Physics and Engineering of Radiation Detection

3.2. Diffusion and Drift of Charges in Gases 155

For a gas mixture, the effective mobility can be computed from the so called
Blanc’s law
1
μ+

=

∑n

j=1

cj

μij+

, (3.2.9)

wherenis the number of gas types in the mixture,μij+is the mobility of ioniin gas
jandcjis the volume concentration of gasjin the mixture.
The drift velocity of ions is roughly two to three orders of magnitude lower than
that of electrons. The slow movement of ions causes problems of space charge
accumulation, which decreases the effective electric field experienced by the charges
decreases. The resulting slower movement of ions has the potential of increasing the
space charge and decreasing the pulse height at the readout electrode. This and
other signal deterioration effects will be discussed later in the Chapter.

B.2 DriftofElectrons........................

If a constant electric field is applied between the electrodes, the electrons, owing to
their small mass, are rapidly accelerated between collisions and thus gain energy.
The energy that these electrons lose through collisions with gas molecules is not
very large (again because of their small mass). Because of these collisions their
mean energy increases and consequently the energy distribution can no longer be
described by a Maxwellian distribution.
Along the electric field lines, the electrons drift with velocityvdwhich is usually
an order of magnitude smaller than the velocity of thermal motionve. However the
magnitude of drift velocity depends on the applied electric field and finds its limits
at the breakdown in the gas. The approximate dependence of drift velocity on the
electric field E is given by (33)

vd=

2 eElmt

3 mev ̄e

, (3.2.10)

wherelmtis the mean momentum transfer path of electrons. Using theory of elec-
tron transport in gases, more precise expressions for drift velocity and other related
parameters have been obtained and reported by several authors (see (39) and refer-
ences therein).
In early days of gaseous detector developments, a number of experimental studies
were carried out to determine the drift velocities of electrons in the usual gases used
in radiation detection. At that time the availability of computing power was a
bottleneck in numerically solving complex transport equations needed to determine
the drift velocities and therefore resort was made to experimental studies. Although
we now have the capability to perform such computations, the published results of
earlier experimental studies are still extensively used in modern detectors.
Fig.3.2.1 shows the variation of electron drift velocity in methane, ethane, and
ethylene with respect to the applied electric field. It is apparent that only in the
low field region, the drift velocity increases with the energy. Beyond a certain value
of the electric field that depends on the type of gas, the velocity either decreases or
stays constant. As evident from figures 3.2.2 and 3.2.3, this behavior is typical of
gases that are commonly used in radiation detectors.
An important result that can be deduced from Fig.3.2.2 is the non-negligible
dependence of electron drift velocity on the pressure of the gas. This, of course, can