In order to examine the effect of Floquet boundary condition in 3D FE analysis, as shown in Figure , we compare the difference between the simulated unit cells of 1 × 1 and 2 × 2 array of Si3
SWS. We find at the wavelengths above 600 nm, the reflectance of 1 × 1 array of Si3
SWS as unit cell is almost consistent with unit cell of 2 × 2 array, meanwhile insignificant discrepancy occurs at wavelengths shorter than 600 nm. Based on this consequence, it is enable us to do simulation with more computational efficient using 1 × 1 array of Si3
SWS as a simulated unit cell with engineering acceptable accuracy. According to our recent RCWA work [4
], the reflectance spectra are first plotted in Figure using the optimal design parameters [1
]. Also, the spectra calculated by a full 3D FE analysis with the same design parameters are indicated by dashed lines. For the cylinder-shaped Si3
SWS, the reflectance spectra for RCWA and FE analysis are similar, but not agreed for the cone-shaped Si3
SWS due to existing evanescent orders along the top of structures. This comparison confirms the importance of 3D FEM simulation which is beyond the RCWA approach [4
Figure 2 Plot of the difference of reflectance spectrum of Si3N4 SWS with the cylinder-, the right circular cone-, and the square pyramid-shaped structures as well as two different periodical configurations: 1 × 1 (solid line) and 2 × 2 arrays (more ...)
Comparison of the reflectance spectra for the cone- and cylinder-shaped Si3N4 SWS calculated by RCWA and 3D FE analysis with the same design parameters.
Figure shows the reflectance spectra with incident angles of 0°, 15°, 30°, 45°, and 60° for the cylinder-, right circular cone-, and square pyramid-shaped Si3
SWS, respectively. For the normal incidence case, the lowest average reflectance among three structural shapes is 3.47% of square pyramid-shaped structure. The others are 6.86 and 4.42% for the cylinder- and the right circular cone-shaped Si3
SWS, respectively. Meanwhile, as shown in Figure , one can observe that the reflectance increases significantly with larger incident angles, resulting in average reflectance beyond 50%. Table summarizes the average reflectance for various incident angles. Height effect on average reflectance of Si3
SWS at normal incident angle with d
= 130 nm and s
= 70 nm is also calculated, as shown in Figure . The resulting average reflectance of pyramid-shaped Si3
SWS nearly keeps lowest in comparison with the cylinder- and the right circular cone-shaped Si3
SWS as the structural height is ranging from 50 to 500 nm. Figure shows the reflectance dependence on the structural height and wavelength. The pyramid-shaped Si3
SWS has lower reflectance and less sensitivity on structure height in comparison with the cylinder-shaped Si3
SWS. Hence, the impact of process variation of structure height on solar cell performance is smaller for pyramid-shaped Si3
SWS. Based on solar spectrum at the sea level revealed in American Society for Testing and Materials (ASTM) Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical 37 Tilted Surface [9
], we further estimate the reflected power density (W/m2
/nm) defined by reflectance times incident power density, as shown in Figure . The higher reflected power density of cylinder-shaped Si3
SWS (red line) indicates the less efficiency in the solar cell application. Therefore, normalized reflectance defined as
Plots of the reflectance spectrum for the (a) cylinder- (b) circular-cone-, (c) and square-pyramid-shaped Si3N4 SWS with incident angles of 0°, 15°, 30°, 45°, and 60°.
Summary of the average reflectance of Si3N4 SWS with various incident angles
Plot of the average reflectance among the studied three shapes of Si3N4 SWS with heights varying from 50 to 500 nm.
3D view for the height effect on the reflectance with respect to different wavelength. (a) The pyramid-shaped Si3N4 SWS has lower reflectance and less sensitivity on structure height in comparison with (b) the cylinder-shaped Si3N4 SWS.
Plot of the reflected power density among three different shapes.
reveals the real power efficiency applied in the solar cell application. Figure shows the normalized reflectance for the cylinder-, right circular cone-, and square pyramid-shaped Si3N4 SWS, respectively. The square pyramid-shaped Si3N4 SWS again shows the lowest normalized reflectance 3.13% while the cylinder- and the right circular cone-shaped Si3N4 SWSs have 6.66 and 4.12%, respectively.
Plot of reflectance with and without considering incident solar spectrum at sea level.