Thin single crystal perovskite solar cells to harvest below-bandgap light absorption

The efficiency of perovskite solar cells has surged in the past few years, while the bandgaps of current perovskite materials for record efficiencies are much larger than the optimal value, which makes the efficiency far lower than the Shockley–Queisser efficiency limit. Here we show that utilizing the below-bandgap absorption of perovskite single crystals can narrow down their effective optical bandgap without changing the composition. Thin methylammonium lead triiodide single crystals with tuned thickness of tens of micrometers are directly grown on hole-transport-layer covered substrates by a hydrophobic interface confined lateral crystal growth method. The spectral response of the methylammonium lead triiodide single crystal solar cells is extended to 820 nm, 20 nm broader than the corresponding polycrystalline thin-film solar cells. The open-circuit voltage and fill factor are not sacrificed, resulting in an efficiency of 17.8% for single crystal perovskite solar cells.


Supplementary Notes. Calculation of the efficiency upper limit:
The J SC was calculated by the integration of: where q is the electronic charge, I is the incident spectral photon flux density, α is the absorption coefficient, d is the thickness. A full reflection of light by the electron transport layer and the metal back electrode was assumed. The reflection of ITO glass was considered by assuming 90% EQE over the whole absorption spectrum which is reasonable because many high-efficiency perovskite solar cells demonstrated this high EQE. The bandgap of PTAA is large enough and its thickness is thin enough to avoid notable absorption, as demonstrated by the EQE of ~90% or above for the thin film polycrystalline perovskite solar cells with the same PTAA layer. Therefore, the parasitic absorption of PTAA was not considered. The UV-visible light is completely absorbed before approaching the PCBM/C 60 /BCP layers due to the large absorption coefficient of perovskite in this wavelength region and large thickness of perovskite.
The only portion of light that can partially approach the PCBM/C 60 /BCP layers is almost at the band edge. But PCBM, C 60 and BCP have negligible light absorption in the near-infrared region. Therefore, the light reflection was considered but parasitic absorption of these layers was not considered in the simulation.
The V OC was calculated from the quasi-Fermi level splitting based on the nonequilibrium carrier concentration, resulting a relation of V OC with J SC , τ eff and crystal thickness (d): where T and k are the absolute temperature and Boltzmann constant, N D is the concentration of the donor atom, τ eff is effective recombination lifetime, n i is the intrinsic carrier concentration, d is the film thickness. The τ eff was obtained on measured effective lifetime and extracted lifetime at different MAPbI 3 film thickness (Supplementary Figure 12). The dependence of τ eff on crystal thickness was derived based on: where τ s and τ b are surface recombination lifetime and bulk recombination lifetime, k b is the bulk recombination rate constant, P is the irradiance of the incident light, E is the average energy of incident photons. The dependence of τ eff on crystal thickness is derived to be: If the τ s is much higher than the τ b which is the case for perovskite single crystals, τ eff is found to be proportional to the square root of the crystal thickness, which is consistent with the experimental results (Supplementary Figure 12).
The calculated FF overall remains almost unchanged with value of about 0.89 which is much larger than common values observed in high-efficiency perovskite solar cells.
The FF was fixed at 0.8 when calculating the PCE. Combining the Jsc, V OC and FF, the dependence of PCE on film thickness was calculated.
Supplementary Method.

Measurement of carrier mobility and trap density by SCLC:
The hole-only devices were fabricated in a configuration of ITO/PTAA/MAPbI 3 /Au.
The hole mobility was calculated according to: where V b is applied voltage. The calculated hole mobility is 121±15 cm 2 V −1 s −1 . The hole trap density n t in the thin single crystal was calculated according to: Where V TFL is the voltage at which all the traps are filled, n t is the hole trap density.