88
S. Leu and D. Sontag
In that way, they reach the metal contacts without recombining. The speed at which
the charge carriers (electrons and holes) travel is determined by their mobility μ.
The average time until they recombine is given by their lifetime τ . The quantity
governing the travel of charge carriers is the diffusion length. The diffusion length
L diff is given by
L diff = (D × τ )
1/2 with D =
q
k B T
μ
(4.13)
L diff diffusion length (see also Chap. 3)
μ
mobility, D diffusion constant, k B Boltzmann constant, q charge of the electron,
T absolute temperature
τ
lifetime
4.2 Recombination Losses
4.2.1 General Concepts
When we illuminate a solar cell, more and more electrons are energetically lifted into
the conduction band and become available for the generation of an electric current.
They “jump over” the forbidden zone. This process is called “photo-generation”.
Now, the question arises: how do the electrons come back into the valence band?
The semiconductor has a high conductivity under illumination. As soon as we switch
off the light, the semiconductor loses its increased conductivity again. The electrons,
thus, leave the conduction band after a certain time and recombine with the holes
in the valence band. The time between generation and recombination we call the
lifetime τ. The holes also have a lifetime.
The lifetime is defined by the equation
τ(n) = n/(R(n))
(4.14)
τ
lifetime
n excess carrier density
R recombination rate
This equation indicates how long the excess carriers n exist before they recombine again. The recombination process is governed by the recombination rate
R.
For “direct-bandgap” semiconductors like GaAs, see Sect. 4.1, this is relatively
fast, because after the thermalisation, e.g. after the release of surplus energy to the
crystal lattice, the electron jumps directly into the valence band by skipping over the
forbidden zone and recombines there with a hole. The momentum of the electron
does not have to be changed.
S. Leu and D. Sontag
In that way, they reach the metal contacts without recombining. The speed at which
the charge carriers (electrons and holes) travel is determined by their mobility μ.
The average time until they recombine is given by their lifetime τ . The quantity
governing the travel of charge carriers is the diffusion length. The diffusion length
L diff is given by
L diff = (D × τ )
1/2 with D =
q
k B T
μ
(4.13)
L diff diffusion length (see also Chap. 3)
μ
mobility, D diffusion constant, k B Boltzmann constant, q charge of the electron,
T absolute temperature
τ
lifetime
4.2 Recombination Losses
4.2.1 General Concepts
When we illuminate a solar cell, more and more electrons are energetically lifted into
the conduction band and become available for the generation of an electric current.
They “jump over” the forbidden zone. This process is called “photo-generation”.
Now, the question arises: how do the electrons come back into the valence band?
The semiconductor has a high conductivity under illumination. As soon as we switch
off the light, the semiconductor loses its increased conductivity again. The electrons,
thus, leave the conduction band after a certain time and recombine with the holes
in the valence band. The time between generation and recombination we call the
lifetime τ. The holes also have a lifetime.
The lifetime is defined by the equation
τ(n) = n/(R(n))
(4.14)
τ
lifetime
n excess carrier density
R recombination rate
This equation indicates how long the excess carriers n exist before they recombine again. The recombination process is governed by the recombination rate
R.
For “direct-bandgap” semiconductors like GaAs, see Sect. 4.1, this is relatively
fast, because after the thermalisation, e.g. after the release of surplus energy to the
crystal lattice, the electron jumps directly into the valence band by skipping over the
forbidden zone and recombines there with a hole. The momentum of the electron
does not have to be changed.