Abstract

Although nanowire (NW) antireflection coating can enhance light trapping capability, which is generally used in crystal silicon (CS) based solar cells, whether it can improve light absorption in the CS body depends on the NW geometrical shape and their geometrical parameters. In order to conveniently compare with the bare silicon, two enhancement factors ET and EA are defined and introduced to quantitatively evaluate the efficient light trapping capability of NW antireflective layer and the effective light absorption capability of CS body. Five different shapes (cylindrical, truncated conical, convex conical, conical, and concave conical) of silicon NW arrays arranged in a square are studied, and the theoretical results indicate that excellent light trapping does not mean more light can be absorbed in the CS body. The convex conical NW has the best light trapping, but the concave conical NW has the best effective light absorption. Furthermore, if the cross section of silicon NW is changed into a square, both light trapping and effective light absorption are enhanced, and the Eiffel Tower shaped NW arrays have optimal effective light absorption.

© 2015 Optical Society of America

1. INTRODUCTION

Nanowire (NW) antireflective coating has a significant effect in reducing the reflection of light; thus, it is especially important and widely used to improve the light trapping capability in the field of crystal silicon (CS) solar cells [1,2]. Several studies have reported that optical absorption performance of NW solar cells is greatly influenced by the NW geometric parameters, such as the NW diameter, length, arrays density, volume filling ratio, etc. [36]. The optimal optical properties of NW solar cells can be obtained by reasonably modulating these parameters. Most of the studies have considered the NW antireflection coating and CS substrate as a whole and mainly focus on how to minimize the light reflection (R) and transmission (T) to increase the light absorption (A) by A=1RT. There is no doubt that the light trapping performance of CS solar cells is significantly enhanced after etching a NW antireflection layer, but it is often to neglect the difference of light absorption distribution between the NW antireflection layer (ANW) and CS body (ASi) where A=ANW+ASi, as shown in Fig. 1(a).

 

Fig. 1. (a) Distribution of light absorption (ANW and ASi are light absorption of antireflection layer and CS, respectively). (b) Structure diagram of NW arrays (D is the NW diameter, L is the period length, and T is the thickness of CS). (c) Shapes of NW (I, cylindrical, m=0; II, parabolic truncated conical, m=0.50; III, convex conical, m=1.0; IV, conical, m=2.0; V, concave conical, m=4.0).

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In this paper, compared with the naked CS, the enhancement factor of efficient light trapping ET and effective light absorption EA are defined as follows:

ET=NAPtotalNAPnSiNAPnSi,
EA=NAPSiNAPnSiNAPnSi,
where
NAPtotal=A(λ)F(λ)λ/(h0c0)dλ,
NAPSi=ASi(λ)F(λ)λ/(h0c0)dλ,
NAPnSi=AnSi(λ)F(λ)λ/(h0c0)dλ.
NAPtotal is the total number of absorbed photons (each absorbed photon with energy greater than the bandgap produces one and only one electron-hole pair) in the whole body, including the CS body and the NW antireflective coating. NAPSi represents the number of absorbed photons in the CS body itself, which is a part of the whole, and NAPnSi means the number of absorbed photons of the naked CS. A, ANW, and ASi and their respective parts in light absorption are shown in Fig. 1(a). F(λ) is the distribution of solar radiation spectral intensity on the Earth’s surface under AM1.5 spectrum. λ is the wavelength of incident light, h0 and c0 are Planck constant and speed of light in vacuum, respectively. As shown in Fig. 1(b), the CS body with an antireflection layer of tapered silicon NW arrays arranged in a square is taken as an example. The cross section of NW is first considered a circle, and its contour shape is described by using a super-parabola profile function, i.e., Eq. (6):
r=(L/2)(z/H)m/2,L=(1/ρ)1/2,
where r is the NW radius, H is the NW length, L is the array’s period length, ρ is the NW array’s density. The thickness of CS is 100 μm, and the z axis is perpendicular to the CS surface. The top of the NW is at z=0 and the bottom at z=H. When m=0, the NW shape is cylindrical; for m<2 or m>2, the NW has a convex or concave shape, and, when m=2, the NW has a conical shape. It is convenient to use the expression to depict different types of shapes by only changing the value of the parameter m, as shown in Fig. 1(c).

2. SIMULATION METHODS

The net radiation method (NRM) [7,8] and effective medium approximation (EMA) [9,10] are used in our theoretical calculations. NRM is suitable for illustrating the transmission, absorption, and reflection characteristics of a multilayer medium for incident radiation based on its good matching between simulation and experimental results. As shown in Fig. 2(a), a system of N layers, a, c and b, d represent the incoming and outgoing light radiation, respectively. The interfaces are labeled i=1,,N1, where i is the total number of interfaces, and Ni is the refractive index of the ith medium. The relations between the outgoing and incoming energy fluxes (Q) at each interface can be expressed in terms of the reflection at the interface and the transmission passing through the medium. For every interface i, there are four equations:

{Qi,a=τiQi,dQi,b=ri,i+1Qi,a+ti+1,iQi+1,cQi+1,c=τi+1Qi+1,bQi+1,d=ti,i+1Qi,a+ri+1,iQi+1,c.
The reflectivity and transmittivity at each of the interface is ri,i+1 and ti,i+1 (subscripts indicate energy fluxes transferring from layer i to layer i+1), which are determined using Fresnel’s laws, ri,i+1+ti,i+1=1, and vice versa, ri+1,i+ti+1,i=1. τi is the absorption attenuation rate of layer i, defined by
τi=exp(αdi/cosφ),
where α=4πk/λ is the absorption coefficient and di/cosφ is the distance traveled through the layer of thickness di with propagation angle φ. k is the imaginary part of the complex refractive index Nnk=nik. Both the real refractive index n and the extinction coefficient k are functions of λ. Assuming the incident energy flux Q1,a=1 and QN,c=0, then, for each layer, the spectral reflectance Ri,i+1=Qi,b, transmittance Ti,i+1=Qi+1,d and absorptance Ai,i+1=Qi,aRi,i+1Ti,i+1 can be worked out.

 

Fig. 2. (a) Schematic multilayer structure, with numbering convention of interfaces (1,,i,,N1), refractive index (N1,,Ni,,NN), and energy fluxes (Qi,a,Qi,b,Qi+1,c,Qi+1,d,). (b) Schematic representation of silicon NW and effective multilayer structure.

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The effective multilayer structure of silicon NW is shown in Fig. 2(b), and the refractive indices of different NW layers can be solved by the EMA formula:

f1(NSi2NEff2)(NSi2+2NEff2)+f2(NAir2NEff2)(NAir2+2NEff2)=0,
where f1 and f2 are the ratio of volume filling of silicon NW and air, respectively, and f1+f2=1. NSi, NAir, and NEff are the complex refractive indices of CS, air, and the interlayer of NW, respectively.

Before starting the calculations, related parameters are assumed as follows: the NW array’s density ρ is set as 100μm2, so the array’s period length L=100nm; the maximum value of NW bottom diameter D=L=100nm and the NW length H=1.0μm; the thickness of CS substrate T=100μm; the layer thickness di=10nm, and it is also the minimum step in calculating.

3. RESULTS

First, taking the NW antireflection layer and the CS body as a whole, the effect of different shapes of NW arrays on optical performance is studied. As shown in Fig. 3, compared with the naked CS, there is a better light trapping effect with the NW antireflection coating than without it. Among the five NW shapes, the shape of “I” (the cylindrical NW) has the weakest ability to lower the light reflection, and the other tapered NW has better antireflection capability, as shown in Figs. 3(a) and 3(b). This means that the bigger top cross-sectional area will block the light incidence [3,11]. Furthermore, the shape of “III” (the convex conical NW) has better antireflection and absorption capability than others, as seen in Figs. 3(d) and 3(e). For the whole structure, the light absorption is enhanced for wavelengths less than 1.17 μm; for the longer wavelength region, the more the light antireflection, the more the light transmission because the light in this wavelength range cannot be absorbed by CS, as shown in Figs. 3(c) and 3(f). For the five NW shapes, if taken as a whole, the ranking order of light trapping performance is III>IV>II>V>I. This result is consistent with previous research findings and the conclusion that the tapered Si NW has strong light trapping ability [12,13].

 

Fig. 3. (a)–(c) Calculated reflectivity, absorptivity, and transmissivity of the CS substrate covered with NW antireflection coating compared with the naked CS. (The five simulation shapes: I, cylindrical; II, parabolic truncated conical; III, convex conical; IV, conical; V, concave conical, respectively.) Right inset (d)–(f): partially enlarged corresponding to the left.

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The NW antireflection coating can enhance light trapping characteristics, but, in the meantime, the increased surface recombination losses represent a handicap for high-efficiency solar cells [11]. Therefore, our concern is about how to increase the amount of photons that be absorbed after the surface texturization. In our research, the absorbed photons are divided into two parts: ΦNW and ΦSi, which are absorptivity of photon flux (APF) of NW antireflection coating and CS body, respectively. Here, for comparison’s sake, it is assumed that the photons, which are absorbed by NW antireflection coating, are used to compensate for surface recombination losses and that the photons, which are absorbed by the CS body, can be efficiently utilized and completely converted into electron-hole pairs. Thus, for ASi, a higher value is better, and, for ANW, a lower value is better. The differences of light absorptivity and APF between the NW antireflection layer and CS body are shown in Fig. 4. For shape of “I,” as a whole, although there is a little contribution to the light trapping effect than that of naked silicon, which can be seen in Fig. 3(a), there is little enhancement in improving the light absorption in the CS body and even worse than naked CS, as seen in Figs. 4(b) and 4(d). The main cause of this situation is that the NW antireflection layer has absorbed part of the photons. For other shapes, obviously, the NW antireflection layer basically absorbs part of the high-energy photons. The light absorptivity and APF show a decreasing trend with decrease in NW volume, and the absorption peak declines and appears to shift to the shorter wavelength, as shown in Figs. 4(a) and 4(c). Other high-energy photons, which are not absorbed by the NW antireflection layer, enter the CS body and are absorbed by it, as shown in Figs. 4(b) and 4(d). In this sense, the light trapping ability of NW antireflection coating is further enhanced, and the NW has a similar effect on the antenna [14,15].

 

Fig. 4. (a) and (c) Light absorptivity ANW and absorptivity of photon flux (APF) ΦNW of silicon NW coating, respectively. (b) and (d) Light absorptivity ASi and absorptivity of photon flux (APF) ΦSi of CS body compared with the naked silicon under AM, respectively. 1.5 spectrum.

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As previously mentioned, our concern is about how to increase the amount of photons that can be absorbed by the CS body compared with the naked CS, and this is what the NW antireflection layer really does. To make the difference between them more intuitionistic, a 3D illustration is necessary.

There is an important parameter, the ratio of the NW diameter to the array period length, i.e., D/L. This parameter is closely related to the effective refractive index of the NW antireflection layer, which affects the change of photon absorption. variations of the enhanced factors ET and EA under different geometric parameters are studied and shown in Fig. 5. First, for the cylindrical NW shown in Figs. 5(a) and 5(f), only when the value of D/L is in the range of 0.69–0.82 and H is greater than 0.440 μm, there is improved best light trapping property and ET is the biggest and near 0.21, which is consistent with the present results [3]. However, under these conditions, EA is less than zero and cannot compete with the naked CS. It means the NW alone absorbs all of the photons, instead of being absorbed by the CS body. For EA, its maximum value is near 0.13 only when the value of D/L is in the range of 0.70–0.89, H is less than 0.300 μm, and, under the same conditions, ET is only about 0.17, less than 0.21. This implies that better light trapping does not translate into better light absorption. Next, for other NW shapes, values of ET are greater than that for the shape of “I” under the same conditions, and, for the shape of “III,” it can reach the biggest value of 0.52. Among them, ET of shape of “III” has a little advantage as compared with others shown as the larger area, where ET is greater than 0.5, as shown in Fig. 5(c). It reflects the parabolic contours of NW having least resistance to the flow of photons and improves the light absorption. Quite unexpectedly, EA of shape of “III” is not the largest, while EA of shape of “V” is the largest of about 0.31, as shown as the larger area, where EA is greater than 0.3, as shown in Fig. 5(j). Through the analysis, it can be concluded that photon absorption is not only related to the NW volume but also on the NW shape, which mainly depends on the small tip and the larger base [13,16]. The number of photons, which should be absorbed by the NW antireflection layer, is reduced due to the unique NW morphology, so there are more photons penetrating through the NW antireflection layer and then absorbed by the CS body.

 

Fig. 5. (a)–(e) Contour map of enhancement factor ET under different values of H and D/L, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the circle cross section. (f)–(j) Contour maps of enhancement factor EA under different values of H and D/L, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the circle cross section.

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Several conclusions can be reached through analysis of Fig. 5. First, the tapered NW (shape of “II,” “III,” “IV,” and “V”) has better optical properties than the cylindrical NW (shape of “I”), no matter for light trapping or effective light absorption. Second, with longer NW, there is better light trapping ability [17,18] but poor effective light absorption. Third, for the tapered NW, the larger the ratio of D/L and the closer it is to equal 1, the better are the light trapping and effective light absorption. The third conclusion implies that the best arrangement for the NW arrays is that the NW should be arranged closely and without gaps. Therefore, the square cross-section NW arrays are considered next.

With the NW array density unchanged, the performances of light trapping and effective light absorption of square cross-section NW are studied and are shown in Fig. 6. Compared with the circle cross-section NW shown in Fig. 5, there is a tendency of blueshift for both ET and EA corresponding to the maximum value of their optimal properties. Under the same conditions, the square cross-section NW arrays have the larger values of ET and EA than does the circle cross-section NW. Among the five shapes of NW, in the same way, the shape of “V,” whose apparent shape is like the Eiffel Tower’s, has the most obvious advantage.

 

Fig. 6. (a)–(e) Contour map of enhancement factor ET under different values of H and D/L, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the square cross section. (f)–(j) Contour map of enhancement factor EA under different values of H and D/L, which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the square cross section.

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4. CONCLUSIONS

We have investigated the optical absorption of silicon NW-based solar cells, which can be divided into two parts: the light absorption of the surface NW arrays; the CS body. The main function of the antireflection layer is to reduce light reflection and increase light transmission; the CS substrate is the main place where photons are absorbed and converted. Computer simulations demonstrate that the NW arrays can increase the optical absorption, and it depends on not only the NW diameter, length, and volume filling ratio but also on the shape of the cross section. By studying the circular and square cross-section NW, based on the definition of enhancement factors ET and EA, we found that silicon NW, which is shaped like the Eiffel Tower, has the largest amount of photon absorption even when its light trapping capability is not the best. Therefore, the enhancement factor EA should be considered as the key index in the design of a light-trapping structure.

Funding

Fundamental Research Funds for the Central Universities (11ZG02); National Natural Science Foundation of China (NSFC) (50972032, 51172069, 51372082, 91333122); Ph.D. Programs Foundation of Ministry of Education of China (20110036110006, 20120036120006, 20130036110012).

REFERENCES

1. Z. Xu, J. Jiang, and G. L. Liu, “Lithography-free sub-100 nm nanocone array antireflection layer for low-cost silicon solar cell,” Appl. Opt. 51, 4430–4435 (2012). [CrossRef]  

2. M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014). [CrossRef]  

3. Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014). [CrossRef]  

4. J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013). [CrossRef]  

5. K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014). [CrossRef]  

6. Y. Zhan, X. Li, S. Wu, K. Li, Z. Yang, and A. Shang, “Enhanced photoabsorption in front-tapered single-nanowire solar cells,” Opt. Lett. 39, 5756–5759 (2014). [CrossRef]  

7. R. Santbergen and R. J. C. van Zolingen, “The absorption factor of crystalline silicon PV cells: a numerical and experimental study,” Sol. Energy Mater. Sol. Cells 92, 432–444 (2008). [CrossRef]  

8. R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013). [CrossRef]  

9. A. Najar, J. Charrier, P. Pirasteh, and R. Sougrat, “Ultra-low reflection porous silicon nanowires for solar cell applications,” Opt. Express 20, 16861–16870 (2012). [CrossRef]  

10. H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013). [CrossRef]  

11. F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014). [CrossRef]  

12. J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010). [CrossRef]  

13. B. Wang, E. Stevens, and P. W. Leu, “Strong broadband absorption in GaAs nanocone and nanowire arrays for solar cells,” Opt. Express 22, A386–A395 (2014). [CrossRef]  

14. E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014). [CrossRef]  

15. Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015). [CrossRef]  

16. B. Wang and P. W. Leu, “Enhanced absorption in silicon nanocone arrays for photovoltaics,” Nanotechnology 23, 194003 (2012). [CrossRef]  

17. R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011). [CrossRef]  

18. V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

References

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  1. Z. Xu, J. Jiang, and G. L. Liu, “Lithography-free sub-100 nm nanocone array antireflection layer for low-cost silicon solar cell,” Appl. Opt. 51, 4430–4435 (2012).
    [Crossref]
  2. M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
    [Crossref]
  3. Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
    [Crossref]
  4. J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
    [Crossref]
  5. K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
    [Crossref]
  6. Y. Zhan, X. Li, S. Wu, K. Li, Z. Yang, and A. Shang, “Enhanced photoabsorption in front-tapered single-nanowire solar cells,” Opt. Lett. 39, 5756–5759 (2014).
    [Crossref]
  7. R. Santbergen and R. J. C. van Zolingen, “The absorption factor of crystalline silicon PV cells: a numerical and experimental study,” Sol. Energy Mater. Sol. Cells 92, 432–444 (2008).
    [Crossref]
  8. R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013).
    [Crossref]
  9. A. Najar, J. Charrier, P. Pirasteh, and R. Sougrat, “Ultra-low reflection porous silicon nanowires for solar cell applications,” Opt. Express 20, 16861–16870 (2012).
    [Crossref]
  10. H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
    [Crossref]
  11. F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
    [Crossref]
  12. J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010).
    [Crossref]
  13. B. Wang, E. Stevens, and P. W. Leu, “Strong broadband absorption in GaAs nanocone and nanowire arrays for solar cells,” Opt. Express 22, A386–A395 (2014).
    [Crossref]
  14. E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014).
    [Crossref]
  15. Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
    [Crossref]
  16. B. Wang and P. W. Leu, “Enhanced absorption in silicon nanocone arrays for photovoltaics,” Nanotechnology 23, 194003 (2012).
    [Crossref]
  17. R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
    [Crossref]
  18. V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

2015 (1)

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

2014 (8)

V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

B. Wang, E. Stevens, and P. W. Leu, “Strong broadband absorption in GaAs nanocone and nanowire arrays for solar cells,” Opt. Express 22, A386–A395 (2014).
[Crossref]

E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014).
[Crossref]

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
[Crossref]

Y. Zhan, X. Li, S. Wu, K. Li, Z. Yang, and A. Shang, “Enhanced photoabsorption in front-tapered single-nanowire solar cells,” Opt. Lett. 39, 5756–5759 (2014).
[Crossref]

2013 (3)

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013).
[Crossref]

H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
[Crossref]

2012 (3)

2011 (1)

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

2010 (1)

2008 (1)

R. Santbergen and R. J. C. van Zolingen, “The absorption factor of crystalline silicon PV cells: a numerical and experimental study,” Sol. Energy Mater. Sol. Cells 92, 432–444 (2008).
[Crossref]

Abbes, O.

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Abouda Lachiheb, M.

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Bai, F.

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Bang, J. H.

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

Bouaïcha, M.

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Bui, H.

V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

Charrier, J.

Dong, G.

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Dong, J. R.

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

Duan, Z.

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Dutta, M.

V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

Fang, M.

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Fu, P.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Fukata, N.

V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

Grzeskiewicz, B.

E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014).
[Crossref]

Guo, Z.

Ho, J. C.

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Jee, S.-W.

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010).
[Crossref]

Jiang, J.

Jung, J.-Y.

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010).
[Crossref]

Kotkowiak, M.

E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014).
[Crossref]

Lee, J.-H.

K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
[Crossref]

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010).
[Crossref]

Leu, P. W.

B. Wang, E. Stevens, and P. W. Leu, “Strong broadband absorption in GaAs nanocone and nanowire arrays for solar cells,” Opt. Express 22, A386–A395 (2014).
[Crossref]

B. Wang and P. W. Leu, “Enhanced absorption in silicon nanocone arrays for photovoltaics,” Nanotechnology 23, 194003 (2012).
[Crossref]

Li, K.

Li, M.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Li, R.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Li, X.

Y. Zhan, X. Li, S. Wu, K. Li, Z. Yang, and A. Shang, “Enhanced photoabsorption in front-tapered single-nanowire solar cells,” Opt. Lett. 39, 5756–5759 (2014).
[Crossref]

K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
[Crossref]

Li, Y.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Lin, H.

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Liu, G. L.

Liu, S.

K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
[Crossref]

Liu, X.

H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
[Crossref]

Mwenya, T.

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Nafie, N.

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Najar, A.

Park, K.-T.

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010).
[Crossref]

Pirasteh, P.

Robak, E.

E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014).
[Crossref]

Santbergen, R.

R. Santbergen, A. H. M. Smets, and M. Zeman, “Optical model for multilayer structures with coherent, partly coherent and incoherent layers,” Opt. Express 21, A262–A267 (2013).
[Crossref]

R. Santbergen and R. J. C. van Zolingen, “The absorption factor of crystalline silicon PV cells: a numerical and experimental study,” Sol. Energy Mater. Sol. Cells 92, 432–444 (2008).
[Crossref]

Shang, A.

Shao, B.

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

Shen, C.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Smets, A. H. M.

Song, D.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Sougrat, R.

Stevens, E.

Trinh Pham, V.

V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

Um, H.-D.

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

J.-Y. Jung, Z. Guo, S.-W. Jee, H.-D. Um, K.-T. Park, and J.-H. Lee, “A strong antireflective solar cell prepared by tapering silicon nanowires,” Opt. Express 18, A286–A292 (2010).
[Crossref]

van Zolingen, R. J. C.

R. Santbergen and R. J. C. van Zolingen, “The absorption factor of crystalline silicon PV cells: a numerical and experimental study,” Sol. Energy Mater. Sol. Cells 92, 432–444 (2008).
[Crossref]

Wang, B.

B. Wang, E. Stevens, and P. W. Leu, “Strong broadband absorption in GaAs nanocone and nanowire arrays for solar cells,” Opt. Express 22, A386–A395 (2014).
[Crossref]

B. Wang and P. W. Leu, “Enhanced absorption in silicon nanocone arrays for photovoltaics,” Nanotechnology 23, 194003 (2012).
[Crossref]

Wang, H.

H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
[Crossref]

Wang, L.

H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
[Crossref]

Wu, S.

Xiu, F.

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Xu, Z.

Yakoubi, J.

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Yang, H.

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

Yang, Z.

Yip, S.

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Zeman, M.

Zhan, Y.

Zhang, J. C.

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

Zhang, R. Y.

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

Zhang, Z.

H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
[Crossref]

Zhao, Y.

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Zhou, K.

K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
[Crossref]

Zrir, M. A.

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Adv. Nat. Sci. (1)

V. Trinh Pham, M. Dutta, H. Bui, and N. Fukata, “Effect of nanowire length on the performance of silicon nanowires based solar cell,” Adv. Nat. Sci. 5, 045014 (2014).

Appl. Opt. (1)

Int. J. Therm. Sci. (1)

H. Wang, X. Liu, L. Wang, and Z. Zhang, “Anisotropic optical properties of silicon nanowire arrays based on the effective medium approximation,” Int. J. Therm. Sci. 65, 62–69 (2013).
[Crossref]

J. Appl. Phys. (1)

R. Y. Zhang, B. Shao, J. R. Dong, J. C. Zhang, and H. Yang, “Absorption enhancement analysis of crystalline Si thin film solar cells based on broadband antireflection nanocone grating,” J. Appl. Phys. 110, 113105 (2011).
[Crossref]

Nanotechnology (2)

B. Wang and P. W. Leu, “Enhanced absorption in silicon nanocone arrays for photovoltaics,” Nanotechnology 23, 194003 (2012).
[Crossref]

K. Zhou, X. Li, S. Liu, and J.-H. Lee, “Geometric dependence of antireflective nanocone arrays towards ultrathin crystalline silicon solar cells,” Nanotechnology 25, 415401 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Opt. Mater. (1)

E. Robak, B. Grzeskiewicz, and M. Kotkowiak, “Absorption enhancement in silicon nanowire-optical nanoantenna system for photovoltaic applications,” Opt. Mater. 37, 104–109 (2014).
[Crossref]

Phys. Status Solidi A (1)

Z. Duan, M. Li, T. Mwenya, F. Bai, Y. Li, and D. Song, “Geometric parameter optimization to minimize the light-reflection losses of regular vertical silicon nanorod arrays used for solar cells,” Phys. Status Solidi A 211, 2527–2531 (2014).
[Crossref]

Pure Appl. Chem. (1)

F. Xiu, H. Lin, M. Fang, G. Dong, S. Yip, and J. C. Ho, “Fabrication and enhanced light-trapping properties of three-dimensional silicon nanostructures for photovoltaic applications,” Pure Appl. Chem. 86, 557–573 (2014).
[Crossref]

Sci. Rep. (1)

Y. Li, M. Li, P. Fu, R. Li, D. Song, C. Shen, and Y. Zhao, “A comparison of light-harvesting performance of silicon nanocones and nanowires for radial-junction solar cells,” Sci. Rep. 5, 11532 (2015).
[Crossref]

Sol. Energy (1)

M. Abouda Lachiheb, M. A. Zrir, N. Nafie, O. Abbes, J. Yakoubi, and M. Bouaïcha, “Investigation of the effectiveness of SiNW used as an antireflective layer in solar cells,” Sol. Energy 110, 673–683 (2014).
[Crossref]

Sol. Energy Mater. Sol. Cells (2)

J.-Y. Jung, H.-D. Um, S.-W. Jee, K.-T. Park, J. H. Bang, and J.-H. Lee, “Optimal design for antireflective Si nanowire solar cells,” Sol. Energy Mater. Sol. Cells 112, 84–90 (2013).
[Crossref]

R. Santbergen and R. J. C. van Zolingen, “The absorption factor of crystalline silicon PV cells: a numerical and experimental study,” Sol. Energy Mater. Sol. Cells 92, 432–444 (2008).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Distribution of light absorption ( A NW and A Si are light absorption of antireflection layer and CS, respectively). (b) Structure diagram of NW arrays ( D is the NW diameter, L is the period length, and T is the thickness of CS). (c) Shapes of NW (I, cylindrical, m = 0 ; II, parabolic truncated conical, m = 0.50 ; III, convex conical, m = 1.0 ; IV, conical, m = 2.0 ; V, concave conical, m = 4.0 ).
Fig. 2.
Fig. 2. (a) Schematic multilayer structure, with numbering convention of interfaces ( 1 , , i , , N 1 ), refractive index ( N 1 , , N i , , N N ), and energy fluxes ( Q i , a , Q i , b , Q i + 1 , c , Q i + 1 , d , ). (b) Schematic representation of silicon NW and effective multilayer structure.
Fig. 3.
Fig. 3. (a)–(c) Calculated reflectivity, absorptivity, and transmissivity of the CS substrate covered with NW antireflection coating compared with the naked CS. (The five simulation shapes: I, cylindrical; II, parabolic truncated conical; III, convex conical; IV, conical; V, concave conical, respectively.) Right inset (d)–(f): partially enlarged corresponding to the left.
Fig. 4.
Fig. 4. (a) and (c) Light absorptivity A NW and absorptivity of photon flux (APF) Φ NW of silicon NW coating, respectively. (b) and (d) Light absorptivity A Si and absorptivity of photon flux (APF) Φ Si of CS body compared with the naked silicon under AM, respectively. 1.5 spectrum.
Fig. 5.
Fig. 5. (a)–(e) Contour map of enhancement factor E T under different values of H and D / L , which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the circle cross section. (f)–(j) Contour maps of enhancement factor E A under different values of H and D / L , which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the circle cross section.
Fig. 6.
Fig. 6. (a)–(e) Contour map of enhancement factor E T under different values of H and D / L , which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the square cross section. (f)–(j) Contour map of enhancement factor E A under different values of H and D / L , which are corresponding to NW shape of “I,” “II,” “III,” “IV,” and “V” having the square cross section.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

E T = NAP total NAP n Si NAP n Si ,
E A = NAP Si NAP n Si NAP n Si ,
NAP total = A ( λ ) F ( λ ) λ / ( h 0 c 0 ) d λ ,
NAP Si = A Si ( λ ) F ( λ ) λ / ( h 0 c 0 ) d λ ,
NAP n Si = A n Si ( λ ) F ( λ ) λ / ( h 0 c 0 ) d λ .
r = ( L / 2 ) ( z / H ) m / 2 , L = ( 1 / ρ ) 1 / 2 ,
{ Q i , a = τ i Q i , d Q i , b = r i , i + 1 Q i , a + t i + 1 , i Q i + 1 , c Q i + 1 , c = τ i + 1 Q i + 1 , b Q i + 1 , d = t i , i + 1 Q i , a + r i + 1 , i Q i + 1 , c .
τ i = exp ( α d i / cos φ ) ,
f 1 ( N Si 2 N Eff 2 ) ( N Si 2 + 2 N Eff 2 ) + f 2 ( N Air 2 N Eff 2 ) ( N Air 2 + 2 N Eff 2 ) = 0 ,

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