development of micro-pattern gaseous detectors – gem - LMU

1.2. Free Charges in Gases 17
involving a constant defined by the gas.
dn = −const n + · n − · dt (1.33)
Certain impurities in the gas volume, as O2, Cl2 or water are able to capture electrons, since they
have outer shells, which are nearly fully occupied ( so-called electron affinity). This effect may keep
electrons from reaching the readout to be detected. For instance, a pollution of 1 % air in Argon
and a drift fields of 500 V/cm leads to a removal of about 33% of the liberated electrons per cm
drift [Saul 77].
1.2.3 Drift of Ions and Electrons
Applying an electric field to the active detector volume leads to acceleration of free charges and gives
rise to drift velocity. The proportional constant between the field E and the mean drift velocity vD of
the charged particle is called mobility µ :
vD = µ · E · p0
p
(1.34)
where p is the gaseous pressure and p0 the standard pressure of 1013 mbar. The mobility of ions is
typically smaller than that of electrons. Explicitly:
cm2 Gas Ion mobility µ V s
Ar Ar + 1.7
CO2 CO + 2 1.09
Ar CO + 2 1.72
Table 1.1: Mobility of ions in Argon and CO2. Argon-ions in CO2 gas are not reported by the literature.
The mobility of electrons is about 100 to 1000 times higher than of ions. The greater mean free path
λ enables the electrons, differently to ions, to gain considerably energy between collisions with the
gas molecules. In an electric field, electrons reach energies of some eV which leads to a de-Broglie
wave length of the size comparable to the atomic diameter. Quantum mechanical effects result in
a cross section σ for the electrons that strongly depends on their kinetic energy and therefore also
depending on the free path λ, since λ ∝ 1/σ. This behavior is sketched in Fig. 1.8 for the cross
section of electrons in Argon as a function of their kinetic energy. The characteristic minimum is
called Ramsauer minimum.
The electron drift in gases is described in [Bieb 08] and [Grup 08] where the drift velocity vD is
approximated in terms of the electric field:
vD ≈
2 ∆Ekin
3 3
· eE
m
· λe
(1.35)
where ∆Ekin is the fraction of energy transferred to the gas molecule during collision with the electron.
For the electric fields used in the GEM detector ( typically 1.0...2.0(kV/cm)) in an Ar/CO2 mixture
in the ration 93/7, the drift velocity is about 4 cm/µs.