# Photonic Nanostructures Design and Optimization for Solar Cell Application

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## Abstract

**:**

## 1. Introduction

_{3}HT hybrid nanostructure through interface molecular modification on the ZnO nanowire surface. Wu et al. [19] reported a 74% increase in efficiency of ZnO nanowire dye-sensitized (DSSC) thin film solar cells. Mokkapati et al. [20] provided criteria for optimizing light trapping of metal nanoparticles in periodic arrays in a long wavelength range, allowing for a higher order diffraction mode while maintaining the highest possible fill factor. Therefore, designing a photonic crystal unit cell that combines multilayer thin film structures and multi-shell nanowires with optimized geometric properties can lead to solar cells with a broadband, high-energy absorption rate.

## 2. Theoretical Analysis of One-Dimensional Solar Cell with Multilayer Nano Films

_{l}, µ

_{l}and n

_{l}(l = 1, 2,…, N), respectively. Each layer of the multilayer structure is a medium with complex permittivity and magnetic permeability given by [21]:

_{0}= z

_{l}= 0, z

_{l}= z

_{l−1}+ d

_{l}and d

_{l}is the thickness of the l-th layer (l = 2,…, N − 1). The constants A

_{l}and B

_{l}represent wave components with the propagating velocity components along the positive and negative z directions, respectively. The variables ɛ

_{0}and µ

_{l}are the permittivity and permeability of vacuum, respectively. The total fields for transverse magnetic (TM) waves can then be obtained by interchanging ${E}_{l}\to {H}_{l}$, ${H}_{l}\to -{E}_{l}$, and ${\mu}_{l}\leftrightarrow {\epsilon}_{l}$ in Equation (3). The constants A

_{l}and B

_{l}can be determined by using interfacial conditions at $z={z}_{l}$ (l = 1, 2,…, N − 1), which lead to:

_{l}

^{2}= ɛ

_{l}(l = 1, 2,…, N − 1) is the refraction index. From Equation (4), we can derive the following relation

_{N}= 0, since there is no reflection in the region N. Therefore, the transmission and reflection coefficients can be calculated as $\tilde{t}=1/{M}_{11}$ and $\tilde{r}={M}_{21}/{M}_{11}$, respectively. ${M}_{ij}$ (i, j =1, 2) are the components of the 2 × 2 matrix

**M**. Finally, the power transmittance T and reflectance R can be calculated as:

**Figure 3.**(

**a**) Imaginary parts of the dielectric loss tangent. (

**b**) Real parts of the relative permittivity of ZnO, CdS, and CZTS layers.

**Figure 4.**Theoretical and numerical results of the reflection, transmission and absorption of the five-layer thin film solar cell under (

**a**) 0°. (

**b**) 30°. (

**c**) 60° angle of incident.

## 3. Numerical Simulation and Optimization on Solar Cell Consisting of Core-Shell Nanowire Arrays and Multi-Layer Thin Films

_{1}in Figure 8a,b showing the meshed unit cell which is sandwiched between two bodies of vacuum with finite length.

**Figure 8.**(

**a**) Dimensions of a single unit cell. (

**b**)The meshed FE model. (

**c**) The simulated electric field flux. (

**d**) The simulated Poynting energy field in the unit cell.

_{1}, h

_{2}, h

_{3}, and the height, h, as well as the diameters, d

_{1}, d

_{2}, and the unit cell width, w, of the core/shell are randomly selected until a global minimum is found (optimal fitness). In this case, the GA is utilized to find the geometric parameters that result in the maximum energy absorption over the entire frequency spectrum. This is accomplished by minimizing the reciprocal of the maximum energy absorption. After structural optimization is carried out, excellent absorptions with an average rate of approximately 90% can be observed over a broad high frequency range from 300 to 750 THz, as shown in Figure 9. It can be found that optimization results are achieved in the optical spectrum, 400–1000 nm (300–750 THz), where most energy comes from and different optimized designs have different maximum absorption frequency ranges. For example, the optimized structure with d

_{2}= 170 d

_{i}= 100 can reach the maximum absorption rate in two frequency ranges of 350–500 THz and 650–750 THz, while in 500–650 THz the absorption rate of this design is the least among all three optimized designs. The obtained optimized structures can be used in solar cells with specifically-emphasized operating frequency ranges.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Bermel, P.; Luo, C.; Zeng, L.; Kimerling, L.C.; Joannopoulos, J.D. Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals. Opt. Express
**2007**, 15, 16986–17000. [Google Scholar] [CrossRef] [PubMed] - Zhou, D.; Biswas, R. Photonic crystal enhanced light-trapping in thin film solar cells. J. Appl. Phys.
**2008**, 103. [Google Scholar] [CrossRef] - Chutinan, A.; Li, C.W.W.; Kherani, N.P.; Zukotynski, S. Wave-optical studies of light trapping in submicrometre-textured ultra-thin crystalline silicon solar cells. J. Phys. D Appl. Phys.
**2011**, 44. [Google Scholar] [CrossRef] - Araújo, A.; Barros, R.; Mateus, T.; Gaspar, D.; Neves, N.; Vicente, A.; Martins, R. Role of a disperse carbon interlayer on the performances of tandem a-Si solar cells. Sci. Technol. Adv. Mater.
**2013**, 14. [Google Scholar] [CrossRef] - Zeng, L.; Bermel, P.; Yi, Y.; Alamariu, B.A.; Broderick, K.A.; Liu, J.; Kimerling, L.C. Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector. Appl. Phys. Lett.
**2008**, 93. [Google Scholar] [CrossRef] - Mallick, S.B.; Agrawal, M.; Peumans, P. Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells. Opt. Express
**2010**, 18, 5691–5706. [Google Scholar] [CrossRef] [PubMed] - Yi, G.C.; Wang, C.; Park, W.I. ZnO nanorods: Synthesis, characterization and applications. Semicond. Sci. Technol.
**2005**, 20. [Google Scholar] [CrossRef] - Grandidier, J.; Weitekamp, R.A.; Deceglie, M.G.; Callahan, D.M.; Battaglia, C.; Bukowsky, C.R.; Atwater, H.A. Solar cell efficiency enhancement via light trapping in printable resonant dielectric nanosphere arrays. Phys. Status Solidi
**2013**, 210, 255–260. [Google Scholar] [CrossRef] - Mendes, M.J.; Morawiec, S.; Mateus, T.; Lyubchyk, A.; Águas, H.; Ferreira, I.; Crupi, I. Broadband light trapping in thin film solar cells with self-organized plasmonic nano-colloids. Nanotechnology
**2015**, 26. [Google Scholar] [CrossRef] [PubMed] - Morawiec, S.; Mendes, M.J.; Filonovich, S.A.; Mateus, T.; Mirabella, S.; Águas, H.; Crupi, I. Broadband photocurrent enhancement in a-Si: H solar cells with plasmonic back reflectors. Opt. Express
**2014**, 22, A1059–A1070. [Google Scholar] [CrossRef] [PubMed] - Hu, L.; Chen, G. Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications. Nano Lett.
**2007**, 7, 3249–3252. [Google Scholar] [CrossRef] [PubMed] - Peng, Q.; Qin, Y. ZnO nanowires and their application for solar cells. In Nanowires—Implementations and Applications; Hashim, A., Ed.; INTECH Open Access Publisher: Rijeka, Croatia, 2011; pp. 158–178. [Google Scholar]
- Xia, Y.; Yang, P.; Sun, Y.; Wu, Y.; Mayers, B.; Gates, B.; Yin, Y.; Kim, F.; Yan, H. One-dimensional nanostructures: synthesis, characterization, and applications. Adv. Mater.
**2003**, 15, 353–389. [Google Scholar] [CrossRef] - Garnett, E.; Yang, P. Light trapping in silicon nanowire solar cells. Nano Lett.
**2010**, 10, 1082–1087. [Google Scholar] [CrossRef] [PubMed] - Myung, Y.; Jang, D.M.; Sung, T.K.; Sohn, Y.J.; Jung, G.B.; Cho, Y.J.; Kim, H.S.; Park, J. Composition-Tuned ZnO-CdSSe Core-Shell Nanowire Arrays. ACS Nano
**2010**, 4, 3789–3800. [Google Scholar] [CrossRef] [PubMed] - Seol, M.; Kim, H.; Kim, W.; Yong, K. Highly efficient photoelectrochemical hydrogen generation using a ZnO nanowire array and a CdSe/CdS co-sensitizer. Electrochem. Commun.
**2010**, 12, 1416–1418. [Google Scholar] [CrossRef] - Li, J.; Yu, H.; Wong, S.M.; Zhang, G.; Sun, X.; Lo, P.G.Q.; Kwong, D.L. Si nanopillar array optimization on Si thin films for solar energy harvesting. Appl. Phys. Lett.
**2009**, 95. [Google Scholar] [CrossRef] - Lin, Y.Y.; Lee, Y.Y.; Chang, L.; Wu, J.J.; Chen, C.W. The influence of interface modifier on the performance of nanostructured ZnO/polymer hybrid solar cells. Appl. Phys. Lett.
**2009**, 94. [Google Scholar] [CrossRef] - Wu, J.J.; Chen, Y.R.; Liao, W.P.; Wu, C.T.; Chen, C.Y. Construction of nanocrystalline film on nanowire array via swelling electrospun polyvinylpyrrolidone-hosted nanofibers for use in dye-sensitized solar cells. ACS Nano
**2010**, 4, 5679–5684. [Google Scholar] [CrossRef] [PubMed] - Mokkapati, S.; Beck, F.J.; Polman, A.; Catchpole, K.R. Designing periodic arrays of metal nanoparticles for light-trapping applications in solar cells. Appl. Phys. Lett.
**2009**, 95. [Google Scholar] [CrossRef] - Veselago, V.G. The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp.
**1968**, 10, 509–514. [Google Scholar] [CrossRef] - Zhou, X.; Hu, G. Total transmission condition for photon tunnelling in a layered structure with metamaterials. J. Opt. A Pure Appl. Opt.
**2007**, 9. [Google Scholar] [CrossRef]

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**MDPI and ACS Style**

Liu, Q.; Sandgren, E.; Barnhart, M.; Zhu, R.; Huang, G.
Photonic Nanostructures Design and Optimization for Solar Cell Application. *Photonics* **2015**, *2*, 893-905.
https://doi.org/10.3390/photonics2030893

**AMA Style**

Liu Q, Sandgren E, Barnhart M, Zhu R, Huang G.
Photonic Nanostructures Design and Optimization for Solar Cell Application. *Photonics*. 2015; 2(3):893-905.
https://doi.org/10.3390/photonics2030893

**Chicago/Turabian Style**

Liu, Qian, Eric Sandgren, Miles Barnhart, Rui Zhu, and Guoliang Huang.
2015. "Photonic Nanostructures Design and Optimization for Solar Cell Application" *Photonics* 2, no. 3: 893-905.
https://doi.org/10.3390/photonics2030893