\documentstyle[times,pramana,epsf,floats]{ias}
\begin{document}
\mark{{An Electromagnetic Calorimeter for the Silicon Detector (SiD) Concept}{J.E. Brau et al.}}
\title{An Electromagnetic Calorimeter \\
for the Silicon Detector (SiD) Concept}

\author{J.E. Brau, R.E. Frey, D. Strom}
\address{University of Oregon, Eugene, OR 97403-1274 USA}
\author{M. Breidenbach, D. Freytag, N. Graf, G. Haller, R. Herbst, J. Jaros, T. Nelsen}
\address{Stanford Linear Accelerator Center, Menlo Park, CA 94025 USA}
\author{V. Radeka}
\address{Brookhaven National Laboratory, Upton, NY 11973 USA}
\author{B. Holbook, R. Lander, M Tripathi}
\address{University of California, Davis, CA 95616 USA}
\author{Y. Karyotakis}
\address{Laboratoire d'Annecy�-le�-Vieux de Physique des Particules,  Annecy-�le-�Vieux, CEDEX, FRANCE
}
\keywords{calorimetry, ILC, Linear Collider, high energy physics}
\pacs{2.0}
\abstract{A silicon-tungsten calorimeter for SiD 
at the International Linear Collider is under development.  Recent progress is summarized.
}

\maketitle
\section{Introduction}

To complement LHC
capabilities, ILC detectors must reconstruct hadronic final states, 
including reasonable separability
of $W\rightarrow${\em jets} from $Z\rightarrow${\em jets}.
The LDC and SiD full detector concept designs include silicon-tungsten (Si-W) 
electromagnetic calorimeters (ECal) for particle flow reconstruction 
of jets at the ILC.
With high density and segmentation, they are critical to the physics goal
jet energy 
resolution of $\approx 30\%/\sqrt{E_{\rm jet}}$.

The few mm segmentation possible with a Si-W ECal provides outstanding 
reconstruction and isolation of individual photons. 
At the same time, good electromagnetic energy resolution
is achievable --- $\approx 15\%/\sqrt{E}$. 
Also, excellent lepton reconstruction results from this ``imaging'' calorimeter,
crucial for many new physics signatures. 
For more on the advantages of the Si-W approach see References 
\cite{ref:brau,ref:brient,ref:calor2004,ref:paris,ref:rome}

An outstanding 
technical issue is integration of silicon detectors with readout 
electronics.  With about 50 million detector pixels, 
a solution to the integration issue and the cost of the silicon detectors 
will likely determine viability. 
We proposed\cite{ref:mibtalk,ref:reftalk} a possible integration solution
which naturally allows high transverse segmentation (currently $3.5$ mm)
and a small readout gap (currently 1 mm), maintaining a small Moliere radius.
In the SiD application, this design includes thirty longitudinal sampling
layers, twenty of thickness $5/7\>X_0$, followed by ten
of $10/7\>X_0$. 

The silicon detectors
dominate the cost of our design, so we 
use simple sensor designs to control cost.
The small Moliere radius allows effectively better separability at a reduced ECal
radius, also reducing costs, since other elements of the overall detector are then smaller.
%We have studied various
%options for longitudinal segmentation to provide optimization between
%EM resolution, shower containment, and cost. 
%(In our design, the silicon cost depends
%to first order only on the number of longitudinal layers; transverse segmentation
%is a minor element of cost for granularity of a few mm or larger.)

During the past year we have made important progress. The readout chip  
(KPiX) design was completed and sent to industry, for three prototypes cycles.
The prototype functions, albeit with some issues.
We have made progress characterizing prototype silicon detectors and developing 
a novel readout cable concept for
the thin gap. The critical bump
bonding is being planned for prototypes. 
This progress gives us confidence in the design and we plan
to demonstrate the detector concept with prototypes in an electron test beam, 
and develop a full-depth ECal module, 
incorporating features needed for a realistic ILC detector. This module could be part 
of an international test beam study. 
While we focus on an implementation of our approach for the SiD design, the
ideas and R\&D are applicable to other Si-W ECal designs, notably LDC. 

\section{Overview of Gap Design}

The thrust of our project is to integrate pixels on a large, commercially feasible 
silicon wafer, with the readout electronics, including digitization, contained in a 
single chip, bump bonded to the wafer. 
Pixel size of 12 mm$^2$ (motivated by PFA requirements for 
photon isolation) 
gives $N\approx 10^3$ pixels per 6-inch wafer. The 
beam-crossing duty cycle ($\sim 10^{-3}$) permits heat reduction with power cycling. Our
design has several important features:
(i.) electronics channel count effectively reduced by a factor $N=1024$,
ii.) transverse segmentation down to a few mm naturally accommodated,
(iii.) cost, to first order, independent of the transverse segmentation, and
(iv.) small readout gaps ($\sim$1 mm, Figure \ref{fig:gap}), maintaining a small Moliere radius.
%
%\begin{enumerate}
%\item The electronics channel count is effectively reduced by a factor $N=1024$.
%\item A transverse segmentation down to a few mm can be naturally accommodated.
%\item	The cost, to first order, will be independent of the transverse segmentation.
%\item	Small readout gaps ($\sim$1 mm), maintaining a small Moliere radius.
%\end{enumerate}
%
The first property is necessary for a realistic highly-segmented ECal. 
The electronics is then a relatively small fraction of the ECal cost. The third 
creates flexibility to optimize for physics goals. The 
fourth optimizes the physics capability and reduces cost.





%Our R\&D collaboration consists of the following main elements:
%\begin{itemize}
%\item The silicon detectors, led by the Oregon group. A one-wafer wide, 
%full-depth module has 30 layers in the baseline configuration.
%\item The (kapton) readout cables, led by the Davis group. This development requires
%both prototyping and fabrication.
%\item The readout chips must be bump bonded to the silicon detectors. This procedure
%is to be carried out at the Davis facility. 
%\item The readout ASIC chips, led by the SLAC group. BNL is also contributing to this effort.
%\item The tungsten. We have in hand what we need for the test module. For the
%full ECal, we plan 1 m long plates. We have identified at least one vendor who
%can provide according to our need. Annecy and SLAC will lead this effort.
%\item The mechanical design for the test module and for the real ECal are led by SLAC and
%Annecy.
%\end{itemize}




\section{KPiX Readout Chip}

The most significant development for our project has been completion of the
design of the KPiX readout chip and the
fabrication of the first rounds of prototype chips. 
A recent discussion of the KPiX functionality can be found in Ref.~\cite{ref:LCWS05mib}. 

\begin{figure}[htbp]
\epsfxsize=10cm
\centerline{\epsfbox{gap4.eps}}
\caption{Schematic of the readout gap. With power cycling
    of the readout chip, the heat load of the KPiX readout chip 
    can be handled by passive conduction through the tungsten.}
\label{fig:gap}
\end{figure}


\section{Silicon Sensor Properties}

\noindent
In the past year we continued measurements on 6 inch Hamamatsu
prototypes with an emphasis on parameters relevant to 
use of the sensors with the electronics design.  
The most important measurements in this 
regard are stray capacitance and
leakage  current.  We have also investigated the use of 
a radioactive source for an absolute calibration.
The results here are an update of our presentation\cite{ref:LCWS05strom}
at LCWS05.

\subsection{Pixel Capacitance and Trace Resistance}

In most cases the noise of a pixel charge measurement
is directly proportional to the total capacitance
input to the amplifier,  dominated by
the stray capacitance of traces
connecting pixels to the bump-bonding array.
Our Hamamatsu detectors have oxide metal layers 
about 0.9\,$\mu$m thick, and
6\,$\mu$m thick traces, giving a theoretical capacitance 
of approximately 3.1\,pF$/$cm.
%~\cite{bib:handbuch}.  
The total stray
capacitance of a given pixel has two contributions,  one
from the capacitance of the traces connecting
the pixel to the bump-bonding array, and a second due to
traces from other pixels which cross the given pixel. 
These are compensating 
effects, leading to very similar values for the stray capacitances.

A small fraction of the pixels have a very large number of crossing traces, resulting
in capacitances of somewhat more than 100\,pF.  In a future version
of the sensors we plan to reduce the larger stray capacitances
by narrowing the 
traces in the vicinity of the bump-bonding array.
In Figure~\ref{fig:legosum-model} the measured capacitances are
shown for a large number of pixels in one quadrant for the
Hamamatsu detector, as well as the expected 
capacitance for a future version of the detector with 1024 pixels
and slightly smaller pixels.


\begin{figure}[t]
\parbox{4.2cm}{
\includegraphics[width=46mm]{legosum.eps}
}
%\parbox{0.05cm}{~}
\parbox{4.2cm}{
\includegraphics[width=46mm]{cguess3dsum.eps}}
%\parbox{0.05cm}{~}
\parbox{4.1cm}{
\includegraphics[height=46mm]{peakvscap.eps}}

\caption{Summary of capacitance measurements as a function of pixel position on 
the detector.  
Figure on left is current measurements, 
where the high capacitance of pixels at small row number is due to
large number of traces in that region.  Center figure is the expected 
capacitance in a 1024 pixel verison of the sensor.
Figure on right is the measured position of $^{241}$Am peak signal versus total pixel capacitance.} 
%\caption{Expected capacitance in a 1024 pixel version of the
%silicon sensors with no change in pixel width from
%the current version.  The current version of these detectors have
%757 pixels and 6~$\mu$m wide traces.}
\label{fig:legosum-model} 
\end{figure}

Another important property of the detectors is trace series resistance ($R_s$),
with a  
noise contribution 
proportional to  $C_{tot}\sqrt{R_s}$, where $C_{tot}$ is the total
input capacitance.
It is desirable to keep this noise term 
comparable to  the input FET noise, or
$R_s \sim 300\,\Omega$.
We measure
a trace resistance of $57\pm 2 \Omega/\mbox{cm}$.
For the longest traces ($\sim$ 10\,cm)  the measured value implies 
a maximum resistance of $\sim 600$\,$\Omega$.



\subsection{Leakage Current}

Leakage current (typically a few nA$/$cm$^2$)
 can add an additional term to the electronic noise that
grows with shaping time.   
Leakage current was measured to be $<$2\,nA/pixel for the interior of
the detector. 
The neighboring pixels 
and the guard ring were left ``floating'' .
For pixels on the edge of the detector, with 
the guard ring floating, the
leakage current was less than 10\,nA/pixel.
We expect the noise contribution for leakage current to be
minimal, $\sim$250 electrons.


\subsection{Calibration}

Silicon calorimeters are quite stable.  
Since the largest change in response is due to
the electronics, it is designed
with an internal calibration system.  This internal
calibration should limit the spread within a chip to
$\sim 1\%$.   Chip-to-chip variations could be larger.
Each sensor might be calibrated after the readout chip
has been bump bonded with  60\,keV photons from 
 $^{241}$Am.  Fully contained deposition
gives a signal of approximately 16,000 electrons,
somewhat less than the MIP signal, but well above our noise.
The calibration must be
done before the detector assemblies are placed between the tungsten
sheets.  

To demonstrate this technique we show the measurements of the
$^{241}$Am photon peak versus pixel capacitance in the right plot of
%Figure~\ref{fig:peakvscap}.
Figure~\ref{fig:legosum-model}.
The peak shifts lower at larger capacitance 
because of the finite input capacitance of laboratory electronics.  
The signal-to-noise for the
 $^{241}$Am peak will be about 8 in the final system, which will broaden the peak
 considerably.  The charge measurement will be
 relative to an external bunch clock rather than to 
 the time of arrival of the photon in the laboratory.
 This adds an additional smearing of the observed spectrum
 of less than 5\%.  
 %
 %  This assumes a sample time of 2 microseconds and shaping time
 %  of 1 microsecond and 300 ns bunch clock, ie
 %     (1 - e^{-1.7}) - (1 - e^{-2.0})  = 0.047
 Thus we expect a total width for the
 $^{241}$Am  60keV signal of approximately 15\%.

Since the readout ADC
 will have  a least significant bit approximately equal to the expected 
 noise it should be possible 
 to calibrate each pixel to 1\% with approximately 250 detected 
 photons.   Relating
 the charge scale at 8 ADC counts to that at full scale readout,
 will require care in the design.
 Somewhat easier, but still difficult, will be a wafer-to-wafer 
 calibration at the sub-percent level,  averaging over 
 1024 pixels/wafer.  
%
%
%


%\begin{figure}[htb]
%\begin{center}
%\includegraphics[height=50mm]{peakvscap.eps}
%\end{center}
%\caption{Measured position of peak versus total pixel capacitance.
%\label{fig:peakvscap}}
%\end{figure}

\subsection{Cross Talk}
The cross talk introduced capacitive couplings
between the channels has been found to be at or below
the 1\% level.  The cross talk is a function of both the 
capacitive coupling and the properties of the readout electronics. 
While we have a qualitative understanding of the cross talk, we are
continuing to work on a quantitative model and on incorporating the
properties of the KPiX electronics into the model.  


\begin{acknowledgments}
The authors wish to thank the organizers for hosting a
well run workshop.  
We also wish to thank Mary Robinson for assisting in making some of the measurements 
reported here.  This work is supported by the Office of Science of the U.S.  Department of Energy.
\end{acknowledgments}


\bigskip
\begin{thebibliography}{5}

\bibitem{ref:brau} J. Brau, A. Arodzero, D. Strom, 
%``Calorimetry for the NLC Detector,'' in 
{\it Proc. of the 1996 DPF/DPB Summer Study on New Directions in High-energy Physics}, 
SLAC-PUB-7693.

\bibitem{ref:brient} H.~Videau and J.~C.~Brient,

%``A Si-W calorimeter for linear collider physics,''
%\href{http://www.slac.stanford.edu/spires/find/hep/www?irn=5653983}{SPIRES entry}

in 
{\it Proc. 10th International Conference on Calorimetry in High Energy Physics (CALOR 2002)}, 
Pasadena, California, 25-30 March 2002, pp. 309-320.

\bibitem{ref:calor2004}
D. Strom, R. Frey, M. Breidenbach, D. Freytag, N. Graf, G. Haller, 
O. Milgrome,         V. Radeka, 
%``Design and development of a dense, fine grained silicon 
%tungsten
calorimeter with integrated electronics,''  
CALOR04 March, 2004, Perugia, Italy.

\bibitem{ref:paris}
R. Frey, D. Strom, M. Breidenbach, D. Freytag, N. Graf, G. Haller, 
O. Milgrome,         V.  Radeka, 
%``Silicon/tungsten ECal for SiD - Status and Progress,''  
LCWS04,April 2004 , Paris, France.

\bibitem{ref:rome} D. Strom,        R. Frey, M. Breidenbach, D. Freytag, N. Graf, G. Haller, 
O. Milgrome,         V. Radeka, 
%``Fine Grained Silicon-Tungsten Calorimetry for a Linear Collider Detector'', 
NSS-MIC November 2004, Rome, ITALY.

\bibitem{ref:mibtalk}
M. Breidenbach, talk at Chicago LC Workshop, Jan. 2002, 
http://LCworkshop.uchicago.edu/; updated at Cornell workshop, July 2003, 
http://www.lns.cornell.edu/LC/workshop/. 

\bibitem{ref:reftalk}
R. Frey, talk and proceedings paper from Calorimeter 2002, Pasadena, CA, March 
2002, documents available at http://3w.hep.caltech.edu/calor02/ ;  
talk presented at Linear Collider Workshop, LCWS2002, Korea, Aug. 28, 2002, 
http://lcws2002.korea.ac.kr/.

\bibitem{ref:LCWS05mib} M. Breidenbach, talk presented
at LCWS, Stanford, CA, March 2005. 

\bibitem{ref:LCWS05strom} David Strom, talk presented
at LCWS, Stanford, CA, March 2005. 

\bibitem{ref:sispecs1} Specification document for first version prototype
silicon detectors (2003):\\
http://www.slac.stanford.edu/xorg/lcd/SiW/documents/SiSpec\_v3.pdf

\end{thebibliography}



\end{document}
