## 3 Results of Simulations
### SHJ Cell Characterization under Illumination
#### 3.2.1 Current-Voltage (I-V) Characteristics  
Figure 4a displays the I-V characteristics simulated under illumination for the cells SHJ\({}_{1}\) and SHJ\({}_{4}\) to be investigated here, together with those of two other cells SHJ\({}_{2}\) and SHJ\({}_{3}\) with intermediate doping concentrations in a-Si:H(p\({}^{+}\)) N\({}_{\text{a-Si}}\) = 1 \(\times\) 10\({}^{19}\) cm\({}^{-3}\) and 5 \(\times\) 10\({}^{19}\) cm\({}^{-3}\), respectively [35]. While \(V_{OC}\) and \(I_{\text{SC}}\) maintain their proper values, the FF in the cells degrade considerably to reach 40% in cell SHJ\({}_{1}\) with N\({}_{\text{a-Si}}\) = 5 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) and 75.5% in cell SHJ\({}_{4}\) with N\({}_{\text{a-Si}}\) = 10\({}^{20}\) cm\({}^{-3}\), which is well below what is expected from a high efficiency c-Si cell. It has been suggested, in a merely descriptive way, that such distortion relates to hole reflection at the a-Si:H/c-Si thermionic emission barrier [35]. In order to validate such a model, however, a link to a measurable quantity that satisfies the model predictions must be found. For instance, the shape of the distorted I-V characteristics suggests the presence of a high cell series resistance since \(V_{\alpha}\) is practically unaffected by the distortion. When drift-diffusion rather than thermionic emission transport is assumed, however, the severe distortion disappears from the I-V characteristics of cell SHJ\({}_{1}\) as depicted in Curve 4 of Figure 4b, which confirms that the distortion is related to thermionic emission transport but does not systematically link it to a high series resistance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Cell: N\({}_{\text{a-Si [cm${}^{-3}$]}}\)**} & **A** & **B** & **(B\(-\)A)** \\ \cline{2-4}  & **WF\_c-Si [eV]** & **WF\_a-Si [eV]** & **V\({}_{\text{bi,total [V]}}\)** \\ \hline SHJ\({}_{1}\): 5 \(\times\) 10\({}^{18}\) & 4.245 & 5.414 & 1.169 \\ SHJ\({}_{4}\): 1 \(\times\) 10\({}^{20}\) & 4.245 & 5.580 & 1.335 \\ \hline  & C & D & (C+D) \\  & V\({}_{\text{bi,a-Si [V]}}\) & V\({}_{\text{bi,c-SI [V]}}\) & V\({}_{\text{bi,total [V]}}\) \\ \hline SHJ\({}_{1}\): 5 \(\times\) 10\({}^{18}\) & 0.270 & 0.899 & 1.169 \\ \hline SHJ\({}_{4}\): 1 \(\times\) 10\({}^{20}\) & 0.391 & 0.944 & 1.335 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Built-in potential and its components in cells SHJ\({}_{1}\) and SHJ\({}_{4}\) at equilibrium.  
Different I-V characteristics for SHJ\({}_{1}\) simulated under different conditions with and without TCO at the front contact are compared in Figure 4b. In Curves 1, 2, and 3, the distortion caused by reflection at the thermionic emission barrier is clearly recognized. In Curve 1, however, Voc also degrades considerably due to weak inversion caused by the front Schottky contact when the TCO work function is low. In Curve 2, the TCO work function is high enough to avoid such a \(V_{OC}\) degradation. Curve 3 is identical to Curve 1 in Figure 4a with flat band front contact. Finally, Curve 4 displays I-V characteristics of the reference simulation assuming drift-diffusion transport and flat band front contact. I-V characteristics similar to those of Curves 1 and 2 were reported previously [26; 32], with no clear interpretation for the shape of the distortion.