Absorption generates electrons and holes in the perovskite. After relaxation toward the band edges, their nonequilibrium populations are described by separate electron and hole quasi-Fermi levels. Selective contacts collect electrons through an electron-transport layer and holes through a hole-transport layer, while suppressing the opposite carriers.
For ideal contacts at open circuit,This quasi-Fermi-level splitting is not the band gap itself or simply the equilibrium built-in voltage. At equilibrium there is one common Fermi level and no extractable photovoltage. Under illumination at open circuit, generation is balanced by recombination while a nonzero population splitting persists.
Selective extraction, quasi-Fermi splitting and recombination-limited solar-cell voltage
. Original qualitative energy diagram and stipulated illuminated diode curves. Trap-assisted and interface recombination reduce carrier splitting and open-circuit voltage. Band offsets, energy spacings and current scales are illustrative rather than fitted perovskite data. Details.Important parasitic paths include trap-assisted Shockley-Read-Hall recombination in the bulk, at grain boundaries and at interfaces, and recombination at poorly selective contacts. They lower the steady carrier populations and their quasi-Fermi splitting. Auger recombination can matter at high carrier densities but need not dominate an ordinary one-sun device. Radiative recombination is an unavoidable detailed-balance contribution, rather than an avoidable defect loss of the same kind.
An approximate illuminated diode relation isIncreased nonradiative recombination generally increases the dark recombination current and reduces ; it can also change ideality and fill factor. Shunts add a leakage path. Series resistance mainly reduces voltage under load and fill factor: its simple drop vanishes at zero terminal current, so it should not be invoked as an automatic direct subtraction from open-circuit voltage.
Absorption of photons with creates electron-hole pairs, the upward band-diagram arrow. In the depletion region the built-in field drives electrons towards n material and holes towards p material; diffusion also delivers carriers generated within a diffusion length outside that region. Selective contacts collect the two signs. Illumination maintains a nonequilibrium quasi-Fermi-level splitting, allowing a voltage and useful current through an external load; it is the light, rather than the equilibrium barrier, that supplies the energy.
Taking forward diode current as positive, an ideal illuminated junction haspower is delivered where in this convention. Reflection, below-gap transmission, carrier thermalization, recombination and resistive losses limit real conversion; even an ideal single junction has radiative detailed-balance limits.[ref]
Detailed Balance Limit of Efficiency of p-n Junction Solar Cells by William Shockley and Hans-Joachim Queisser. 1961, Journal of Applied Physics 32, pp.510–519: radiative detailed-balance limit
