\documentclass{PoS}

\title{Performance of CMOS sensors for a digital electromagnetic calorimeter}

\ShortTitle{Performance of CMOS sensors for a digital electromagnetic calorimeter}

%\author{\speaker{Paul Dauncey}%
%        \href{http://www.spider.ac.uk}{\tt http://www.spider.ac.uk}.}\\
\author{Paul Dauncey%
        \thanks{On behalf of the SPiDeR Collaboration;
        {\tt http://www.spider.ac.uk}}\\
        Imperial College London\\
        E-mail: \email{P.Dauncey@imperial.ac.uk}}

%\author{Another Author\\
%        Affiliation\\
%        E-mail: \email{...}}

\abstract{We have developed monolithic silicon pixel sensors as study devices
for a digital electromagnetic calorimetry application at future
collider detectors, such as a linear collider. The motivation for a
digital ECAL and the sensor requirements which arise from this are
discussed.

We present results from the "TPAC" CMOS sensors produced using the
0.18\,$\mu$m INMAPS process. The sensors have 50\,$\mu$m pixel size. The
technology is also applicable to tracking and vertexing applications
where highly granular pixels with integrated in-pixel readout is needed.

Several varieties of the TPAC sensors were fabricated with and without
some of the various processing innovations available in INMAPS,
specifically deep P-wells and high-resistivity epitaxial silicon. The
performance of these sensor variants has been measured both in the
laboratory and at beam tests. Comparisons of these sensors with each
other are presented, showing that the INMAPS
innovations result in significant improvements in the sensor performance.}

\FullConference{35th International Conference of High Energy Physics\\
                 July 22-28, 2010\\
                 Paris, France}

\begin{document}

\section{Motivation for digital electromagnetic calorimetry}
The planned $e^+e^-$ international linear collider 
%(ILC)~\cite{ref:ilc} 
(ILC)\footnote{
J.~Brau, Y.~Okada and N.~Walker (eds.),
\emph{International Linear Collider Reference Design Report}, (2007),
\href{http://www.linearcollider.org/rdr}
{\tt http://www.linearcollider.org/rdr}.
}
will have an energy of 500\,GeV to 1\,TeV,
with a physics programme complementary to LHC.
Many ILC physics processes are characterised by multi-jet final states
so the reconstruction of the invariant mass of two or more jets is critical.
Jet energy resolution is a major driver for ILC detector 
%esigns~\cite{ref:sid,ref:ild,ref:calice}
designs.\footnote{
\emph{SiD Detector Concept},
\href{http://silicondetector.org/}
{\tt http://silicondetector.org/}.}
\footnote{\emph{ILD Detector Concept},
\href{http://www.ilcild.org/}
{\tt http://www.ilcild.org/}.}
\footnote{\emph{CALICE Collaboration},
\href{https://twiki.cern.ch/twiki/bin/view/CALICE/WebHome}
{\tt https://twiki.cern.ch/twiki/bin/view/CALICE/WebHome}.
}
``Particle flow'' techniques will provide the required performance but
require highly granular calorimeters.

Usually, a sampling electromagnetic calorimeter measures the energy deposited 
in the sensitive layers using analogue readout.
%interspersed between the dense layers which cause the shower. 
The concept of a digital electromagnetic calorimeter (DECAL) is to 
measure the number of particles in the sensitive layers instead, which
requires digital readout but with much finer granularity.
Counting particles eliminates the resolution contribution from Landau 
fluctuations of the deposited energy and so the resolution should be
closer to the intrinsic stochastic shower variations.
High granularity, typically 100\,$\mu$m, 
is necessary to reduce the probability of multiple 
particles per pixel. This should also improve pattern recognition
for particle flow.

Simulation comparing analogue and digital calorimeters indicates a 
significant resolution improvement in principle, typically reducing
the stochastic term in $\sigma_E/E$ by 20\% for a given sampling
fraction, see fig~\ref{fig:tpac}.
%However, the exact value is sensitive to the core shower 
%density which has not been measured at high granularity.
%
\begin{figure}[h]
\begin{center}
\begin{picture}(0,125)
\put(-215,-20){\includegraphics[height=156pt]{ErgResn1.png}}
\put(-103,2){\footnotesize $20\times 0.6X_0+10\times 1.2X_0$}
\put(-180,108){\footnotesize Analogue: $\frac{\sigma_E}{E}=0.011\oplus\frac{0.160}{\sqrt{E}}$}
\put(-179,92){\footnotesize Digital:\phantom{X\,\,} $\frac{\sigma_E}{E}=0.009\oplus\frac{0.128}{\sqrt{E}}$}
\put(35,-15){\includegraphics[height=140pt]{TPAC1_photo.png}}
\end{picture}
%\includegraphics[width=0.45\textwidth]{ErgResn1.png}
%\hskip 2cm
%\includegraphics[width=0.35\textwidth]{TPAC1_photo.png}
\end{center}
\caption{Left: Comparison of $\sigma_E/E$ as a function of
$1/\sqrt{E}$ for simulated analogue (green) and digital (red)
electromagnetic calorimeters with a typical
ILC geometry.
% of $20\times 0.6X_0+ 10\times 1.2X_0$.  The stochastic
%terms for the fits shown are 16.0\% for analogue and 12.8% for digital.
Right: Photograph of a TPAC V1.2 sensor.}
\label{fig:tpac}
\end{figure}

\section{The TPAC sensor}
The TPAC (Tera-Pixel Active Calorimeter) sensor 
%V1.2~\cite{ref:tpac},
V1.2,\footnote{
J.~A.~Ballin et al.,
\emph{Monolithic Active Pixel Sensors (MAPS) in a quadruple well
technology for nearly 100\% fill factor and full CMOS pixels},
\emph{Sensors} {\bf 8} (2008) 5336.
}
shown in
fig.~\ref{fig:tpac},
is a study sensor to investigate aspects of digital 
electromagnetic calorimetry.
It was fabricated using the 0.18\,$\mu$m ``INMAPS'' CMOS process, which has 
enhanced features beyond standard CMOS. Specifically, INMAPS includes
deep P-well to prevent signal absorption in circuit N-wells, hence
allowing use of full CMOS (NMOS and PMOS) in-pixel. It also allows
the use of high-resistivity silicon in the epitaxial layer for faster signal 
collection.

The TPAC V1.2 senor has a 50\,$\mu$m pixel pitch on a 1\,cm$^2$ sensor,
giving a $168 \times 168$ pixel array, with 28k pixels total.
A total of four variants of sensors were fabricated, with and without INMAPS
enhancements, namely;
standard CMOS,
INMAPS deep P-well, and
INMAPS deep P-well plus high-resistivity epitaxial layer, with standard (12\,$\mu$m)
and thicker (18\,$\mu$m) layer depth.

\section{CERN and DESY beam tests and results}
All four variants 
of TPAC V1.2 sensors were tested in beam at CERN (August 2009) and DESY
(March 2010), using 120\,GeV pion beams at CERN and
1-5\,GeV electron beams at DESY. A stack of six sensors was exposed to
the beams.
%
Tracks were formed from hits in combinations of sensors and projected
to each layer to measure the probability of a pixel hit as a function of
distance from the track, as shown in fig.~\ref{fig:eff}.
The MIP efficiency was then determined by fitting this distribution,
%to a flat top function, convoluted with a Gaussian to allow 
allowing
for track resolution.
%
\begin{figure}[h]
\begin{center}
\begin{picture}(0,140)
%\put(-200,-20){\includegraphics[width=0.40\textwidth]{Sensor29Eff.png}}
\put(-230,0){\includegraphics[height=140pt]{Sensor29Eff.png}}
%\put(50,-10){\includegraphics[width=0.45\textwidth]{SensorSummaryVsElectron.png}}
\put(-10,-20){\includegraphics[height=180pt]{SensorSummaryVsElectron.png}}
\end{picture}
%\includegraphics[width=0.40\textwidth]{Sensor29Eff.png}
%\hskip 2cm
%\includegraphics[width=0.45\textwidth]{SensorSummaryVsElectron.png}
\end{center}
\caption{Left: Typical distribution for the
probability of a hit as a function of position
relative to the track projection. % for a threshold of 400 electrons.
Right: MIP efficiency as a function of threshold,
for all four sensor variants.}
\label{fig:eff}
\end{figure}

The efficiency was found as a function of the digital threshold.
A MIP leaves an average signal of 1300 electrons in a 12\,$\mu$m 
epitaxial layer
and, due to charge spread, at most half of this is absorbed by any
single pixel. The threshold was varied between 100 and 500 electrons,
which are typical values needed for a DECAL.

The results of this analysis are shown in fig.~\ref{fig:eff}.
The standard CMOS sensors have low efficiency at all thresholds, as expected
due to use of in-pixel PMOS transistors.
The deep P-well reduces N-well signal absorption and so raises the
efficiency very significantly (to nearly 100\% for low thresholds).
Adding the high-resistivity epitaxial layer makes further improvements with
the resulting efficiency being close to 100\% across most of the threshold 
range.

\section{Conclusions}
Very significant improvement in efficiency have been demonstrated 
using INMAPS-enhanced features compared to standard CMOS process.
This allows the use of in-pixel PMOS components, enabling sophisticated
processing per pixel, and shows a complex DECAL sensor is feasible.
%Data were also taken with a tungsten converter
%within the sensor stack and these should allow a measurement of the
%core shower density at high granularity. This will allow a realistic
%estimate of the expected resolution of a digital electromagnetic
%calorimeter.

\end{document}


\begin{thebibliography}{99}
\bibitem{ref:ilc}
J.~Brau, Y.~Okada and N.~Walker (eds.),
\emph{International Linear Collider Reference Design Report}, (2007),
\href{http://www.linearcollider.org/rdr}
{\tt http://www.linearcollider.org/rdr}.

\bibitem{ref:sid}
\emph{SiD Detector Concept},
\href{http://silicondetector.org/}
{\tt http://silicondetector.org/}.

\bibitem{ref:ild}
\emph{ILD Detector Concept},
\href{http://www.ilcild.org/}
{\tt http://www.ilcild.org/}.

\bibitem{ref:calice}
\emph{CALICE Collaboration},
\href{https://twiki.cern.ch/twiki/bin/view/CALICE/WebHome}
{\tt https://twiki.cern.ch/twiki/bin/view/CALICE/WebHome}.

\bibitem{ref:tpac}
J.~A.~Ballin et al.,
\emph{Monolithic Active Pixel Sensors (MAPS) in a quadruple well
technology for nearly 100\% fill factor and full CMOS pixels},
\emph{Sensors} {\bf 8} (2008) 5336.

\end{thebibliography}

\end{document}
