## 3 Results
### Normal Multi-function vs. Super-Multi-Junction; Practical Conditions
#### 3.2.2 Computation Results of the Monte Carlo Simulation in the Practical Conditions  
The distribution of the annual average efficiency of both a multi-junction solar cell and a super- multi-junction solar cell optimized by the spectrum in one year in Miyazaki is shown in Figure 11. The trend of the average of the annual average efficiency in each event in Figure 2, as well as the standard deviation of the distribution, is shown in Figure 12, overviewing the general efficiency trend after optimization. Please note that the spectrum for optimization was not the artificial standard spectrum (AM1.5G), but an accidental annual spectrum given by Monte Carlo simulation calculated by the flowchart in Figure 5, considering both seasonal and accidental fluctuation in the atmospheric parameters and fluctuation of the solar irradiance within the range of the highest and lowest irradiance in Miyazaki taken from the solar irradiance database of METPV-11. The underlying probability model for the calculation of the distribution of the average annual efficiency was given by the flowchart in Figure 2.  
The normal multi-junction solar cell showed the broader distribution of the average annual efficiency depending on the spectrum in that year, as the increase of junction number. This is because the width of the absorbing spectrum band of each junction becomes narrower. This implies that the impact on the annual average efficiency by the spectrum-mismatching loss increases with the increase of the number of junctions. As a result, the annual average efficiency peaked at four junctions and then decreased with the increase of the number of junctions. The super-multi-junction solar cell, on the contrary, showed narrower distribution, but it still shows a slightly broader distribution as the junction number increases. The annual average efficiency in the super-multi-junction solar cells is expected to reach 50% by 6-8 junctions. An example of the distribution of the optimized bandgap energy of 10-junction solar cells is shown in Figure 13. The optimized bandgap was calculated according to the spectrum and other climate conditions given by random numbers, according to Figure 2. The histogram of the calculated  
Figure 10: Quantile–quantile plot that examines the values of two distributions: (**a**) Aerosol density; (**b**) Water precipitation. optimized bandgap energy in each junction is normalized so that the integral of the range becomes unity. The overlap of each peak does not mean that the higher bandgap junction has lower bandgap energy than that of the lower peak. It is constrained that the bandgap structure was equivalently modeled by allowing the bandgap energy of the \((i+1)\)th junction to be equal or greater than that of the \((i)\)th junction, but not allowing the bandgap energy of the \((i+1)\)th junction to be less than that of the \((i)\)th junction. The most distinct difference of the super-multi-junction solar cell from the normal multi-junction solar cell is the level of the top junction. The distribution of the optimized bandgap energy of the top junction was substantially lower than that of the normal multi-junction solar cell. This is because the short-wavelength region of the sunlight is changeable by fluctuation of the aerosol scattering and the lower bandgap energy in the top junction is favorable in generating surplus current, so it compensates for the spectrum-mismatching loss by transferring the photon energy generated by the recombination using the surplus current of the top junction. The set of the bandgap energy of the super-multi-junction solar cell is listed in Table 4. Unlike the current technology, the designed bandgap of each junction has a range, demonstrating that the super-multi-junction solar cell is robust to bandgaps. Figure 11: Optimization design result of the normal multi-junction solar cells (distribution of the annual average efficiency) under the worst-case combination of climate, atmospheric conditions, latitude, and orientation angle.