Environmental Engineering Reference
In-Depth Information
where
P
is the incident light power, and
FF
¼½
eV
oc
=
k
B
T
ln
ð
1
þ
eV
oc
=
k
B
T
Þ=ð
1
þ
eV
oc
=
k
B
T
Þ:
ð
6
:
6
Þ
Looking at these expressions, one canmake a few observations on the ef
ciency. One
must maximize the short-circuit current, which requires optimal absorption of
photons and minimal recombination of the minority carriers before exiting the
junction. One seeks a large open-circuit voltage
V
oc
¼
(
k
B
T
/
e
)ln(1
þ
J
sc
/
J
o
), which
requires, in addition to maximizing
J
sc
,
minimizing the reverse current
1
=
2
1
=
2
J
rev
¼
J
o
¼
e
½
n
p
ð
D
n
=
t
n
Þ
þ
p
n
ð
D
p
=
t
p
Þ
:
ð
3
:
66
Þ
Small reverse current density is promoted by making the thermal
minority
carrier
concentrations small, favored by a low temperature (this is aided by making the
majority
dopings
N
D,A
large) and also by a long recombination lifetime. In practice,
the open-circuit voltage is limited by the built-in voltage
V
B
, because beyond that
voltage the device no longer provides an exponential
I
(
V
) relation in the forward bias
regime. The upper limit of
V
B
is
E
G
/
e
, although, if both sides of the junction are doped
into themetallic regime, the value could be slightly larger than this, given by Equation
3.59. To make an estimate of the optimal
filling factor
behavior, for 300 K and
E
G
¼
1.1 eV for Si, we can take
eV
oc
/
k
B
T
¼
42. This gives FF
[42
ln(43)]/43
¼
[42
0.89. One can see from this that large illumination, that is, con-
centration of the light using mirrors or lenses, is advantageous, to increase the open-
circuit voltage and, hence, the conversion ef
3.76]/43
¼
ciency of the cell.
ciency g approaches 30% for favorable
assumptions, a result that dates to Shockley and Quiesser [63]. These authors also
gave an ultimate ef
ciency of a more general nature, which is quoted as 44%, but is
not as directly applicable to the single-junction solar cell as is the basic ef
ciency g
(Figure 6.2).
These devices work by the photoelectric effect, the release of charge by annihilation
of a quantum of light. Since light photons have nearly zero momentum, the
absorption process favors semiconductors with a direct bandgap, where the electron
and hole have the same momentum. Figure 6.3 shows the absorption coef
cients for
Ge, Si, and GaAs as a function of photon energy. GaAs has the typical direct bandgap
behavior, desirable for a solar cell, while indirect bandgaps for Si and Ge lead to low
optical absorption, especially at energies close to the bandgap value, 1.1 eV for Si.
This means that the thickness of a silicon layer to completely absorb light is
larger than that in direct bandgap semiconductors by the relatively low absorption
constant. Faceting the surface to reduce re
ection and to lengthen the path of the
light within the cell is a means of overcoming this additional cost.
For the single-gap junction, the ef
6.1.1
Silicon Crystalline Cells
The idea of surface texturing and its utility is illustrated in Figure 6.4. It is seen that
the facet makes two re
ections necessary for backscattering of light, so that if the
