\section{Introduction and motivation}
\label{sec:introduction}

In this paper, we present results from a study
of a novel approach
to electromagnetic calorimeters (ECAL).
In this approach, the
readout of the ECAL is binary, meaning that each channel
returns a yes/no result with no further amplitude 
information.

Although the potential applications for a binary ECAL are
wide, the sensor discussed in this paper was designed for
a specific application, namely the International Linear
Collider (ILC)~\cite{ref:introduction:ilc}. 
This is widely assumed to be
the next worldwide particle physics frontier accelerator
and it has a wide and rich physics 
programme~\cite{ref:introduction:ilcphysics1,
ref:introduction:ilcphysics2}.
The work presented in this paper
has been done within the context of the
CALICE Collaboration~\cite{ref:introduction:calice},
which is studying calorimetry for the ILC.

Many of the ILC physics measurements require reconstruction of heavy
particles decaying 
into hadrons. To identify the decaying
particles through the invariant mass of the hadronic jets
requires excellent hadronic jet energy resolution. The
main techniques which should be able to provide this resolution are
based on Particle Flow Algorithms 
(PFA)~\cite{ref:introduction:pfa1,
ref:introduction:pfa2, ref:introduction:pfa3},
which require
very high granularity calorimetry to allow the separation
of the showers into the individual particles in the jet.
For the ECALs, it is widely accepted that a sampling
calorimeter will provide the best PFA performance, due
to having good transverse and longitudinal granularity. The
current state-of-the-art has silicon sensors as the
detecting layers and tungsten as the 
converter and this structure is being
considered by both the major ILC detector
concepts~\cite{ref:introduction:sid, ref:introduction:ild}. 


%\subsection{Electromagnetic shower properties}
An electron, positron or photon interacting in material produces
an electromagnetic (EM) shower containing a large
number of charged particles and photons.
A sampling EM calorimeter (ECAL) measures the charged
particle component of the shower at various positions
in the shower depth by having sensitive layers interspersed
with a dense material which efficiently produces the shower.
The sensitive layers operate
by measuring the
ionisation created by the charged particles in these
layers and normally the shower energy is estimated by
measuring the energy deposited through the ionisation.

In this paper, we present a new technique for a sampling
ECAL, in which an estimate of the number of particles in
the shower is used as the measure of the shower energy,
rather than the energy deposited. Clearly, these
quantities are strong correlated, as each
charged particle in the shower will deposit energy in
the sensitive layer. However, the energy deposited depends
on the speed and angle of the charge particle and also has
fluctuations around the average deposit, as described by
the Landau function~\cite{ref:introduction:landau}.
Hence, it would be expected that
the energy deposited would have a larger spread for any
given shower than the number of particles. 
Therefore, an ECAL which measures the number of particles
would have an intrinsically better resolution.

In the rest of this paper, 
Section~\ref{sec:basic} presents the fundamental properties
of EM showers relevant to the study.
Section~\ref{sec:requirements}
expands on the binary readout ECAL requirements, while
Section~\ref{sec:physics}
gives the expected shower resolution
performance of a binary ECAL.
