1. سه نوع بازترکیب وجو دارد
شاتکی رید هال SRH
اوژه
مستقیم

2. SRH Recombination

7. Generation and recombination
n0  n0 + ∆n = n
Recombination and generation processes. Generation processes depend on absorption and on flow of photons
  G = R 
Life time of minority carriers:
∆n is the surplus concentration
Ri is the rate of recombination
n0 is the concentration at equilibrium
n is the charge concentration
G is the rate of generation
There are different recombination processes, the generated charge carriers will be built back into the cristall.
Each recombination process i has it‘s own recombination rate, and ist own minority charge carrier living time τ
Bulk: the first three processes go on parallel and do not depend on each other. The first three components describe the life time of a minority carrier in a special Volume. But you also have to think about the surface recom. Which goes on parallel too. you get a effective charge carrier life time of τeff
Typical values for solarcells are 1-100μs
Life time:
The functionallity of a solar cell depends on the minority charge carriers, mostly the electrons, because for solar cell p-doped silicon is mostly used.
Life time of an electron is important.  Because n0 is very small you can say n = ∆n
The life time also depends on the density of th holes. p = p0 + ∆p  po depends on the doping, ∆p depends on the excitation  here ∆n = ∆p
∆n depends on the excitation and is also called injection.  ∆n<<p0 is low injection.

8. Generation and recombination
Recombination by radiation Auger-recombination
Radiation:
The inverse process of absorption. A electron goes over into the valenceband by radiation of electromagnetic radiation.
Proportional to occupied state in the conduction band and unoccupied states in the valence band.
B = a material konstant
N0 und p0 are the concentrations of electrons or holes in thermal equilibrium
Ni is the intrinsic charge darrier concentration of the material  for silicium this plays a minor role because here you need a phonon as we know  very improbable
Auger-recombination:
Electron recombinates. Free energy but not in form of a electromagnetic radiation. A second Electron or hole in either band get the energy. This second charge carrier gives ist energy back in form of phonons to the cristall latice.
Mainly in high doped material >1017 cm3  for high doped materials the life time of minority carreirs is highly reduced by this formular
 Stärkster begrenzender faktor bei solarzellen mit dicke <1mm

9. Generation and recombination
Recombination by impurity
τSRH depends on:
Number of impurities
Energy level of impurities
Cross section of impurities
Recombination on the surface
Untreated silicon surfaces S > 106 cm/s
Depends strongly on charge carrier injection
and doping
Recombination by (impurities shokley read hall)
There are impurities because of cristall defects or impureness.  energy levels between the two bands in the forbidden zone  two steps recombination way
Electrons fall into the energylevel of the impuritý and from there in the valence band.
The life time SRH depends on the numper of the impurities and energetic level of these impurities and from the cross section. The more the level in the middel of the two bands, and the bigger the cross section the worse the life time.
SRH theory believes in one defective state between the band gap which interacts with the bands by emission or einfang of electrons and holes.
This process is the limiting recombination process in multicristall silicon and Czochralski-Silicon. If you use moncristall silicon or float zone silicon than there is almost no recombination because of impurities. FZ is monocristall and free of dislocation. One impurity on 1 million particles
Surface:
Correspond to high mistakes in the cristall!! Because the cristall structure breakes up very abruptly
Dangling bonds: free bonds will be filled up with foreign atoms this means new impurities or the bonds will not been filled and stay unoccupied.  many different energy levels at the surface in the forbidden zone. Because of these energy levels many created electron hole couples will be destroyed. This works for the back and the front of the surface.
Die defektniveaus in der Bandlücke bilden ein Kontinuum
An der Oberfläche bildet sich eine Raumladungszone aus  ferminiveaus und ladungsträgerdichten unterscheiden sich von denen im Volumen
Annahme, dass die einzelnen Defektzustände nicht miteinander wechselwirken,  Rekombinationsrate der Oberfläche ist die Summe aus den Beiträgen aller Defektzuständee zur SRH rekombination
S is the surface recombination velocity and the velocity on the back and on the front surface is equally if you look at it simply
S considers the behaviour of the SRH recombination and the influence of the depletion area.
S= Oberflächenrekombinationsrate(Teilchenstromdichte welche in der Oberfläche fließt) / delta n
S depends on the potential of the surface, but even stronger on the charge carrier injectionand the doping
D is the diffusionn constant of the minority carriers which depends on the material, the Temperature and concentration of the doping
W is the thikness of the material
For a untreated silicon material is S > 106 cm/s

10. Generation and recombination
radiation
Low p0  SRH is dominant
and τ independet of p0
High p0  τ ~ p0-2
(Auger recombination)
radiation recombination
plays no role for silicon
Normal sunlight radiation
the basis of the solar cell
is in the are of the SRH
recombination
105
104
103
102
101
100
Auger
τ [µs]
SRH
Experimental
Low hole density  t is constant the SRH is dominant SRH is independent of the equilibrium hole density which is determined by the doping.
High hole density  t ~ po^-2 (auger)#
Because of the doping, and the low injection the basis of the solar cell is in the field of the SRH recombination.
SRH theory believes in one defective state between the band gap which interacts with the bands by emission or einfang of electrons and holes.
Bei niedriger injektion delta n<<p0 ist die lebensdauer unabhängig von der ladungsträgerdichte SRH dominiert.
Wird delta n = p0 überschritten, dann fällt oder steigt die lebensdauer, je nach typ des dominanten rekombinationszentrum.
Für hohe injektion dominiert Auger  lebensdauerabfall mi (delta n)^2 für delta n ~ 10^16-10^18 cm^-3
p0 [cm-3]

11. طول نفوذ در بازترکیب تاثیر گذار است
Is the mean free length of path a charge carrier can travel in a volume of a crystall lattice before recombination takes place.
depends on:
The semiconductor material
The doping
The perfection of the crystall lattice
D is the diffusion constant
Merke:
Ladungsträger bewegen sich aus Bereichen höherer Konzentration in Bereiche geringerer Konzentration
D is the Diffusion constant
After one Diffusion length, the number of light generated charge carriers decreases by 1/e exponentialy.
Silizium
Teff = 1μs - 100μs
Bei 300K im p-type silicon Dn = 26,9 cm^2 /s und Dp=10,7cm^2/s
Bei 300K in n-type Dp = 11,6 cm^2/s und Dn = 32,3cm^2/s

12. Diffusion length Silicon: (10 μm - 100 μm)
λ < 800nm light absorbed within 10μm
λ > 800nm electron-hole generation all over the volume
 for an effectiv solar cell the diffusion
length has to be 2-3 times thicker
than the actual solar cell
Multichristall silicon
τeff = 50μs
Leff,n (cm)
Leff,p (cm)
p-type
0,037
0,023
n-type
0,040
0,024
Silicon:
λ < 800nm a huge part of the sunlight will be absorbed in silicon within 10μm  the pn junction is right under the surface.  most of the light generated carriers will be generated under right next to the pn junction. They just have to diffuse a few microns towards the pn junction to distribute to the solar current
λ > 800nm electron-hole generation all over the volume  longer way into the pn-junction and the probability to reach this junction before they recombinate ist very small.
Silizium
Teff = 1μs - 100μs
Bei 300K im p-type silicon Dn = 26,9 cm^2 /s und Dp=10,7cm^2/s
Bei 300K in n-type Dp = 11,6 cm^2/s und Dn = 32,3cm^2/s