3D simulation of morphological effect on reflectance of Si_{3}N_{4} subwavelength structures for silicon solar cells
 Yiming Li^{1}Email author,
 MingYi Lee^{1},
 HuiWen Cheng^{1} and
 ZhengLiang Lu^{1}
DOI: 10.1186/1556276X7196
© Li et al; licensee Springer. 2012
Received: 17 November 2011
Accepted: 23 March 2012
Published: 23 March 2012
Abstract
In this study, we investigate the reflectance property of the cylinder, right circular cone, and square pyramid shapes of silicon nitride (Si_{3}N_{4}) subwavelength structure (SWS) with respect to different designing parameters. In terms of three critical factors, the reflectance for physical characteristics of wavelength dependence, the reflected power density for real power reflection applied on solar cell, and the normalized reflectance (reflected power density/incident power density) for real reflectance applied on solar cell, a full threedimensional finite element simulation is performed and discussed for the aforementioned three morphologies. The result of this study shows that the pyramid shape of SWS possesses the best reflectance property in the optical region from 400 to 1000 nm which is useful for silicon solar cell applications.
1. Introduction
Silicon solar cell is one of the promising renewable energy technologies in order to relieve the impact of the climate change. In semiconductorbased solar cells, electronhole pairs are generated through absorption of impinging photons. Due to high refraction index of semiconductor materials, especially silicon, the incident sunlight power is largely reflected back, resulting in the reduction of light absorption and poor energy conversion efficiency. Antireflection coating (ARC) is mounted over absorption layers, resulting in three effects: (a) reduction in surface reflection, (b) increase in light absorption due to an increase in optical path length by diffraction, and (c) enhancement of internal reflection that reduces the amount of escaping light. Based on the theory of impedance matching, single layer (SLR) and multilayer of ARC are proposed for reduced reflectance property; however, the resulting reflectance spectra meet the demand only within a narrow spectral domain. Subwavelength structure's (SWS) dimensions are much smaller than the wavelengths of light; therefore, using ARC on the surface of silicon solar cells can substantially reduce the reflectivity and improve the capability of light trapping. It thus will achieve the enhanced efficiency according to our recent both numerical and experimental studies [1–3]. Compared with silicon solar cell with a SLAR, the efficiency of silicon solar cell with Si_{3}N_{4} SWS is promising among various ARC layers in our recent work [4]. A rigorous coupledwave analysis (RCWA) [1, 5–7] has been reported to estimate the reflectance of Si_{3}N_{4} SWS by approximating structural shapes with partitioned uniform homogeneous layers. RCWA is an exact solution of Maxwell's equations for the electromagnetic diffraction by grating structures which is generally applicable for 2D plane with 1D periodicity; however, RCWA may suffer numerical difficulties in presence of evanescent orders and it requires a large amount of calculation for retaining several diffraction orders. These factors limit flexible application of RCWA; in particular, for 3D problems with nonazimuthally symmetric structural shapes. Numerical simulation of 3D morphological effect on reflectance property has not been studied yet. Therefore, a full 3D finiteelement (FE) analysis of Si_{3}N_{4} SWS will be an interesting examination for quantitative understanding of the reflectance property.
In this study, 3D FE simulation for the reflectance of Si_{3}N_{4} SWS with three types of structural shapes, the cylinder, the right circular cone, and the square pyramid shapes, is conducted with respect to different geometry parameters and lighting angles for quantitative understanding of reflectance property. First, proper selection on the boundary conditions can alleviate the computational load from simulating a holistic ARC. The reflectance of Si_{3}N_{4} SWS on the silicon substrate is thus simulated using the 3D finite element method (FEM); consequently, in terms of three critical factors, the reflectance for physical characteristics of wavelength dependence, the reflected power density for real power reflection applied on solar cell, and the normalized reflectance (reflected power density/incident power density) for real reflectance applied on solar cell are calculated and discussed for the aforementioned three morphologies. The analysis of reflectance spectrum with wideangle incidences of electromagnetic wave and the average reflectance with various heights are presented. Besides, according to our recent study, which presented the optimal design parameters of Si_{3}N_{4} SWS based on RCWA [4], numerical verification and comparison is accomplished following the discussion. The engineering findings of this study show that the pyramid shape of SWS possesses the best reflectance property in the optical region from 400 to 1000 nm which is useful for silicon solar cell applications.
This rest of the article is organized as follows. In Section 2, we show the computational structure and model. In Section 3, we report the results and discussion. Finally, we draw conclusions and suggest future work.
2. The SWS and optical model
where λ is the incident wavelength, A = 0.939816, B = 8.10461 × 10^{3}, λ_{1} = 1.1071 μm, and ε = 11.6858. The calculation settings of reflectance were reported and can be found in our recent studies [1, 4].
3. Results and discussion
Summary of the average reflectance of Si_{3}N_{4} SWS with various incident angles
Average reflectance (%)  0°  15°  30°  45°  60° 

Cylinder shape  6.86  6.70  9.95  23.13  52.78 
Circular cone shape  4.42  3.64  7.79  26.68  50.98 
Square pyramid shape  3.47  3.15  8.88  24.40  51.44 
4. Conclusions
In this study, the reflective property of unit cell with a validated Floquet boundary condition has been calculated using a full 3D FE simulation. Considering various incidence angles and height effect on three experimentally observed structural shapes of Si_{3}N_{4} SWS, we have concluded that the pyramidshaped Si_{3}N_{4} SWS has best reflective property in the analysis of morphological effect. Compared with the results of RCWA, the reflective property calculated by the full 3D FEM is significantly deviated from the results from RCWA, giving the hint that a detailed and comprehensive methodology is dispensable for the design of Si_{3}N_{4} SWS. The results of computed reflectance, reflected power density, and normalized reflectance have shown that the pyramid shape of SWS may have the best reflectance property in the optical region from 400 to 1000 nm which is useful for silicon solar cell applications. The optimized pyramidshaped Si_{3}N_{4} SWS is currently under plan for implementation with silicon solar cells.
Abbreviations
 3D:

threedimensional
 ARC:

antireflection coating
 FEM:

finite element method
 RCWA:

rigorous coupledwave analysis
 Si_{3}N_{4}:

silicon nitride
 SLAR:

single layer
 SWS:

subwavelength structure.
Declarations
Acknowledgements
This study was supported in part by the Taiwan National Science Council under contract Nos. NSC992221E009175 and NSC1002221E009018.
Authors’ Affiliations
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