Solar Cells 2
shoomoosh
class09SolarCells2020-08Bulkandsurfacerecombination1.pptxBulk and surface recombination (1)
Prof. Richard R. King
Solar Cells
EEE 565
Arizona State University
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Solar cell efficiency
h =
Iinc
Voc
Jsc
FF
h = solar cell efficiency (unitless)
Voc = open-circuit voltage (V)
Jsc = short-circuit current (A/cm2)
FF = fill factor (unitless)
Iinc = incident light intensity (W/cm2)
Voc
‹#›
Solar cell voltage
Voltage depends on non-equilibrium concentrations of electrons and holes
Bandgap-voltage offset (Eg/q) – V is a useful parameter for gauging solar cell quality, especially when dealing with semiconductors of many different bandgaps
Basically a measure of how close electron and hole quasi-Fermi levels are to conduction and valence band edges
‹#›
Simplified diode equation
Solar cell current J is simply photogenerated current Jph minus recombination current Jrec :
Recombination current increases exponentially with V
Jog is the key parameter expressing the dependence of recombination current on voltage
Jog is strongly dependent on g: Jog is much higher for g = 2 than for g = 1 at the same voltage
= diode ideality
factor
In forward bias (normal operation for solar cells):
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Recombination in semiconductors
Recombination rate term is proportional to the concentration of the “reactants,” the electrons and holes, as in a chemical reaction
Generation term, ensures that net recombination rate Jrec is zero at equilibrium when pn = ni2 .
Net recombination current density
Note that for g = 1:
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Recombination in semiconductors
Recombination of electrons and holes determines solar cell voltage, and ultimately, solar cell efficiency
Fundamental recombination processes:
Radiative recombination
Auger recombination
Non-fundamental recombination processes – can be reduced in principle to zero:
Trap-assisted (TA) recombination
(also called SRH recomb.)
→ mediated by traps in the energy gap, due to defects
Recombination can take place in the semiconductor bulk or, especially for TA recombination, at semiconductor interfaces
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Radiative recombination
Radiative recombination
Energy of recombining electron-hole (e-h) pair given to emitted photon
Inverse process of e-h pair generation by absorbing a photon
Note dependence on pn product: concentrations of reacting species
B is radiative recombination coefficient 1.8 X 10-10 cm3/s for GaAs
Recombination current density and Jo due to radiative recombination:
Fairly weak quadratic increase of B with increasing Eg
For low-level injection (LLI), e.g., for minority electrons in p-type material:
Radiative recombination rate
# of e-h pairs recombining per unit time, per unit volume [s-1cm-3]
w = thickness of volume in which recombination takes place
trad = lifetime of minority carriers due to radiative recombination
‹#›
Auger recombination
Auger recombination
Energy of recombining e-h pair given to another free carrier
Inverse process is carrier multiplication: hot carriers generating other carriers
Auger recombination is a 3-body interaction recombination rate depends on np2 and pn2
Especially important for high doping concentration and for high incident light intensities (optical concentration)
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SRH (defect-mediated) recombination
Trap-assisted (TA) recombination
Density of trap states in bandgap that mediate SRH recombination
Energy level of trap states in bandgap
Capture cross sections for electrons and holes
Thermal velocity for electrons
Thermal velocity for holes
Smallest possible lifetime for electron capture
Smallest possible lifetime for hole capture
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SRH (defect-mediated) recombination
Trap-assisted (TA) recombination
Trap state with energy Et in forbidden gap catalyzes e-h recombination
Energy of recombining e-h pair given to lattice vibrations (heat)
SRH recombination is proportional to the trap density Nt Can be eliminated in principle by removing all defects, impurities
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SRH recombination
Trap-assisted (TA) recombination
This equation can be arranged in a way that might be more intuitive, showing the linear dependence of recombination rate RSRH on trap density, capture cross section, and thermal velocity:
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SRH recombination, low-level injection
Trap-assisted (TA) recombination
For low-level injection (LLI), e.g., in p-type base with p NA >> n this reduces to:
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SRH recombination, high-level injection
Trap-assisted (TA) recombination
For high-level injection (HLI), e.g., in p-type base with n ≈ p this reduces to:
For
‹#›
Recombination in semiconductors
Old slides
‹#›
Recombination in semiconductors
Recombination of electrons and holes determines solar cell voltage, and ultimately, solar cell efficiency
Fundamental recombination processes:
Radiative recombination
Auger recombination
Non-fundamental recombination processes – can be reduced in principle to zero:
Shockley-Read-Hall (SRH) recombination mediated by traps in the energy gap, due to defects
Recombination can take place in the semiconductor bulk or, especially for SRH recombination, at semiconductor interfaces
‹#›
Radiative recombination
Radiative recombination
Energy of recombining electron-hole (e-h) pair given to emitted photon
Inverse process of e-h pair generation by absorbing a photon
Note dependence on pn product: concentrations of reacting species
B is radiative recombination coefficient 1.8 X 10-10 cm3/s for GaAs
Recombination current density and Jo due to radiative recombination:
Fairly weak quadratic increase of B with increasing Eg
For low-level injection (LLI), e.g., for minority electrons in p-type material:
Radiative recombination rate
# of e-h pairs recombining per unit time, per unit volume [s-1cm-3]
w = thickness of volume in which recombination takes place
trad = lifetime of minority carriers due to radiative recombination
‹#›
Auger recombination
Auger recombination
Energy of recombining e-h pair given to another free carrier
Inverse process is carrier multiplication: hot carriers generating other carriers
Auger recombination is a 3-body interaction recombination rate depends on np2 and pn2
Especially important for high doping concentration and for high incident light intensities (optical concentration)
‹#›
SRH (defect-mediated) recombination
Shockley-Read-Hall (SRH) recombination
Energy state Et in forbidden gap catalyzes e-h recombination
Energy of recombining e-h pair given to lattice vibrations (heat)
SRH recombination is proportional to the trap density Nt Can be eliminated in principle by removing all defects, impurities
hole and electron capture cross sections [cm2]
carrier thermal velocity [cm/s]
intrinsic Fermi level
‹#›
SRH recombination, low-level injection
Shockley-Read-Hall (SRH) recombination
For low-level injection (LLI), e.g., in p-type base with p NA >> n this reduces to:
‹#›
SRH recombination, high-level injection
Shockley-Read-Hall (SRH) recombination
For high-level injection (HLI), e.g., in p-type base with p n this reduces to:
‹#›
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