## Nature Communications》The research team led by Tze Chien Sum from Nanyang Technological University in Singapore - Use mixed materials achieve high-efficiency carrier multiplication with internal quantum efficiency exceeding 100%

#### Carrier Multiplication Effect Helps Break Shockley-Queisser Limit of Single-Junction Perovskite Solar Cells

The carrier multiplication (CM) effect in perovskite solar cells has long been highly anticipated for its potential to break the Shockley-Queisser limit for single-junction solar cells. Despite compelling evidence of strong CM effects observed in lead halide perovskites, studies in actual solar cell devices are still sorely lacking. This work utilizes the Cs0.05FA0.5MA0.45Pb0.5Sn0.5I3 system as a testbed, exhibiting highly efficient CM with a low threshold of 2Eg (~500 nm) and remarkable efficiency of 99.4 ± 0.4%. The robust CM effect enables an unbiased internal quantum efficiency exceeding 110% and reaching as high as 160% in optimal devices. More importantly, our findings provide fresh insights into the complex interplay between various factors (optical and parasitic absorption losses, charge recombination and extraction losses, etc.) undermining CM contributions to the overall performance. Surprisingly, CM effects may already exist in perovskite solar cells but are suppressed by the present architecture. A comprehensive redesign of the existing device configuration is required to leverage CM effects for next-generation perovskite solar cells.

#### Overview of Carrier Multiplication Effect

The carrier multiplication effect refers to when a high-energy photon excites an electron, which then transfers its energy to another electron in the valence band, exciting it into the conduction band as a hot electron. Thus, one photon can generate two electron-hole pairs, i.e. “carrier multiplication”. This effect can increase the maximum photoconversion efficiency limit of solar cells.

#### Experiments Show Nearly Perfect CM Efficiency in Cs0.05FA0.5MA0.45Pb0.5Sn0.5I3 System

Researchers utilized the Cs0.05FA0.5MA0.45Pb0.5Sn0.5I3 system for experiments and discovered its highly efficient CM with a low threshold of 2Eg (~500 nm) and remarkable efficiency of 99.4%. This means nearly perfect multiplication is triggered when the incident photon energy exceeds 2Eg.

#### CM Boosts Quantum Efficiency but Room for Improvement Exists

Thanks to the CM effect, an unbiased internal quantum efficiency exceeding 110% and reaching 160% is achieved in test devices. However, factors like optical absorption loss and carrier recombination loss weaken the CM contributions to efficiency. Surprisingly, CM effects may already exist in perovskite solar cells but are suppressed by the present architecture.

#### Outlook

A complete redesign of existing solar cell devices is required to fully tap the CM effects. This research provides important insights for developing next-generation high-efficiency perovskite solar cells.

a Steady-state absorption spectrum of the perovskite thin film. FA is the fraction of absorbed light or absorptance and is the photon energy. The first dotted line from the left demarcates the regions below/above 2Eg. The other two dotted lines indicate the energies for 3Eg and 4Eg. The arrows designate the pump energies used in TA spectroscopy measurements. The pump energies range from 1.54 eV (dark red) to 4.96 eV (purple), the same as that shown in panel (c). Inset is the Tauc plot indicating the bandgap. b TA spectra of the mixed Pb-Sn perovskite film excited with 3.06 eV (405 nm) pulses. The color indicates the amplitude ΔA which varies from −8 mOD (yellow) to 2 mOD (dark blue). c Initial amplitude |ΔA| for different pump energies as a function of the required IA. The dashed lines show that |ΔA| increases linearly with IA. The red, green and blue solid lines indicate carrier multiplication (CM) quantum yield (QY) = 1, 2 and 3, respectively. d CM QY variation with increasing pump energy. The blue dots represent the CM QY calculated from panel (c), and the error bars represent the uncertainties of the CM QY determined using the error propagation formula. The red line is a fit to the data based on a previously published model25,28. The fitted CM efficiency is 99.8%. The dashed gray line and dashed dark yellow line show the influence of uncertainty of the data on the fitted result. The dashed green line indicates the ideal case.

a, b Jsc and c, d IQE as a function of absorbed photon flux (IA) under different pump energies in Cs0.05FA0.5MA0.45Pb0.5Sn0.5I3 (a, c) and MAPbI3 (b, d) PSCs illuminated by monochromatic CW lasers. The solid lines in (a) and (b) show that the Jsc increases linearly with IA. The horizontal dotted black lines in (c) and (d) indicate IQE = 100%. The violet-shaded regions in (c) and (d) indicate IQE > 100%. Source data are provided as a Source Data file.

a J–V curves of Cs0.05FA0.5MA0.45Pb0.5Sn0.5I3 PSC devices with two perovskite layer thicknesses (i.e., the thinnest and thickest layers) measured under one sun. The dashed lines indicate J = 0 mA cm−2 (horizontal) and V = 0 V (vertical). b The corresponding EQE (black Y-axis on the left, indicated by the black dotted circle) and the integrated Jsc (red Y-axis on the right, indicated by the red dotted circle) of PSC devices with different perovskite layer thicknesses. c Relationship between the EQE, IQE and perovskite absorptance Absperovskite. The dotted line is the EQE = 100% boundary. On the left (from yellow to green), the EQE is smaller than 100%, although IQE is larger than 100%. The low EQE is due to decreased Absperovskite. On the right (from green to blue), both the EQE and IQE are larger than 100%. d IQE of the PSCs. The dashed lines indicate IQE = 100% (horizontal) and wavelength = 500 nm (vertical). The arrow points to the CM threshold at around 2Eg. The violet-shaded region in (d) indicates IQE > 100%. Source data are provided as a Source Data file.

a IQE as a function of variation in PSCs with 1.2 M thin perovskite layer and 2.0 M thick perovskite layer. The arrows show that the highest IQE of ~161.5% and ~142.5% are obtained in the 1.2 M thin sample and 2.0 M thick samples at 3.33Eg with CM threshold of 2Eg and 2.08Eg, respectively. b Comparison of peak IQE value of Pb-Sn mixed PSCs, PbSe solar cells and PbS photovoltaic devices. Blue squares are the average peak IQE of the glass and quartz-based Pb-Sn mixed PSCs with both thick and thin perovskite layers, and the error bars are the standard deviation. Orange circles are the normalized IQE value of PbSe solar cells taken from reference34. Green open circles are the peak IQE value of PbS devices taken from reference35. CM threshold for PSCs is ~2Eg which is smaller than the 3Eg of PbSe solar cells and 2.5Eg of PbS devices. The horizontal dashed black lines in (a) and (b) indicate IQE = 100%. The vertical dashed lines and arrows in (b) indicate the CM thresholds of the PSCs (blue), PbS devices (green) and PbSe solar cells (orange). The dashed curves indicate the variation trend of the IQE values. The violet-shaded regions in (a) and (b) indicate IQE > 100%. Source data are provided as a Source Data file.