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Energy Express

  • Editor: Christian Seassal
  • Vol. 20, Iss. S6 — Nov. 5, 2012
  • pp: A941–A953
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A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length

Wooyoung Lee, Seung-Yeol Lee, Jungho Kim, Sung Chul Kim, and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 20, Issue S6, pp. A941-A953 (2012)
http://dx.doi.org/10.1364/OE.20.00A941


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Abstract

We propose a method for calculating the optical response to partially-coherent light based on the coherence length. Using a Fourier transform of a randomly-generated partially-coherent wave, we demonstrate that the reflectance, transmittance, and absorption with the incidence of partially-coherent light can be calculated from the Poynting vector of the incident coherent light. We also demonstrate that the statistical field distribution of partially-coherent light can be obtained from the proposed method using a rigorous coupled wave analysis. The optical characteristics of grating structures in photovoltaic devices are analyzed as a function of coherence length. The method is capable of providing a general procedure for analyzing the incoherent optical characteristics of thick layers or nano particles in photovoltaic devices with the incidence of partially-coherent light.

© 2012 OSA

1. Introduction

Photovoltaic devices have gained increasing attention, due to their potential usage for solving energy problems. Because recent photovoltaic technologies have low energy conversion efficiencies compared to other technologies [1

1. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl. 20(1), 12–20 (2012). [CrossRef]

], replacing existing energy sources such as fossil-fuel and nuclear-fuel is not urgently important. In order to solve this problem, various structures and fabrication methods such as crystalline silicon, thin-films, and organic solar cell technology have been proposed by several research groups [2

2. M. A. Green, “Silicon photovoltaic modules: a brief history of the first 50 years,” Prog. Photovolt. Res. Appl. 13(5), 447–455 (2005). [CrossRef]

6

6. S. Günes, H. Neugebauer, and N. S. Sariciftci, “Conjugated polymer-based organic solar cells,” Chem. Rev. 107(4), 1324–1338 (2007). [CrossRef] [PubMed]

].

Many recent studies for improving light absorption in photovoltaic devices have concluded that metallic nanoparticles or corrugated metallic films, supporting surface plasmon scattering and coupling, can be used to enhance light absorption in the active region [7

7. M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett. 12(6), 2894–2900 (2012). [CrossRef] [PubMed]

10

10. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

]. Those light trapping structures can significantly increase energy conversion efficiency at a specific frequency but only if the structure is appropriately designed. Optimization of the geometry, with a view to improving the absorption in the active region has been studied by many groups using a variety of numerical methods, which are based on the assumption that the incident light is perfectly coherent, analogous to a monochromatic laser. However, radiated light from the sun is not perfectly coherent because radiated waves from the sun have a finite coherent length and a finite spectral width. Moreover, this incoherent characteristic of incident light can significantly change the optical characteristic of photovoltaic devices [11

11. C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt. 41(19), 3978–3987 (2002). [CrossRef] [PubMed]

]. In the absorption power spectrum, narrow oscillation peaks that are numerically calculated under the assumption of coherent light may decrease or not be observable in practical experiments. Thus, improving numerical methods for calculating the relation between the optical responses and incoherent characteristics of a source that has a finite coherent length becomes a necessity [11

11. C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt. 41(19), 3978–3987 (2002). [CrossRef] [PubMed]

16

16. J. S. C. Prentice, “Optical generation rate of electron-hole pairs in multilayer thin-film photovoltaic cells,” J. Phys. D Appl. Phys. 32(17), 2146–2150 (1999). [CrossRef]

].

2. Numerical model

The same process is repeated until the sampling time interval (T) is sufficient for representing the characteristics of the partially-coherent source. By sampling the pseudo wave with the number of samples (N), the real part of the optical field (xre[n]) then can be discretely expressed as
xre[n]=sin(2πfnNT+ϕi),
(2)
where f is the frequency of the source, n is the sampling sequence number, N is an odd number, and ϕi is the phase shift at the end of the i-th phase-maintaining interval. The term ϕiin Eq. (2) is determined from the relation given by
ϕi=ϕi1+ϕrand(fori=1,2,3,),
(3)
where ϕ0is the initial phase and ϕrand is the random phase that is maintained during the phase-maintaining interval. By using discrete Fourier transform of xre[n], the pseudo source can be decomposed into the sum of coherent sources in the frequency domain. The Xk is the weighted value of frequency component, which is defined as
Xk=1Nn=N12N12xre[n]ejk2πNn.
(4)
Since xre[n] is the discrete set of purely real input, Xk is equal to the complex conjugate of X-k. Thus, the respective real and imaginary parts (xim[n]) of complex partially-coherent source are expressed as
xre[n]=X0+2k=1N12Re(Xkejk2πNn), (5.a)
xim[n]=2k=1N12Im(Xkejk2πNn). (5.b)
The entire expression for a partially-coherent wave (x[n]) then can be expressed as
x[n]=xre[n]+jxim[n]=X0+2k=1N12Xkejk2πNn.
(6)
Starting with the real form of a pseudo wave in time domain, the complex form of the pseudo source can be modeled as the sum of coherent sources. The pseudo source in the Fourier domain is illustrated in Fig. 1(b). Since only data within the specific range is sufficient to represent the characteristics of the partially-coherent light and this can increase the speed of the calculation, we find the maximum component in the Fourier domain, using data only within the effective spectral width (Weff), and data that remains outside of it can be discarded, as shown in Fig. 1(b). Since the process of discarding data reduces the total energy of the wave, the sum of the energy should be normalized to satisfy the conservation of energy law. This modified source is the partially-coherent source, which we are interested in modeling in the Fourier domain. By using an inverse discrete Fourier transform (IDFT), this partial coherent source in the Fourier domain can be converted back into the wave in the time domain as shown in Fig. 1(c). The modified wave in the time domain is not exactly equal to the pseudo source in Fig. 1(a). However, it is sufficient to represent the incoherent optical characteristics of the partially-coherent source itself. Therefore, a randomly-generated partially-coherent source, which has a specific frequency both in the time and frequency domains can be obtained.

Moreover, the partially-coherent simulation result can be easily calculated by superposing the simulation results of the coherent sources, which can be obtained by using existing numerical simulation methods such as RCWA, the finite element method (FEM), and the finite-difference time-domain method (FDTD). This superposition principle can be justified as follows:

The electric and magnetic fields in Cartesian coordinates can be expressed as
E=m=1MEm=m=1M(Em,x,Em,y,Em,z)ejωmt, (7.a)
H=m=1MHm=m=1M(Hm,x,Hm,y,Hm,z)ejωmt, (7.b)
where Em and Hm represent the electric and magnetic fields with specific frequency, and ωm is the frequency of wave. The z component of instantaneous Poynting vector (Sz) is given by
Sz=ExHy*EyHx*=(m=1MEm,xejωmt)(m=1MHm,y*ejωmt)(m=1MEm,yejωmt)(m=1MHm,x*ejωmt).
(8)
The exponential components in Eq. (8) do not vanish when the frequency of the electric and magnetic fields are different. Due to the oscillation terms in Eq. (8), we integrate the instantaneous Poynting vector over the sampling time interval (T) and obtain the time-average Poynting vector (Pz) as
Pz=1T0TSzdt=1T0T[m=1M(Em,xHm,y*Em,yHm,x*)]dt=m=1MPz,m,
(9)
where Pz,m is the time-average Poynting vector calculated from the wave with a single frequency component like a monochromatic wave. The Pz,m is expressed as
Pz,m=1T0TSz,m=1T0T(Em,xHm,y*Em,yHm,x*)dt,
(10)
where Sz,m is the z component of an instantaneous Poynting vector with a monochromatic wave. Since ωn is not an arbitrary number and is chosen from the sampling time interval (ωn = 2πfn = 2πn/T), the sampling time interval (T) is a multiple of each period (Tn = 1/fn = T/n). Thus, the oscillation terms, which appear in Eq. (8), vanish in Eq. (9) and only non-oscillation terms remain in the time-average Poynting vector. Therefore, it is possible to easily calculate the optical characteristics of reflectance and transmittance from the sum of the time-average Poynting vector with coherent waves.

3. Simulation results

Figure 2(a)
Fig. 2 (a) Schematic diagram of Si thin film. Calculated (b) reflectance and (c) absorption spectra with coherent and partially-coherent lights.
shows a Si thin film on a gold layer. The 225-nm thick Si film is bonded to the 75-nm thick gold layer. A 1-mm thick glass is used as a substrate at the bottom. The refractive index and extinction coefficient of Si and Au were obtained from the literature [22

22. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

]. The calculated results for the reflectance and absorption spectra with the normal incidence of TM-polarized light are shown in Figs. 2(b) and 2(c), respectively. In all simulations presented in this section, the sampling time (T) and number (N) are 104 and 2 × 103 fs, respectively. The sampling time was selected so as to include at least 500 periods of incident wavelength. Moreover, it can include at least about 20 times the coherence packet as the coherence length changes. The effective spectral width is 100 THz, in which most of the energy of the original source is contained. The degree of partial coherence is represented by the coherence time (Tc), which can be expressed as
Tc=Lcc.
(11)
Here, Lc is obtained from Eq. (1) and the spectral width can be properly selected to model the characteristics of the source itself. The solid blue curve shown in Figs. 2(b) and 2(c) represents the coherent case, while the green, red, azure, violet, and brown curves represent the partially-coherent case with coherence times of 95, 41, 20, 10, and 5 fs, respectively. Throughout this paper, the same coherence times and line colors are used to represent the spectral response of partially-coherent wave. The solid black curve represents incoherent limit, which is calculated from GTMM. The GTMM is used for comparison with our method only in simple layer structures since the GTMM cannot calculate complex geometry that contains grating structures or nanoparticles. Those results can be used to compare the difference between incoherent simulation results and partially-coherent results. As the coherence time decreases from 95 to 5 fs, the calculated reflection and absorption spectra based on the proposed method become closer to those based on the GTMM, which shows the accuracy of the proposed numerical method.

As shown in Fig. 2(c), absorption peaks can be seen near 430, 480, 565, and, 735 nm whereas absorption dips appear near 415, 455, 520, and 650 nm. The narrow resonance peaks and dips in the solid blue curve originate from Fabry-Perot resonance of the Si layer. The absorption and reflectance spectra are dominantly affected by the thickness of the Si layer in the coherent case.

An interesting feature is that the absorption near the wavelengths of the peak resonance decreases with decreasing coherence length, whereas the absorption near the wavelength of the dip resonance increases with decreasing coherence length. This simulation result indicates that the narrow oscillations, which occur in conventional simulations based on the assumption of coherent light, do not occur or decrease with the incidence of partially-coherent light. Since a partially-coherent wave, having a finite coherence length, contains numerous frequency components, it cannot create precisely the same resonance as the coherent wave. Thus, the degree of resonance behavior in a layer structure decreases as shown in Figs. 2(b) and 2(c). Moreover, the sharpness of the resonance peaks and dips also decrease with decreasing coherence length. The calculated spectra for reflection and absorption approaches the result for the incoherent limit calculated based on GTMM as the coherence length of the partially-coherent light decreases.

Our proposed method can be extended to calculate the optical response with partially coherent light as a function of incident angle. Since a representative advantage of RCWA is that it is capable of calculating an optical response with oblique incidence in nano structures, our method, when combined with RCWA, can easily be used to calculate an optical response with oblique incidence. The same structure shown in Fig. 2(a) was chosen to analyze an optical response with obliquely incident light. Figures 3(a)
Fig. 3 Calculated absorption spectra with oblique incidence (a) 30°, (b) 60°, and (c) 70°.
, 3(b), and 3(c) show absorption spectra for incident angles of 30°, 60°, and 70°. In each case, the optical responses with partially- and perfectly-incoherent incident light are analyzed. As the incident angle increases, multiple reflections or interference effects in the layer decrease. Moreover, the difference between the partially coherent and coherent cases decreases with increasing incident angle. The reason for this is that the magnitude of the interference effect decreases in oblique cases: The incoherent characteristics of the source result in a smooth interference effect.

Figure 4(a)
Fig. 4 (a) Schematic diagram of Si thin film with grating structures. Calculated (b) reflectance and (c) absorption spectra with coherent and partially-coherent lights.
shows a Si thin film with the corrugated back metal contact, which can be used as a backscatter in photovoltaic devices. The 50-nm-height and 400-nm-period gold grating is attached to a 50-nm gold layer. The fill factor of this gold grating is 0.5. The 250-nm thick Si film is placed on the surface of the grating structure. This geometry is well known for serving as a basic structure in photovoltaic devices [10

10. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

]. The calculated results for the reflectance and absorption spectra in Si layer with the normal incidence of TM-polarized light are shown in Figs. 4(b) and 4(c), respectively. Since the geometry shown in Fig. 4(a) is similar to that shown in Fig. 2(a), similar absorption and reflectance spectra appear in the coherent case, except for one resonance, which appears near 665 nm. This new resonance originates from the effect of the gold grating. Since the gold grating and nanoparticles can create a sharp resonance at a specific frequency, this can enhance the absorption in the active region at a specific frequency. This is the reason why a gold grating is used as a back contactor in this structure. However, the resonance peak near 665 nm contributes not to the

The statistical amplitude distribution of the electric field is illustrated in Fig. 5
Fig. 5 The amplitude distributions of the electric fields (a) with 525 nm (coherent), (b) with 525 nm (partially-coherent), (c) with 560 nm (coherent), and (d) with 560 nm (partially-coherent). The coherence time of partially-coherent wave is 5 fs.
. Figures 5(a) and 5(b) are calculated at a wavelength of 525 nm, which corresponds to the resonance peak of the absorption spectra in Fig. 4(c). On the other hand, Figs. 5(c) and 5(d) are obtained at a wavelength of 560 nm, which is matched with the resonance dip of the absorption spectra. Figures 5(a) and 5(c) represent the case where the incident wave is coherent. Figures 5(b) and 5(d) correspond to the case where the incident wave is partially-coherent and the wave has a coherence time of 5 fs. As shown in Figs. 5(a) and 5(b), the overall intensity of the electric field in the absorption layer is higher in the case of a coherent wave than for a partially-coherent wave. In contrast, the overall intensity in the absorption layer is higher in the partially-coherent wave than in the coherent wave when the wavelength is located near the resonance dip, as shown in Figs. 5(c) and 5(d).

Our method was extended to the analysis of the optical characteristics of photovoltaic devices as a function of coherence length. The typical geometry of a copper indium gallium (di)selenide (CIGS) photovoltaic device is shown in Fig. 6(a)
Fig. 6 (a) Device structure of the CIGS solar cell. (b) Calculated absorption spectra with coherent and partially-coherent lights.
. Since RCWA has an advantage in calculating thick layers, it is an appropriate example to show how our method can be extended to real photovoltaic devices that include a layer of thick glass. A 150-nm CIGS is attached on a 400-nm layer of molybdenum (Mo). The 50-nm thick zinc oxide (ZnO) and 20-nm thick zinc sulfide (ZnS) layers are attached to the CIGS layer. The 1000-nm thick boron doped zinc oxide (BZO), which functions as a transparent conducting layer, is attached on the top of the ZnO. A 1-mm thick glass is used as a substrate at the bottom. The refractive index and extinction coefficients of Mo, ZnO, and ZnS are taken from the literature [22

22. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

24

24. M. Bass, ed., Handbook of Optics, 3rd ed., vol. 4 (McGraw-Hill, 2009).

]. The refractive index and extinction coefficients of BZO and CIGS are taken from experiment data. The absorption spectra in the CIGS active layer with the normal incidence of TM-polarized light are shown in Fig. 6(b). Since the calculated absorption spectra have many dips or peaks, as shown in Fig. 6(b), the absorption spectra and corresponding total absorption vary as the coherence length changes. This is a quite different result compared with the simulation based on coherent assumption.

The spectral current densities of a CIGS solar cell and a CIGS solar cell with a grating structure are shown in Figs. 8(a) and (b)
Fig. 8 (a) Spectral current density of CIGS solar cell. (b) Spectral current density of CIGS solar cell with grating structure.
. The spectral current density between 450 and 700 nm is calculated when the normal incident light is TM polarized. We assume that the solar spectrum has AM 1.5 conditions, all absorbed energy contributes to generating electrons, and all of the generated electrons are converted into current without any loss. The results show that the spectral current density variation in a photovoltaic device with varying coherence length is significantly different from the coherent result.

The total calculated current density between 450 and 800 nm is shown in Table 1

Table 1. Total Current Density (mA/cm2) in the Absorption Layer of CIGS Solar Cells

table-icon
View This Table
. The CIGS with grating structures show a lower efficiency than CIGS without a grating when the coherence time exceeds 49 fs. However, a CIGS with grating structures show a higher efficiency when the coherence time is smaller than 49 fs. The results also demonstrate that our method can provide a more accurate simulation for designing photovoltaic devices with various coherence lengths.

4. Conclusion

Acknowledgment

The authors acknowledge the support of the National Research Foundation and the Ministry of Education, Science and Technology of Korea through the Creative Research Initiative Program (Active Plasmonics Application Systems).

References and links

1.

M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl. 20(1), 12–20 (2012). [CrossRef]

2.

M. A. Green, “Silicon photovoltaic modules: a brief history of the first 50 years,” Prog. Photovolt. Res. Appl. 13(5), 447–455 (2005). [CrossRef]

3.

G. K. Mor, O. K. Varghese, M. Paulose, K. Shankar, and C. A. Grimes, “A review on highly ordered, vertically oriented TiO2 nanotube arrays: fabrication, material properties, and solar energy applications,” Sol. Energy Mater. Sol. Cells 90(14), 2011–2075 (2006). [CrossRef]

4.

I. Repins, M. A. Contreras, B. Egaas, C. DeHart, J. Scharf, C. L. Perkins, B. To, and R. Noufi, “19.9%-efficient ZnO/CdS/CuInGaSe2 solar cell with 81.2% fill factor,” Prog. Photovolt. Res. Appl. 16(3), 235–239 (2008). [CrossRef]

5.

T. Ameri, G. Dennler, C. Lungenschmied, and C. J. Brabec, “Organic tandem solar cells: a review,” Energy Environ. Sci. 2(4), 347–363 (2009). [CrossRef]

6.

S. Günes, H. Neugebauer, and N. S. Sariciftci, “Conjugated polymer-based organic solar cells,” Chem. Rev. 107(4), 1324–1338 (2007). [CrossRef] [PubMed]

7.

M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett. 12(6), 2894–2900 (2012). [CrossRef] [PubMed]

8.

P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt. 14(2), 024002 (2012). [CrossRef]

9.

S. C. Kim and I. Sohn, “Simulation of energy conversion efficiency of a solar cell with gratings,” J. Opt. Soc. Kor. 14(2), 142–145 (2010). [CrossRef]

10.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

11.

C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt. 41(19), 3978–3987 (2002). [CrossRef] [PubMed]

12.

E. Centurioni, “Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers,” Appl. Opt. 44(35), 7532–7539 (2005). [CrossRef] [PubMed]

13.

M. C. Troparevsky, A. S. Sabau, A. R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. Express 18(24), 24715–24721 (2010). [CrossRef] [PubMed]

14.

S. Jung, K.-Y. Kim, Y.-I. Lee, J.-H. Youn, H.-T. Moon, J. Jang, and J. Kim, “Optical modeling and analysis of organic solar cells with coherent multilayers and Incoherent glass substrate using generalized transfer matrix method,” Jpn. J. Appl. Phys. 50(12), 122301 (2011). [CrossRef]

15.

J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D Appl. Phys. 33(24), 3139–3145 (2000). [CrossRef]

16.

J. S. C. Prentice, “Optical generation rate of electron-hole pairs in multilayer thin-film photovoltaic cells,” J. Phys. D Appl. Phys. 32(17), 2146–2150 (1999). [CrossRef]

17.

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 12(5), 1068 (1995). [CrossRef]

18.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077 (1995). [CrossRef]

19.

H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A 24(8), 2313–2327 (2007). [CrossRef] [PubMed]

20.

H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC, 2012).

21.

N. A. Stathopoulos, L. C. Palilis, S. R. Yesayan, S. P. Savaidis, M. Vasilopoulou, and P. Argitis, “A transmission line model for the optical simulation of multilayer structures and its application for oblique illumination of an organic solar cell with anisotropic extinction coefficient,” J. Appl. Phys. 110(11), 114506 (2011). [CrossRef]

22.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

23.

M. Bass, ed., Handbook of Optics, 2nd ed., vol. 2 (McGraw-Hill, 1994).

24.

M. Bass, ed., Handbook of Optics, 3rd ed., vol. 4 (McGraw-Hill, 2009).

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(040.5350) Detectors : Photovoltaic
(240.6680) Optics at surfaces : Surface plasmons
(310.0310) Thin films : Thin films

ToC Category:
Photovoltaics

History
Original Manuscript: August 27, 2012
Revised Manuscript: October 12, 2012
Manuscript Accepted: October 12, 2012
Published: October 17, 2012

Citation
Wooyoung Lee, Seung-Yeol Lee, Jungho Kim, Sung Chul Kim, and Byoungho Lee, "A numerical analysis of the effect of partially-coherent light in photovoltaic devices considering coherence length," Opt. Express 20, A941-A953 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S6-A941


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References

  1. M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, “Solar cell efficiency tables (version 39),” Prog. Photovolt. Res. Appl.20(1), 12–20 (2012). [CrossRef]
  2. M. A. Green, “Silicon photovoltaic modules: a brief history of the first 50 years,” Prog. Photovolt. Res. Appl.13(5), 447–455 (2005). [CrossRef]
  3. G. K. Mor, O. K. Varghese, M. Paulose, K. Shankar, and C. A. Grimes, “A review on highly ordered, vertically oriented TiO2 nanotube arrays: fabrication, material properties, and solar energy applications,” Sol. Energy Mater. Sol. Cells90(14), 2011–2075 (2006). [CrossRef]
  4. I. Repins, M. A. Contreras, B. Egaas, C. DeHart, J. Scharf, C. L. Perkins, B. To, and R. Noufi, “19.9%-efficient ZnO/CdS/CuInGaSe2 solar cell with 81.2% fill factor,” Prog. Photovolt. Res. Appl.16(3), 235–239 (2008). [CrossRef]
  5. T. Ameri, G. Dennler, C. Lungenschmied, and C. J. Brabec, “Organic tandem solar cells: a review,” Energy Environ. Sci.2(4), 347–363 (2009). [CrossRef]
  6. S. Günes, H. Neugebauer, and N. S. Sariciftci, “Conjugated polymer-based organic solar cells,” Chem. Rev.107(4), 1324–1338 (2007). [CrossRef] [PubMed]
  7. M. G. Deceglie, V. E. Ferry, A. P. Alivisatos, and H. A. Atwater, “Design of nanostructured solar cells using coupled optical and electrical modeling,” Nano Lett.12(6), 2894–2900 (2012). [CrossRef] [PubMed]
  8. P. Spinelli, V. E. Ferry, J. van de Groep, M. van Lare, M. A. Verschuuren, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Plasmonic light trapping in thin-film Si solar cells,” J. Opt.14(2), 024002 (2012). [CrossRef]
  9. S. C. Kim and I. Sohn, “Simulation of energy conversion efficiency of a solar cell with gratings,” J. Opt. Soc. Kor.14(2), 142–145 (2010). [CrossRef]
  10. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010). [CrossRef] [PubMed]
  11. C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt.41(19), 3978–3987 (2002). [CrossRef] [PubMed]
  12. E. Centurioni, “Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers,” Appl. Opt.44(35), 7532–7539 (2005). [CrossRef] [PubMed]
  13. M. C. Troparevsky, A. S. Sabau, A. R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. Express18(24), 24715–24721 (2010). [CrossRef] [PubMed]
  14. S. Jung, K.-Y. Kim, Y.-I. Lee, J.-H. Youn, H.-T. Moon, J. Jang, and J. Kim, “Optical modeling and analysis of organic solar cells with coherent multilayers and Incoherent glass substrate using generalized transfer matrix method,” Jpn. J. Appl. Phys.50(12), 122301 (2011). [CrossRef]
  15. J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D Appl. Phys.33(24), 3139–3145 (2000). [CrossRef]
  16. J. S. C. Prentice, “Optical generation rate of electron-hole pairs in multilayer thin-film photovoltaic cells,” J. Phys. D Appl. Phys.32(17), 2146–2150 (1999). [CrossRef]
  17. 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. A12(5), 1068 (1995). [CrossRef]
  18. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A12(5), 1077 (1995). [CrossRef]
  19. H. Kim, I.-M. Lee, and B. Lee, “Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis,” J. Opt. Soc. Am. A24(8), 2313–2327 (2007). [CrossRef] [PubMed]
  20. H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC, 2012).
  21. N. A. Stathopoulos, L. C. Palilis, S. R. Yesayan, S. P. Savaidis, M. Vasilopoulou, and P. Argitis, “A transmission line model for the optical simulation of multilayer structures and its application for oblique illumination of an organic solar cell with anisotropic extinction coefficient,” J. Appl. Phys.110(11), 114506 (2011). [CrossRef]
  22. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  23. M. Bass, ed., Handbook of Optics, 2nd ed., vol. 2 (McGraw-Hill, 1994).
  24. M. Bass, ed., Handbook of Optics, 3rd ed., vol. 4 (McGraw-Hill, 2009).

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