3D simulation of morphological effect on reflectance of Si3N4 sub-wavelength structures for silicon solar cells
© Li et al; licensee Springer. 2012
Received: 17 November 2011
Accepted: 23 March 2012
Published: 23 March 2012
In this study, we investigate the reflectance property of the cylinder, right circular cone, and square pyramid shapes of silicon nitride (Si3N4) 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 three-dimensional 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.
Silicon solar cell is one of the promising renewable energy technologies in order to relieve the impact of the climate change. In semiconductor-based solar cells, electron-hole 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 Si3N4 SWS is promising among various ARC layers in our recent work . A rigorous coupled-wave analysis (RCWA) [1, 5–7] has been reported to estimate the reflectance of Si3N4 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 non-azimuthally symmetric structural shapes. Numerical simulation of 3D morphological effect on reflectance property has not been studied yet. Therefore, a full 3D finite-element (FE) analysis of Si3N4 SWS will be an interesting examination for quantitative understanding of the reflectance property.
In this study, 3D FE simulation for the reflectance of Si3N4 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 Si3N4 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 wide-angle 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 Si3N4 SWS based on RCWA , 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, λ1 = 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 Si3N4 SWS with various incident angles
Average reflectance (%)
Circular cone shape
Square pyramid shape
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 Si3N4 SWS, we have concluded that the pyramid-shaped Si3N4 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 Si3N4 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 pyramid-shaped Si3N4 SWS is currently under plan for implementation with silicon solar cells.
finite element method
rigorous coupled-wave analysis
This study was supported in part by the Taiwan National Science Council under contract Nos. NSC-99-2221-E-009-175 and NSC-100-2221-E-009-018.
- Sahoo KC, Li Y, Chang EY: Numerical calculation of reflectance of sub-wavelength structures on silicon nitride for solar cell application. Comput Phys Commun 2009, 180: 1721–1729. 10.1016/j.cpc.2009.04.013View Article
- Sahoo KC, Lin MK, Chang EY, Tinh TB, Li Y, Huang JH: Silicon nitride nanopillars and nanocones formed by nickel nanoclusters and inductively coupled plasma etching for solar cell application. Jpn J Appl Phys 2009, 48: 126508. 10.1143/JJAP.48.126508View Article
- Sahoo KC, Chang EY, Lin MK, Li Y, Huang JH: Fabrication and configuration development of silicon nitride sub-wavelength structures for solar cell application. J Nanosci Nanotechnol 2010, 10: 5692–5699. 10.1166/jnn.2010.2553View Article
- Sahoo KC, Li Y, Chang EY: Shape effect of silicon nitride sub-wavelength structure on reflectance for solar cell application. IEEE Trans Electron Dev 2010, 57: 2427–2433.View Article
- Moharam MG, Gaylord TK: Rigorous coupled-wave analysis of planar-grating diffraction. J Opt Soc Am 1981, 71: 811–818. 10.1364/JOSA.71.000811View Article
- Moharam MG, Gaylord TK: Rigorous coupled-wave analysis of metallic surface-relief gratings. J Opt Soc Am A 1986, 3: 1780–1787. 10.1364/JOSAA.3.001780View Article
- Moharam MG, Pommet DA: Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings. J Opt Soc Am A 1995, 12: 1077–1086. 10.1364/JOSAA.12.001077View Article
- Sahoo KC, Lin MK, Chang EY, Lu YY, Chen CC, Huang JH, Change CW: Fabrication of antireflective sub-wavelength structures on silicon nitride using nano cluster mask for solar cell application. Nanoscale Res Lett 2009, 4: 680–683. 10.1007/s11671-009-9297-7View Article
- ASTM Standard G173–03: Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface.2008. [http://www.astm.org/Standards/G173.htm]
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.