Environmental Engineering Reference
In-Depth Information
Figure 3.17 Current
-
voltage characteristics of a silicon solar cell under illumination [41].
If the device is terminated in a load resistor, the power density is
P ¼ JV ¼ J
rev
V½
exp
ðeV=k
B
TÞ
1
J
L
V;
ð
3
:
70
Þ
where the actual
V
will depend on the choice of the load resistance (Figure 3.17).
3.8
Metals and Plasmas
The fundamental properties of the plasma are independent motion of charges of
opposite sign and charge neutrality. Each charge
q
is locally surrounded by its electric
potential
V¼ k
c
q
/
r
, but this potential will be felt by neighboring charges, which are
mobile. Thus, a
shielding property
is inherent to a plasma. If a disturbance of potential,
say,
V
appears, it will alter the local density of electrons to a perturbed value
n
0
¼n
exp
(
eV
/
k
B
T
)
n
(1
þ eV
/
k
B
T
) assuming
eV
is small compared to
k
B
T
. Recalling Equa-
tion 3.64, where we can identify the relevant charge density as
e
(
n
0
n
) and
nd, since
n
0
nneV
/
k
B
T
,
2
ðVÞ¼ne
2
V
=l
D
;
r
=
k
B
Te
o
¼ V
ð
3
:
71
Þ
where
1
=
2
ne
2
l
D
¼ðk
B
Te
o
=
Þ
ð
3
:
71a
Þ
is the Debye length, which is important in plasmas and also in solution chemistry
where ions are mobile and can shield surface potentials, for example.
To solve (3.71) in spherical geometry as surrounding a point charge
q
, one
nds
VðrÞ¼ðk
c
q
=
rÞ
exp
ðr
=l
D
Þ
ð
3
:
71b
Þ
