Lead Telluride Quantum Dot Solar Cells Displaying External Quantum Efficiencies Exceeding 120%

Multiple exciton generation (MEG) in semiconducting quantum dots is a process that produces multiple charge-carrier pairs from a single excitation. MEG is a possible route to bypass the Shockley-Queisser limit in single-junction solar cells but it remains challenging to harvest charge-carrier pairs generated by MEG in working photovoltaic devices. Initial yields of additional carrier pairs may be reduced due to ultrafast intraband relaxation processes that compete with MEG at early times. Quantum dots of materials that display reduced carrier cooling rates (e.g., PbTe) are therefore promising candidates to increase the impact of MEG in photovoltaic devices. Here we demonstrate PbTe quantum dot-based solar cells, which produce extractable charge carrier pairs with an external quantum efficiency above 120%, and we estimate an internal quantum efficiency exceeding 150%. Resolving the charge carrier kinetics on the ultrafast time scale with pump–probe transient absorption and pump–push–photocurrent measurements, we identify a delayed cooling effect above the threshold energy for MEG.


S1 -Absorbance and Transmission Spectra and Electron Microscopy
The size distribution (SD) was determined optically by fitting a Gaussian function to the first excitonic peak. For an independent analysis via TEM a histogram of the diameter distribution of more than 3000 individual particles was produced using Image J (http://imagej.nih.gov/ij/). The QD size distribution was then derived via the standard deviation of the histogram produced (see Table S1).

Size Distribution
Absorbance S3 -Photovoltaic performance of small-and large-bandgap PbTe QDs if TiO 2 is employed as an electron-collecting layer

S5 -Integrated EQE
The photocurrent under short-circuit conditions was reconstructed by multiplying the EQE at each wavelength with the corresponding incident power under AM1.5 irradiation. Integration over all wavelengths produced a short-circuit current (J SC ) of 18.4±0.6 mA/cm 2 . The average measured J SC is 17.8 ± 0.3 mA/cm 2 , which is ca. 3 % lower than the calculated value. We note that the EQE measurements performed under various white light background (WLB)

S6 -EQE measurements under tuneable background illumination
illuminations were performed 10 days after the EQE measurement conducted without a WLB (see Figure   1(c) of the main text) and show a lower photocurrent under similar measurement conditions. We explain this phenomenon with QD surface oxidation effects 1,2 which are likely to reduce the extractable photocurrent under short-circuit conditions (see Figure S6).
The lower quantum efficiency at higher white-light intensity is indicative of a carrier-density dependent charge recombination. Transient photovoltage measurements under different white light intensities (see Figure S7) confirm this.
S7 -Transient photovoltage decay measurements under tuneable back ground illumination for devices consisting of PbTe QDs. In Figure S10(a) we show the transient absorption spectrum after an excitation at 2.0 eV, which is below the ground state bleach (GSB) energy observed in Figure 4(a) of the main text. In agreement with previous transient absorption measurements on PbS and PbSe QDs 6 we find no notable GSB signal in this region. We note that the excitation density generated by the 2.0eV pump is significantly smaller than for the 3.1eV pump. This phenomenon arises due to three effects: First, the PbTe QD sample absorbs ca. 6.0 times less at 2.0 eV compared to 3.1eV (see Figure S10(b)); second, we doubled the pump fluence for the lower pump excitation; and third, the generated photon flux at 2.0 eV is ca. 1.5 times higher than at 3.1 eV. Considering all three effects we estimate the excitation density generated by the 2.0eV pump to be a factor of 1.9 times smaller than for the 3.1eV pump S11 -Long-time Pump-Push Photocurrent Figure S11: Photocurrent response as a function of (long) time delay between pump and push pulse. The fluence of the pump excitation has been adjusted to produce 5 nA for each excitation energy. The transients were corrected for the response at negative delay times. The transients clearly contain two components where the early dynamics can be interpreted in the framework of MEG. The long-lived signal including the growing component at >100 ps delay have been previously assigned to the delayed charge-transport-assisted trapping of photogenerated charge carriers. S12 -Kinetics of the pump-push-photocurrent experiment Figure S12: Photocurrent response as a function of time delay between pump and push pulse. The photocurrent due to the pump pulse only was 5nA. The transient has not been corrected for the response at negative delay times. The red line is a fit to the data using an exponential 800fs decay function convolved with the 80fs Gaussian response function of the setup. Bibliography: