## 4 Conclusions  
We analyzed the DB of the MEGSC with nonradiative recombination. In the ideal MEGSC, the excited electron after AR emits high photon energy under the stringent blackbody radiation condition (=QY\({}_{\mathrm{max}}\cdot\)E\({}_{\mathrm{g}}\), where QY\({}_{\mathrm{max}}\) is the maximum QY). However, an excited electron in the actual materials loses its kinetic energy through a phonon-assisted cooling process. The NQY from the pump-probe measurements depends on the material status (defects and effective mass), so its related parameters, E\({}_{\mathrm{th}}\) and QY, deviate from IQY.  
In the DB of the MEGSC, we introduced the ratio \(\mathrm{f_{NR}}\) between radiative and nonradiative recombination to see the impact of the ideal reverse saturation current. Typically, E\({}_{\mathrm{th}}\) = 2E\({}_{\mathrm{g}}\) with \(\mathrm{f_{NR}}\) = \(10^{-1}\) is the critical point to regard the QD status for the effect of MEG under one-sun illumination. Increasing the light concentration improves MEG. The minimum point for the MEGSC under NQY (in actual material systems) is \(\mathrm{f_{NR}}=10^{-4}\) at E\({}_{\mathrm{th}}\) = 2E\({}_{\mathrm{g}}\), 3E\({}_{\mathrm{g}}\), and 4E\({}_{\mathrm{g}}\). J\({}_{0}\) must be lower than \(10^{4}\) times J\({}_{0}\) under full-light concentration to maintain the performance of the MEGSC. We compared the proposed approach with the experimental results to explain the effect of nonradiative recombination on MEGSCs. Minimizing nonradiative recombination can significantly improve \(\mathrm{V_{OC}}\) by reducing surface defects.  
The following are available online at [[http://www.mdpi.com/2076-3417/10/16/5558/s1](http://www.mdpi.com/2076-3417/10/16/5558/s1)]([http://www.mdpi.com/2076-3417/10/16/5558/s1](http://www.mdpi.com/2076-3417/10/16/5558/s1)), Table S1: The theoretical maximum efficiency with the variation of \(\mathrm{f_{NR}}\) under one-sun illumination (C = 1), where \(\mathrm{\eta}\) is the efficiency. Table S2: The theoretical maximum efficiency for different values of \(\mathrm{f_{NR}}\) under full-light concentration (C = 46,200), where \(\mathrm{\eta}\) is the efficiency. Figure S1: Variations of \(\mathrm{f_{NR}}\) with theoretical efficiencies of the MEGSC. For this simulation, we use IQY and NQY (E\({}_{\mathrm{th}}\) = 2.E\({}_{\mathrm{g}}\), 3-E\({}_{\mathrm{g}}\), and 4-E\({}_{\mathrm{g}}\)) under one-sun illumination. Figure S2: Variations of \(\mathrm{f_{NR}}\) with theoretical efficiencies of the MEGSC. For this simulation, we use IQY and NQY (E\({}_{\mathrm{th}}\) = 2:E\({}_{\mathrm{g}}\), 3-E\({}_{\mathrm{g}}\), and 4-E\({}_{\mathrm{g}}\)) under full-light concentration.  
Conceptualization, [PERSON]; Supervision, [PERSON]; Writing--original draft, J.L.; Writing--review & editing, [PERSON] All authors have read and agreed to the published version of the manuscript.  
This research paper is based upon work supported in part by the Engineering Research Center Program of the National Science Foundation and the Office of Energy Efficiency and Renewable Energy of the Department of Energy under NSF Cooperative Agreement No. EEC-1041895. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the National Science Foundation or Department of Energy.  
The authors declare no conflict of interest.