# The Outdoor Field Test and Energy Yield Model of the Four-Terminal on Si Tandem PV Module
Four-terminal (4T) tandem cells were designed so that the output of the Si cell and other top junctions were taken independently, thus robust to the spectrum change. In the case of III-V/Si three-junction solar cells that are frequently considered as an excellent candidate for high-efficiency solar cells, the output terminal from the top cell comes from two-junction III-V solar cells, and the top two-junction cell is still susceptible to spectrum change. Therefore, a long-term field test of the module using III-V/Si 4T solar cells is essential to the validation of the use of this configuration. Currently, the best efficiency confirmed by the third-party is 33.3% [85]. Other groups of the 4T type tandem cells are partial concentrator cells and 3T tandem cells. The partial concentrator solar cell was first proposed in 2017 [86], using wide-acceptance concentrator optics that selectively concentrate onto the top III-V cells stacked on the larger size Si bottom cell. This type of tandem solar cell was considered for the application to VIPV [87] and various design methods and models were invented [88; 89; 90]. Several prototypes were made [28], and an annual average efficiency as high as 27.4% was anticipated [77]. 3T type tandem cells basically connect one of the terminals of the pairs of the two-terminal. This method has an advantage of simplifying the interconnection of the solar cells among the PV module. There are several types of tandem cells, including Ge-based III-V \begin{table}
\begin{tabular}{c c c} \hline \hline  & **CPV 1** & **Normal Installation** \\ \hline Solar spectrum & Only direct & A mixture of direct, diffused from the sky, and reflection \\ Angle & Always normal & Varies by time and seasons \\ Spectrum by angle & Constant (only normal) & Needs consider coupling to angle \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The difference in performance modeling between concentrator photovoltaic (CPV) and standard installation [1]. The outdoor performance of CPV was intensively studied in more than 20 years considering the spectrum mismatching problem of the tandem solar cells. cell [91], polymer type [92], III-V monolithic [93], and III-V on Si [94]. The advantage of the better spectrum matching operation using this 3T configuration was also studied [95]. The background of this study and our motivation are summarized as follows:  
1. Tandem solar cells are highly efficient, and various types of the device structure were studied. On-Si tandem is one of them, and it has a distinct advantage of cost, using well-established Si solar cell technology. 2. Regardless of the type of material, the annual performance of the tandem solar cells does not perform well due to spectrum mismatching loss. 3. The modeling of the spectrum mismatching loss was studied relying on the airmass variation. The intensive study on CPV performance in more than 20 years revealed that the fluctuation of atmospheric parameters played an essential role. 4. Due to the development of the new application of the high-efficiency solar cell, including vehicle-integrated solar cells, the precise annual energy yield modeling of the tandem solar cells is required. The knowledge on precise spectrum-mismatching modeling in CPV is expanded to the non-concentration standard installation. 5. 4T on Si tandem solar cell is a good candidate for the robustness to the spectrum variation. Its outdoor operation and energy yield modeling was intensively studied in this article. The model did not rely only on airmass but considered real fluctuation of the spectrum in all kinds of climate, considering atmospheric fluctuation.