Welcome to the PV online course, in this chapter we will cover how a solar cell works.
In this teaching unit we deal with the transport of charge carriers.
We are looking at a box.
This box has 4 sides that are closed and 2 sides that are open.
In the illustration, these are the right
and left sides respectively.
There are a total of 10 particles in the box,
which can move completely freely and chaotically.
You can imagine the particles as gas.
On average, as many particles
will leave the box to the right side as to the left side.
Of course, this is only a thought experiment.
In reality, the box is a semiconductor crystal
with 10 million free charge carriers.
On average, 5 million would leave the crystal to
one of the two sides.
Now let's look at 5
of these boxes with freely moving particles.
The boxes are connected to each other.
The number of particles in the boxes
decreases from left to right.
The box on the right has 2 particles less than the box on the left.
We now look at the interface between the box
with the 6 and the 4 particles.
From the left box 3 particles will diffuse to the right.
From the right box 2 particles will diffuse to the left.
In sum, 1 particle moves to the right,
so there is a particle flow
of one particle to the right.
This particle flow can be described by the diffusion law:
The number n of particles diffusing through a given area A
is proportional to the particle concentration gradient dn/dx.
D is the
constant of proportionality between the particle flow
and the concentration gradient and is called the diffusion constant.
The particles diffuse to the location
with lower particle density.
The direction of diffusion is therefore opposite to the direction
of the concentration gradient - this is the reason for the minus sign
in front of the diffusion constant.
Diffusion takes place as long as there is a concentration gradient.
The diffusion law is shown here once again.
If the particles are now charged particles,
e.g. electrons, the equation shown is obtained,
in which both sides have been multiplied by e the elementary charge.
But e by A times D_n by dt is an electric current density.
we get the diffusion current density of the electrons.
Analogously, we get the diffusion current density of the holes.
Here there is no "-" in the equation.
However, the equation describes the dependence on dn/dx, i.e.
the concentration gradient of the electrons;
if there were dp by dx, there would also be
a minus sign aswell.
We now come to
another type of charge carrier transport: the field current.
We consider a crystal, to which
an electric voltage U is applied.
Electrons are accelerated in the direction of the positive pole,
but are slowed down by core atoms.
This creates the movement shown.
The strength of the electric field in V/cm
can be determined by the applied voltage and the distance l between the plates.
While the electrons move against the electric field,
the holes move in the direction of the electric field.
The field current density of the electrons
is proportional to the electric field strength.
The proportionality constant
is called electric conductivity.
This can be calculated with the help of the elementary charge,
the concentration of the electrons and again with the mobility of the electrons.
The result is that the field current density
is equal to the elementary charge times the concentration of the electrons times
the mobility of the electrons times the electric field strength.
Analogous to the field
current density of the electrons, we can also calculate
the field current density of the holes.
We conclude:
The movement of charge carriers from higher concentration
to lower concentration generates a diffusion current.
The movement of charge carriers due to an electric field
generates a drift current.
Holes move in the same direction as the electric field,
while electrons move in the opposite direction.
Thank you for your attention.