7.6
Note that the product v th σN sT has the unit of a velocity; it is called the surface
recombination velocity
with σ p or σ n for an n- or p-type semiconductor, respectively. A low surface recombination
velocity means that little recombination takes place while a (theoretical) value of S r = ∞
would mean that every minority carrier coming to the proximity of the surface
recombines.
For high quality solar cells it is crucial to have a low surface recombination velocity
S r , which can be achieved in two different ways: first, S r can be made low by reducing the
trap density N sT . In semiconductor technology, N sT can be reduced with so-called
passivation. This means that the defect density is reduced by depositing a thin layer of a
suitable material onto the semiconductor surface. Because of this layer, the valence
electrons on the surface can form covalent bonds, such that N sT is reduced.
Secondly, the excess minority carrier concentration at the surface (p s or n s ) can be
reduced, for example by high doping of the region just underneath the surface in order to
create a barrier. Because of this barrier, the minority carrier concentration is reduced and
hence the recombination rate R s . We discuss both ways in more detail during our
discussion on crystalline silicon solar cells in Section 12.4.
More detailed discussions for the extreme cases S R → ∞ and S r = 0 are found in
Appendix C.
Carrier concentration in non-equilibrium
When a semiconductor is illuminated additional electrons and holes are generated in the
material by the absorption of photons. The photogenerated carriers interact with the
semiconductor lattice. The extra energy that the electron-hole pairs receive from the
photons with energies larger than the band gap of the semiconductor is released into the
lattice in the form of heat. After this so–called thermalization process, which is very fast
and takes approximately 10
−12 s, the carrier concentrations achieve a steady state. In this
non-equilibrium state the electron and hole concentrations differ from those in the
equilibrium state. In non-equilibrium states two Fermi distributions are used to describe
the electron and hole concentrations. One Fermi distribution with the quasi-Fermi energy
for electrons, E Fn , describes the occupation of states in the conduction band with electrons.
Another Fermi distribution with the quasi-Fermi energy for holes, E Fp , describes the
occupation of states in the valence band with electrons, and therefore determines also the
concentration of holes. Using the band diagram with the quasi-Fermi levels the process of
Note that the product v th σN sT has the unit of a velocity; it is called the surface
recombination velocity
with σ p or σ n for an n- or p-type semiconductor, respectively. A low surface recombination
velocity means that little recombination takes place while a (theoretical) value of S r = ∞
would mean that every minority carrier coming to the proximity of the surface
recombines.
For high quality solar cells it is crucial to have a low surface recombination velocity
S r , which can be achieved in two different ways: first, S r can be made low by reducing the
trap density N sT . In semiconductor technology, N sT can be reduced with so-called
passivation. This means that the defect density is reduced by depositing a thin layer of a
suitable material onto the semiconductor surface. Because of this layer, the valence
electrons on the surface can form covalent bonds, such that N sT is reduced.
Secondly, the excess minority carrier concentration at the surface (p s or n s ) can be
reduced, for example by high doping of the region just underneath the surface in order to
create a barrier. Because of this barrier, the minority carrier concentration is reduced and
hence the recombination rate R s . We discuss both ways in more detail during our
discussion on crystalline silicon solar cells in Section 12.4.
More detailed discussions for the extreme cases S R → ∞ and S r = 0 are found in
Appendix C.
Carrier concentration in non-equilibrium
When a semiconductor is illuminated additional electrons and holes are generated in the
material by the absorption of photons. The photogenerated carriers interact with the
semiconductor lattice. The extra energy that the electron-hole pairs receive from the
photons with energies larger than the band gap of the semiconductor is released into the
lattice in the form of heat. After this so–called thermalization process, which is very fast
and takes approximately 10
−12 s, the carrier concentrations achieve a steady state. In this
non-equilibrium state the electron and hole concentrations differ from those in the
equilibrium state. In non-equilibrium states two Fermi distributions are used to describe
the electron and hole concentrations. One Fermi distribution with the quasi-Fermi energy
for electrons, E Fn , describes the occupation of states in the conduction band with electrons.
Another Fermi distribution with the quasi-Fermi energy for holes, E Fp , describes the
occupation of states in the valence band with electrons, and therefore determines also the
concentration of holes. Using the band diagram with the quasi-Fermi levels the process of