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

The results shown in the previous section
motivate the development of an ECAL
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.

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.

Implement as CMOS sensor. Epitaxial layer is sensitive
area~\cite{ourstuff}.

\subsection{Pixel size}
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 per event, in the layer at which the density is
a maximum, for 100\,GeV EM showers is shown in
figure~\ref{fig:requirements:core}. This simulation uses
the nominal geometry described 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 is assumed to have 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}

This pixel size 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 order
$10^{12}$ pixels; hence this concept has been labelled the 
``tera-pixel'' ECAL.

\subsection{Noise}
The ILC physics interaction rate for producing 
the high energy events of interest
will be low; less than one per bunch 
train~\cite{ref:introduction:ilcphysics1}.
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
hit rate 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.

Size of typical shower times 30 layers to estimate number
of pixel hits. Use previous plots to give number of particles.

\subsection{Charge diffusion}


\subsection{Dead areas}


\subsection{Sensor assumptions}

Assume: noise per pixel is 50\,eV, charge spread is given by
deep p-well~\cite{ref:physics:inmaps}, the sensor sensitive
layer is 12\,$\mu$m thick and the layer has an average dead
area of 10\%.

These are varied from 25\,eV to 75\,eV, zero charge diffusion
to no deep p-well diffusion, 6\,$\mu$m to 12\,$\mu$m
and 5\% to 15\%, respectively.
