## 1 Introduction  
Multiple exciton generation solar cells (MEGSCs) are promising future-generation solar cells that are capable of creating several electron and hole pairs (EHPs) via impact ionizations. This can overcome the theoretical single-junction efficiency limit by decreasing the carrier thermalization loss in nanostructured materials [1; 2; 3]. A quantum efficiency of \(>\)100% has been observed in silicon solar cells, which has motivated the development of theoretical and empirical approaches for MEGSCs [4; 5]. The theoretical efficiency of MEGSCs has been calculated [5; 6; 7; 8; 9] based on the ideal quantum yield (QY), which is the number of EHPs generated under blackbody radiation. In the detailed balance (DB) limit, single-junction solar cells (SJSCs) consider only one radiative recombination (Figure 1a), and the MEGSC undergoes multiple-carrier recombination (MR) via Auger recombination (AR). The M \(-\) 1 electrons directly recombine into holes and transfer their energy to the remaining electron, where M is the maximum generated EHPs. By absorbing the energy, the electron excites to a high-energy state. Thereafter, it emits single-photon energy (which is equal to the product of the maximum quantum yield and the bandgap energy) without losses (Figure 1b) [7]. The amount of photon energy emitted is comparable to that of the topmost junction in a tandem solar cell under blackbody radiation. An MEGSC under blackbody radiation shows efficient carrier management, undergoing no other nonradiative recombination processes. However, the MR in the actual materials describes nonradiative AR to occur via phonon-assisted electron or hole relaxation [10] (Figure 1c). Experiments show that the excited electrons or holes release their kinetic energy to reach the valence band. Subsequently, the carrier experiences direct recombination or capture at the trap. Therefore, this relaxation process limits the performance of an MEGSC as the carrier cooling rate is slowed down, moving from one state to another [11]. In the context of carrier dynamics of the MEGSCtheory, the excited carriers experience multiple exciton generation (MEG) via impact ionization, release energy via phonons, and produce additional decay paths through surface state or defects. Thus, these conditions produce a less-ideal MEG because of the generation of nonradiative recombination paths of quantum dots (QDs) in MEGSCs [11]. The discrepancy between ideal and actual performance depends on MEGSC idealities. Two parameters are crucial to test the characteristics of an MEGSC: QY and threshold energy (\(=\) E\({}_{\text{th}}\)). The ideal quantum yield (IQY) increases according to a staircase step function, and the threshold energy describes the onset point over 100% of QY. The E\({}_{\text{th}}\) for IQY is twice that of the bandgap energy (E\({}_{\text{th}}\) = 2.E\({}_{\text{g}}\)) without carrier losses [5; 6; 7; 8; 9], but the actual material shows a difference in QY and E\({}_{\text{th}}\) because of nonidealities related to surface state or defects. Thus, the nonideal quantum yield (NQY) shows a delayed E\({}_{\text{th}}\) and a linearly increasing QY. During initial measurements of QY in PbSe QDs up to 300% and 700% [12; 13], various groups have examined the NQY by pump-probe measurements with CdTe [14], CdSe [15], InAs [16; 17], and Si [18]. The uncertainties related to surface states and long-lived QD photocharging in the pump-probe measurements [19; 25] have limited the QY up to 300% in QD systems. The experimental results of measurements in QD MEGSCs are much lower than the theoretical limit owing to nonradiative recombination and insufficient light absorption [26; 27; 28; 29; 30]. Therefore, these shortcomings have initiated developments in the DB limit of an MEGSC for quantitative analysis of the impact of nonradiative recombination. The conventional AR depends on the material parameters (carrier lifetime, doping concentration, and Auger constant) in the DB [31].