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.
Figure 1.
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 is
Increased 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 has
power 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]