Chemistry Reference
In-Depth Information
At φ
=
π and for
H
1 it follows for the ion sheath voltage
ϕ
s
k
B
·
e
·¯
9
32
·
ϕ
sh
=−¯
ϕ
s
T
e
=
π
2
·
H
2
(3.258)
and for the sheath thickness
s
max
s
eff
=
5
12
·
z
=
s
max
π
·
H
(3.259)
respectively.
Finally, we obtain with the Bohm current density an expression similar to the
Child-Langmuir law
2
1
/
2
e
m
+
·
ϕ
3
/
2
s
s
max
¯
j
+
=
e
·
n
0
·
v
Bohm
=
C
+
·
ε
0
·
·
(3.260)
w
ith
C
+
=
200
/
243 (in the DC Child-Langmuir law
C
+
=
4
/
9) and
s
max
=
50
s
child
.
In the case of collisional sheath a corresponding formula to (3.243) is derived [36]
/
27
·
2
1
/
2
λ
1
/
2
+
e
m
+
·
ϕ
3
/
2
s
¯
·
j
+
=
e
·
n
0
·
v
Bohm
≈
1.68
·
ε
0
·
·
.
(3.261)
s
5
/
2
max
3.6.3.2 Strongly Asymmetric Capacitively Coupled RF Plasma
In a capacitively coupled, unconfined, and for that reason asymmetrical RF discharge,
a negative self-bias voltage
appears at the powered electrode which is little less
than half the peak-to-peak RF voltage
(
ϕ
sb
)
. Assuming capacitive sheath model
and strong asymmetry, the idealized potentials over the RF cycle is represented in
Figure 3.29.
(
ϕ
pp
)
ϕ
RF
(
t
)
=−
ϕ
SB
+
ϕ
0
·
sin
(
ω
·
t
)
,
(3.262)
1
2
·
(
−
ϕ
pl
(
t
)
=
ϕ
sf
+
ϕ
SB
+
ϕ
0
)
·
[1
+
sin
(
ω
·
t
)
]
(3.263)
with
ϕ
0
.
The negative self-bias potential results from the fact that no net DC current
can flow over one RF cycle due to the capacitive coupling, and that the sur-
face ratio between the powered and grounded electrode is significantly different
(
|
ϕ
SB
|≤
1
/
2
·
ϕ
pp
=
.
The electrons can follow the alternating electric field and leads to a moving
electron edge which modulates the positive space charge region, the sheath potential,
and the thickness, see Figures 3.28 and 3.29. Increasing RF voltage amplitudes mainly
affect the self-bias voltage and sheath properties at the powered electrode. It has only
little influence on the plasma potential in strongly asymmetric RF discharges. As the
result, the self-bias voltage at the powered electrode increases with the applied RF
A
rf
A
grounded
)
