Benefit from Photon Recycling at the Maximum-Power Point of State-of-the-Art Perovskite Solar Cells

Photon recycling is required for a solar cell to achieve an open-circuit voltage $(V_{\mathrm{OC}})$ and power conversion efficiency (PCE) approaching the Shockley-Queisser theoretical limit. The achievable performance gains from photon recycling in metal halide perovskite solar cells remain uncertain due to high variability in material quality and the nonradiative recombination rate. We quantify the enhancement due to photon recycling for state-of-the-art perovskite ${\mathrm{Cs}}_{0.05}({\mathrm{MA}}_{0.17}{\mathrm{FA}}_{0.83}{)}_{0.95}\mathrm{Pb}({\mathrm{I}}_{0.83}{\mathrm{Br}}_{0.17}{)}_3$ (triple-cation) films and corresponding solar cells. We show that, at the maximum power point (MPP), the absolute PCE can increase up to 2.0% in the radiative limit, primarily due to a 77 mV increase in $(V_{\mathrm{MPP}})$. For this photoactive layer, even with finite nonradiative recombination, benefits from photon recycling can be achieved when nonradiative lifetimes and external light-emitting diode (LED) electroluminescence efficiencies, $Q_e^{\mathrm{LED}}$, exceed 2 µs and 10%, respectively. This analysis quantifies the significance of photon recycling in boosting the real-world performance of perovskite solar cells toward theoretical limits.

Figure 1

Detailed-balance simulation of J-V curves for an ideal ${\mathrm{Cs}}_{0.05}({\mathrm{MA}}_{0.17}{\mathrm{FA}}_{0.83}{)}_{0.95}\mathrm{Pb}({\mathrm{I}}_{0.83}{\mathrm{Br}}_{0.17}{)}_3$ perovskite photovoltaic device in the radiative limit (no nonradiative recombination) with (red trace) and without (black dashed trace) photon recycling (PR).

Figure 2

Simulated J-V curves (triple-cation, 1.6 eV band gap) with and without PR for $k_1$ values of (a) $1\times {10}^4{\mathrm{s}}^{-1}$, (b) $2\times {10}^5{\mathrm{s}}^{-1}$, and (c) $3\times {10}^6{\mathrm{s}}^{-1}$ ($k_2^{\mathrm{int}}=2\times {10}^{-10}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$ and $k_3=1\times {10}^{-28}\mathrm{c}{\mathrm{m}}^6{\mathrm{s}}^{-1}$). (d) $V_{\mathrm{OC}}$ (red lines) and $V_{\mathrm{MPP}}$ (black lines) as a function of $k_1$, revealing differences in the onset of performance improvements due to PR. Dotted vertical red and black lines indicate $k_1$ thresholds ($2\times {10}^6$ and $7\times {10}^5{\mathrm{s}}^{-1}$, respectively) below which PR improves performance at open circuit and the MPP, respectively.

Figure 3

Simulated J-V curves (black traces) for $k_1=2\times {10}^5{\mathrm{s}}^{-1}$, $k_2^{\mathrm{int}}=2\times {10}^{-10}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$, and $k_3=1\times {10}^{-28}\mathrm{c}{\mathrm{m}}^6{\mathrm{s}}^{-1}$ (a),(c) without and (b),(d) with PR are shown with the magnitude of SRH, radiative, and Auger recombination currents as a function of voltage (blue traces). (c),(d) The fractions of total recombination current due to SRH, radiative, and Auger recombination are shown at each voltage (red traces) (c) without and (d) with PR. The fraction of radiative recombination as a function of voltage with and without PR is equivalent to $Q_e^{\mathrm{LED}}$ and $Q_i^{\mathrm{lum}}$, respectively.

Figure 4

The voltage with PR $(V^{\mathrm{PR}})$ for P_esc = 4.7% at the MPP and open circuit is shown as a function of $Q_e^{\mathrm{LED}}(V_{\mathrm{OC}})$, which, as nonradiative recombination decreases, approaches unity. Inset: $\mathrm{\Delta }{V}^{\mathrm{PR}}$ for P_esc = 4.7% at MPP and open circuit as a function of $Q_e^{\mathrm{LED}}(V_{\mathrm{OC}})$.

Figure 5

The effect of PR on the MPP steady-state carrier density and $Q_e^{\mathrm{LED}}(V_{\mathrm{OC}})$ as a function of $k_1$ for (a) P_esc = 4.7%, (b) 9.4%, and (c) 14.1%.

Figure 6

(a) The $V_{\mathrm{OC}}$ with PR in the radiative limit $(V_{\mathrm{OC}}^{\mathrm{rad}})$ is shown along with (b) the nonradiative subtractive effect on $V_{\mathrm{OC}}^{\max }(V_{\mathrm{OC}}^{\mathrm{nonrad}})$. Combined, $V_{\mathrm{OC}}^{\mathrm{rad}}+V_{\mathrm{OC}}^{\mathrm{nonrad}}$ yield (c) the total $V_{\mathrm{OC}}^{max}$ as a function of $k_1$ and P_esc, with a dashed line at $k_1=1\times {10}^5{\mathrm{s}}^{-1}$ showing that increasing P_esc for a fixed $Q_i^{\mathrm{lum}}$ decreases $V_{\mathrm{OC}}$.