## 5 Summary and Conclusions  
A model is developed that accurately interprets the distortion of the I-V characteristics of SHJ cells under illumination linked to hole reflection at the thermionic emission barrier. In the proposed model, the reflected holes at the thermionic emission energy barrier pile up at the hetero-interface and create an excess dipole with negative ions in the a-Si:H(p\({}^{+}\)) layer. The enhanced electric field crossing the a-Si:H(i) layer sweeps the free holes spilling-over from the a-Si:H(p\({}^{+}\)) layer back, strongly depleting the intrinsic layer and widening the depletion of the doped layer, which enhance the total cell series resistance. With such a model, the large forward bias V\({}_{\text{SC}}\) established at the pn junction even at short circuit terminals compensates the voltage drop on the enhanced series resistance under illumination. Also, since the model explains the bias dependence of V\({}_{\text{SC}}\), which follows that of the enhanced a-Si:H resistance linked to the bias dependence of the excess electric field at the hetero-interface. In addition, the model predicts that cells with heavily doped a-Si:H(p\({}^{+}\)) would suffer less from hole reflection at the thermionic emission under illumination because the relative excess hole concentration piling-up at the hetero-interface is smaller. Therefore, the enhanced field, a-Si:H depletion and resistance are undermined, which results in smaller values of V\({}_{\text{SC}}\) and to improved I-V characteristics and cell \(FF\).  
Moreover, since the proposed model assimilates the impact of hole reflection at the thermionic barrier to a series resistance effect, it gives an answer to why only the cell \(FF\) is degraded, while the cell open circuit is unaffected. Accordingly, the degradation associated with the thermionic barrier can be clearly differentiated from that related to the front Schottky contact in the presence of an inadequate TCO usually characterized by a degradation in both the Voc and the \(FF\).  
Figure 12: Simulated (**a**) free hole concentration profile and (**b**) electric Field distribution at equilibrium (_Cont. line_) and under illumination-SC (_Dash_) for cell SHJ\({}_{4}\) assuming thermionic emission hole transport at the hetero-interface with a default value of A\({}^{*}\).  
Figure 13: Simulated valence band diagram of cell SHJ\({}_{4}\) at equilibrium and under illumination-SC assuming thermionic emission transport across the hetero-interface with the default A\({}^{*}\) value.  
**Author Contributions:** Both authors have made significant contribution to this study and have approved this submission. [PERSON] originated the idea and defined the methodology. Both authors contributed to running the simulations and in discussing and validating the interpretations. Conceptualization: M.G.; data curation: M.G.; formal analysis: M.G.; funding acquisition: Y.A.; investigation: M.G. and Y.A.; methodology: M.G.; project administration: Y.A.; software: M.G. and Y.A.; validation: M.G. and Y.A.; writing--original draft: M.G.; writing--review & editing: M.G.  
**Funding:** This research was funded by Kuwait Foundation for the Advances of Science [KFAS] grant number [P115-15 EE-01].  
**Acknowledgments:** This work is supported by the Kuwait University Research Administration project GE01/08 and the KFAS/KU-IMEC funded project P115-15 EE-01.  
**Conflicts of Interest:** The authors declare no conflict of interest.