3 Solar Cells: Basics
47
current carried by these holes is a diffusion current; its current density J p.diff is given
by the equation:
J p.diff = −D p
∂ p(x)
∂ x
,
(3.2)
where D p is the diffusion constant of the holes and p(x) the carrier profile of the
holes.
On the other hand, L p is the minority-carrier diffusion length (of the holes). L p is,
in its turn, given by the expression
L p =
D p × τ p ,
(3.3)
where τ p is the lifetime of the holes.
The minority carrier diffusion length L p governs the carrier transport on the right
side of the device.
p-i-n solar cells: In p-i-n solar cells the transport of the photo-generated carriers is
mainly by drift (and not by diffusion). Thus, p-i-n solar cells are drift-controlled
devices. The transport length that now intervenes is the drift length (for electrons
and holes)
L drift = μ × τ × E,
(3.4)
where μ is the carrier mobility, τ the carrier lifetime and E the electric field.
The link between diffusion and drift is given by the so-called «Einstein relation»:
D = (μkT )/q,
(3.5)
where k is the Boltzmann constant, T the absolute temperature and q the charge of
an electron.
For further details, the reader is referred to Chap. 6, Sect. 6.2.1.
We will now:
Discuss in more detail, whilst using the corresponding equations, the functioning
of a solar cell; the goal here is to look at the main parameters of the solar cell: shortcircuit current density J sc , open-circuit voltage V oc , Fill Factor FF and efficiency η.
We will also give approximate relationships for the dependence of η on temperature
and intensity of the incoming light.
3.4 Solar Cell Characteristics, Equivalent Circuits and Key
Parameters
We have just stated, in Sect. 3.3, that, in general, solar cells are simply semiconductor
diodes, which are exposed to light. We will now look at the behaviour of a diode in
47
current carried by these holes is a diffusion current; its current density J p.diff is given
by the equation:
J p.diff = −D p
∂ p(x)
∂ x
,
(3.2)
where D p is the diffusion constant of the holes and p(x) the carrier profile of the
holes.
On the other hand, L p is the minority-carrier diffusion length (of the holes). L p is,
in its turn, given by the expression
L p =
D p × τ p ,
(3.3)
where τ p is the lifetime of the holes.
The minority carrier diffusion length L p governs the carrier transport on the right
side of the device.
p-i-n solar cells: In p-i-n solar cells the transport of the photo-generated carriers is
mainly by drift (and not by diffusion). Thus, p-i-n solar cells are drift-controlled
devices. The transport length that now intervenes is the drift length (for electrons
and holes)
L drift = μ × τ × E,
(3.4)
where μ is the carrier mobility, τ the carrier lifetime and E the electric field.
The link between diffusion and drift is given by the so-called «Einstein relation»:
D = (μkT )/q,
(3.5)
where k is the Boltzmann constant, T the absolute temperature and q the charge of
an electron.
For further details, the reader is referred to Chap. 6, Sect. 6.2.1.
We will now:
Discuss in more detail, whilst using the corresponding equations, the functioning
of a solar cell; the goal here is to look at the main parameters of the solar cell: shortcircuit current density J sc , open-circuit voltage V oc , Fill Factor FF and efficiency η.
We will also give approximate relationships for the dependence of η on temperature
and intensity of the incoming light.
3.4 Solar Cell Characteristics, Equivalent Circuits and Key
Parameters
We have just stated, in Sect. 3.3, that, in general, solar cells are simply semiconductor
diodes, which are exposed to light. We will now look at the behaviour of a diode in