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Recent research in the rapidly emerging field of plasmonics has shown the potential to significantly enhance light trapping inside thin-film solar cells by using metallic nanoparticles. In this article it is demonstrated the plasmon enhancement of optical absorption in amorphous silicon solar cells by using silver nanoparticles. Based on the analysis of the higher-order surface plasmon modes, it is shown how spectral positions of the surface plasmons affect the plasmonic enhancement of thin-film solar cells. By using the predictive 3D modeling, we investigate the effect of the higher-order modes on that enhancement. Finally, we suggest how to maximize the light trapping and optical absorption in the thin-film cell by optimizing the nanoparticle array parameters, which in turn can be used to fine tune the corresponding surface plasmon modes.
©2009 Optical Society of America
1. Introduction
At present, thin-film solar cells are considered as a main and low-cost alternative to conventional wafer-based cells. With the thickness of a few microns and below, they can significantly decrease the amount of the semiconductor material required, and thus, reduce the production costs of such cells [1]. In addition, carrier diffusion paths are much shorter in thin-film materials, which lead to a reduction of the losses from minority carrier recombination.
However, due to relatively poor light absorption of thin-films, more efficient light trapping mechanisms are required for better performance as compared to wafer-based solar cells. Usual methods such as surface texturing used in wafer-based cells for light trapping [2, 3] cannot be applied to thin-film cells: micron texturing has a relatively large size, while submicron surface texturing inevitably increases the surface area and hence the minority carrier recombination on the surface. A promising way found recently [4] is to use the rapidly emerging field of plasmonics and nanoplasmonics in particular, to enhance the optical absorption of the photo-active layer.
Recent experimental studies on both organic [5–8] and inorganic [9–12] solar cells have shown that performance of thin-film cells can be improved significantly by metallic nanoparticles deposited on top of the photo-active layer. It was shown that the enhanced performance of such cells is attributed to the improved optical absorption of thin-film photo-active layers [7]. This more effective optical absorption is caused by scattering from the metallic nanoparticles [13], which strongly increases the light trapping within thin-film cells by coupling with waveguide modes of the active layer [14, 15].
Through coupling with surface plasmons, which are the eigenmodes of metals [16], the incident light very effectively interacts with the metal nanoparticles over cross-sections much larger than the geometrical cross-sections of these nanoparticles [17]. In other words, the excitation of multiple surface plasmons leads to the extraordinary scattering [18] and strong electromagnetic field enhancement in the vicinity of nanoparticle surfaces [19,20]. Due to enhanced near-fields, the scattered light can very efficiently couple into waveguide modes of the active layer [14,15], dramatically increasing the optical path and absorption of the light inside the active layer [21]. As a result, the total absorbed power by the photo-active layer in a solar cell containing metallic nanoparticles can be significantly enhanced.
An additional advantage of metallic nanoparticles is in the resonant nature of plasmonic enhancements. This makes the nanoparticles a very efficient and flexible tool for solar cell applications, which can be used to manipulate the light trapping and energy conversion efficiency. By tuning the plasmon resonance frequencies of the nanoparticles (by changing their material, size, or arrangement) one can modify spectral profiles of the absorbed power in the photo-active layer, as well as the total absorbed power.
However, despite several experimental attempts to enhance the solar cell performance using very different nanoparticle materials, sizes, shapes, and surface coverages, there is still no systematic study on the optimum light trapping that can be achieved by proper adjustment of nanoparticle parameters. Many efforts have been done to study the influence of the nanoparticle shapes [21,22] on the localized field enhancement and light trapping. However, such important questions as tuning of the surface plasmons and the role of the higher-order modes in plasmonic enhancements still remain essentially open. At the same time, the plasmonic mechanism of the enhancement by metal nanoparticles, as well as the key role of surface plasmon modes (and especially the higher-order modes) in those enhancements, is undeniable [4, 21]. Thus, finding the optimum nanoparticle parameter space by tuning the higher-order surface modes to enable the effective plasmon enhancement still remains one of the major challenges in this direction.
In this paper, we present a systematic study on plasmon enhancement by high-order surface modes of the absorbed power in thin-film hydrogenated amorphous silicon (a-Si:H) solar cells. Based on predictive 3D modeling for a thin-film a-Si:H cell with spherical silver nanoparticles, we demonstrate how the high-order surface plasmons in different nanoparticle arrays can be used to enhance the absorbed power. Finally, we perform an optimization study for the nanoparticle array parameters to achieve better optical enhancement and light trapping inside the amorphous silicon layer.
2. Surface plasmons
According to the Mie theory for a single spherical nanoparticle in air [23], both scattering and absorption by the nanoparticle are caused by interaction of the incident light with all the normal modes of the nanoparticle. In other words, the overall cross-sections are the sums of contributions from all the normal modes
where σ(n) sca and σ(n) abs are the contributed cross-sections from the n-th normal mode.
Coupling of the incident light with the nanoparticle normal modes strongly depends on the mode number n and size parameter q=kR, where R is the nanoparticle radius and k=ω/c is the vacuum wavenumber with frequency of the incident light ω and speed of light c. Since higher modes feature the distance between any two adjoining poles in the field patterns that decreases with the mode number n, the coupling with higher-order modes is less effective [24]. In the case of very small nanoparticles (much smaller than the wavelength of the incident light, when q≪1), mainly the dipolar normal mode (n=1) is excited. This results in strong absorption and weak scattering of the light, σabs≫σsca. However, as the nanoparticle size increases, the contribution of higher-order modes becomes larger and can no longer be ignored. As a result, the scattering induced by higher-order modes in large nanoparticles becomes comparable and may even dominate over the absorption.
For metal particles, the absorption and scattering of the light become even more complex. It is related to free electrons in metals and collective oscillations of the induced surface charges known as surface plasmons [16,25]. Collective oscillations of the surface charges at the nanoparticle interface create a resonant structure with a very specific field pattern. Since these fields are related to the surface charges at the metal interface, they decrease very rapidly with the distance from the interface in both directions [16] (i.e., inside and outside the nanoparticle). Moreover, at frequencies close to the surface plasmon resonance, the incident light strongly couples with the induced internal surface charges, leading to extraordinary scattering and absorption by the metal particles [18].
According to the Mie theory [23], each normal mode of metal nanoparticles contains a surface plasmon resonance. Thus, there exist an infinite number of surface plasmons characterized by their own order n and possessing different resonant frequencies ω (n) res. These frequencies decrease with the size of metallic particles as can be seen in Fig. 1, which shows the associated red-shifts of the surface plasmon resonances for silver nanoparticles. Moreover, the sensitivity of ω (n) res to the particle size is determined by the order number n: higher-order plasmons are less sensitive to changes in the particle size. Thus, the surface plasmon frequencies for the lowest modes with n=1, 2, 3 can be heavily dispersed, especially for relatively large nanoparticles with R≥30 nm.
The resonant contributions of surface plasmons to light absorption and scattering by a single metal nanoparticle also depend on the radius R and the mode number n [23]. The contributions of the first three plasmon modes of silver nanoparticles with different radii R are shown in Fig. 2. One can see that the scattering of the first three resonant surface plasmon modes always increases with the nanoparticle radius. Meanwhile, the resonant contributions to the total absorption of the nanoparticles decrease with the nanoparticle size after reaching their critical (peak) radius. Thus, the Q factor of the resonant absorption significantly decreases for low-mode plasmons excited in relatively large nanoparticles (R>50 nm). For such nanoparticles, the Q factor of the dipolar absorption resonance is so small that it becomes negligible as shown by the dashed line in Fig. 1. The decrease of the modal (n=1, 2, 3, …) absorption for relatively large nanoparticles plays a key role in plasmonic enhancement of the optical absorption of thin-film solar cells. Hence, it is important to identify the effect of the modal absorption in order to obtain the optimal plasmonic enhancement in a thin-film solar cell.
Fig. 1. Frequencies of the surface plasmon resonances in both scattering and absorption spectra for single spherical silver nanoparticles with radius R. The dashed curve shows the region where there is no resonant absorption on the dipolar mode.
Fig. 2. Absorption and scattering cross-sections as a function of the radius R of a single silver nanoparticle for the n=1, 2, 3 surface plasmon modes, corresponding to the resonant frequencies in Fig. 1.
3. Plasmonic enhancement
To study the role of the dipolar and higher-order surface modes in plasmonic enhancement of thin-film solar cells, let us consider optical absorption of a hydrogenated amorphous silicon (a-Si:H) solar cell with a 240 nm thick photo-active layer, a 20 nm thick ITO coating, and an 80 nm thick Al back contact (Fig. 3). We assume that the top surface of the ITO coating is uniformly covered by spherical silver nanoparticles of radius R with surface coverage η. Here, the surface coverage characterizes the part of the total surface area of the cell covered by the spherical nanoparticles.
Fig. 3. Sketch of a thin-film a-Si:H solar cell structure with an array of Ag nanoparticles on top of an ITO layer.
In this set of numerical experiments, we have used the Finite Element Method to solve a full set of 3D Maxwellian equations with perfectly matched layer boundary conditions for monochromatic, normally incident plane waves. Simulations were performed for the square array of the nanoparticles by applying periodic boundary conditions. The employed boundary conditions account for multiple scattering caused by nanoparticle-nanoparticle, nanoparticle-substrate, and nanoparticle-substrate-nanoparticle interactions, as well as describe the coupling of the scattered light into waveguide modes of the a-Si:H layer. Thus, the performed simulations take into account all the major effects of the metal nanoparticles deposited on top of the cell.
The results of our calculations for optical absorption rates for both the a-Si:H photo-active layer (solid lines) and Ag nanoparticle array with the radius R=20 nm (dashed lines) and different values of the surface coverage of 0, 10, and 20% are shown in Fig. 4. This figure reveals the mixed and complex influence of the surface plasmons on the cell optical absorbance.
The analysis of the higher-order surface plasmons (Fig. 2) shows that the main interaction of the sunlight with small silver nanoparticles of R=20 nm is realized mainly through the coupling with the dipolar mode (n=1). The corresponding resonant region is depicted in Fig. 4 as the shadow area. This figure shows that, in the resonant region, where the dipolar surface plasmon shows up more strikingly, the nanoparticle-enhanced cells have decreased optical absorption in the photo-active layer [12, 22]. This happens because of very high losses caused by excitation of surface plasmons in such small metallic nanoparticles (the dashed curves in Fig. 4). Despite this fact, the enhanced scattering from metallic nanoparticles (also influenced by the surface plasmons) occurs at longer wavelengths [26], thus improving the light trapping inside the photo-active a-Si:H layer. Since most of the energy of the solar radiation in the AM1.5 global spectrum is concentrated between 0.55 and 2.5 eV, the positive effect of the improved light trapping can compensate the negative effect from plasmonic absorption inside the nanoparticles, giving a positive total gain from the plasmonic effects integrated over the overall solar spectrum.
From here, we can summarize that to optimize the performance of plasmonic solar cells, one needs the two main things:
i) to maximize the forward light scattering from the plasmons into the photo-active layer;
ii) to minimize the plasmon-induced light absorption by the metal nanoparticles in the peak region of the solar spectrum.
Fig. 4. Spectral absorption rate of the a-Si:H photo-active layer (solid lines) and silver nanoparticles with R=20 nm (dashed lines) as a function of frequency ω[eV]. The shadow depicts position of the n=1 surface plasmon resonance.
Fig. 5. Spectral absorption rate of the a-Si:H photo-active layer (solid lines) and silver nanoparticles with R=90 nm (dashed lines) as a function of frequency ω[eV]. The shadow regions correspond to the n=1, 2, 3 surface plasmon resonances.
This approach benefits from the results of the analysis of the higher-order plasmon modes (Figs. 1 and 2). Our results suggest that for large nanoparticles the contributions of higher-order surface plasmon modes become more important. The resonant frequencies of the lowest-order modes for such nanoparticles are no longer around 3.5 eV as in the small nanoparticle case. By increasing the nanoparticle size, one can shift the low-order plasmon modes towards the peak area of the solar spectrum. This significantly improves the light scattering by the higher-order modes in the peak region of the solar spectrum as quantified in Fig. 2. Moreover, in this case the nanoparticle absorption caused by the lowest-order modes and especially by the dipolar mode, is significantly decreased, making the higher-order absorption dominant. This is very advantageous, as the low-order modes of large nanoparticles have resonant frequencies within the peak range of the solar spectrum. In other words, by increasing the nanoparticle size, one can separate the plasmon-induced scattering and nanoparticle absorption into different frequency/photon energy ranges, improving the light scattering in the peak range of the solar spectrum and leaving the plasmon-induced absorption outside of this region.
Figure 5 demonstrates this substantially improved plasmon enhancement, by using silver nanoparticles with R=90 nm. Compared to the case of R=20 nm, these nanoparticles feature strong coupling of the sunlight with the first three surface plasmon modes and shift resonant energy of the dipolar mode by more than 1 eV towards the peak region of the solar spectrum. Even though each surface mode induces additional absorption in the nanoparticles, the total level of this absorption in the peak region of the solar spectrum remains quite small and can be attributed to a huge decrease of the dipolar absorption compared to the case of small nanoparticles. As a result, the absorption rate of the photo-active layer can be increased by up to 20% over a broad frequency range.
One might argue the applicability of the Mie theory, which does not account for the effect of the highly-absorbing substrate. Here, we show that because of the relatively small dielectric permittivity of the ITO layer, the change in the resonant frequencies of the metallic nanoparticles caused by the a-Si:H layer is very small. This frequency shift is not significant since the resonant absorption peaks of the Ag nanoparticle arrays (dashed lines) in Figs. 4 and 5 are still very close to the resonant frequencies of the surface plasmons predicted by the Mie theory (the shadow regions).
4. Optimization
In the above, we have shown that by tuning the spectral position of the higher-order surface modes (e.g. by changing the size and surface coverage of the nanoparticles) one can improve performance of plasmonic solar cells. Now, let us consider how the nanoparticle array parameters affect this enhancement.
The performed analysis of the effect of the higher-order plasmon modes suggests that optical absorption in the photo-active layer may be enhanced through the excitation of surface plasmons in large metal nanoparticles, resulting in the effective light trapping inside thin-film solar cells. However, we should note that larger nanoparticle sizes, as well as larger surface coverages, inevitably lead to the increased absorbed and reflected (by the array of metal nanoparticles) power thus effectively reducing the optical absorption in the photo-active layer. Therefore, there exists an optimum combination of the nanoparticle array parameters which maximizes the positive effect of higher-order surface plasmon modes on the optical absorption and photocurrent response of plasmonic solar cells [17].
4.1. Coverage optimization
To perform optimization of the optical absorption, one needs to investigate the influence of both the radius R and the surface coverage η on the absorbed light-power. The total absorbed power, P tot, has been calculated by integration of the absorption rate of the photo-active layer over the AM1.5 global spectrum for a wide range of the array parameters R and η. The calculated dependences of the plasmon enhancement
on the surface coverage η are shown in Fig. 6, where P tot(R,0) is the total absorbed power by the plain cell without nanoparticles.
These results suggest that for any given radius of nanoparticles R, there exist a value of surface coverage η max (Fig. 7) maximizing the plasmon-related enhancement of the absorbed power. By deposition of nanoparticles with the average surface density of η max/(πR 2) that cover the η max (%) of the top cell surface, one can achieve the maximum enhancement F max for the particular radius R of the nanoparticles.
The existence of the optimum surface coverage η max to obtain the maximum plasmon-related light trapping in the solar cells enhancement can be understood by examining the scattering of the nanoparticles. For small nanoparticle coverages, the energy scattered to the forward semi-sphere and then transmitted into the a-Si:H photo-active layer increases with η, while for large values of η, above a certain limit, the main part of the scattered energy is reflected back due to the dominant backward scattering. In such a way, for very large surface coverage by metallic particles, the incident light is strongly shielded by the induced surface charges and is reflected back by the higher-order surface modes. As a result of this competition, the most effective light trapping, and hence, optical absorption by the cell, occurs at η max.
In addition to the main peak at intermediate values η max, Fig. 6 also shows a complimentary maximum of the plasmon enhancement by small nanoparticles with R=10 nm. This enhancement corresponds to extremely small surface coverages, η<5%, when multiple scattering from the nanoparticles is very weak. Recently, similar effects have been obtained for crystalline silicon solar cells [10, 17], where it was demonstrated that metallic nanoparticles with low surface coverages can provide significant individual contribution to the overall light absorption.
4.2. Size optimization
We have already mentioned the big difference in the plasmon enhancement by small and large nanoparticles caused by the higher-order plasmon modes. This difference also leads to very different behavior of ηmax for small and large particles depicted in Fig. 7. One can see from this figure that η max for small nanoparticles decreases with the radius R, owing to the dominant dipole absorption, whose cross-section increases with the nanoparticle radius (Fig. 2). This observation is in contrast to the large nanoparticle case, when the coupling of the incident sunlight with the higher-order surface plasmon modes makes the light absorption a dominant effect, thus dramatically changing the behavior of η max.
The optimized scattering and absorption of the sunlight by the higher-order surface plasmon modes also explain why the maximum enhancement for large nanoparticles is higher than for the small ones (Fig. 8). The stronger forward scattering from higher-order plasmon modes of large nanoparticles can more effectively trap the light inside the amorphous silicon layer.
Fig. 7. Dependence of the surface coverage η max when the maximum enhancement of the a-Si:H optical absorption is obtained for silver nanoparticles with radius R.
Fig. 8. Size-dependence of the maximum achievable enhancement F max by silver nanoparticles with radius R.
As a result, the plasmon enhancement can be increased from 10.95%, being the maximum enhancement for small nanoparticles achieved at R=30 nm and η=33.45%, to 15.15%, for large nanoparticles with R=80 nm and η=11.23%, (Fig. 7, 8).
Recently, a similar ITO(20 nm)/a-Si:H(240 nm)/stainless steel plasmonic cell was experimentally studied in [11]. It showed the 8.3% enhancement by using Au nanoparticles with R=50 nm and η=3%. Despite quite significant differences in the nanoparticle shapes and solar cell structures, these results are in good quantitative agreement with our computations (Fig. 6). Moreover, our numerical experiments suggest that the enhancement obtained in paper [11] can be almost doubled by using larger Ag nanoparticles.
We should also note that, despite the evident advantage of using large nanoparticles, small nanoparticles offer another distinctive advantage: the width of their plasmon enhancement peak in the η-space is wider than that for large particles (the inset on Fig. 8). In other words, although small nanoparticles provide a weaker enhancement, the range of the surface coverage η, which results in at least 10% plasmonic enhancement, is broader than for larger nanoparticles; this enables better reproducibility of the plasmon enhancement in experiments.
5. Conclusion
We have studied the plasmonic effect of silver nanoparticles deposited on the top surface of the thin-film hydrogenated amorphous silicon solar cell on light trapping inside the photo-active layer. We have discussed and analyzed the role of higher-order surface plasmon modes in the plasmonic enhancement of the thin-film solar cells. It has been shown that by excitation of higher-order surface plasmon resonances in larger nanoparticles, one can increase the energy transmitted into the amorphous silicon layer, as well as decrease the optical absorption related to the metallic nanoparticles. Thus, the overall broadband optical absorption in the photo-active layer can be significantly improved.
Based on the numerical full-wave solution, we have investigated the effect of the nanoparticle array parameters on the efficiency of the higher-order surface plasmon mode coupling and the associated enhancement of the optical absorption in the cell. We have also performed the optimization of the plasmon enhancement and elaborated the optimum characteristics of the nanoparticle arrays maximizing the light trapping and hence the photocurrent response inside the thin-film a-Si:H photo-active layer.
The obtained results have shown that there exist two optimal configurations of the silver nanoparticles enhancing the optical absorption by 10.95% and 15.15%, respectively. The former is caused by the small nanoparticles with R≈30 nm and η≈ 33%, while the latter can be achieved with the nanoparticles of R ≈ 80 nm and η≈11%. Thus, proper adjustment of the nanoparticle array parameters, which takes into account the higher-order plasmon modes, may lead to the new generation of efficient and cheap plasmonic solar cells.
References and links
1. M. A. Green, Third Generation Photovoltaics (Springer, Berlin, 2003).
2. M. A. Green, Solar Cells: Operating Principles, Technology and System Applications (The University of New South Wales, Sydney, 1998).
3. J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77, 917–930 (2004). [CrossRef]
4. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008). [CrossRef] [PubMed]
5. M. Westphalen, U. Kreibig, J. Rostalski, H. Lüth, and D. Meissner, “Metal cluster enhanced organic solar cells,” Sol. Energy Mater. Sol. Cells 61, 97–105 (2000). [CrossRef]
6. A. J. Morfa, K. L. Rowlen, T. H. Reilly III, M. J. Romero, and J. v. d. Lagemaatb, “Plasmon-enhanced solar energy conversion in organic bulk heterojunction photovoltaics,” Appl. Phys. Lett. 92, 013504 (2008). [CrossRef]
7. S. S. Kim, S. I. Na, J. Jo, D. Y. Kim, and Y. C. Nah, “Plasmon enhanced performance of organic solar cells using electrodeposited Ag nanoparticles,” Appl. Phys. Lett. 93, 073307 (2008). [CrossRef]
8. S. W. Tong, C. F. Zhang, C. Y. Jiang, G. Liu, Q. D. Ling, E. T. Kang, D. S. H. Chan, and C. Zhu, “Improvement in the hole collection of polymer solar cells by utilizing gold nanoparticle buffer layer,” Chem. Phys. Lett. 453, 73–76 (2008). [CrossRef]
9. H. R. Stuart and D. G. Hall, “Island size effects in nanoparticle-enhanced photodetectors,” Appl. Phys. Lett. 73, 3815 (1998). [CrossRef]
10. D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86, 063106 (2005). [CrossRef]
11. D. Derkacs, S. H. Lim, P. Matheu, W. Mar, and E. T. Yu, “Improved performance of amorphous silicon solar cells via scattering from surface plasmon polaritons in nearby metallic nanoparticles,” Appl. Phys. Lett. 89, 093103 (2006). [CrossRef]
12. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101, 093105 (2007). [CrossRef]
13. M. D. Yang, Y. K. Liu, J. L. Shen, C. H. Wu, C. A. Lin, W. H. Chang, H. H. Wang, H. I. Yeh, W. H. Chan, and W. J. Parak, “Improvement of conversion efficiency for multi-junction solar cells by incorporation of Au nanoclusters,” Opt. Express 16, 15754–15758 (2008). [CrossRef] [PubMed]
14. B. J. Soller and D. G. Hall, “Scattering enhancement from an array of interacting dipoles near a planar waveguide,” J. Opt. Soc. Am. B 19, 2437–2448 (2002). [CrossRef]
15. K. R. Catchpole and S. Pillai, “Absorption enhancement due to scattering by dipoles into silicon waveguides,” J. Appl. Phys. 100, 044504 (2006). [CrossRef]
16. N. A. Azarenkov and N. K. Ostrikov, “Surface magnetoplasma waves at the interface between a plasma-like medium and a metal in a Voigt geometry,” Phys. Rep. 308, 333–428 (1999). [CrossRef]
17. Yu. A. Akimov, K. Ostrikov, and E. P. Li, “Surface plasmon enhancement of optical absorption in thin-film silicon solar cells,” Plasmonics 4, 107–113 (2009). [CrossRef]
18. B. S. Luk’yanchuk, M. I. Tribelsky, Z. B. Wang, Y. Zhou, M. H. Hong, L. P. Shi, and T. C. Chong, “Extraordinary scattering diagram for nanoparticles near plasmon resonance frequencies,” Appl. Phys. A 89, 259–264 (2007). [CrossRef]
19. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Spectral response of plasmon resonant nanoparticles with a non-regular shape,” Opt. Express 6, 213–219 (2000) [CrossRef] [PubMed]
20. W. B. Ewe, H. S. Chu, and E. P. Li, “Volume integral equation analysis of surface plasmon resonance of nanoparticles,” Opt. Express 15, 18200–18208 (2007). [CrossRef] [PubMed]
21. K. P. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93, 191113 (2008). [CrossRef]
22. C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92, 013113 (2008). [CrossRef]
23. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (Wiley, New York, 1998). [CrossRef]
24. Yu. A. Akimov, V. P. Olefir, and N. A. Azarenkov, “Influence of azimuth structure of surface waves on efficiency of their excitation by tubular electron beams,” Contr. Plasma Phys. 46, 817–825 (2006). [CrossRef]
25. Yu. A. Akimov, N. A. Azarenkov, and V. P. Olefir, “Non-symmetric surface waves in cylindrical waveguide structures with radially non-uniform plasma filling,” Phys. Scr. 67, 329–336 (2003). [CrossRef]
26. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93, 121904 (2008). [CrossRef]
