Chemistry Reference
In-Depth Information
4. Hydrogenation can return state
d
to state
c
or, for temperatures above
∼
400 K, the radical can de-excite by split-off of the neighboring methyl
group and return the carbon atoms involved to their initial graphitic state
a
k
x
exp
−
,
d
[
CH
sp
x
]
E
x
kT
−
=[
CH
sp
x
]
(8.64)
dt
where
k
x
=
10
13
s
−
1
is the frequency factor and
E
x
=
1.604 eV is the
activation energy for release of methyl group.
5. For graphite temperatures in excess of
1100 K, thermal annealing can
return state
c
to state
a
via elimination of some of the ion-induced damage
accumulated in the implantation zone
∼
k
an
exp
−
,
d
[
CH
sp
3
]
E
an
kT
CH
sp
3
−
=[
]
(8.65)
dt
where
k
an
=
10
13
s
−
1
is the frequency factor
E
an
=
2.42 eV is the activation energy for the annealing
Thus, at low temperatures, exposure of the film to thermal hydrogen atoms results
in the conversion of carbon from the
sp
2
to the
sp
3
hybridization state with some
fraction of radical centers, determined by the ratio of σ
D
/
σ
H
. At higher temperatures
(400-650 K), an equilibrium balance between the supply of
sp
x
radical carbon centers
from hydrogenation and abstraction and their loss through thermal decomposition due
to methyl and hydrogen split-off is established, leading to measurable erosion rates.
At even higher temperatures, however, the rapid decomposition of the radical states
by H-atom split-off prevents significant hydrogenation to
sp
3
hybridization states.
This, in turn, means that there is little or no abstraction occurring, and if so, there
is no significant production of carbon in the radical carbon state. Thus, chemical
erosion is suppressed at higher temperatures.
The steady-state solution to the aforementioned set of differential equations
leads to a very weak dependence in
Y
m
(maximum erosion yield) and a very strong
dependence in
T
m
(temperature at which the yield is maximum) on the flux density φ.
Such dependencies are not observed in experiments. Roth and García-Rosales [299]
proposed that since the absolute concentration of carbon in the
sp
3
hybridization state
with attached methyl groups is unknown, they use
k
x
and
k
−
H
as fitting parameters
adjustable to all the available experimental data in the relevant energy and temperature
ranges, taking into account the flux dependence of
Y
m
and
T
m
. The formula resulting
from this fitting procedure is
0.033exp
−
1.7 eV
kT
Y
therm
=[
CH
sp
3
]
exp
−
1.7 eV
kT
.
(8.66)
2
×
10
−
32
φ
+
