\section{Requirements}
\label{sec:requirements}

The results shown in the previous section
motivate the development of a
sensor which is capable of estimating the
number of charged particles in a shower.
The method considered here is to propose
an ECAL with binary readout, such that each
pixel of the calorimeter gives a yes/no result
to the presence of a charged particle. Any charged
particle gives an average energy deposit which 
has a universal minimum at a particular particle 
velocity and for
normal incidence. Any other speed or incident
angle gives a larger mean deposit, so a threshold
set below the minimum ionising particle (MIP) level,
allowing also for the Landau spread, should be
efficient for detecting all charged particles.

\subsection{EM shower requirements}
To give an accurate estimate, a sensor for counting
charged particles
would
need to have a low probability of two charged
particles crossing the same pixel. The density of
charged particles in the layer at which the density is
a maximum for 100\,GeV EM showers is shown in
figure~\ref{fig:requirements:core} for the example
sampling ECAL used in Section~\ref{sec:introduction}.
The peak value corresponds to 70 charged particles per mm$^2$;
this would therefore require a
pixel size significantly smaller than 0.014\,mm$^2$. 
The sensor discussed
in the rest of this paper has a pixel size of 
0.0025\,mm$^2$, implemented as a square pixel
of size $50 \times 50$\,$\mu$m$^2$.
%
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=6cm]{requirements/density.png}
\caption{\sl 
Maximum density of charged particles per layer
within 100\,GeV EM showers, as a function of the layer
in the shower.
}
\label{fig:requirements:core}
\end{center}
\end{figure}


\subsection{ILC requirements}
As shown above, the pixel size for a binary ECAL need to
be of the order of 50\,$\mu$m. This is two orders of
magnitude smaller than any of the analogue pad ECALs being
considered for the 
ILC~\cite{ref:introduction:sid, ref:introduction:ild} 
and will be more than
sufficient to allow PFA separation of particles. The size 
of the ECALs assumed in the ILC detector 
studies
is large with a total sensor surface area of around 2000\,m$^2$.
For 50\,$\mu$m pixels, this would require a total of around
$10^{12}$ pixels; hence this concept has been labelled the 
``tera-pixel''
ECAL.

The ILC will run with bunch trains, whereby the beams
will collide (a ``bunch crossing'') at a rate of around 200-400\,ns 
but only for a short time, of around 1\,ms (a ``bunch train'').
Each bunch train will therefore contain up to 5000 bunch
crossings. The bunch train rate will be around 5\,Hz,
meaning that there will be 199\,ms with no beam collisions
following each 1\,ms bunch train. Hence, the ILC detectors will
buffer data during the 1\,ms bunch train and then read out
in the 199\,ms of dead time.

The physics interaction rate for producing 
the high energy events of interest
will be low; less than one per bunch 
train~\cite{ref:introduction:ilcphysics}.
There will be
significant levels of background from the ILC machine itself,
as well as low energy physics events. However, with such a
large number of pixels in a binary ECAL, then the overall
data rate from most of the detector
will be dominated by the rate of noise. Assuming
a threshold of around five times the noise, then the noise
rate will be $\sim 10^{-6}$ per pixel per bunch crossing.
This means for the 5000 bunch crossings in a bunch train,
each pixel will have an average of $\sim 0.005$ hits. Hence, the
sensor needs to be able to buffer at least this number of
hits per pixel during the bunch train.

The one area where other sources of hits will not be negligible
will be in the most forward regions, where backgrounds from
the machine will be substantial.
The beam simulation programme 
Guinea Pig~\cite{ref:requirements:guineapig} 
allows such backgrounds to be estimated.
Figure~\ref{fig:requirements:guineapig} shows the expected number
of hits in the endcap region as a function of radius from
the beam line for the ILD detector. The peak at the innermost radius 
corresponds to 150 hits per bunch crossing
at 300\,mm radius, within a 2\,mm band in radius. 
This corresponds to a
total area of 4000\,mm$^2$ and so an average occupancy of 
$10^{-4}$. Hence for the
innermost endcap pixels, the probability of getting a hit in a
bunch train could be as high as 0.5.
%
\begin{figure}[ht!]
\begin{center}
\includegraphics[width=6cm]{requirements/guin.png}
\caption{\sl 
Simulated number of ILC machine background hits per bunch crossing
in the endcap region, as a function of the radius from
the beam line.
}
\label{fig:requirements:guineapig}
\end{center}
\end{figure}

\subsection{Other issues}
An ECAL designed to deliver good PFA performance will also
need to be compact, minimising any gaps between the converter
layers. This keeps the transverse spread of the EM showers
small, measured by the effective Moli\`ere radius, as this
helps separate particles close to each other in jets. Hence,
the sensitive layers have to be as thin as possible
compared to the converter
thicknesses. For example, tungsten has a radiation length 
of $X_0 = 3.5$\,mm. Most ILC ECAL 
designs~\cite{ref:introduction:sid, ref:introduction:ild} 
have only $\sim 0.5X_0$
in each of the first few layers, which therefore 
corresponds to $\sim 2$\,mm of tungsten. Hence, sensitive
detectors based on thin silicon sensors seem a sensible choice.

The compactness requirement also significantly limits the
amount of cooling infrastructure which can be included
between the converter layers. Any pipework will increase
the space, degrading the effective Moli\`ere radius. Hence,
this requires very low power sensors and readout electronics.
The timing structure of the ILC means there are significant
gains to be made by powering off any parts of the sensors
which are not required during the 199\,ms dead period. Even
including this reduction of O(100) in power consumption,
the requirements are tight. For example, one 
design~\cite{ref:introduction:ild} has no active cooling
in the bulk of the ECAL, relying purely on conduction through
the converter material and the electronics PCBs. The target
average power consumption for this design is 1\,$\mu$W/mm$^2$.

A very significant issue with all such calorimeters is
cost. With a sensitive area of 2000\,m$^2$, then the
total cost will be dominated by the silicon detectors
themselves. Hence, there is a strong motivation to reduce
the sensor unit area cost. This pushes for simple sensors
which can be produced through a large number of vendors
and require no low-yield processing features.

%\subsection{The TPAC sensor}
%In this paper, we present results from a test sensor
%which was designed to investigate a binary ECAL
%and to demonstrate the feasibility of this approach.
%A complete ECAL
%for this application would require around 30 layers of
%sensors, covering a total surface of the order of 2000\,m$^2$. Given
%a pixel pitch of the order of 50\,$\mu$m, this corresponds to a total
%number of pixels of the order of $10^{12}$, so this development has
%been named the Tera-Pixel Active Calorimeter (TPAC) sensor.
%This paper reports on results from the first test version of the
%sensor, TPAC1.0.
%
%The sensor is based on a 0.18\,$\mu$m CMOS process,
%which was modified to include a ``deep P-well'' implant.
%This modified process is called INMAPS and is described
%in detail elsewhere~\cite{ref:introduction:inmaps}.
%This protects signal charge from absorption by the
%circuit electronics and so allows a significant amount of
%signal processing and data handling in the 
%pixels.
