Chemistry Reference
In-Depth Information
Phase boundary
φ(
z
)
Wall
Plasma
Presheath
Sheath
φ
pl
Δφ
Bohm
z
=0
z=s
z
φ(0) = φ
0
= 0
Δφ
sh
~λ
De
~λ
+
λ
De
n
-
=
n
e
=
n
pl
n
+
~
n
e
n
+
>
n
e
φ
s
FIGURE 3.27
Qualitative behavior of the electric potential for the transition region from the
bulk plasma over the presheath and space charge sheath to the phase boundary of condensed
matter.
The resulting self-consistent electric field of the space charges determines the
charge carrier transport to the surface.
Taking additionally into account no collisions and in the sheath (λ
+
s
) and
cold plasma ions, the transport of ions can be simplified described by use of
z
as the
distance normally toward the surface and the boundary condition for the potential
ϕ
0 at the sheath edge. The equations for continuity of the ion flux and
conservation of the ion energy in the space charge sheath are given by (3.198) and
(3.199), respectively.
(
z
=
0
)
=
n
+
(
z
)
·
v
+
(
z
)
=
n
+
(
0
)
·
v
+
(
0
)
+
const
.,
(3.198)
1
2
m
+
·
1
2
m
+
·
v
2
+
(
)
=
v
2
+
(
)
−
·
(
)
(
>
)<
z
0
e
ϕ
z
ϕ
z
0
0.
(3.199)
The combination of both equations provides the positive ion density
n
+
(
z
)
inside the
sheath
1
−
1
/
2
2
e
·
ϕ
(
z
)
n
+
(
z
)
=
n
+
(
0
)
·
−
.
(3.200)
m
+
·
v
2
+
(
0
)
The corresponding electron density in the sheath region is described by the Boltzmann
distribution in the repulsive sheath potential.
exp
e
.
·
ϕ
(
z
)
n
e
(
z
)
=
n
e
(
0
)
·
(3.201)
k
B
·
T
e
