Chemistry Reference
In-Depth Information
4
0.8
Plasma potential
V
s
i
0.15
0.6
3
Argon - ICP - discharge
p
= 1 Pa,
P
= 100 W
0.4
2
0.10
i
'
1
0.00
0.2
V
s
- 2 (
V
s
-
V
f
)
i
''
0
-0.10
0.0
Floating potential
V
f
-0.2
-1
-10
0
10
20
30
Titel X-Achse
FIGURE 6.3
Example for a probe characteristic
i
(
V
)
and its first and second derivative.
of a current of attracted positive ions and also a current
i
e
,
ret
of retarded electrons:
i
=
i
e
,
ret
+
i
+
,
sat
. At plasma potential no charge carriers
a
re attracted or repelled by
the probe. Here the random currents
i
e
0,
+
0
=
(
e
0
N
e
,
+
v
e
,
+
S
p
of electrons and ions
flow to the probe (
e
0
: elementary charge,
n
: density,
v
: mean velocity,
S
p
: probe sur-
face). Because of high ion mass and low ion temperature the relation
i
e
0
1
/
4
)
i
+
0
holds
and often
i
+
0
is neglected (cold ion approximation [4,22,23]). At voltages higher
than plasma potential only attracted electrons reach the probe (electron saturation
current). Mostly the second derivative of a correctly measured probe characteristic
has only two extreme values: a minimum and a maximum value near the plasma
potential, see Figure 6.3. An additional maximum value at strongly negative probe
bias may be caused by a group of fast isotropic electrons and an additional maximum
near plasma potential can be caused by negative ions, but in most cases additional
extreme values indicate problems with missing or incomplete rf-compensation or
probe surface contamination (see below).
An isotropic electron velocity distribution function
F
(
v
)
=
4π
v
2
f
(
v
)
occurs often
in good approximation in most regions of a discharge.
F
(
v
)
is normalized to unity
(
F
(
v
)
dv
=
1). An EEDF
F
(
U
)
with
eU
=
(
m
e
/
2
)
v
2
(
m
e
,
v
: mass and velocity of
electrons) may be defined in this case as
F
(
U
)
=
F
(
v
)(
dv
/
dU
)
=
4π
v
2
f
(
v
)(
dv
/
dU
)
.
Thisdefinitionensuresthatalso
F
isnormalizedtounity.Thefollowingexpression
for the electron retarding current
i
e
,
ret
to any non-concave probe may be derived from
a detailed consideration of the orbital motion of the electrons without having to
assume the existence of a sheath region across which the probe to plasma potential
is developed [4,24]
(
U
)
1
dU
,
∞
e
3
/
0
N
e
S
p
2
3
/
2
m
1
/
2
V
s
−
V
U
1
/
2
F
i
e
,
ret
(
V
)
=
(
U
)
−
V
≤
V
s
.
(6.1)
U
e
V
s
−
V
