Open Access
Add to BibSonomyAbstract
In this study we report novel silicon nanowire (SiNW) array structures that have near-unity absorption spectrum. The design of the new SiNW arrays is based on radial diversity of nanowires with periodic diamond-like array (DLA) structures. Different array structures are studied with a focus on two array structures: limited and broad diversity DLA structures. Numerical electromagnetic modeling is used to study the light-array interaction and to compute the optical properties of SiNW arrays. The proposed arrays show superior performance over other types of SiNW arrays. Significant enhancement of the array absorption is achieved over the entire solar spectrum of interest with significant reduction of the amount of material. The arrays show performance independent of angle of incidence up to 70 degrees, and polarization. The proposed arrays achieved ultimate efficiency as high as 39% with filling fraction as low as 19%.
© 2015 Optical Society of America
1. Introduction
Semiconductor nanowire (NW) arrays, in general, but more specifically, silicon nanowire (SiNW) arrays are considered highly attractive and promising for light trapping in photovoltaic applications. NW arrays show unique optical properties relative to thickness-equivalent slab of the same material. Properly designed NW array has lower reflectance and higher absorptance, and at the same time uses less material in comparison with flat films. The optical properties of the vertically aligned NW arrays can be modified and controlled by adjusting their geometric parameters such as height, radius, NW cross section, and lattice constant [1,2]. Numerous researchers have proposed different array configurations to enhance absorption spectrum [1–4]. Some studies show the tunability of the optical properties of SiNW arrays by adjusting the radius value of NW [5]. Other studies propose randomizing geometrical parameters to enhance the absorption spectrum of SiNW arrays [6,7]. This randomness can be in the form of random height, radius, and (or) positioning of the NWs. Random NW arrays show enhancement in the absorption spectrum compared to the uniform periodic SiNW arrays. Other studies propose different geometries of the NW cross section, such as elliptical, square, and hexagonal cross sections to enhance arrays performance [8–11]. In the current study, we introduce for the first time the concept of employing diversity of SiNW radii in certain distributions that is inspired from diamond crystal lattice structure. The proposed distribution of diverse radius NWs produces significantly broadened and enhanced absorption spectra with significantly reduced amount of material in the SiNW arrays. Such highly ordered SiNW arrays can be realized for PV applications by using nano-imprinting lithography techniques [12].
2. Methods and simulation strategy
Numerical electromagnetic simulation is used in our study. The high frequency structure simulation (HFSS) commercial software package is used to calculate the reflectance, transmittance, and absorptance of the SiNW arrays. HFSS implements finite element method (FEM) for solving Maxwell equations, which offers the capability to conduct 3D full wave simulation of structures with sub wavelength features. In addition, HFSS offers the capability to employ the experimental optical properties of materials. The scattering matrix of the nanowire structures are used to determine the reflectance, R(λ), and transmittance, T(λ), and from there the absorptance, A(λ), is calculated as:
Normal incident plane wave is assumed to illuminate the arrays with parallel polarization, and the standard AM1.5 solar spectrum is used with wavelength range of λ = 315 to 4000 nm. To study the optical properties of the arrays in isolation from other effects, the arrays are assumed to be suspended in air. The SiNW arrays are considered 2D infinite periodic arrays in the X and Y directions, and circular cylinders are used to model the SiNWs. The infinite array is realized in the simulation domain by using a periodic unit cell with perfect electric conductor (PEC) and perfect magnetic conductor (PMC) walls. The experimental optical properties of the crystalline silicon are employed in the simulations, as proposed by [13], Palik et al. The performance of the SiNW arrays is quantified by calculating the ultimate efficiency as:where λ is the wavelength in nm, λg is the wavelength corresponding to the crystalline silicon band gap, I(λ) is the standard AM1.5 solar spectrum, and A(λ) is the absorptance of the array. To study the angular response of arrays at different polarization and orientation angles with respect to the lattice structure of the array, Bloch periodic boundary conditions are used, which can be realized by using Floquet ports and the master-slave boundary conditions on the unit cell walls [14].3. Principles of design
The focus of this study is on employing diversity of the geometrical parameters of a NW array to produce an enhanced and broadband absorption spectrum. In this manuscript, two geometrical parameters are investigated: the radii and the distribution of NWs in an array. The design of the proposed SiNW array is based on employing diversity of NW radii with a specific distribution in array lattice structure. The main goal is to achieve optimal performance in terms of ultimate efficiency and the amount of material used. To this end, four types of SiNW array structures are studied (i) uniform periodic arrays (ii) modified radii NW arrays (iii) diamond-like arrays (DLA) with limited radial diversity and (iv) DLA with broad radial diversity. Enhancing the performance of these NW arrays depends on the radial diversity as well as the distribution of the NWs. In order to show the effect of radius value on the absorption spectrum of an array structure, we first study a uniform periodic array with fixed height (h) and lattice constant (a). Then, to study the effect of radial diversity of NWs on the absorption spectrum, a uniform periodic array is modified to include two different NW radii, representing limited diversity. Furthermore, to show the effect of broadening the diversity of the NW radius values, the uniform periodic SiNW array is modified into two different arrays. One includes three different radii NWs, while the other one includes four different radii NWs. To study the distribution effect of diverse radii NWs, two lattice configurations are considered: rectangular and hexagonal. Finally, designs of SiNW arrays inspired from the diamond lattice structure are studied, analyzed, and optimized for the ultimate efficiency and the amount of material.
3.1 Uniform periodic arrays
The absorption spectrum of a uniform SiNW array with fixed height and lattice constant has peak positions that depend on the NW radius. As an example, the absorption spectrum of a diluted uniform rectangular array with fixed lattice constant (a = 400nm) and height (h = 2.3µm) is calculated at different radius values. The absorption spectra have peak positions that depend on the radius value of the SiNW, and red-shift as the NW radius increases, as shown in Fig. 1. The absorption peak position and the optical property dependence on the radius of the NWs have been explored by different studies analytically [15], experimentally [16], and numerically [4].
Fig. 1 (a) 3D depiction of a uniform periodic SiNW array, and the top view of the unit cell that is used in simulation domain to represent the array, and (b) absorption spectra of uniform periodic SiNW arrays, with fixed lattice constant and height (h) at different radius values (R). The absorption peaks that correspond to each radius value are shown, where the red shift due to radius increases is clearly observed.
In the current study, this phenomenon of red-shift of the absorption peaks is utilized to design new SiNW arrays with broadband absorption spectra. Our approach is based on the inclusion of NWs with diverse radii values in an array to generate an absorption spectrum with different overlapping peaks. Broad diversity of NW radius values is employed to obtain a more enhanced and broadband absorption spectrum. In this manner, several adjacent overlapping absorption peaks are created which broadens absorption spectrum. In the following sections, numerical modeling is used to highlight this concept.
3.2 Modified periodic arrays
To demonstrate the concept of radii diversity and its effect on absorption spectrum, four arrays are studied: uniform periodic array with single-valued NW radius, modified periodic arrays with two, three, and four radius values. The absorption spectrum of each array is shown in Fig. 2. The insets in the figure represent a 3D depictions of the arrays with color coded NWs based on their radius value. It is obvious that the multi NW radius inclusion in an array leads to multi absorption peaks, and as the diversity of the radii value is broadened the absorption spectrum becomes broader and the filling fraction reduces.
Fig. 2 Absoption spectra of the four different SiNW arrays: (a) uniform periodic array, and modified periodic array with (b) two, (c) three, and (d) four nanowires radii. The insets show 3D depections and top views of the unit cells of the NW arrays with color codes based on NW radius values as in Fig. 1. Lattice constant and the NW hieght in all arrays are 400 nm and 2.3 µm, respectively.
In addition, the lattice structure of the multi radius NWs array has an effect on the array optical properties. To illustrate this, two SiNW array lattice structures composed of multi radii NWs are arranged in square and hexagonal lattice configurations, as shown in insets of Fig. 3. To make fair comparison, the values of NW radii and the lattice constant are kept as in the modified periodic array in Fig. 2(b). Both arrays in Fig. 3 are composed of similar NW radius values (R1 = 60, R2 = 50, R3 = 40, and R4 = 30 nm). We observe that the lattice structure has noticeable impact on the absorption spectrum of diverse arrays, as inferred from Fig. 3. This effect of lattice configuration and arrangement of NWs can be attributed to the changing of the coupling conditions of the incident plane wave into the asymmetric radial modes in the NW array. These conclusions open up the possibility of proposing new SiNW arrays with diverse radii and structures inspired from diamond lattice structure.
Fig. 3 Absorption spectra of diverse SiNW arrays for two different distributions: (a) rectangular lattice structure (b) hexagonal lattice structure. The insets show 3D depiction and top view of the arrays.
3.3 Diamond-like array structures
In this configuration, the distribution of the NWs in a unit cell is inspired by the diamond crystal lattice structure. The top view of the periodic unit cell has resemblance with the view of the diamond crystal unit cell as seen from the [100] direction, as shown in Fig. 4.
Fig. 4 (a) Unit cell of the diamond crystal structure, (b) planar view of the diamond crystal unit cell as seen from the [100] direction, and (c) top view of the periodic unit cell with diamond-like distribution of the SiNWs that are color coded based on the radius value.
In the current study, two SiNW DLA structures are proposed: the first one with limited radii diversity while the second with broad radii diversity. The proper selection of the radius values and the spatial distribution of these NW arrays are key factors in enhancing the performance of SiNW arrays.
3.3.1 DLA with limited radii diversity
In this configuration, four different NW radii are selected representing limited diversity. The NWs are arranged in a square unit cell as shown in Fig. 5. The initial radius values are selected as (R1 = 135, R2 = 110, R3 = 90, and R4 = 65 nm), which are based on our previous work [17]. Thirteen SiNWs are arranged in a square periodic unit cell based on a certain strategy. The largest radius NWs are positioned at the corners of the unit cell, and the smallest radius at the middle of the edge lines of the unit cell. Such arrangement of nanowires yields optimal performance in terms of ultimate efficiency and filling fraction. The remaining NWs are positioned inside the unit cell which has initial width and length (W × L) of 1 × 1 µm.
Fig. 5 Schematic of the limited diversity DLA: (a) 3D depiction of the DLA with different colors coding the values of the NWs radius, (b) top view of the array, and (c) the unit cell of the DLA.
3.3.2 DLA with broad radii diversity
In this configuration, thirteen different values are assigned to thirteen NW radii that are arranged in the unit cell. A similar strategy of arranging the NWs in the limited diversity DLA is repeated. The largest radius NWs are positioned at the corners of the unit cell, and the smallest radii at the middle of the edge lines of the unit cell. The remaining NW are positioned inside the unit cell. Figure 5 shows a schematic of 3D depiction of DLA with color code indicating NW radius values. The initial values of NW radii are selected as (R1 = 135, R2 = 125, R3 = 115, R4 = 110, R5 = 105, R6 = 90, R7 = 85, R8 = 80, R9 = 75, R10 = 70, R11 = 65, R12 = 60, R13 = 55 nm). These values represent a broad diversity of the NW radius values. To make fair comparison, the unit cell dimensions are kept as in the limited diversity DLA.
4. Results and discussion
Previously, we reported the effect of employing diversity of geometrical parameters on enhancing SiNW array performance [17,18]. The design concepts, used in those studies, are deployed in the current study in order to achieve higher performance arrays (see Fig. 6). The effect of the diversity of NWs radius values and distribution on the absorption spectrum is investigated through different array configurations. The angular response of one of the proposed structures is also studied. These structures show enhanced and broadband absorption spectra that cover the wavelengths (λ = 315 to 1000nm).
Fig. 6 Schematic of the broad diversity DLA: (a) 3D depiction of the DLA with different colors coding the values of the NWs radius, (b) top view of the array, and (c) the unit cell of the DLA.
4.1 Radii diversity effect
The effect of employing NW radii diversity for diluted periodic and non-optimized SiNW array is shown by the illustrative example in Section (3.2). In this section, we apply the same approach to an optimized periodic SiNW array for ultimate efficiency and filling fraction. Parametric sweeping of the radii and lattice constant in the range of 40-350 nm and of 100-800 nm, respectively, is conducted which yields optimal values of R = 182 nm and a = 600 nm. In order to show the advantages of diversity, this array is modified into two diverse arrays. In the first, the array is composed of four different radii SiNW with 10 nm incremental steps (R1 = 182, R2 = 172, R3 = 162, R4 = 152 nm), while in the second with 20 nm incremental steps, the radii chosen are R1 = 182, R2 = 162, R3 = 142, R4 = 122 nm. The distributions of these NW are demonstrated by the insets in Fig. 7. Absorption spectra of these SiNW arrays are compared with the uniform periodic array absorption spectrum as shown in Fig. 7. These results show that applying radii diversity enhances absorption spectrum and reduces the amount of material used. The span of the radii values affects the absorption spectrum and can enhance the array performance. This issue is the further studied for DLA in the next section.
Fig. 7 Absorption spectra for optimized uniform periodic SiNW array, and diverse arrays (modified optimized uniform periodic arrays). NWs with four different radius values are included in the modified arrays as depicted in the inset.
The calculated ultimate efficiency and filling fraction of the three arrays are shown in Table 1. These results indicate that the radii diversity in an array causes gain in the efficiency and reduction in the amount of the material used. The radii diversity with a proper distribution of the NW is a key element for enhancing and broadening the absorptance of the SiNW arrays.
Table 1. The ultimate efficiency and the filling fraction of the SiNW arrays
4.2 Nanowires distribution effect
In addition to SiNW radii diversity, distribution of such SiNW plays a significant role in shaping the absorption spectrum as demonstrated in the previous sections. The diamond-like distribution of SiNW in a unit cell is studied for two configurations, the limited and broad diversity.
4.2.1 DLA with limited radii diversity
In the DLA, diversity and distribution of the NW are deployed to produce an enhanced absorption spectrum. The radius values are selected in a manner to produce an absorption spectrum that has multiple peaks. The initial unit cell dimensions and radius values lead to an enhanced and broadened absorption spectrum over uniform periodic arrays [17]. Further optimization is conducted for the ultimate efficiency of the limited diversity array. Since the array includes large number of parameters, the optimization is performed in two ways. In the first, NW radii are scaled while keeping the cell size the same; in the second, both the cell size and the NW radii are scaled simultaneously. For the first case, the ultimate efficiency vs the filing fraction is shown in Fig. 8(a). While for the second case, the filling fraction is kept constant as the initial value (24%), and the ultimate efficiency vs cell size scaling factor is shown in Fig. 8(b). The scaling factor is defined as the ratio of the size of the unit cell to the initial size of unit cell. Ultimate efficiency as high ~34% can be achieved with ~50% filling fractions. The optimal performance of the array, in the sense of filling fraction and ultimate efficiency, is achieved at scaling factor of 1.3 of the initial cell, as shown in Fig. 8(b). An interesting result out of the optimization of DLA is that ultimate efficiency can exceed 20% with a filling fraction as low as ~11%, as Fig. 8(a) shows. The absorption spectrum of the optimized array is shown in Fig. 9 in the next section.
Fig. 8 (a) Constant value lattice constant, variable NW radius values using 10% scaling increments, (b) fixed filling fraction 24% with scaling of the unit cell and the radii values in 10% increments.
Fig. 9 Absorption spectra of thin film, optimized uniform periodic array, modified periodic array with diversity, limited diversity DLA, and broad diversity DLA. The height (h) of the arrays and thickness of the thin film are 2.3 µm.
4.2.2 DLA with broad radii diversity
Broad diversity is shown to enhance the performance of the uniform periodic arrays, in terms of the ultimate efficiency and the amount of material used, as demonstrated in Section (3.2). Broad radii diversity is applied to the DLA, which leads to enhance the absorption over the entire solar spectrum as shown in Fig. 9. The absorption level of the diverse DLA outperforms all other arrays over the entire spectrum. The enhancement of absorption over uniform periodic arrays is significant especially in the IR band in the diverse arrays. For the broad diversity SiNW arrays, the enhancement is quite remarkable. Optimization is conducted to the initial broad diverse DLA structure in a similar manner to the limited diversity DLA arrays. The initial filling fraction (~19%) is kept constant, and the optimal scaling factor is found to be ~1.3, similar to that of the limited diversity DLA.
The role of diversity in broadening and enhancing the absorption spectrum can be seen in Fig. 9. Both DLAs show almost the same absorption trend in the band of λ = 315-500 nm, which means that the optical effects and mechanisms are not affected by broadening the diversity of radii in this band. In other words, the radii diversity has more impact on enhancing the absorption in the IR band with minor impact in the visible band if compared with that of the limited diversity. The absorption of the DLAs is significantly enhanced in the band greater than λ = ~500 nm over the uniform and the modified periodic arrays. This indicates that other optical effects arise as a result of diversifying the radii, which leads to enhance the absorption.
Table 2 shows the filling fraction for thin film, optimized uniform periodic array, modified periodic array, DLA with limited diversity, and DLA with broad diversity. The achieved ultimate efficiency and filling fraction in the broad diversity SiNW DLA are superior to other types of arrays. The calculated ultimate efficiency and the filling ratio are ~40% and ~19%, respectively. This means that ~77% enhancements in the efficiency and ~34% reductions in the amount of the material are achieved, relative to the uniform periodic array. This confirms the role of diversity coupled with the proper distribution of the NWs in enhancing the efficiency and reducing the material used over the uniform periodic arrays.
Table 2. Ultimate efficiency and filling fraction for different optimized SiNW arrays
4.3 Angular response
The calculations in this study assumed normal plane wave incidence. To test performance of the DLA arrays under different angles of incidence, the angular response is studied. In addition to perpendicular (s) and parallel (p) polarizations, the effect of the orientation of the lattice to these polarizations is investigated. Two different orientations labeled as (10) and (11) respectively are shown in the insets of Fig. 10. To quantify the angular response, the ultimate efficiency is calculated at different off normal angles (θ). In Fig. 10(a) and Fig. 10 (b) we show the ultimate efficiency as a function of incidence angle for the limited diversity DLA. For comparison, we plot the ultimate efficiency for optimized uniform SiNW array (a = 600 nm, R = 182 nm). The response of the arrays is independent of the angle of incidence up to 70 degree and 60 degrees for the p-polarization and s- polarization respectively. The trend of the angular response is consistent with previous studies [19]. The increase of the efficiency above that of the normal incidence can attributed to the various resonance modes that occur as a result of different angles of incidence [15].
Fig. 10 The angular response of the limited radii diversity DLA at: (a) parallel, and (b) perpendicular polarizations at different orientations of the plane of incidence with respect to the lattice structure expressed by 11 and 10 vectors.
4.4 Qualitative analysis
Light interaction with SiNW arrays encompasses different optical effects. For weakly absorbing materials like silicon, these optical effects play a key role in determining NW arrays optical properties and absorption strength. The strong absorption spectrum in the SiNW array can be attributed to multiple and coupled optical effects. The main optical effects that arise in light interaction with SiNW DLAs are the guided and leaky guided waves, Fabry-Perot resonance, and dielectric resonance antenna (DRA).
A single silicon nanowire can be modeled as a circular cylinder dielectric waveguide with loss at wavelengths below the band gap wavelength due to absorption. Free space plane wave can couple with the leaky modes of dielectric waveguide and result in resonant absorption peaks due to the wave confinement in the wire. The leaky waveguide model of the SiNW, on one hand, can predict the absorption spectrum of dilute arrays. On the other hand, this model alone cannot accurately explain absorption spectrum of dense NW arrays. Despite this, the leaky waveguide behavior of NWs plays very important role in determining the optical properties of SiNW arrays. The leaky modes in dielectric wave guide depend on the radius and the refractive index of the waveguide and the surrounding material. Derived from solving Maxwell’s equations, the leaky mode resonances are defined by a characteristics equation, found in [20], Balanis. In dense arrays, due to the strong coupling between the adjacent NWs, other modes and optical effects can take place such as radiation effect by NWs [15].
Fabry-Perot resonances, which are a product of the finite length of NW, can trap light by the multiple internal reflections between the interfaces of the wire with air. This creates longer effective propagation path that results in enhanced absorption and can create standing waves. The Fabry-Perot resonances are dominant in the IR band, which explains the strong absorption of IR despite silicon weak absorptance in this band. The weakly guided modes and (Fabry-Perot)-like resonances are the two main optical effects responsible for the peaks in SiNW arrays absorption spectra.
A dielectric wave guide, under specific conditions, can radiate in the radial direction making the circular cylinder dielectric acting like optical antenna [20]. Detailed analyses about the conditions under which a dielectric waveguides behave as a radiating optical antenna are contained in [20], Balanis. This effect in SiNW arrays helps in deflecting the normal incident light into lateral propagation. This can be seen as creating an infinite path length for light propagation. The radiated light from the NWs is either absorbed or scattered in a Mie-like scattering by the adjacent NWs. Radii diversity results in an increase of the density of the modes in an array, which increases the probability that NWs act as an optical antenna at different modes. These intuitive analyses can explain the significant enhancement of absorption in SiNW DLA, especially in the IR band. The broadening and enhancement of the absorption spectrum in SiNW DLA can be attributed to the above mentioned optical effects. We emphasize that at specific regions in solar spectrum there are particular dominant optical effects.
5. Conclusions
We demonstrated that the distribution of SiNWs of radial diversity in a lattice structure is a key element in achieving broadband and strong absorption spectrum for the SiNW arrays. The effect of radial diversity of NWs and their distribution in a lattice on arrays absorption spectrum are studied and compared with uniform periodic arrays. Novel SiNW arrays structures, inspired from diamond crystal lattice structure, are proposed and studied. They show significant enhancement in the ultimate efficiency of ~186% over equivalent thickness thin film, and material amount reduction in the order of ~81%. By employing broad diversity of NW radii in the diamond-like SiNW array, a broadband near-unity absorption spectrum is obtained. Despite that silicon is a weak absorber in the near band gap, the proposed SiNW arrays exhibit strong absorption. Although the presented results are for normal incident, we have verified that the enhanced absorption persists for off normal incidence at different polarizations.
Acknowledgments
This material is based on work supported in part by the National Science Foundation under Grants ARI # 0963249, MRI #0959124 (Razor), EPS #0918970 (CI TRAIN), Award No. EPS-1003970, and a grant from the Arkansas Science and Technology Authority, managed by the Arkansas High Performance Computing Center. This work is also a part of research that is partially funded by a scholarship from United States Department of State Bureau of Educational and Cultural Affairs (ECA)/ FULBRIGHT Commission.
References and links
1. B. Hua, Q. Lin, Q. Zhang, and Z. Fan, “Efficient photon management with nanostructures for photovoltaics,” Nanoscale 5(15), 6627–6640 (2013). [CrossRef] [PubMed]
2. H.-P. Wang, D.-H. Lien, M.-L. Tsai, C.-A. Lin, H.-C. Chang, K.-Y. Lai, and J.-H. He, “Photon management in nanostructured solar cells,” J. Mater. Chem. C 2(17), 3144–3171 (2014). [CrossRef]
3. N. Huang, C. Lin, and M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012). [CrossRef]
4. E. C. Garnett, M. L. Brongersma, Y. Cui, and M. D. McGehee, “Nanowire Solar Cells,” Annu. Rev. Mater. Res. 41(1), 269–295 (2011). [CrossRef]
5. Y. Zeng, Q. Ye, and W. Shen, “Design principles for single standing nanowire solar cells: going beyond the planar efficiency limits,” Sci. Rep. 4, 4915 (2014). [CrossRef] [PubMed]
6. Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Opt. Lett. 36(10), 1884–1886 (2011). [CrossRef] [PubMed]
7. H. Bao and X. Ruan, “Optical absorption enhancement in disordered vertical silicon nanowire arrays for photovoltaic applications,” Opt. Lett. 35(20), 3378–3380 (2010). [CrossRef] [PubMed]
8. R. Ren, Y.-X. Guo, and R.-H. Zhu, “Enhanced absorption in elliptical silicon nanowire arrays for solar energy harvesting,” Opt. Eng. 53(2), 027102 (2014). [CrossRef]
9. J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, and D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009). [CrossRef] [PubMed]
10. O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. A. M. Bakkers, and A. Lagendijk, “Design of Light Scattering in Nanowire Materials for Photovoltaic Applications,” Nano Lett. 8(9), 2638–2642 (2008). [CrossRef] [PubMed]
11. F. Khan, S.-H. Baek, and J. H. Kim, “Dependence of performance of si nanowire solar cells on geometry of the nanowires,” Sci. World J. 2014, 358408 (2014). [CrossRef] [PubMed]
12. K. J. Morton, G. Nieberg, S. Bai, and S. Y. Chou, “Wafer-scale patterning of sub-40 nm diameter and high aspect ratio (>50:1) silicon pillar arrays by nanoimprint and etching,” Nanotechnology 19(34), 345301 (2008). [CrossRef] [PubMed]
13. E. D. Palik, Handbook of Optical Constants of Solids (Academic,1985).
14. I. Bardi, R. Remski, D. Perry, and Z. Cendes, “Plane wave scattering from frequency-selective surfaces by the finite-element method,” IEEE Trans. Magn. 38(2), 641–644 (2002). [CrossRef]
15. K. T. Fountaine, W. S. Whitney, and H. A. Atwater, “Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to Bloch photonic crystal modes,” J. Appl. Phys. 116(15), 153106 (2014). [CrossRef]
16. M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. S. Saini, “Color Matrix Refractive Index Sensors Using Coupled Vertical Silicon Nanowire Arrays,” Nano Lett. 12(8), 4228–4234 (2012). [CrossRef] [PubMed]
17. O. H. Alzoubi and H. Naseem, “Broad band absorption silicon nanowire array using diverse radii for photovoltaic applications,” in Proceedings of IEEE Conference on Photovoltaic Specialist Conference (PVSC) (IEEE 40th, 2014), pp. 2197–2201. [CrossRef]
18. O. H. Alzoubi, H. Abu-Safe, K. Alshurman, and H. A. Naseem, “Broadband Absorptance High Efficiency Silicon Nanowire Fractal Arrays for Photovoltaic Applications,” in Proceedings of MRS meeting, 1707 (2014). [CrossRef]
19. B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, C. M. de Sterke, and R. C. McPhedran, “Modal analysis of enhanced absorption in silicon nanowire arrays,” Opt. Express 19(S5Suppl 5), A1067–A1081 (2011). [CrossRef] [PubMed]
20. C. A. Balanis, Advanced Engineering Electromagnetics (John Wiley & Sons, 2012), Chap. 9.
