Chemistry Reference
In-Depth Information
The scattering cross sections derived from (9.79) or (9.86) are only as good as the
optical potential,
V
opt
, the potential energy surfaces
V
0
(
R
)
and
V
d
(
R
)
, and the coupling
function
V
d
k
(
. These quantities have to be obtained from separate calculations,
ideally using ab initio techniques of molecular structure theory, or directly from
experiments. But even then, the cross sections forming the resonance model are
semiempirical in the sense that a priori assumptions about the relevance or irrelevance
of molecular ion and target states have to be made from the very beginning. This
weakness of the model, however, also leads to its strength: Technically tractable
equations with an intuitive physical interpretation, which, in the local approximation,
can be even solved analytically with semiclassical techniques [86-88].
R
)
9.2.2 T
YPICAL
P
ROCESSES
Now representative elementary processes are discussed in more detail, focusing,
in particular, on reactive and inelastic collisions, which change the internal energy
and composition of the scattering fragments. Elastic scattering between the various
species is not explicitly included although the associated cross sections are usually
much larger than the cross sections for inelastic and reactive collisions combined.
But they only randomize the directed motion of the electrons in the electric field.
The thereby induced changes of the electron energy distribution function affects the
plasma chemistry only indirectly, as far as an increase of energy in the electronic
subsystem makes certain collisions more probable than others.
9.2.2.1 Production of Ions
The main production processes for ions in a molecular, electronegative gas discharge
are electron impact ionization and dissociative electron attachment. Both processes
share the same compound state,
AB
−
, but the former leads to positive molecular
ions whereas the latter to negative atomic ions. Impact ionization is additionally also
the main source for electrons that, depending on their energy, trigger a multitude of
excitation and dissociation collisions.
Electron impact ionization
is similar to electronic excitation (see the following
text), except that the excited state belongs to the two-electron continuum. In the
notation of the previous subsection, the differential cross section is thus proportional
to the modulus of the reaction amplitude squared,
(
+
)
α
k
d
σ
I
α
→
β
∼|
β
k
1
k
2
|
V
|
|
2
d
1
d
2
dE
2
,
(9.87)
where
1
is the solid angle associated with
k
1
, the momentum of the primary electron
2
is the solid angle associated with
k
2
, the momentum of the secondary electron
E
2
is the energy of the secondary electron
φ
AB
+
β
The exit channel state,
, describes the internal state of the
positive ion and the 6D relative motion between the two electrons and the ion, which
is controlled by
V
, that is, the Coulomb interaction of the primary and secondary
electron with each other and with the positive ion. The entrance channel of the set
|
β
k
1
k
2
=|
ψ
k
1
k
2
