Chapter 8. ORGANIC SOLAR CELLS - from and for SET students

Chapter 2
c-Si Technology
2.1 Continuity Equation
In the first section the generation-recombination mechanism will be outlined followed by the the surface recombination.
2.1.1 Generation-Recombination
In thermal equilibrium the thermal generation is equal to thermal recombination. Also in static equilibrium the
excess generation is equal to excess recombination. One can study recombination by investigating the effect by
simply switching off a disturbance. By doing so the relaxation time (life time) of the system to return to its
initial state can be measured. When working out some equation for that then we get that the carrier density is
given by:
in which τn,0 is the lifetime of the minority carrier, which is given by:
δn(t) = δn(0)e −t
τ n,0 (2.1)
τn,0 = 1
Other recombination mechanism are the Shockley-Read-Hall recombination in which we have states in the
band-gap that can facilitate recombination. In that case the life time is given by:
τpt =
αrp0
1
vthσpNt
in which σp is the capture cross section for holes and Nt is the density of states in the gap.
Now let us get back to the continuity equation. The recombination rate is determined by the minority
carrier concentration, however the life time depends on the majority concentration. The continuity equation is
now needed to work out the density of minority carriers. The minority concentration will determine the current
density. This can be done in the following way:
Basically one looks at a volume element in which one looks at the carriers that come in and which go out
and check how that changes over a period of time. The the governing equation is given by:
This is given for n type material.
2.1.2 Surface Recombination
∂p
∂t = −∂F + p
∂x + gp − p
Let us now try to apply the continuity equation for surface recombination. For that we have to materials where
the atom structure does not match. Obviously at the surface it will not fit, thus there are faults at the surfaces
and interfaces. This is a sources of defects and also efficient recombination centres.
Now we can determine the generation, assuming it to be constant. A specific lifetime is given. Now the
recombination rate at the surface is given by:
R = ∂ps
τp0s
9
τpt
(2.2)
(2.3)
(2.4)
(2.5)