Environmental Engineering Reference
In-Depth Information
the
p
-type and
n
-type semiconductor layers, respectively. The external circuit that receives the
electrical power generated by the cell is connected to these electrodes.
The
n
-type and
p
-type semiconductor materials consist of a pure semiconductor, such as
silicon, doped with a small amount of another element. In the
n
-type layer, silicon is doped with P
or As, elements that readily give up an electron from the outer shell and are thereby called
donors
.
In the
p
-type layer, silicon is doped with B or Ga, which accept an electron into their outer shell
and are called
receptors
. The mobile electrons in the
n
-type layer and the mobile “holes” in the
p
-type layer provide charge carriers that permit an electric current to flow through the cell. At the
junction of the two layers, there exists an electric potential difference between them required to
maintain thermodynamic equilibrium between the charge carriers in either layer.
When sunlight falls upon the cell, some photons penetrate to the region of the interface and can
create there an electron-hole pair, provided that the photon energy equals or exceeds the gap energy
E
g
needed to move an electron from the valence band to the conduction band; that is, provided
that the wavelength
E
g
. The electron and hole then move to the negative and
positive electrodes respectively and provide a current that moves through the external circuit from
the positive to the negative electrodes with an accompanying electric potential drop, both sustained
by the flow of photons into the cell.
In these processes only a fraction of the solar energy flux is utilized to create electrical power
to feed into the external circuit. Long-wavelength photons
λ
is less than
hc
/
have insufficient energy
to create an electron-hole pair, so their absorption merely heats the cell. Short-wavelength photons
(λ <
(λ >
hc
/
E
g
)
appearing as heating, not
electrical power. Typically, only about half of the solar irradiance is available to produce electrical
power. Of this amount, only a fraction eventually results in electric power flowing to the external
circuit because of various additional internal losses in the cell.
When exposed to sunlight, a photovoltaic cell generates electric current and a cell potential
difference, depending upon the solar irradiance level and the electrical characteristics of the load in
the external circuit. In the limit where the external circuit is not closed, no current can flow but an
open-circuit voltage
V
oc
is generated that increases with solar irradiance, but not proportionately
so, as sketched in Figure 7.14(a). At the opposite limit of an external short circuit, where the cell
voltage is zero, a short-circuit current (current density
j
ss
A/m
2
) flows through the cell in an amount
proportional to the solar irradiance [see Figure 7.14(a)]. In both these extremes, no electrical power
is generated because either the current or voltage is zero. For intermediate cases where the cell
delivers electrical power to a load, the cell voltage and current density,
V
and
j
, are each less than
the limiting values of
V
oc
and
j
ss
. For a given value of the irradiance, the relationship between
V
and
j
, sketched in Figure 7.14(b), depends upon the electrical characteristics of the load. The
power output is the product
Vj
, which reaches a maximum
hc
/
E
g
)
have more energy than needed, with the excess
(
hc
/λ
−
E
g
)
)
max
at a point intermediate between
the open- and short-circuit conditions. The maximum power per unit area that the cell can deliver,
(
(
Vj
Vj
)
max
, is generally about 60-80% of the product
V
oc
j
ss
.
The efficiency
η
of a photovoltaic cell is the ratio of the electrical power generated per unit
area
(
Vj
)
to the solar irradiance
(
I
)
impinging on the cell surface:
Vj
I
η
≡
(7.9)
The efficiency increases with increasing irradiance and, for any level of irradiance, is a maximum
at the maximum of output power. Photovoltaic cell efficiencies are rated for a solar irradiance of
