Chemistry Reference
In-Depth Information
If a Maxwellian EEDF occurs, then it follows from (6.1)
i
e
0
exp
V
V
e
,
i
e
,
ret
(
V
)
=
V
≤
V
s
(6.2)
where
S
p
e
0
N
e
e
0
V
e
2π
m
e
1
/
2
i
e
0
=
(6.3)
is the thermal electron current, that is, the random electron current at a Maxwellian
EEDF.
V
e
is the electron temperature in voltage units:
V
e
=
kT
e
/
e
0
(
k
: Boltzmann
constant,
T
e
: electron temperature).
In case of a Maxwellian EEDF the following evaluation of the probe characteristic
has to be made:
1. Determination of the plasma potential from the inflection point, that is, from
the maximum value of the first derivative or from the zero cross of the second
derivative of the probe characteristic:
V
s
=
.
2. After extracting the electron retarding current from the total probe current
i
e
,
ret
(
V
(
i
max
)
=
V
(
i
=
0
)
)
=
(
)
−
i
+
,
sat
(
)
<
V
s
[25,26] the electron temperature
is obtained from the slope of the logarithmic electron retarding current
ln
V
i
V
V
for
V
V
s
, see Equation 6.2.
3. The electron density
N
e
is obtained from (6.3) with
i
e
0
=
(
i
e
,
ret
(
V
))
for
V
<
. The positive
ion density
n
+
follows from the quasi neutrality of the plasma:
n
+
=
i
(
V
)
N
e
.
6.1.3 P
ROBE
M
EASUREMENTS ON
M
ORE
C
OMPLICATE
C
ONDITIONS
6.1.3.1 Plasmas with Isotropic Non-Maxwellian EEDF
A non-Maxwellian EEDF is indicated by the fact that the logarithmic electron
retarding current is not a straight line. Then the EEDF is obtained by the twofold
differentiation of (6.1) with respect to the probe potential
V
(
U
=
V
s
−
≤
V
,
V
V
s
)
[1,27], see also [4,24]
2
3
/
2
m
1
/
2
e
e
3
/
0
N
e
S
p
U
1
/
2
d
2
i
e
,
ret
(
V
)
F
(
U
)
=
.
(6.4)
dV
2
Using the normalization
F
(
U
)
dU
=
1 the electron density and the mean electron
e
0
UF
energy
=
(
U
)
dU
follow from (6.4) as
V
s
2
3
/
2
m
1
/
2
e
e
3
/
0
S
p
N
e
=
(
V
s
−
V
)
1
/
2
i
e
,
ret
(
V
)
dV
,
(6.5)
−∞
e
0
V
s
−∞
(
V
s
−
V
)
3
/
2
i
e
,
ret
(
V
)
dV
=
.
(6.6)
V
s
−∞
(
V
s
−
V
)
1
/
2
i
e
,
ret
(
V
)
dV
