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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 6274–6285
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Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics

Peng Wang and Rajesh Menon  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 6274-6285 (2013)
http://dx.doi.org/10.1364/OE.21.006274


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Abstract

Nanophotonic light trapping offers a promising approach to increased efficiency in thin-film organic photovoltaics. In this paper, an extension of the direct-binary-search algorithm was adopted to optimize dielectric nanophotonic structures for increasing power output of ultra-thin organic solar cells. The optimized devices were comprised of an absorber layer sandwiched between two patterned, transparent, conducting cladding layers. Light trapping in such devices with an absorber thickness of only 10nm increases power output by a factor of 16 when compared to a flat reference device. We further show that even under oblique illumination with angles ranging from 0 to 60degrees, such a device could produce over 7 times more power compared to a flat reference device. Finally, we also performed a spectral and parametric analysis of the optimized design, and show that the increase is primarily due to guided-mode resonances. Our simulations indicate that this new design approach has the potential to significantly increase the performance of ultra-thin solar cells in realistic scenarios.

© 2013 OSA

1. Introduction

The simulated organic solar cell sandwiched between two nanostructured light-trapping layers is illustrated in Fig. 1(a)
Fig. 1 Schematics of the simulation models. (a) Ultra-thin absorber layer sandwiched between two nanostructured light-trapping layers. (b) First reference cell with bare, unpatterned surface. The incident angle is defined as θ. (c) Second reference cell with an optimal anti-reflection coating.
. The device is comprised of (from top to bottom) a top-cladding layer, an active layer, a bottom-cladding layer, and finally, a back-contact layer. The simulation region is defined in one dimension and it is assumed to be periodic with a spacing of Λ. Note that the two cladding layers are patterned with rectangular profiles as indicated. The cladding layers are made of indium tin oxide (ITO), which offers excellent charge-carrier collection properties [22

22. Y. Yang, X. W. Sun, B. J. Chen, C. X. Xu, T. P. Chen, C. Q. Sun, B. K. Tay, and Z. Sun, “Refractive indices of textured indium tin oxide and zinc oxide thin films,” Thin Solid Films 510(1-2), 95–101 (2006). [CrossRef]

]. The active layer is composed of two thin-film materials: a 20nm-thick PEDOT:PSS layer, which serves as the top contact to enhance charge-collection efficiency [23

23. A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys. 384(1-3), 44–51 (2011). [CrossRef]

25

25. L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron. 3(3-4), 143–148 (2002). [CrossRef]

], and the absorber, P3HT:PCBM as the carrier-generation medium [1

1. H. Hoppe and N. S. Sariciftci, “Organic solar cells: An overview,” J. Mater. Res. 19(07), 1924–1945 (2004). [CrossRef]

7

7. S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics 3(5), 297–302 (2009). [CrossRef]

,12

12. A. Raman, Z. Yu, and S. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express 19(20), 19015–19026 (2011). [CrossRef] [PubMed]

17

17. S. Kim, S. Na, J. Jo, D. Kim, and Y. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett. 93(7), 073307 (2008). [CrossRef]

,26

26. J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater. 6(7), 497–500 (2007). [CrossRef] [PubMed]

]. Two reference devices were used as controls in our simulations. The first device in Fig. 1(b) was comprised of a 3-layer stack of PEDOT:PSS, P3HT:PCBM and a back-reflector. Although this device lacks a top electrode and hence, would not be functional, we used it as a simplified reference for optimization and parametric analysis to gain insight into the mechanisms of nanophotonic light trapping. The second reference device shown in Fig. 1(c) represents a more realistic architecture as it included an optimized anti-reflection coating as the top layer. This layer also serves as the top-electrical contact and is composed of ITO. Our optimized devices were compared to this reference geometry in the final discussions. The back-contact was assumed to be a perfect-electric conductor.

The variables for optimization were the parameters that describe the 1D geometry of the device in Fig. 1(a). These are: the period of the simulated region (Λ), the fill-factor of the top-cladding layer (ff1), the fill-factor of the bottom-cladding layer (ff2), the displacement factor, s between the patterned areas of the top and bottom cladding layers, the etch-depth of the top-cladding layer (ts), the thickness of the remaining top-cladding layer (tc1), the thickness of the unetched bottom-cladding layer (tc2) and the etch-depth into the bottom electrode (tb). The two reference devices both have fixed geometric parameters and have the same film thicknesses for the PEDOT:PSS (tPED = 20nm) and P3HT:PCBM (ta) layers as the optimized device.

We applied the FDTD method for rigorous numerical simulations. A broadband plane-wave light source was positioned above the cell. Its spectrum was weighted according to the standard AM1.5 solar spectrum ranging from 350nm to 800nm [27

27. American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra for Photovoltaic Performance Evaluation, http://rredc.nrel.gov/solar/spectra/am1.5/.

]. For computational simplicity, only normal incidence is assumed during optimization. However, the optimized devices were analyzed under broad-angle illumination and their performance was compared to the reference devices. Perfectly-matched layers (PML) were included in the model to avoid numerical reflection in the direction of wave propagation (Y-direction as indicated in Fig. 1(a)) [28

28. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

]. The PMLs were located at the top and bottom boundaries of the simulation region and placed parallel to X-axis. Bloch-periodic boundary conditions were imposed in the X-direction [29

29. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

,30

30. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). [CrossRef] [PubMed]

]. The execution time of FDTD simulation is sufficiently long to guarantee numerical convergence to steady state.

2. Optimization algorithm and figure-of-merit

The FOM for optimization was the output electrical power-density of the solar cell. We first computed the light intensity distribution, Iλ(x,y,λ) within the absorber layer of the device for a given geometry. Then, the short-circuit current density was computed as
jsc=qtaΛactive(λminλmaxΦλ(x,y,λ)IQE(λ)dλ)dxdy,
(1)
where q is the electronic charge, IQE(λ) is the internal quantum efficiency, Φλ(x,y,λ)=I(x,y,λ)hc/λ is the local photon flux in the absorber region, and ta is the thickness of the active region. The IQE for the organic absorber was taken from ref [7

7. S. H. Park, A. Roy, S. Beaupre, S. Cho, N. Coates, J. S. Moon, D. Moses, M. Leclerc, K. Lee, and A. J. Heeger, “Bulk heterojunction solar cells with internal quantum efficiency approaching 100%,” Nat. Photonics 3(5), 297–302 (2009). [CrossRef]

]. The current-voltage performance of the solar cell was modeled as [31

31. J. Nelson, The Physics of Solar Cells (Imperial College Press, 2004).

]:
j(V)=jscj0(exp(qVkBT)1),
(2)
where V is the bias voltage, kB is the Boltzmann’s constant and T is the operating temperature. In addition, j0=q(n2+1)Eg2kBT4π2ħ3c2eEgkBT is the dark current density, which is a function of the refractive index n, bandgap Eg and temperature T [31

31. J. Nelson, The Physics of Solar Cells (Imperial College Press, 2004).

]. ħ is the reduced Plank’s constant and c is the speed of light in vacuum. The power-density is then calculated as:
P(V)=j(V)V.
(3)
From this curve, the peak of the output power-density is calculated. The same calculation is performed for the reference cell in Fig. 1(b). The FOM is finally defined as E, the ratio of the peak power-density of the nanostructured device to that of the reference device.

3. Optimization results

The thickness of the absorber plays a critical role in determining the ultimate enhancement [18

18. P. Wang and R. Menon, “Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping,” Opt. Express 20(2), 1849–1855 (2012). [CrossRef] [PubMed]

]. Here, we applied the optimization algorithm on devices with three different absorber thicknesses,10nm, 30nm and 50nm.

The simulation and optimization results of the first design with a 10-nm thick P3HT:PCBM layer are summarized in Fig. 2
Fig. 2 Results of the optimized device with 10-nm thick absorber. (a) Evolution of the enhancement factors as a function of the iteration number. The optimized design is shown in the inset. (b) Calculated J-V and P-V curves for both the optimized device and the reference device (inset). (c) Enhancement spectrum analysis (inset: electric-field-intensity distributions inside the active layer at the peaks of the TE and TM polarizations). (d) Angular response analysis of the optimal design (inset: spectral-angular analysis).
. A power-enhancement factor, E = 31 is reached after 19 iterations (see Fig. 2(a)). A random parameter set was used as the initial condition. The geometry of the optimized design is shown in Fig. 2(a). In the optimized design, the period, Λ = 320nm, and the fill factor of the top-cladding layer, ff1 = 0.19, which gives a width of the scattering line of 60nm. The bottom-cladding layer is offset by a half period from the center of the top-cladding layer and it has a fill factor, ff2 = 0.43, which gives a width of 138nm for the scattering line. Interestingly, the heights of scattering lines for the top and bottom cladding layers are 75nm and 25nm, respectively. This suggests that strong optical scattering and hence, light trapping is achievable even with relatively shallow structures. Note that such low-aspect ratio nanostructures can be reliably replicated using nanoimprint lithography [33

33. L. J. Guo, “Recent progress in nanoimprint technology and its applications,” J. Phys. D Appl. Phys. 37(11), R123–R141 (2004). [CrossRef]

]. As plotted in Fig. 2(a), both E and J follow F in the process of optimization. This further demonstrates that both the increased short-circuit current density and the increased power output are due to the enhanced light absorption enabled by the periodic dielectric nanostructures. As we show later, such nanostructures generate guided-mode resonances, which dramatically increase the light intensities within the active layer. The electrical characteristics of the optimized and the reference devices were simulated and plotted in Fig. 2(b). The short-circuit current density and the peak power-density are both increased dramatically in the nanostructured device.

We also computed the enhancement spectrum (see Fig. 2(c)), which is defined as the ratio of the total light intensity integrated over the active region for each wavelength for the optimized design to that for the reference device. The spectrum is plotted for both TM and TE polarizations as indicated. There is broadband enhancement over the entire spectrum, which is likely due to the anti-reflection properties of the top-cladding layer. However, there are multiple resonance peaks that make large contributions to the overall enhancement. For the TE mode with electric field polarized parallel to the nanostructures (Z-direction), the enhancement-spectrum peak appears at λ = 414nm. The strongest resonance for the TM mode with electric field polarized perpendicular to the nanostructure (X-direction) is located at λ = 652nm. Intriguingly, the peaks at the two polarizations approach the peak of the solar spectrum (~500nm for AM1.5) and the bandgap of the absorber (~750nm for P3HT:PCBM). The intensity distributions of electric fields of both polarizations inside the active layer at their corresponding resonance peaks are illustrated in the insets in Fig. 2(c). The enhancement factors were calculated as a function of the incident angle, θ for the optimized design and plotted in Fig. 2(d). This plot is a good measure of the performance of the device when not tracking the sun or under diffuse illumination. The broadband enhancement of output power remains greater than 5 × for incidence angles as large as 60°. Furthermore, a closer look at the enhancement spectrum as a function of incident angle (inset of Fig. 2(d)) shows that guided-mode resonances exist even at large angles (>40°) although a shift in resonance wavelength with incident angle is also seen. This shift could be advantageous when both broadband and broad-angle enhancement is desired. Note that the effect of an anti-reflection coating is typically characterized by enhancement with very little wavelength dependence. Therefore, we can also conclude that the light scattering effects of both cladding layers predominate over the anti-reflection effects of the top-cladding layer for angles less than about 60°.

In the second design, an absorber thickness of 30nm was assumed and the results are summarized in Fig. 3
Fig. 3 Results of the optimized device with 30-nm thick absorber. (a) Evolution of the enhancement factors as a function of the iteration number. The optimized design is shown in the inset. (b) Calculated J-V and P-V curves for both the optimized device and the reference device (inset). (c) Enhancement spectrum analysis (inset: electric-field-intensity distributions inside the active layer at the peaks of the TE and TM polarizations). (d) Angular response analysis of the optimal design (inset: spectral-angular analysis).
. A power-enhancement, E = 11 is obtained after 23 iterations. Interestingly, in the optimized design the top-cladding layer is absent, and light trapping arises from the relatively thin patterned bottom-cladding layer. Although this optimized design represents an unrealistic device (since there is no top electrode), we can evaluate the performance of nanophotonic light-trapping by numerically studying the properties of such a device. Note that this situation may be readily avoided in the future by including a minimum thickness constraint on the top-cladding layer (recall that this also serves as the top electrode) during optimization. The J-V and P-V curves are plotted in Fig. 3(b), and the spectral and the angular responses are shown in Figs. 3(c) and 3(d), respectively. The electric field intensities at the peaks of the enhancement spectrum for TE and TM polarizations are shown as insets in Fig. 3(c). The first peak at λ = 430nm for TE polarization is close to the maximum of the AM1.5 solar spectrum, offering strong light enhancement at the maximal power input. The second peak at 690nm for TM polarization approaches the bandgap of the P3HT:PCBM absorber, which attempts to boost the low intrinsic absorption there, by enhanced light-trapping. The performance of the optimized device under oblique incidence is relatively good since the enhancement has a slower drop-off with incident angle compared to the first design (see Fig. 2(d)). The enhancement spectrum as a function of incident angle is shown in the inset of Fig. 3(d). The presence of sharp peaks in the spectra even at large incidence angles (~40° and greater) confirms that the nanophotonic light trapping dominates the total contribution to power enhancement compared to the anti-reflection effect.

4. Parametric analysis

The sensitivity of power-enhancement to variations in the geometric parameters of the optimized design is important, since fabrication of these devices will inevitably introduce errors. Furthermore, such a parametric analysis can provide additional insight into the mechanisms of light trapping involved. We conducted such an analysis and these results are summarized in Fig. 5
Fig. 5 Parametric analysis of the optimized device with an active-layer thickness of 10nm. (a) (E) vs. Λ; (b) Enhancement spectrum vs. Λ; (c) (E) vs. s; (d) Enhancement spectrum vs. s; (e) (E) vs. ff1; (f) Enhancement spectrum vs. ff1; (g) (E) vs. ts; (h) Enhancement spectrum vs. ts; (i) (E) vs. ff2; (j) Enhancement spectrum vs. ff2; (l) (E) vs. tb; (l) Enhancement spectrum vs. tb; (m) (E) vs. tc1; (n) Enhancement spectrum vs. tc1; (o) (E) vs. tc2; (p) Enhancement spectrum vs. tc2.
. Each parameter was scanned over a predetermined range of values while the other parameters were kept constant at the optimal design. For each parameter, we plot the power-enhancement factor as well as the enhancement spectrum as a function of the parameter value. Only the first design with the 10nm-thick active layer is analysed for brevity.

The first parameter we analyzed was the period of the computational domain of the device, Λ, which was varied from 50nm to 800nm. The power-enhancement factor peaks at about Λ = 350nm (see Fig. 5(a)). This arises from multiple resonances over the incident spectrum. These resonances are particularly strong at wavelengths shorter than 500nm as observed in the enhancement spectra shown in Fig. 5(b).

The second parameter we analyzed was s, the relative displacement factor between the patterned regions of the top- and bottom-cladding layers. Although, the power-enhancement factor shown in Fig. 5(c) has low sensitivity to changes in s, the enhancement spectra shown in Fig. 5(d) illustrate very interesting behavior. For all values of s, there is a strong resonance at λ~650nm. However, when s is close to 0.5, i.e., when the patterned regions of the top- and bottom-cladding layers are shifted relative to each other by Λ/2, a second strong resonance starts to appear at λ~400nm. We can relate this to the field distribution plots shown in the insets of Fig. 2(c). It looks like the top-cladding layer concentrates TE polarized light in the center of the active region, while the bottom-cladding layer concentrates TM polarized light along the edges of the active region. The net result of this design is that for unpolarized light, the active region is uniformly illuminated with enhanced light intensities. Note that uniform illumination is important to avoid hot-spots within the absorber material.

The analysis of the top-cladding structure is shown in Figs. 5(e)-5(h). When the fill-factor, ff1 or the thickness of the layer, ts becomes 0, a single resonance at λ~600nm is seen in the enhancement spectra (Figs. 5(f) and 5(h)). This resonance clearly arises due to light scattering from the patterned bottom-cladding layer. As ff1 or ts increases, multiple resonances emerge until the power-enhancement factor peaks at ff1 = 0.2 or ts = 70nm. We can surmise that the bottom-cladding layer primarily affects the resonance at long wavelength, while the short-wavelength resonance (where the AM1.5 spectrum peaks) is a result of the interaction between the top- and bottom-cladding layers. As ff1 increases further, two distinct regions of resonance arise. The top-cladding layer modulates the position and strength of the second resonance. This resonance shifts to longer wavelength with increasing fill factor and thickness of scattering layer (see Figs. 5(f) and 5(h)). The long-wavelength resonance lies slightly above the bandgap and hence, doesn’t contribute significantly to device performance and the overall power-enhancement drops. In Fig. 5(h), the resonance is weakened gradually at ts>50nm and the secondary peak in Fig. 5(g) is likely due to the third resonance occurring at λ~500nm when ts>100nm.

The analysis of the impact of the bottom-cladding structure is shown in Figs. 5(i)-5(l). As hinted earlier, the bottom-cladding layer disproportionally impacts the second resonance peak close to the bandgap of P3HT:PCBM absorber. At lower values of ff2, a broad resonance exists from 400nm to 600nm. However, as ff2 increases, the resonance shifts to wavelengths above 600nm. The biggest impact on the power-enhancement factor arises from absorption near the peak of the AM1.5 spectrum (~500nm) and this seems to occur when ff2~0.4. On the other hand, as the thickness, tb increases beyond 30nm, the second resonance splits into three peaks, and the power-enhancement E is reduced. This is likely due to the sharing of energy between these three distinct resonances.

Intriguingly, the parametric analyses of tc1 and tc2, the thicknesses of the unpatterned regions of the top- and bottom-cladding layers, respectively, indicate that these are essential to optimal light-trapping performance (see Figs. 5(m)-5(p)). A minimum thickness is required to support guided-mode resonances. In addition, these layers act as optimal electrodes with high transparency and low carrier-recombination. Despite the peak of the power-enhancement factor, E at tc1 = 120nm via our optimization algorithm, the parametric analysis reveals another peak when tc1 = 0nm (see Fig. 5(m)). From the enhancement spectrum at tc1 = 0nm, we can observe that there is a relatively flat broadband enhancement from 400nm to 650nm, and very high enhancements beyond 650nm (see Fig. 5(n)). Although this peak has a higher value for E, it clearly will not be a practical device since no top electrode would be present. Yet a design with cladding layer thickness close to the second data point in Fig. 5(m) may serve as an optimal design with higher enhancement factor compared to that with tc1 = 120nm. This particular example also demonstrates that our DBS algorithm is apt to converge to local maxima and care must be taken to interpret and analyze the optimized designs. As illustrated in Figs. 5(o) and 5(p), the unpatterned region of the bottom-cladding layer sustains strong broadband resonance at tc2 = 60nm. It is also clear that the power-enhancement factor is strongly influenced by tc2 and care must be taken to ensure its precision during fabrication.

Parasitic absorption in ITO can partially explain the effects of tc1 and tc2. Despite relatively good transparency of ITO, thicker top cladding layer may still potentially consume a significant amount of solar energy, compromising the power output, as plotted in Fig. 5(m) where E at tc1 = 0 is higher than E at tc1 = 120nm. The calculated fractions of light absorbed by ITO layers are 29%, 9% and 16% for the three designs above with 10nm, 30nm and 50nm thick absorbers, respectively.

5. Conclusions

The nanostructured geometries in the optimized devices are challenging to fabricate at low-cost using conventional patterning technologies such as scanning-electron-beam lithography or photolithography [35

35. T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature 406(6799), 1027–1031 (2000). [CrossRef] [PubMed]

]. This can be mitigated somewhat by the recent advances in nanopatterning such as absorbance modulation [36

36. T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009). [CrossRef] [PubMed]

], optically-saturable transitions [37

37. N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett. 107(20), 205501 (2011). [CrossRef] [PubMed]

], two–photon absorption [38

38. S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express 14(6), 2300–2308 (2006). [CrossRef] [PubMed]

] and interference lithography [39

39. J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater. 17(16), 3027–3041 (2007). [CrossRef]

]. Furthermore, developments in roll-to-roll nanoimprint lithography [33

33. L. J. Guo, “Recent progress in nanoimprint technology and its applications,” J. Phys. D Appl. Phys. 37(11), R123–R141 (2004). [CrossRef]

,40

40. C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett. 11(2), 661–665 (2011). [CrossRef] [PubMed]

] can enable the mass replication of such nanostructures.

Acknowledgment

The authors would like to thank Daniel Jacobs in the Department of Material Science and Engineering at the University of Utah for providing resources on the material properties of the organic materials used in this work.

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A. Lenz, H. Kariis, A. Pohl, P. Persson, and L. Ojamae, “The electronic structures and reflectivity of PEDOT:PSS from density functional theory,” Chem. Phys. 384(1-3), 44–51 (2011). [CrossRef]

24.

M. Leclerc and A. Najari, “Organic thermoelectrics: Green energy from a blue polymer,” Nat. Mater. 10(6), 409–410 (2011). [CrossRef] [PubMed]

25.

L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron. 3(3-4), 143–148 (2002). [CrossRef]

26.

J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater. 6(7), 497–500 (2007). [CrossRef] [PubMed]

27.

American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra for Photovoltaic Performance Evaluation, http://rredc.nrel.gov/solar/spectra/am1.5/.

28.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

29.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

30.

Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). [CrossRef] [PubMed]

31.

J. Nelson, The Physics of Solar Cells (Imperial College Press, 2004).

32.

P. Wang and R. Menon, “Simulation and analysis of the angular response of 1D dielectric nanophotonic light-trapping structures in thin-film photovoltaics,” Opt. Express 20(S4Suppl 4), A545–A553 (2012). [CrossRef] [PubMed]

33.

L. J. Guo, “Recent progress in nanoimprint technology and its applications,” J. Phys. D Appl. Phys. 37(11), R123–R141 (2004). [CrossRef]

34.

M. A. Green, “Enhanced evanescent mode light trapping in organic solar cells and other low index optoelectronic devices,” Prog. Photovolt. Res. Appl. 19(4), 473–477 (2011). [CrossRef]

35.

T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature 406(6799), 1027–1031 (2000). [CrossRef] [PubMed]

36.

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science 324(5929), 917–921 (2009). [CrossRef] [PubMed]

37.

N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett. 107(20), 205501 (2011). [CrossRef] [PubMed]

38.

S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express 14(6), 2300–2308 (2006). [CrossRef] [PubMed]

39.

J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater. 17(16), 3027–3041 (2007). [CrossRef]

40.

C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett. 11(2), 661–665 (2011). [CrossRef] [PubMed]

41.

S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett. 12(6), 2971–2976 (2012). [CrossRef] [PubMed]

42.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012). [CrossRef] [PubMed]

43.

A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett. 12(6), 2792–2796 (2012). [CrossRef] [PubMed]

OCIS Codes
(350.6050) Other areas of optics : Solar energy
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(310.6188) Thin films : Spectral properties
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Solar Energy

History
Original Manuscript: December 12, 2012
Revised Manuscript: February 8, 2013
Manuscript Accepted: February 24, 2013
Published: March 5, 2013

Citation
Peng Wang and Rajesh Menon, "Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics," Opt. Express 21, 6274-6285 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6274


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  24. M. Leclerc and A. Najari, “Organic thermoelectrics: Green energy from a blue polymer,” Nat. Mater.10(6), 409–410 (2011). [CrossRef] [PubMed]
  25. L. A. A. Pettersson, S. Ghosh, and O. Inganas, “Optical anisotropy in thin films of poly(3,4-ethylenedioxythiophene)-poly(4-styrenesulfonate),” Org. Electron.3(3-4), 143–148 (2002). [CrossRef]
  26. J. Peet, J. Y. Kim, N. E. Coates, W. L. Ma, D. Moses, A. J. Heeger, and G. C. Bazan, “Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols,” Nat. Mater.6(7), 497–500 (2007). [CrossRef] [PubMed]
  27. American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra for Photovoltaic Performance Evaluation, http://rredc.nrel.gov/solar/spectra/am1.5/ .
  28. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  29. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002). [CrossRef]
  30. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107(41), 17491–17496 (2010). [CrossRef] [PubMed]
  31. J. Nelson, The Physics of Solar Cells (Imperial College Press, 2004).
  32. P. Wang and R. Menon, “Simulation and analysis of the angular response of 1D dielectric nanophotonic light-trapping structures in thin-film photovoltaics,” Opt. Express20(S4Suppl 4), A545–A553 (2012). [CrossRef] [PubMed]
  33. L. J. Guo, “Recent progress in nanoimprint technology and its applications,” J. Phys. D Appl. Phys.37(11), R123–R141 (2004). [CrossRef]
  34. M. A. Green, “Enhanced evanescent mode light trapping in organic solar cells and other low index optoelectronic devices,” Prog. Photovolt. Res. Appl.19(4), 473–477 (2011). [CrossRef]
  35. T. Ito and S. Okazaki, “Pushing the limits of lithography,” Nature406(6799), 1027–1031 (2000). [CrossRef] [PubMed]
  36. T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining light to deep subwavelength dimensions to enable optical nanopatterning,” Science324(5929), 917–921 (2009). [CrossRef] [PubMed]
  37. N. Brimhall, T. L. Andrew, R. V. Manthena, and R. Menon, “Breaking the far-field diffraction limit in optical nanopatterning via repeated photochemical and electrochemical transitions in photochromic molecules,” Phys. Rev. Lett.107(20), 205501 (2011). [CrossRef] [PubMed]
  38. S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express14(6), 2300–2308 (2006). [CrossRef] [PubMed]
  39. J. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, and E. L. Thomas, “3D micro- and nanostructures via interference lithography,” Adv. Funct. Mater.17(16), 3027–3041 (2007). [CrossRef]
  40. C. Battaglia, J. Escarré, K. Söderström, L. Erni, L. Ding, G. Bugnon, A. Billet, M. Boccard, L. Barraud, S. De Wolf, F. J. Haug, M. Despeisse, and C. Ballif, “Nanoimprint lithography for high-efficiency thin-film silicon solar cells,” Nano Lett.11(2), 661–665 (2011). [CrossRef] [PubMed]
  41. S. Jeong, E. C. Garnett, S. Wang, Z. Yu, S. Fan, M. L. Brongersma, M. D. McGehee, and Y. Cui, “Hybrid silicon nanocone-polymer solar cells,” Nano Lett.12(6), 2971–2976 (2012). [CrossRef] [PubMed]
  42. K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett.12(3), 1616–1619 (2012). [CrossRef] [PubMed]
  43. A. Mavrokefalos, S. E. Han, S. Y. Yerci, M. S. Branham, and G. Chen, “Efficient light trapping in inverted nanopyramid thin crystalline silicon membranes for solar cell applications,” Nano Lett.12(6), 2792–2796 (2012). [CrossRef] [PubMed]

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