A metallic hole-array structure was inserted into a tandem solar cell structure as an intermediate electrode, which allows a further fabrication of a novel and efficient hybrid organic-inorganic tandem solar cell. The inserted hole-array layer reflects the higher-energy photons back to the top cell, and transmits lower-energy photons to the bottom cell via the extraordinary optical transmission (EOT) effect. In this case light absorption in both top and bottom subcells can be simultaneously enhanced via both structural and material optimizations. Importantly, this new design could remove the constraints of requiring lattice-matching and current-matching between the used two cascaded subcells in a conventional tandem cell structure, and therefore, the tunnel junction could be no longer required. As an example, a novel PCBM/CIGS tandem cell was designed and investigated. A systematic modeling study was made on the structural parameter tuning, with the period ranging from a few hundreds nanometers to over one micrometer. Surface plasmon polaritons, magnetic plasmon polaritons, localized surface plasmons, and optical waveguide modes were found to participate in the EOT and the light absorption enhancement. Impressively, more than 40% integrated power enhancement can be achieved in a variable structural parameter range.
© 2014 Optical Society of America
The tandem solar cell, made of at least two different p-n junctions connected in series, has been receiving extensive attentions in recent years [1–3]. In a conventional tandem structure, a semiconductor with a larger band gap is usually placed on top in order to absorb photons with higher energies, while the other one with a smaller band gap is at the bottom to absorb those transmitted lower-energy photons. In this case the open-circuit voltage is the addition of voltages of the two cascaded subcells. Therefore, in theory a tandem design can avoid the trade-off between reaching either maximum absorption band or maximum voltage, and can be then made to realize a full use of the incident solar energy. However, the challenge for constructing such a tandem cell is to select suitable materials. Ideally, the materials used for both top and bottom subcells must be lattice-matched, so that they can be grown up tightly together. Their band gaps should be chosen to ensure that photocurrents generated in each subcell being matched. A tunnel junction between the two subcells needs to be carefully designed too, in order to transport electrons (holes) from the n (p) side to the p (n) side. Otherwise the unwanted voltage drop across the tunnel junction will be inevitable. Apparently, novel and revolutionary solar cell designs able to relieve such constrains will be highly needed, especially in the current downside period of the solar cell industry.
Plasmonic structures at the nanoscale have been widely investigated in thin-film solar cells in order to enhance the light absorption [4–9]. Surface plasmons (SPs) are thought to be useful because the absorbed energy is proportional to the energy density of the local electromagnetic field. The near-field electrical field enhancement and the large scattering cross section of SPs may result in a highly concentrated energy thus a large light absorption in a much thinner semiconductor layer [10, 11]. Therefore both localized surface plasmons excited in metallic nanoparticles and surface plasmon polaritons propagating at the periodic metal/semiconductor interfaces have been extensively investigated with greater interests in designing newer solar cells. In a 2010 article, we proposed a new scheme of embedding metallic nanogratings at the bottom of an amorphous silicon thin-film solar cell, and achieved a ~33% broadband absorption enhancement . The embedded metallic gratings have the advantages to avoid the blocking of incident lights as compared to those using top gratings, and to achieve a broadband and polarization-insensitive absorption enhancement via a simultaneous excitation of SPs, waveguide modes and Fabry-Perot (FP) resonances altogether inside the cell.
Depression in current solar cell industrials requires new techniques, which are able to realize a further increase in efficiency but with a much reduced cost. In this work, a metallic hole-array (HA), which exhibits an extraordinary optical transmission (EOT) effect, was firstly inserted into a hybrid tandem solar cell [12, 13]. This novel hybrid tandem design comes together with many apparent advantages. First, this metallic HA can be viewed as a wavelength-selective filter, which reflects the high-energy photons back into the top subcell and transmits the lower-energy photons into the bottom subcell. Second, the metallic HA can also act as an intermediate electrode. The electric power generated from both top and bottom subcells can be extracted independently or serially-connected. Besides, both top and bottom subcells will be separated by this intermediate layer, thus the two absorbing materials can be selected in a much wider scope simply according to their performances for each wavelength band, with no lattice-matching condition required. The novel hybrid design has no need for a tunnel junction between the top and the bottom cells too, thus the voltage drop across the tunnel junction can be fully avoided. Intermediate reflectors made up of micro-structured conducting dielectrics were previously proposed to enhance the efficiency in a-Si/μc-Si tandem cells [14–19]. Here, use of a metallic HA indicates an alternative way as intermediate reflectors in tandem solar cells, which may be more flexible for using different combinations of photovoltaic materials. Importantly, the high concentration of SPs and other types of possible resonant polaritons from the metallic HA will further enhance the absorption in both top and bottom subcells, which are difficult to be provided by the dielectric reflectors.
2. Structures and Numerical considerations
The proposed new hybrid solar cell structure is shown in Fig. 1(a).A metallic hole-array was inserted between the top and the bottom subcells, which are different from the commonly used tandem structures (Figs. 1(a) and 1(b)). The holes can be filled with either the used photovoltaic materials or a transparent dielectric medium. The contact layers made of transparent conducting oxides can be optionally inserted between the HA and the top (or the bottom) subcell. Two-dimensional (2D) schematic diagrams of the electrical connection and the optical filtering effect of both novel hybrid and the common tandem structures are shown in Figs. 1(c) and 1(d), respectively. As the metallic HA will act as an electrode, the two subcells can be electrically connected in either a four-terminal way or a two-terminal way, and it will be able to remove the current matching restriction if a four-terminal connection is used (Figs. 1(a) and 1(c)).
As the first attempt in this study, poly (3-hexylthiophene) (P3HT)/6,6-phenyl C61-butyric acid methyl ester (PCBM) blend (band gap Eg = 1.9 eV), which is a widely used organic photovoltaic material suitable for the short visible range, is chosen as the top subcell material . Copper indium gallium selenide (CuInxGa(1-x)Se2, CIGS) (band gap Eg = 1.7-1.0 eV, x = 0-1) is used as the bottom cell material, because of it’s excellent performances in the long visible and infrared spectrum . In the calculation, we chose x = 0.4, and the band gap of CIGS at this case is 1.1 eV. The three-dimensional (3D) and two-dimensional (2D) schematic of the hybrid structure is shown in Figs. 2(a) and 2(b). The optical constants of PCBM and CIGS from references [20, 21] are shown in Figs. 2(c) and 2(d). An Indium Tin Oxide (ITO) contact layer is inserted between the HA and the bottom CIGS subcell, considered to be able to realize the optical impedance matching. (PCBM and ITO have similar refractive indices, and CIGS has a much larger refractive index.) Here Ag was selected as the metal to be used as the intermediate electrode. We also assume that the holes of the HA are filled with PCBM. The light absorption and photo-current generation in this part of PCBM is also included together with those in the PCBM subcell in the calculation. Here we ignored the fabrication consideration, due to the fact that it may be difficult to spin dielectrics into the mesh holes. In reality, this may not be a big issue since that overall electrical and optical performances are mainly determined by the metallic mesh. Detailed geometric and structural parameters of the HA are shown in the inset of Fig. 2(d). In this study, we fixed the thicknesses of both top and bottom subcells to be 100 nm (considered to be as thin as possible), and the thickness of the bottom ITO contact layer to be 10 nm, aiming at minimizing the use of ITO material quantities and thus lowering the overall costs.
In order to match the solar spectrum with both absorption bands of the two selected photovoltaic materials, a wavelength range of 300 nm to 1300 nm was selected in this study. Frequency-dependent dielectric constants of the four materials used were interpolated from the experimental data reported in the corresponding references [20–23]. The modeling software used is a commercially available 3D finite element method (FEM) software Comsol 4.3b. The computational domain was considered as a single unit cell of the periodic cells with an air environment, surrounded by two pairs of lateral periodic boundaries, top and bottom perfect matching layers (PMLs) . Since the solar energy is equally distributed in each polarization and our structure is identical to x and y directions, optical performances of the structure shall be considered independent on the incident polarization. In the following discussions, we fixed the incident plane as the y-z plane, and investigated the Hx component of the electromagnetic field (as shown in Fig. 2(a)). Therefore steady-state electromagnetic field distributions across the structure and the light absorption in both PCBM and CIGS active layers were then fully investigated. The light absorption was calculated as the integral of the Poynting vectors over the surface of the considering active layer. The normal incidence situation was considered throughout the paper.
3. Results and discussions
3.1 Transmission of the Ag HA
Transmissions of the Ag HA with three typical periods of p = 300, 550, and 1000nm were shown in Figs. 3(a)-3(c), when fixing the duty cycle of the holes f = w/p = 0.5, and the thickness of the Ag HA tm = 50 nm. Thicknesses of both top and bottom subcells are also fixed at 100 nm, and the thickness of the ITO contacting layer is 10 nm. Ratios of the power transmitting into the top and the bottom subcells are defined as Tt and Tb. (Tt and Tb are calculated as the integration of the Poynting vector at the top surface and at the interface of the top and the bottom subcells, when a unit incident power is used.) For all used structures, those photons within the absorption band of PCBM (< 650 nm) are almost fully trapped inside the top subcell, with little penetrating into the bottom subcell. The difference between Tt and Tb is then the portion of power absorbed by the top subcell and the intermediate HA layer. For those wavelengths longer than 650 nm, nearly all light power will transmit into the bottom subcell. The trivial difference between Tt and Tb in this spectrum is due to the absorption in Ag and ITO. The metallic HA is highly reflective in the short-wavelength spectrum. For the longer-wavelength spectrum, loss coefficient by Ag is small. Thus the absorption by Ag can be trivial and can be nearly neglected. Tb can all reach 90% in the selected wavelength range for the three chosen periods, while the total hole area only covers 25% (f 2) of the whole Ag HA area. This ratio does not follow the Bethe-Bouwkamp power law . This is believed that the EOT acts effectively. The transmittance differs a lot for the different periods, possibly due to different resonant transmission mechanisms. In order to investigate the details, mapping of the Tb spectrum with the varying period is shown in Fig. 3(d). Five obvious EOT branches exist in the spectrum from 300 to 1300 nm. The five branches all red-shift when increasing the period. The widths of these branches become narrower when the wavelength is beyond the absorption band of CIGS (~1150 nm), as the widths of the resonance curves are related to the absorption loss of the used structures .
In order to understand the mechanisms behind the five branches, we first focused on the first two branches, and investigated the case with details around p = 300 nm. The normalized field distribution of |Hx| at the y-z cross-section located exactly on two transmittance peaks of 780 nm and 820 nm are shown in Figs. 4 (a) and 4(b), corresponding to the second and the first branches in Fig. 3(d), respectively. From the two field distributions, the maximum field enhancement is at the interface between Ag and the surrounding semiconductors, which are typical field distributions of SPs. The two peaks red-shift when increasing the period (Fig. 4(c)). This is coincident with the phase matching conditions of SPs. The first peak red-shifts when the Ag thickness tm increases, while the second one blue-shifts (Fig. 4(d)). Distances between the two peaks (Δλ) increase when reducing the tm (as shown in the inset of Fig. 4(d)). This is because of stronger coupling of SPs at top and bottom interfaces of the Ag layer . Apparently, the first two EOT branches are attributed to the coupling of SPs at the two interfaces of the Ag HA.
Further looking into the case for a longer period at p = 550 nm (Fig. 5). All five EOT branches appeared at this case, and we only pay attention to the third one i.e. the peak at 920 nm. In this case, the magnetic field all concentrated inside the hole, and the electric displacement vectors form approximately a loop. This indicates the existence of the Magnetic Plasmon Polaritons (MPP) [27, 28]. While fixing the f and increasing the p, the resonance peak red-shifts. The peak red-shifts with increasing hole width w, also with increasing tm. These two tuning effects are all coincident well with the typical properties of MPPs.
For the 4th and 5th branches, we investigated the case around p = 1000 nm (Fig. 6). The peak at 1050 nm exhibits a maximum field enhancement at the Ag-semiconductor interfaces, and a strong scattering near the hole (Fig. 6(b)). When fixing the w and increasing the width of the Ag strip (i. e. p increases with the Ag strip width), this peak red-shifts (Fig. 6(c)). This can be attributed to the Localized Surface Plasmons (LSP), excited by scattering of the nanoscale metallic structures. The peak at 820 nm exhibits a waveguide mode inside the hole and in the absorbing subcells. Most of the resonance peak red-shifts with increasing tm and tb, and also red-shifts with increasing p (Fig. 6(d) and 6(e)), this is ascribed to the optical waveguide mode resonating inside the holes. However, the tb = 100 nm curve in Fig. 6(d) does not follow the trend as other curves. This may be ascribed to the interference of different resonant modes. As the period has reached the micrometer scale, multiple resonant modes may participate in both EOT and absorption enhancement. The two dominant mechanisms are ascribed to LSP and the waveguide mode. However, there are other minor resonant modes which can transmit through the holes to the bottom subcell. As shown in Fig. 6 and the mapping plot in Fig. 3(d), some of the resonant peaks seem to be overlapping of different peaks. All these modes will interfere with each other.
3.2 Absorption enhancement and structural optimization of the Ag HA
When varying the period in the broad range from 200 nm to 1.5 μm, 5 resonant mechanisms were identified to participate in the EOT. For different period ranges, dominant mechanisms will be different. Noticeably, high transmittance always exists in the 650-1150 nm spectrum, as wanted in the solar cell applications. Absorptance of the top (At) and the bottom (Ab) subcells for varying periods are shown in Fig. 7. Results for 100 nm PCBM/ 100 nm ITO/100 nm CIGS planar cell without the Ag HA were also given for comparison. This is clear that absorptance inside the top subcell in the new structure can be always enhanced. This is due to the back-reflection of the Ag HA for those short wavelengths, and the photons of short wavelength are confined and intensively absorbed by the top subcell. The absorption by the top subcell is insensitive to structural parameters of the Ag HA. For the bottom subcell, the absorptance at the spectrum <650 nm is suppressed, and the absorptance for the longer-wavelength range is greatly enhanced. Comparing Ab in Fig. 7 and Tb in Fig. 3, the peaks of Ab always coincide well with those of Tb. This indicates that same mechanisms participate in EOT and in the absorption enhancement simultaneously. For wavelengths >1150 nm, there’s no absorption though EOT still exists.
Absorption in the Ag HA for varying periods was also exhibited in Fig. 7(c). The absorptance in Ag was calculated with the same way as the absorption in subcells. There is a sharp absorption peak under the ultraviolet irradiation, due to the interband transition . For the visible and near-infrared spectra where the loss of Ag is moderate, the absorptance curves are mediated by both dispersion of Ag and the resonant absorption of the SPs. The absorption coefficient (the imaginary part of the complex permittivity) of Ag decreases with increasing the wavelength. For the visible band where the absorption is relatively high, the Ag HA exhibits a high reflection and reflect the high-energy photons back to the top subcell. For the longer-wavelength spectrum at near-infrared, where photons transmit through the Ag HA to the bottom subcell, the absorption coefficient of Ag is quite small and the loss is trivial also. However, the parasitic absorption of the Ag HA is almost 5% or more in a quite broad wavelength range.
In order to quantitatively investigate the enhancement, integrated power enhancement factor was defined in this work, which is slightly different from the commonly used integrated current enhancement factor. Integrated current enhancement factor is usually used to evaluate the enhancement effect in solar cells, which takes into account not only the absorptance spectrum, but also different quantum energy of photons at different wavelengths. In the new hybrid solar cell here, short-wavelength photons are preferred to be absorbed inside the top subcell rather than in the bottom subcell. The power associated with per photon-generated carrier will be proportional to the open-circuit voltage Voc (a typical I-V curve is assumed here). The open-circuit voltage Voc strongly depends on the material property, and can be considered as being proportional to the bandgap at most cases . Take this effect into account, the integrated power generation Power in an arbitrary unit can be then defined as
in which I(λ) is the AM1.5 solar spectrum, h is the Plank constant, and c is the speed of light in vacuum. Eg,t (b) is the band gap of the top (bottom) subcell material. P is the power in an arbitrary unit, and only the enhancement factor Epower (Pnovel/Pcompare) is meaningful here. Under this definition, Epower for the structures discussed are 18.41% (p = 300 nm), 17.23% (p = 550 nm), and 15.92% (p = 1000 nm).The current enhancement factors are 14.3%, 10.91%, and 7.99% respectively. To investigate the effects of the metal loss on the overall performance, we also investigate the cases removing the absorption coefficient of Ag (assuming the imaginary parts of optical constants of Ag to be 0). Epower in these cases are 29.31%, 25.28% and 17.01% for p = 300 nm, 550 nm and 1000 nm respectively. The absorption and overall efficiency can be further enhanced by reducing the absorption losses in the metallic HA.
Having figured out the mechanisms accounting for both EOT and the absorption enhancement, we then move on to find an optimized structure for the Ag HA, while still fixing the thicknesses of the top and bottom subcells and the ITO contact layer. Firstly, Epower varying with p with fixed f = 0.5 was shown in Fig. 8. Epower is quite small and even <0 when the period < 200 nm, and then increases quickly with p to the maximum at p = 275 nm. When p>275 nm, Epower declines slowly with increasing p. However, high transmittance always exists when the period varying from 200 nm to 1500 nm. Here we define a relative absorptance AR as AR = Ab/Tb, i.e. the portion of absorption in the power transmitted to the bottom subcell. (Ab is the portion of absorption in the incident power.) As shown in Fig. 8(b), AR for the planar cell declines continuously with the wavelength, which has the same trend with that of the imaginary part of the optical constant of PCBM. Thus the AR variation excludes the influence of the top subcell and the intermediate layer, and concentrates on the absorption in the bottom subcell only. For the tandem cells with the Ag HA, however, the AR curves exhibit many tiny oscillations, as AR includes not only the absorption enhancement effect but also the absorption dispersion of the material. If ignoring those tiny oscillations and paying attention only to the overall trend, for p = 300 nm, AR >0.9 in the spectrum when SPs are excited, and it achieves a perfect absorption (AR = 1) at the peak range. For p = 550 nm, as all five resonance branches participate in, AR is higher than 0.8 in a quite broad band, but the peaks are lower than those of p = 300 nm. However, for p = 1000 nm, AR drops to 0.6. The dominating mode at p = 1000 nm is the waveguide mode, and the absorption enhancement effect from this effect is much weaker than that from SPs.
Except p, tm and f also affect the optical performance of the cell, and in fact that the three parameters will interact to the incident light in a coupled chain. We analyzed the effects from all three parameters here and tried to give simple guidelines for further structural optimization. We fixed the periods and investigated effect of f, in Fig. 9. For p = 300 nm, the broadened absorptance firstly increases with f, and their shapes and peak positions exhibit little changes with f. When f increases further, the Ag strips between neighboring holes are too small to interact with infrared light, and the Ab curve at this case is becoming similar to that of the planar structure for comparison (Fig. 9(a)). Epower firstly increases with f, and then decreases when it is around 0.7 (Fig. 9(d)). For longer period 550 nm, the trend is similar, while the optimized f becomes 0.8. When p = 1000 nm, the optimized f becomes 0.9. The increasing of the optimized f with increasing p can be attributed to the LSP, excitation of which is independent of the period, and but relies on the width of the Ag strip.
When fixing f = 0.5, Epower decreases with increasing p after p = 275 nm. However, for large f and large period, i.e. larger hole width, more light transmitted through the holes via the waveguide mode. Epower at larger periods (such as 500 nm and 1000 nm) also exceed that at p = 300 nm when f >0.6. This will be good if considering the fabrication cost, as it will be easier to make hole-arrays with much larger periods. However, the enhancement effect will weaken with even larger periods. For example, Epower at p = 2 μm is smaller than those at p = 550 nm and 1000 nm in Fig. 9(d), and it will continuously decreases if further increasing p. For such large periods, the diffraction becomes weak and the waveguide mode can’t be sustained, not to mention the SPs which can be only excited at the sub-wavelength scale. The only mechanism that could exist will be the LSP when f is large enough that the Ag strips are still at the sub-wavelength scale. For the last case, the absorption enhancement will be quite weak.
Effects of varying tm are exhibited in Fig. 10. tm has slight influences on the positions and amplitudes of all absorption peaks, except those of MPP and the waveguide mode (Figs. 10(b) and 10(c)). From the overall trend, tm has a weak modification on Epower, much weaker than that from p and f.
At last we investigate the tuning effect of the thickness of the ITO contact layer (tITO), which is fixed at 10 nm in above discussions. This is of great importance as the electrical conductivity of the ITO film depends on its thickness, and this effect must be taken into consideration in a practical design. As exhibited in Fig. 11(d), Epower changes little with varying tITO when p = 550 nm and 1000 nm, while it is very sensitive to tITO when p = 300 nm. . Variation trends of Ab spectra are shown in Figs. 11(a)-11(c). As discussed in Section 2, the ITO contact layer was inserted between the Ag HA and the CIGS subcell for optical impedance matching. The ITO contact layer improves light transmission into the bottom subcell, thus improves the total absorption when compared with the no-ITO case. However, for small periods when SPPs dominate in EOT and the absorption enhancement, the total absorption decreases with increasing tITO as SPPs are concentrated near the interfaces of Ag and semiconductors. When the period increased to the range where MPPs or the waveguide dominates, tITO affects the absorption very little.
In practical applications, optimization of the HA structure needs to simultaneously balance the absorption enhancement, the fabrication cost, and the electrical performance. It would be easier to make hole-arrays with larger periods, and with f which shall not be close to 0 or 1. Associating the above numerical results, hole-arrays with periods between 300 nm and 1000 nm all have the expected great enhancement effects, and the optimized f shall be between 0.5 and 0.8, tm shall be from 50 to 100 nm, tITO shall be on the order of ten nanometers. In these optimized geometric ranges, more than 40% integrated power enhancement can be achieved. This enhancement factor is remarkable in efficiency improvement for the solar cell industry.
3.3 Further discussions
In above discussions, we proposed a novel hybrid tandem solar cell structure, which includes only the basic components of a solar cell. In practical applications, other components such as surface textures and metallic back reflectors can be integrated into the cell as well. The surface texture will increase the chance of reflected light bouncing back into the surface, rather than out to the surrounding air. The back reflector could reflect the leaked light power back into the cell. Both of them will enhance the absorption inside the cell, and these mechanisms do not conflict with our metallic HA. Combination of the surface texture and the back reflector with the metallic HA will for sure able to further enhance the total absorption and the overall efficiency.
All above discussions are under normal incidence. However, as multiple resonant modes participate in the EOT and absorption enhancement, phase-matching conditions can always be fulfilled while varying the incident angle. For a certain mode, resonance will occur at different wavelengths when varying the incident angles. The overall absorption and then the efficiency shall be less sensitive to the incident angle, similar to the plasmonic solar cell reported in our previous work .
In conclusion, a novel hybrid tandem solar cell with a metallic hole-array structure as the intermediate electrode was proposed and the structure was numerically investigated. Besides the convenience in material selection and the structural design brought by the metallic HA, the HA also acts as a selective filter, highly transmits lower-energy photons to the bottom subcell via the EOT and reflects higher-energy photons to the top subcell. Surface plasmon polaritons, magnetic plasmon polaritons, localized surface plasmons, and waveguide modes were identified to participate in the EOT and in the absorption enhancement. A remarkable integrated power enhancement, which is over 40%, was achieved for the PCBM/CIGS hybrid tandem solar cell. The novel design resulted in a significant efficiency improvement, and it is also versatile for further different combinations of active materials.
This work was supported by the National Basic Research Program of China (2012CB922000).
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