Chemistry Reference
In-Depth Information
3.6.1.4 Plasma Sheath in Front of the Floating Surface
Taking into consideration an electric insulating surface immersed in a quasi-neutral
plasma consisting of cold ions and Maxwellian electrons, the net charge flow will be
zero under steady-state conditions
j
+
,
sf
+
j
e
,
sf
=
0
|
surface
.
(3.219)
ϕ
sh
, see (3.222), is
calculated taking into account the current density for ions
j
+
,
sf
, see (3.220), corre-
sponding to the Bohm current density, and for electrons electrons
j
e
,
sf
, see (3.221).
Thereby, the electron density is reduced in the repulsive potential in the space charge
sheath according to the Boltzmann distribution.
From (3.219) the potential drop over the plasma sheath
exp
k
B
·
1
/
2
1
2
T
e
m
+
j
+
,
sf
=
e
·
n
pl
·
−
·
,
(3.220)
exp
k
B
·
1
/
2
exp
−
.
1
2
T
e
e
·
ϕ
sh
j
e
,
sf
=
e
·
n
pl
·
−
·
·
(3.221)
2
·
π
·
m
e
k
B
·
T
e
is the reduced plasma density at the sheath edge. The
solution for the potential drop over the sheath provides
The term
n
pl
·
exp
(
−
1
/
2
)
ln
m
+
2
k
B
·
k
B
·
1
2
·
T
e
e
·
T
e
ϕ
sh
=
ϕ
0
−
ϕ
sf
=
≈
...
·
3
4
.
(3.222)
·
π
·
m
e
e
Finally, the total potential drop between the plasma potential ϕ
pl
and the floating
surface potential ϕ
sf
<
0 results in
ϕ
pl
−
ϕ
sf
=
ϕ
Bohm
+
ϕ
sh
=
ϕ
pl
−
ϕ
0
+
ϕ
0
−
ϕ
sf
1
ln
,
1
2
·
k
B
·
T
e
e
·
m
=
+
(3.223)
·
·
2
π
m
e
ln
0.43
1
2
·
k
B
·
T
e
e
·
m
m
e
ϕ
pl
−
ϕ
sf
≈
·
≈
4.3
·
10
−
5
·
T
e
[
K
]·
(
6.7
+
ln
(
A
+
[
u
]
))
with
A
+
is the mass number of the positive ion.
For example, the floating surface potential for the electron temperature of 2
·
10
4
K
and argon ion (
u
=
40) amounts to about 9 V negative compared with the plasma
potential.
3.6.2 H
IGH
-V
OLTAGE
P
LASMA
S
HEATHS
The high-voltage plasma sheath is defined for the case of high potential drop between
the plasma and an external or self-biased surface potential characterized by the
condition
e
·|
ϕ
sh
|
k
B
·
T
e
. Two approximations are usually applied to describe
