Extracting Decay-Rate Ratios From Photoluminescence Quantum Efficiency Measurements in Optoelectronic Semiconductors

This paper is a contribution to the Physical Review Applied collection titled Photovoltaic Energy Conversion.

Recombination rates in optoelectronic semiconductors are typically recorded using time-intensive and expensive measurements. Here we present a method to extract decay rate ratios in a facile and rapid manner using only photoluminescence quantum efficiency measurements, which we demonstrate on halide perovskite thin-film samples. We combine these ratios with time-resolved photoluminescence data to extract absolute recombination rates, with excellent agreement when our approach is benchmarked against the more time- and infrastructure-intensive technique of transient absorption spectroscopy. This approach also enables direct quantification of the ratio between total second-order and radiative second-order recombination rates. We demonstrate that radiative recombination is only a fraction of total second-order recombination in the range of halide perovskite samples relevant for photovoltaics. We showcase the implications of rapid extraction of decay rates by extracting decay rate ratios on a microscale and by calculating the expected maximum efficiency of a solar cell fabricated from a measured perovskite film. We show that reducing first-order losses will significantly improve solar cell efficiency for our samples until time-resolved photoluminescence lifetimes are longer than approximately 1 µs (at low excitation pulse intensity), at which point second-order nonradiative recombination limits the efficiency of perovskite solar cells. This work presents a framework for rapidly screening optoelectronic semiconductors with techniques widely accessible to many research groups, identifies decay processes that would otherwise be missed, and directly relates the extracted values to predicted device performance metrics.

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Figure 1

(a) Measured PLQE of a passivated MAPbI₃ film (sample 3) as a function of incident laser intensity, alongside the optimal fit to the data based on the model presented in Eq. (3). The excitation density, n, is estimated using values obtained from TAS and TRPL measurements (see Supplemental Material, Note 2 [13]). Error bars on PLQE data are calculated in accordance with the method outlined in Supplemental Material, Note 3 [13]. (b) Natural logarithm of TRPL counts plotted as a function of time for two different initial excitation densities stated in the legend (for sample 1). Solid lines show the fit to each data set. (c) Scaling of initial time-resolved photoluminescence counts for sample 1 on a log scale, $I_{\mathrm{TRPL},0}$, for different excitation densities, used to estimate $p_0$. (d) First-order decay rates extracted from fittings in (b), for measurements at four different positions across the surface of sample 1 and 2.

Figure 2

(a) 1/n versus time, as measured for sample 1 in TAS. Two fits to this data are shown: a linear fit to the high power data [Eq. (10)], and an exponential fit [Eq. (9)], to all the data. The inset shows the recorded TAS signal with time (with each fluence offset in time to overlay the decays). In both plots each color represents a different incident fluence. (b) All second-order rates extracted from PLQE/TRPL and TAS measurements. For samples 1 and 2, TAS and TRPL error bars are obtained from the spread of data at different points on the surface, while for sample 3 and 4, 20% and 30% error bars are assumed, based on the quality of data taken.

Figure 3

(a) Micro-PLQE map (for a 2 mW/cm² excitation density) of a halide perovskite MAPbI₃ film (sample 3). The PLQEs with power were fitted for this map. Poor fits were removed from the data (see Supplemental Material, Note 7 [13]), and results for $a/(\sqrt{{\eta }_{\mathrm{esc}}{b}_r})$ and $b/({\eta }_{\mathrm{esc}}{b}_r)$ are presented in (b). Overlaid on these plots are the maximum, minimum, median, upper and lower quartiles as box and whisker plots. Samples were excited by a 405 nm beam. (c) Measured PLQEs alongside those predicted from TAS and TRPL for samples 1 and 2. (d) The $b/({\eta }_{\mathrm{esc}}{b}_r)$ ratio from PLQE measurements for the four MAPbI₃ samples measured. We note that sample 4 was extremely thick (more than 800 nm) and had low PLQE, so there is larger error in some values obtained. All PLQE error bars represent a 95% confidence interval for fits (for samples 1 and 2, these are the maximum intervals obtained from any measurement on the sample surface; see Supplemental Material, Note 2 [13]).

Figure 4

Predicted solar cell efficiencies for an MAPbI₃ absorber film studied here (sample 3). (a) Current-voltage curves for decay rates measured, with no nonradiative (NR) second-order loss, no first-order loss, and the (fully idealized) case of only intrinsic recombination. The solar cell’s absorptance is that measured for the encapsulated sample at its given thickness (see Supplemental Material, Note 10 [13]). (b) the efficiency of a solar cell made from the same sample, but with optimal absorption, as a function of first-order trapping and ratio of total to radiative second-order recombination $[b/({\eta }_{\mathrm{esc}}{b}_r)]$. The cross marks measured decay rates.