beam to determine the spatial, temporal resolution, and detection efficiencies. The spatial resolution is studied as a function of threshold and applied reverse bias voltage (\textcolor{red}{Fig: spatial res V threshold and bias voltage}). The best spatial resolution achieved in this work corresponds to ($14.78 \pm 0.05)$\si{\micro\meter} and ($15.08 \pm 0.06$)\si{\micro\meter} along the x- and y-direction respectively at operating condition of 1160 LSB and \SI{-30}{\volt}. The temporal resolution is investigated as a function of applied bias voltage. The best timing resolution after appying timewalk correction (\textcolor{red}{ssec: TWC}) to the test beam data is ($1.078 \pm 0.003$)\si{\nano\second} at an over depletion of \SI{-65}{\volt} and a threshold of $1205$ LSB. The detection efficiency of the chip is also studied as a function of threshold and bias voltage. While a detection efficiency $ > 99.8679\substack{+0.0131362 \\ -0.0119965}$\,\% is achieved at all the bias voltages under investigation, the maximum efficiency of $99.8821\substack{+0.0116151\\ -0.010615}$\,\% is obtained at a threshold of 1160 LSB. The efficiency has a steep fall off with increasing threshold as illustrated in \textcolor{red}{Fig: Eff Vs. Threshold}.
\vspace{0.5cm}
As the entire community is currently gearing up for a post MIMOSA26 telescope era, the aforementioned results regarding the short-term solution of using Timepix3 tracking plane to perform track time tagging in nanosecond range are very promising, thus moving one step closer towards the realization of the dream pixel telescope featuring 4D tracking.
\chapter{Introduction}
\label{ch:Introduction}
Test beam facilities are vital infrastructures for studies in instrumentation in particle physics and research and development (R\&D) of sensors and detectors used in high energy physics (HEP) experiments. Testing detector prototype performance using particle beams is a mandatory step to assess the viability of technologies and geometries before the final design of a detector or calibrate assembled modules. Thus, Beam tests in precisely defined environmental conditions are indispensable to study new detector prototypes during R\&D phases and final detector assemblies before going into the production phase for HEP experiments. The detector to be studied is placed and operated in a particle beam of known energy and rate that mimics the actual experimental environment. Although most of the experiments conducted at test beam facilities are in particle detector development, these facilities have played pivotal roles in studies on the interaction of high momentum particles with matter, e.g. for the imaging techniques \cite{paulSchutze} and general studies on multiple Coulomb scattering \cite{MC_scattering_desy}.
\begin{figure}[tbp]
\centering
\includegraphics[width =0.5\linewidth]{files/pictures/areal_view_TB.png}
\caption[]{Aerial view of the DESY Campus at Hamburg-Bahrenfeld with the DESY II synchrotron (blue) and the location of the test beam lines (red) in Hall 2. From \cite{Diener_2019}. }
\label{fig:areal_view_TB}
\end{figure}
\vspace{0.5cm}
DESY (Deutsches Elektronen-Synchrotron) operates a test beam facility at campus Hamburg-Bahrenfeld (\cref{fig:areal_view_TB}), located in building 27 ("Halle 2"), one of the experimental halls at DESY. The facility offers three independent beamlines with electron or positron particles with selectable momenta from $1$-\SI{6}{\giga\electronvolt\per c}. The beam generation mechanism is introduced in \textcolor{red}{Chapter Test Beam at the DESY-II synchrotron} and is illustrated in \textcolor{red}{Figure: Beam generation in chapter TB}. The beamlines are attached to the DESY II synchrotron, which typically runs electron beams with oscillating energy from $0.45$-\SI{6.3}{\giga\electronvolt}, serving as an injector for the PETRA III synchrotron \cite{PETRA-III}. The DESY test beam facility is of the few places worldwide offering users access to multi-\si{\giga\electronvolt} beams. This facility also offers unique infrastructure, including a high field solenoidal magnet and three permanently installed high-precision pixel beam telescopes.
\vspace{0.5cm}
Pixel beam telescopes (see \textcolor{red}{ssec:Pixel beam telescope}), for precise particle tracking, are integral equipment of any test beam facility. The Beam telescope allows investigating novel particle detectors (DUT = Device Under Test). At DESY, EUDET-type pixel beam telescopes \cite{EUDET_INTRO} are available as a high-precision tracking tool for detector development. This type of beam telescope originated from a EUDET project \cite{EUDET_PROJECT} using MIMOSA26 monolithic active pixel sensors, and responding to the increasing demand of the sensor R\&D community, replicas of this pixel telescope are operated at CERN, SLAC and ELSA (University of Bonn). The telescope provides a high-precision beam tracking ($\approx$ \SI{3}{\micro\meter} ), a sufficient event rate ($\approx$ \SI{2}{\kilo\hertz} rate at \SI{10}{\kilo\hertz} beam rate) and an easy integration capability of DUTs \cite{Beamtele_into}. Operated by the EUDAQ2 framework( \cite{eudaq_into} DAQ software, see \textcolor{red}{sec: EUDAQ} and analyzed with the state-of-the-art Corryvreckan offline reconstruction software (\cite{corry_into}, see \textcolor{red}{sec:Corryvreckan}), the beam telescopes offer the whole infrastructure for detector development from measurement to results \cite{Beamtele_into}.
\vspace{0.5cm}
The EUDET-type beam telescopes are an extremely successful set of tracking telescopes providing unprecedented tracking resolution for more than ten years with stable operation. However, the requirements of the current and future detectors in terms of readout bandwidth and time resolutions ($\mathcal{O( \si{\pico\second})}$) exceed the capabilities of the current telescopes(rolling shutter readout mode, \SI{115}{\micro\second}/cycle). Thus, with the approaching end of life of the current beam telescope and to meet the stringent requirements of future detector test beam campaigns, midterm solutions are already being implemented at the DESY-II test beam facility, thus, allowing for the investigation of novel sensor technologies, pico-second timing layer (using low gain avalanche diodes, LGADs), and modern electronics to build the next-generation pixel beam telescope.
\vspace{0.5cm}
This work explores the short-term upgrade solution of using Timepix3 ASIC (application-specific integrated circuit) as a timing layer at the DESY II test beam facility to perform track time-stamping in the nanosecond range. Timepx3 \cite{tpx3_into} is a general-purpose readout ASIC designed in \SI{130}{\nano\meter} CMOS technology and contains $256 \times 256$ pixel channels each of which is $55 \times 55$ \si{\micro\meter}$^2$. Although the Timepix3 readout ASIC is mainly used in particle racking applications where timing and spatial resolution are important, the chip can also be programmed in event counting or photon counting mode for imaging applications with particle rates higher than \SI{40}{\mega hits}/\si{\centi\meter}$^2$/\si{\second}. The choice of the sensor will depend on the particularities of the application. In the presented work, an n-in-p planar silicon sensor of \SI{100}{\micro\meter} thickness, bump-bonded to the Timepix3 ASIC (W5\_E2 assembly), is tested in the laboratory as well as in a test-beam campaign at the DESY II test beam facility. The lab measurements and the test beam data are used to characterize the assembly in terms of charge sharing, spatial and temporal resolution, and detection efficiencies.
\vspace{0.5cm}
The thesis is structured as follows: After a brief introduction of the silicon detector concepts in \textcolor{red}{Chapter 2: Semiconductor detectors}, an overview on the DESY II test beam facility, the EUDET-type pixel beam telescopes, the EUDAQ2 data acquisition (DAQ), and Corryvreckan test beam analysis framework is provided in \textcolor{red}{Chapter 3: Test Beam at the DESY-II synchrotron}. In the first half of the \textcolor{red}{Chapter: Pixel readout ASICs and assembly calibration}, the general characteristics of the Timepix3 ASIC are discussed in detail, followed by a short introduction on the SPIDR readout board. The remaining half focuses on the results obtained from the laboratory and test beam measurements. Finally, \textcolor{red}{Chapter : Conclusions} summarizes the obtained results and gives conclusions.
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\begin{titlepage}
\centering
\vspace*{5cm}
{\Huge\bfseries Commissioning and Time Resolution Studies of a Timepix3 Tracking Plane \par}
\vspace*{0.5cm}
\vspace*{4cm}
{\Large Keerthi Nakkalil\par}
\vfill
{\large \today\par}
\end{titlepage}
\newpage
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