## A comprehensive study for the plasmonic thin-film solar cell with periodic structure

Optics Express, Vol. 18, Issue 6, pp. 5993-6007 (2010)

http://dx.doi.org/10.1364/OE.18.005993

Acrobat PDF (2221 KB)

### Abstract

A comprehensive study of the plasmonic thin-film solar cell with the periodic strip structure is presented in this paper. The finite-difference frequency-domain method is employed to discretize the inhomogeneous wave function for modeling the solar cell. In particular, the hybrid absorbing boundary condition and the one-sided difference scheme are adopted. The parameter extraction methods for the zeroth-order reflectance and the absorbed power density are also discussed, which is important for testing and optimizing the solar cell design. For the numerical results, the physics of the absorption peaks of the amorphous silicon thin-film solar cell are explained by electromagnetic theory; these peaks correspond to the waveguide mode, Floquet mode, surface plasmon resonance, and the constructively interference between adjacent metal strips. The work is therefore important for the theoretical study and optimized design of the plasmonic thin-film solar cell.

© 2010 Optical Society of America

## 1. Introduction

3. K. L. Chopra, P. D. Paulson, and V. Dutta, “Thin-film solar cells: An overview,” Prog. Photovoltaics **12**, 69–92 (2004). [CrossRef]

4. L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett . **89**, 111111 (2006). [CrossRef]

5. C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett . **91**, 061116 (2007). [CrossRef]

6. H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, “Enhancement of light trapping in thin-film hydrogenated microcrystalline Si solar cells using back reflectors with self-ordered dimple pattern,” Appl. Phys. Lett . **93**, 143501 (2008). [CrossRef]

7. W. Zhou, M. Tao, L. Chen, and H. Yang, “Microstructured surface design for omnidirectional antireflection coatings on solar cells,” J. Appl. Phys . **102**, 103105 (2007). [CrossRef]

_{r}

^{d}and a metal with the negative dielectric constant ε

_{r}

^{m}. Meanwhile, SPR, which is the eigenstate of the Maxwell’s equations for the dielectric-metal structure, only exist when Re(-ε

_{r}

^{m}) > ε

_{r}

^{d}is satisfied [8

8. R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A **21**, 2442–2446 (2004). [CrossRef]

9. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sens. Actuator B . **54**, 3–15 (1999). [CrossRef]

10. H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett . **80**, 404–406 (2002). [CrossRef]

12. K. Kato, H. Tsuruta, T. Ebe, K. Shinbo, F. Kaneko, and T. Wakamatsu, “Enhancement of optical absorption and photocurrents in solar cells of merocyanine Langmuir-Blodgett films utilizing surface plasmon excitations,” Mater. Sci. Eng. C-Biomimetic Supramol. Syst . **22**, 251–256 (2002)
[CrossRef]

13. K. Tvingstedt, N. K. Persson, O. Inganas, A. Rahachou, and I. V. Zozoulenko, “Surface plasmon increase absorption in polymer photovoltaic cells,” Appl. Phys. Lett . **91**, 113514 (2007). [CrossRef]

14. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett . **8**, 4391–4397 (2008) [CrossRef]

15. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater . **21**, 3504–3509 (2009) [CrossRef]

16. M. Qiu and S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys . **87**, 8268–8275 (2000). [CrossRef]

17. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett . **31**, 2972–2974 (2006). [CrossRef] [PubMed]

18. K. G. Ong, O. K. Varghese, G. K. Mor, K. Shankar, and C. A. Grimes, “Application of finite-difference time domain to dye-sensitized solar cells: The effect of nanotube-array negative electrode dimensions on light absorption,” Sol. Energy Mater. Sol. Cells **91**, 250–257 (2007). [CrossRef]

19. Z. M. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express **10**, 853–864 (2002) [PubMed]

20. C. P. Yu and H. C. Chang, “Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals,” Opt. Express **12**, 1397–1408 (2004). [CrossRef] [PubMed]

21. R. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, “A frequency-dependent finite-difference time-domain formulation for dispersive materials,” IEEE Trans. Electromagn. Compat . **32**, 222–227 (1990). [CrossRef]

22. D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propag . **44**, 792–797 (1996). [CrossRef]

16. M. Qiu and S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys . **87**, 8268–8275 (2000). [CrossRef]

24. M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: Oblique-incidence case,” J. Electromagn. Waves Appl . **7**, 1595–1607 (1993). [CrossRef]

26. S. Zhao and G. W. Wei, “High-order FDTD methods via derivative matching for Maxwell’s equations with material interfaces,” J. Comput. Phys . **200**, 60–103 (2004). [CrossRef]

19. Z. M. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express **10**, 853–864 (2002) [PubMed]

20. C. P. Yu and H. C. Chang, “Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals,” Opt. Express **12**, 1397–1408 (2004). [CrossRef] [PubMed]

28. A. F. Oskooi, L. Zhang, Y. Avniel, and S. G. Johnson, “The failure of perfectly matched layers and towards their redemption by adiabatic absorbers,” Opt. Express **16**, 11376–11392 (2008). [CrossRef] [PubMed]

## 2. Theoretical modeling

9. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sens. Actuator B . **54**, 3–15 (1999). [CrossRef]

*H*, and

_{z}, E_{x}*E*. The exp(

_{y}*j*

_{0}

*ω*) time convention is used. For the SCs, all the materials are non-magnetic (i.e.

_{t}*μ*= 1).

_{r}### 2.1. Finite-difference equation

*ε*(

_{r}*x,y*), the wave function of the total field

*H*is given by [29]

_{z}^{t}*k*

_{0}is the wave number of free space. Figure 3 shows the general geometry for the inhomogeneous material treatment. Using the second-order central differences, we have

_{x}is the spatial step along the

*x*direction. For the p-polarized incident light, the following averaging techniques can be adopted for the dielectric constants, i.e.

_{1}=

*H*(

_{z}^{t}*i, j*− 1), Φ

_{2}=

*H*(

_{z}^{t}*i*− 1,

*j*), Φ

_{3}=

*H*(

_{z}^{t}*i, j*), Φ

_{4}=

*H*(

_{z}^{t}*i*+ 1,

*j*), and Φ

_{5}=

*H*(

_{z}_{t}*i, j*+ 1), the continuous inhomogeneous wave equation Eq. (1) can be discretized into FDFD equation as

30. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express **8**, 173–190 (2001). [CrossRef] [PubMed]

*H*is known (the incident light) and the FDFD equation of

_{z}^{inc}*H*is expressed as Eq. (5), the FDFD equation for the scattered-field

_{z}^{t}*H*can be derived by

_{z}^{s}### 2.2. Boundary conditions

*y*directions are used to avoid the spurious reflections of waves at the top and bottom boundaries of computational domain. The complex-coordinate PML [31

31. W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett . **7**, 599–604 (1994). [CrossRef]

32. W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett . **15**, 363–369 (1997). [CrossRef]

*ε*

_{0}is the permittivity of free space, and ω is the angular frequency of the incident light. The polynomial variation of the conductivities σ is employed, i.e.

*L*is the layer number of the PML,

*Q*is the order of the polynomial, and

*C*is a constant. For reducing the spurious numerical reflections, the optimized settings are set to

*L*= 8,

*Q*= 3.7, and

*C*= 0.02. The proper discretization form [33

33. C. M. Rappaport, M. Kilmer, and E. Miller, “Accuracy considerations in using the PML ABC with FDFD Helmholtz equation computation,” Int. J. Numer. Model.-Electron. Netw. Device Fields **13**, 471–482 (2000). [CrossRef]

34. G. Mur, “Absorbing boundary-conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat . **23**, 377–382 (1981). [CrossRef]

*y*= 0 as an example, the second-order Mur ABC can be written as

35. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys . **114**, 185–200 (1994). [CrossRef]

*x*directions need to be implemented. Based on the Floquet theorem, we have

*P*is the periodicity and

*θ*is the incident angle with respect to

*x*direction. Compared with the FDFD method, the second equation of Eq. (20) is not easy to be treated by the FDTD method, particularly for the oblique incidence case because one does not know the scattered-field values at a future time in periodic device structures. It should be noted that the periodic boundary conditions should also be implemented at the regions of the hybrid ABC.

*y*=

*y*) between the media 1 and the media 2, the boundary condition for the scattered magnetic field is

_{h}### 2.3. Parameter extraction

*N*nodes in the solution region, a sparse matrix equation is formed because only the nearest adjacent nodes affect the value of

*H*at each node. Hence, the scattered magnetic field can be solved by the iterative methods with the memory and computational complexity of

_{z}^{s}*O*(

*N*). After this, the total electric field components are calculated by

*S*denotes the region of the absorbing material, ∆

_{a}_{Sa}is the area of

*S*, and σ

_{a}_{a}= −ωε

_{0}Im(

*ε*) is the conductivity of the absorbing material.

_{ra}*A*is the amplitude of the incident light, and

*y*and

_{r}*y*are the virtual boundaries for computing the zeroth-order reflectance

_{t}*R*and the zeroth-order transmittance

_{p}*T*, respectively.

_{p}*k*

_{0}= 2π. The dielectric constant of each strip is taken as

*ε*= 4 − 0.1

_{r}*j*The periodicity is

*P*= 0.6

*m*, the thickness of each strip is

*d*

_{3}= 0.5

*m*, and the distance between the adjacent dielectric strips is

*d*= 0.3

_{s}*m*. The spatial steps are set to ∆

_{x}= ∆

_{y}= 0.01

*m*. The zeroth-order reflectance and transmittance are calculated by the FDFD method and the rigorous coupled-wave algorithm [36

36. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A-Opt. Image Sci. Vis . **12**, 1068–1076 (1995). [CrossRef]

## 3. Simulation results

*H*fields in the A-Si and Au layers can be assumed as

_{z}*k, β*, and

*α*are the propagation, phase, and attenuation constants, respectively. For the p-polarized plane wave, the reflection coefficient for the upgoing wave in the A-Si layer reflected by the Au layer is given by

*x̃*-directed propagation constant is

*k*is also the momentum of the SPR. It is well known that SPR will exist if the condition Re(−

_{x}*ε*

_{r}^{Au}) >

*ε*

_{r}

^{Si}is satisfied. But the condition is based on the assumption that

*ε*

_{r}^{Si}and

*ε*

_{r}^{Au}are predominately real. For the real situation, the loss of them cannot be ignored. As a result, the condition is not accurate.

*ỹ*-directed propagation constants in the A-Si and Au layers are the double-value functions of

*k*. Considering that the SPR is a surface wave decayed away from the dielectric-metal interface (

_{x}*ỹ*= 0), we have

*k*

_{y}^{Si}and

*k*

_{y}^{Au}, i.e. Im(

*k*

_{y}^{Si}) < 0 and Im(

*k*

_{y}^{Au}) < 0. As shown in Fig. 5, from solving for the root of Eq. (35), the attenuation constant of the field at A-Si layer change sign when the incident wavelength goes through 560 nm. Meanwhile, the locations of the poles of Eq. (34) are changed from the improper Riemann sheets to the proper Riemann sheets. According to the Drude model, the metallic dielectric function is approximated as

*ω*is the plasma frequency of Au. Hence, the SPRs exist at long wavelength range where the metal is opaque. This also agrees with the fact that the SPRs exist when the incident wavelength is larger than 560nm. Thus the eigenstates of the Maxwell’s equations for the semi-infinite A-Si/Au structure are the SPRs if the conditions of Eq. (39) are satisfied. Besides the attenuation constants conditions, the SPRs should satisfy the phase constants conditions also, i.e.

_{p}*E*field at 735nm, where the maximum phase constant

_{x}*β*of the SPR is achieved by the resonance condition

_{x}*ε*

_{r}^{Si}+

*ε*

_{r}^{Au}≈ 0. It is interesting to note that the field profile looks very symmetric because

*k*becomes very large at 735nm and thus

_{x}*k*

_{y}^{Si}in Eq. (36) and

*k*

_{y}^{Au}in Eq. (37) are comparable to each other. At the wavelength, the maximum amplitudes of the attenuation constants (i.e. the minimum attenuation lengths along

*ỹ*directions) are achieved as well.

_{2}). The complex dielectric constants of the materials (Au, A-Si, etc) are taken from [37, 38

38. X. W. Chen, W. C. H. Choy, and S. L. He, “Efficient and rigorous modeling of light emission in planar multilayer organic light-emitting diodes,” J. Disp. Technol . **3**, 110–117 (2007). [CrossRef]

*d*

_{1}= 25nm,

*d*

_{2}= 120nm,

*d*

_{3}= 40nm,

*d*

_{4}= 30nm,

*d*= 100nm, and

_{s}*P*= 200nm. The

*y*-directed incident field is the p-polarized plane wave with the amplitude of 1 and the frequency spectrum from 400nm to 800nm. The spatial step is set to ∆

_{x}= ∆

_{y}= 0.5nm. Fig. 7 shows the absorbed power density of the A-Si layer. Using the planar Au layer, the non-strip (planar) structure is also modeled. For the non-strip structure,

*d*

_{2}= 140nm is adopted for achieving the same A-Si area while other parameters are unchanged.

**E**|

^{2}. Moreover, the strip structure shows even stronger absorption due to the excited SPR and the constructive interference between strips. In fact, the efficient absorption can enhance the external quantum efficiency.

*y*directions, we consider the structures as the multilayered medium. The waveguide modes can be approximately found by computing the generalized reflection coefficient

*R̃*

_{i,i+1}of the medium between the i

^{th}layer and the (

*i*+ 1)

^{th}layer where (

*d*

_{i+1}-

*d*) is the thickness of the (

_{i}*i*+ 1) layer. Considering that the excitation is

*y*-directed plane-wave,

*k*

_{i+1,y}=

*k*

_{i+1}=

*k*

_{0}√

*ε*

_{r,i+1}. The waveguide modes can be obtained from the local minima of the generalized reflection coefficient as shown in Fig. 8. As shown in Fig. 7 and Fig. 8, the waveguide modes contribute to all the absorption peaks (A and B) of the non-strip structure. In this case, the interface between the A-Si and Au layers can be considered as a good mirror for trapping the light in the non-strip structure. This is the reason why the absorption enhancement still happens in the planar structure. However, for the non-strip structure, the SPR cannot be excited due to the momentum mismatch. For the strip structure, Fig. 9 shows

*H*field distributions at the absorption peaks. There are two different multilayered media in the strip structure as shown in Fig. 2. At the regions where the Au strips are present, the medium is Air/ITO/A-Si/Au/SiO2/Air. In the other region, the medium is Air/ITO/A-Si/SiO2/Air. The waveguide modes of the former medium contribute to the absorption peaks 1, 2, and 6 (See Fig. 7). The absorption peaks 2 and 4 are mainly due to the waveguide modes of the medium without the Au strip.

_{z}^{t}*H*field distributions for the peaks 3 and 4 show the resonant states (Floquet modes) along

_{z}^{t}*x*directions. The periodic boundaries (PBC in Fig. 2) behave like a magnetic wall or electric wall for the peaks of 3 and 4 respectively. The concentrated field at the absorption layer is due to the Floquet modes that can be observed clearly in Fig. 9(c) and Fig. 9(d).

_{k}with the continuous spectrum up to 2π/

*d*

_{3}. The field profile is shown in Fig. 9(e). The

*x*-directed boundaries of the strips achieve better field concentration than the

*y*-directed boundaries. The phenomenon agrees well with the semi-infinite model in which the momentum of the SPR is approximately calculated by Eq. (35)-Eq. (38).

## 4. Conclusion

## A. Integral form of the wave equation

*S*denotes the four small rectangles enclosing the center square point as shown in Fig. 3 and ∂

_{m}*H*/∂

_{z}^{t}*n*denotes the derivatives of

_{m}*H*normal to the contours ∂

_{z}^{t}*S*. Applying the central differences to Eq. (A-1) yields

_{m}## Acknowledgement

## References and links

1. | J. Nelson, The Physics of Solar Cells (Imperial College Press, London, 2003) |

2. | P. Würfel, Physics of Solar Cells: From Principles to New Concepts (Wiley-VCH, Berlin, 2004). |

3. | K. L. Chopra, P. D. Paulson, and V. Dutta, “Thin-film solar cells: An overview,” Prog. Photovoltaics |

4. | L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett . |

5. | C. Haase and H. Stiebig, “Thin-film silicon solar cells with efficient periodic light trapping texture,” Appl. Phys. Lett . |

6. | H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, “Enhancement of light trapping in thin-film hydrogenated microcrystalline Si solar cells using back reflectors with self-ordered dimple pattern,” Appl. Phys. Lett . |

7. | W. Zhou, M. Tao, L. Chen, and H. Yang, “Microstructured surface design for omnidirectional antireflection coatings on solar cells,” J. Appl. Phys . |

8. | R. Zia, M. D. Selker, P. B. Catrysse, and M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A |

9. | J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: Review,” Sens. Actuator B . |

10. | H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett . |

11. | H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988). |

12. | K. Kato, H. Tsuruta, T. Ebe, K. Shinbo, F. Kaneko, and T. Wakamatsu, “Enhancement of optical absorption and photocurrents in solar cells of merocyanine Langmuir-Blodgett films utilizing surface plasmon excitations,” Mater. Sci. Eng. C-Biomimetic Supramol. Syst . |

13. | K. Tvingstedt, N. K. Persson, O. Inganas, A. Rahachou, and I. V. Zozoulenko, “Surface plasmon increase absorption in polymer photovoltaic cells,” Appl. Phys. Lett . |

14. | V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett . |

15. | R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater . |

16. | M. Qiu and S. L. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys . |

17. | A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by subpixel smoothing in the finite-difference time domain,” Opt. Lett . |

18. | K. G. Ong, O. K. Varghese, G. K. Mor, K. Shankar, and C. A. Grimes, “Application of finite-difference time domain to dye-sensitized solar cells: The effect of nanotube-array negative electrode dimensions on light absorption,” Sol. Energy Mater. Sol. Cells |

19. | Z. M. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express |

20. | C. P. Yu and H. C. Chang, “Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals,” Opt. Express |

21. | R. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, “A frequency-dependent finite-difference time-domain formulation for dispersive materials,” IEEE Trans. Electromagn. Compat . |

22. | D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propag . |

23. | G. Veronis and S. Fan, “Overview of Simulation Techniques for Plasmonic Devices,” in Surface Plasmon Nanophotonics, M. L. Brongersma and P. G. Kik, eds., (Springer, Dordrecht, The Netherlands, 2007) |

24. | M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: Oblique-incidence case,” J. Electromagn. Waves Appl . |

25. | A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, Third Edition (Artech House, Boston, 2005). |

26. | S. Zhao and G. W. Wei, “High-order FDTD methods via derivative matching for Maxwell’s equations with material interfaces,” J. Comput. Phys . |

27. | D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE Press, New York, 2000). |

28. | A. F. Oskooi, L. Zhang, Y. Avniel, and S. G. Johnson, “The failure of perfectly matched layers and towards their redemption by adiabatic absorbers,” Opt. Express |

29. | W. C. Chew, Waves and Fields in Inhomogenous Media (Van Nostrand Reinhold, New York, 1990). |

30. | S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express |

31. | W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett . |

32. | W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett . |

33. | C. M. Rappaport, M. Kilmer, and E. Miller, “Accuracy considerations in using the PML ABC with FDFD Helmholtz equation computation,” Int. J. Numer. Model.-Electron. Netw. Device Fields |

34. | G. Mur, “Absorbing boundary-conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat . |

35. | J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys . |

36. | M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A-Opt. Image Sci. Vis . |

37. | E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, London, 1998). |

38. | X. W. Chen, W. C. H. Choy, and S. L. He, “Efficient and rigorous modeling of light emission in planar multilayer organic light-emitting diodes,” J. Disp. Technol . |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(310.6628) Thin films : Subwavelength structures, nanostructures

(310.6805) Thin films : Theory and design

**ToC Category:**

Solar Energy

**History**

Original Manuscript: February 9, 2010

Revised Manuscript: March 4, 2010

Manuscript Accepted: March 5, 2010

Published: March 10, 2010

**Citation**

Wei E. I. Sha, Wallace C. H. Choy, and Weng Cho Chew, "A comprehensive study for the plasmonic thin-film solar cell with periodic structure," Opt. Express **18**, 5993-6007 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5993

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### References

- J. Nelson, The Physics of Solar Cells (Imperial College Press, London, 2003)
- P. Würfel, Physics of Solar Cells: From Principles to New Concepts (Wiley-VCH, Berlin, 2004).
- K. L. Chopra, P. D. Paulson, and V. Dutta, "Thin-film solar cells: An overview," Prog. Photovoltaics 12, 69-92 (2004). [CrossRef]
- L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, "Efficiency enhancement in Si solar cells by textured photonic crystal back reflector," Appl. Phys. Lett. 89, 111111 (2006). [CrossRef]
- C. Haase, and H. Stiebig, "Thin-film silicon solar cells with efficient periodic light trapping texture," Appl. Phys. Lett. 91, 061116 (2007). [CrossRef]
- H. Sai, H. Fujiwara, M. Kondo, and Y. Kanamori, "Enhancement of light trapping in thin-film hydrogenated microcrystalline Si solar cells using back reflectors with self-ordered dimple pattern," Appl. Phys. Lett. 93, 143501 (2008). [CrossRef]
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