## 3 Results and Discussion  
We tested seven cases of \(\mathrm{f_{NR}}\) (\(10^{-10}\), \(10^{-5}\), \(10^{-4}\), \(10^{-3}\), \(10^{-2}\), \(10^{-1}\), and 1) to see the impact of nonradiative recombination. The results are summarized in Figures 3-5, Tables S1 and S2, and Figures S1 and S2 (in the supplementary materials). \(\mathrm{J_{0}}\) is inversely proportional to \(\mathrm{f_{NR}}\) (Equation (9)). A small \(\mathrm{f_{NR}}\) represents a high nonradiative recombination rate. For all cases, \(\mathrm{f_{NR}}=1\) is the case for the IQY of MEGSC. We used both IQY (see Figures 3-5, Table S1, and Figures S1a and S2a) and NQY under one-sun (C = 1; Figures 3a and 4, Table S1, and Figure S1b-d) and full-light concentration (C = 46,200;Figures 3b and 5, Table S2, and Figure S2b-d). For NQY, we chose \(\rm E_{th}=2E_{g}\), 3E\({}_{g}\), and 4E\({}_{g}\) to determine the impact of the nonradiative recombination. Equation (10) can predict the status of the QD MEGSC with NQY because of the nonidealities in the DB of an MEGSC. The MEGSC effect disappears after \(\rm f_{NR}\) = \(10^{-3}\) (1000 times \(\rm J_{0}\)) (Figure 3a). We determined the critical point to maintain MEGSC at \(\rm f_{NR}\) = \(10^{-2}\) and \(\rm E_{th}\) = 2E\({}_{g}\) under one-sun illumination (Figure 3a and Figure S1b). Finally, increasing the light concentration shifts the critical point (from MEG to SJSC) after \(\rm f_{NR}\) = \(10^{-5}\) (\(10^{5  
NQY under light-concentration conditions shows dual peaks after E\({}_{\rm th}\) = 3\(\cdot\)E\({}_{\rm g}\) (Figure 5 and Figure S2b-d). This represents the transition from the MEGSC to the SJSC, where the first peak is for the MEGSC and the second peak is for the SJSC. Thus, the delayed E\({}_{\rm th}\) results in less efficient MEGSCs because of the shifting of the optimum point from the MEGSC to an SJSC under light-concentration conditions. Therefore, E\({}_{\rm th}\) must be maintained at 2\(\cdot\)E\({}_{\rm g}\) with a low nonradiative recombination rate (e.g., 10 times J\({}_{0}\)), typically under one-sun illumination. The material condition for MEGSC is crucial in that the nonradiative recombination impact must be small to maximize the radiative limit. Overall, the results explain the low efficiency of the QD MEGSCs. For instance, the theoretical efficiency is 30.6% for E\({}_{\rm g}\) = 0.98 eV at E\({}_{\rm th}\) = 3E\({}_{\rm g}\) when f\({}_{\rm NR}\) is 1. In the proposed MEGSC detailed balance approach, the theoretical efficiency is 4.6% at f\({}_{\rm NR}\) = 10\({}^{-10}\), which is similar to 4.5% for PbSe QDs [27]. We compared other materials such as PbSe and CdTe and summarized the results in Table 1[27; 28; 29]. This shows that even if a QDSC can present excellent conditions for creating multiple EHPs, its high nonradiative recombination decreases the expected results [27; 28; 29]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multicolumn{3}{c}{**This work (Theoretical Efficiency)**} & \multicolumn{3}{c}{**Experiment**} \\ \hline E\({}_{\rm th}\) = 3E\({}_{\rm g}\) & f\({}_{\rm NR}\) & E\({}_{\rm g}\) (eV) & \(\eta\) (\%) & PbSe [27] & E\({}_{\rm th}\) = 3E\({}_{\rm g}\) & E\({}_{\rm g}\) (eV) & \(\eta\) (\%) \\ \hline  & 10\({}^{-10}\) & 0.98 & 4.6 & & & 0.98 & 4.5 \\ \hline E\({}_{\rm th}\) = 3E\({}_{\rm g}\) & f\({}_{\rm NR}\) & E\({}_{\rm g}\) (eV) & \(\eta\) (\%) & PbSe [28] & E\({}_{\rm th}\) = 3E\({}_{\rm g}\) & E\({}_{\rm g}\) (eV) & \(\eta\) (\%) \\ \hline  & 10\({}^{-11}\) & 0.95 & 2.1 & & & 0.95 & 1.61 \\ \hline E\({}_{\rm th}\) = 2.9E\({}_{\rm g}\) & f\({}_{\rm NR}\) & E\({}_{\rm g}\) (eV) & \(\eta\) (\%) & CdTe [29] & E\({}_{\rm th}\) = 2.9E\({}_{\rm g}\) & E\({}_{\rm g}\) (eV) & \(\eta\) (\%) \\ \hline  & 10\({}^{-11}\) & 0.95 & 1.38 & & & 0.95 & 1.9 \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison between theoretical efficiency and experimental efficiency of an MEGSC.