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The authors numerically investigate the absorption enhancement of an amorphous Si solar cell, in which a periodical one-dimensional nanowall or two-dimensional nanopillar structure of the Ag back-reflector is fabricated such that a dome-shaped grating geometry is formed after Si deposition and indium-tin-oxide coating. In this investigation, the effects of surface plasmon (SP) interaction in such a metal nanostructure are of major concern. Absorption enhancement in most of the solar spectral range of significant amorphous Si absorption (320-800 nm) is observed in a grating solar cell. In the short-wavelength range of high amorphous Si absorption, the weakly wavelength-dependent absorption enhancement is mainly caused by the broadband anti-reflection effect, which is produced through the surface nano-grating structures. In the long-wavelength range of diminishing amorphous Si absorption, the highly wavelength-sensitive absorption enhancement is mainly caused by Fabry-Perot resonance and SP interaction. The SP interaction includes the contributions of surface plasmon polariton and localized surface plasmon.
©2011 Optical Society of America
1. Introduction
To reduce the electron and hole paths such that the photo-generated carrier collection rate can be increased in a solar cell, a trend of development is to decrease the thickness of the absorption layer in such a device. However, with decreased absorption layer thickness in a solar cell, the absorption efficiency is reduced and the device performance becomes ineffective. To solve this problem, several approaches have been proposed to increase the effective absorption rate, including the use of surface nano-textures for producing the broadband anti-reflection effect [1–9], photonic crystals for enhancing light trapping [10–13], metal or dielectric nanoparticles for increasing light scattering and hence the propagation path in the absorption layer [9, 14], multilayered structure for reducing device reflection [15], and surface plasmon (SP) interaction for enhancing light energy conversion [16–40].
A surface nanostructure can produce a gradient distribution of effective refractive index and leads to the broadband anti-reflection effect. Various surface nanostructures have been designed and fabricated for producing such an anti-reflection effect. The accomplishments include nano-grating structures on Si fabricated with the techniques of lithography and etching [1, 2], a polymer film on a substrate based on the phase separation process of a macromolecular liquid [3], a reversibly erasable nanoporous coating based on polyelectrolyte multi-layers [4], random nanoneedles on Si formed with a specific etching technique [5], a silica nanorod array on Si fabricated with the technique of oblique deposition [6], p-GaN nanorods on n-Si grown with chemical vapor deposition for forming a heterojunction photovoltaic cell [7], and tapered ZnO nanorods on a Si solar cell fabricated with solution growth [8]. Such anti-reflection surface structures have been applied to enhance the absorption of thin-film solar cells.
SP represents collective electron oscillation on the surface of a metal structure, including surface plasmon polariton (SPP) of propagating nature and localized surface plasmon (LSP) of local electron oscillation [41, 42]. Normally, SPP requires certain momentum matching mechanisms, such as a metal grating, for absorbing light from or radiating light into the surrounding medium. However, LSP can always absorb light from or emit light into the surrounding medium when the resonant wavelength is matched. Either SPP or LSP extends its energy distribution (a near-field electromagnetic field distribution) in the dielectric or semiconductor material when an SP mode is generated at the interface between a dielectric (semiconductor) and a metal structure. Such a near-field energy distribution can be absorbed or amplified by the dielectric or semiconductor depending on its excitation condition. In a solar cell, the effective absorption of an SP mode on a metal nanostructure and hence the transfer of SP energy into the solar cell absorbing material create an extra channel for harvesting sunlight photons. The SP interaction in a solar cell is particularly useful in enhancing the absorption efficiency in the spectral range of a low material absorption coefficient. SP interaction with the absorbing layer of a solar cell for enhancing its absorption efficiency has been widely applied to the solar cells of various materials, including Si [17–26, 39, 40], GaAs [27, 28], organic and polymers [29–36], dye-sensitized structure [37], and InGaN [38]. Such a technique has been proved to be useful for enhancing solar cell efficiency.
In this paper, we demonstrate the numerical simulation results of absorption enhancement in an amorphous Si solar cell with embedded periodical Ag nanowalls or nanopillars based on the reported solar cell structures [9, 40]. Because of the structure of metal nanowall or nanopillar, the deposited Si absorbing layer becomes periodically grooved following the pattern of metal nanostructure. We consider one-dimensional (1-D) and two-dimensional (2-D) periodical groove (grating) structures and evaluate the absorption enhancements by comparing to the solar cells with flat Si structures of reasonable parameters. Also, the dependencies of solar cell absorption behaviors on sunlight incidence angle and polarization are illustrated. In this study, we are particularly concerned with the effects of SP interaction on the absorption enhancement in such a solar cell structure. Such effects in a solar cell with a similar nanostructure were not well investigated yet. By using the similar parameters of device geometry reported in literature [9, 39, 40], we demonstrate significant absorption enhancements (more than 50% under certain conditions), when compared with a flat device. Also, we show the important contribution to the absorption enhancement from the SP interactions. Meanwhile, both contributions from SPP and LSP are identified. Although only the results of changing the heights of the nanowall and nanopillar are illustrated, their variation trends are useful for guiding the design of a solar cell with a similar nanostructure. In section 2 of this paper, the designated solar cell structure and the numerical method used for evaluating the solar cell absorption are described. The numerical results are presented in section 3. The SPP and LSP contributions are discussed in section 4. Finally, the conclusions are drawn in section 5.
2. Solar cell structures and numerical method
Figure 1(a) shows the cross-sectional view of the solar cell structure under study. This structure represents the one-period element of a 1-D or a 2-D grating solar cell. In a solar cell with 1-D grating, the structure extends to infinity along the x axis and repeats to form a periodical pattern along the y axis, as schematically shown in Fig. 1(b). Also, Fig. 1(a) demonstrates the structure across the center of a square base of a solar cell with a 2-D grating, as schematically shown in Fig. 1(c). As shown in Fig. 1(a), the designed solar cell has an Ag back-reflector of g in thickness on a certain substrate. In our calculations, we assume that g is infinity. The structure shown in Fig. 1(a) has a width of p, which corresponds to the period of either 1-D or 2-D grating. At the center, there is an Ag nanostructure of c and h in width and height, respectively. In a solar cell of 1-D grating, this metal structure extends to infinity to form a nanowall along the x axis. In a solar cell of 2-D grating, it represents a square nanopillar. The structure shown in Fig. 1(a) is designed by assuming that when amorphous Si is deposited on the Ag nanowall or nanopillar, a 1-D or 2-D dome is formed such that the dimension parameters a, d and t are fixed, no matter how large h is. After the deposition of amorphous Si, a uniform layer of indium-tin-oxide (ITO) of b in thickness and 1.7 in refractive index is coated in conformity with the shape of the dome. The sunlight incident angle is defined as θ. In our study, we vary the height of Ag nanowall or nanopillar, h, from 50 through 150 nm and fix all other dimension parameters at a = 120 nm, b = 20 nm [39], c = 80 nm, d = 120 nm, t = 80 nm, and p = 280 nm. Slight changes of these parameters do not affect the key physical behaviors in this study. It is noted that in choosing the device geometric parameters, we have tried to simulate the fabrication conditions under the constraint of numerical computation time. Among those parameters, the chosen thickness of the amorphous Si layer (120 nm) is smaller than those (160-280 nm) previously reported [9, 39, 40]. We use such a thinner amorphous Si layer for demonstrating that with a proper device design, a thinner Si layer can lead to a comparable photon absorption rate. The value of the period (p = 280 nm) is chosen for effectively generating SPP, as to be discussed in section 4. The size of the computation domain is limited by the used software. Although the real solar cell structure in an experimental implementation may not be exactly the same as what is designed here, the solar cell behaviors must be similar and the concerned physics must be the same.
Fig. 1 (a) Cross-sectional view of the solar cell structure (one period) under study. This figure shows the one-period structure of a 1-D or a 2-D grating solar cell. The solar cells with 1-D and 2-D gratings are schematically shown in parts (b) and (c), respectively.
In numerical computations, the commercial software COMSOL Multiphysics is used for evaluating the absorption of the amorphous Si layer. The numerical technique of this software is based on the finite element method. Because of the periodic structures of the solar cells, we use the periodic boundary condition along the x and y directions. On the top and bottom of the solar cell structure, we use the boundary condition of perfectly matched layers for simulating the infinitely extended layers of air and Ag along the z direction. The maximum mesh size of an individual dielectric region is set to be one tenth the shortest wavelength of our concern (320 nm in vacuum) in the material. The accuracy of the numerical result is verified with the convergence test. By solving Maxwell’s equations, we can find the electric field distribution in the whole solar cell structure. The electric field distribution in the absorption layer (amorphous Si) is used for evaluating the photon absorption rate G(λ) (in the unit of s−1nm−1), defined as
Here, Np(λ) is the incident photon flux density as a function of wavelength under the condition of AM1.5G, is the angular frequency, is the permittivity in free space, and is the imaginary part of the dielectric constant of amorphous Si. The denominator in Eq. (1) is the time-average Poynting power of the incident wave. The integrated photon absorption rate GT (in the unit of s−1) contributed by the entire AM1.5G spectral range of amorphous Si absorption (320-800 nm) is then given byIt is noted that with the simulation model above, the diffraction effects of the periodical Ag nanostructures are included. In numerical computations, the dielectric constants of amorphous Si and Ag are obtained from literatures [26, 43].
3. Numerical results
Figure 2 shows the photon absorption rates of the solar cells with 1-D gratings as functions of wavelength with h = 50, 70, 110, and 150 nm in an area of 280 nm x 280 nm when the sunlight incident angle is θ = 0 and the incident polarization is in the y-z plane (the TM polarization). The result of a reference sample (denoted by “flat”) with a flat Ag surface (no Ag nanowall) and a flat Si layer of 163 nm in thickness is also shown in Fig. 2 for comparison. The thickness of the Si layer of the reference sample is designed to make the total volume of Si about the same as that in the case of h = 110 nm. In the case of flat Si surface, one can see a major peak around 620 nm and a broad hump around 500 nm. The peak around 620 nm originates from Fabry-Perot resonance in the planar structure. The broad hump around 500 nm is caused by the maximum solar spectral intensity distribution around this wavelength. The Fabry-Perot resonance peak becomes weaker (also slightly shifted in wavelength) or disappears when the grating structure is introduced. In general, the photon absorption rate increases with increasing h until it becomes larger than 110 nm. The enhancements of photon absorption rate in the wavelength range shorter than 560 nm are believed to be due to the broadband anti-reflection effect. The enhancements of photon absorption rate beyond 560 nm caused by those peaks are attributed to Fabry-Perot resonance and SP interaction. Among various cases of different h values, several prominent common peaks around 600, 670, 700, and 750 nm can be identified. To show the broadband anti-reflection effect, in Fig. 3 , we plot the reflectivity from the whole solar cell structure as a function of wavelength in the case of the 1-D grating solar cell with h = 110 nm, θ = 0, and TM-polarized incident sunlight. The similar result of the reference device of flat surface is also shown for comparison. In the curve of the flat surface device, one can see a major dip and a minor minimum around 620 and 500 nm, respectively, which correspond to the sharp peak and the broad hump in the curve of the same device shown in Fig. 2. We can also find the correspondences between the individual depressions in the curve of h = 110 nm and the peaks in the curve of the same device shown in Fig. 2. In Fig. 3, one can see the low reflectivity of the grating device in the short-wavelength range, particularly below 560 nm. In this wavelength range, no clear Fabry-Perot resonance or SP interaction behavior, which will produce a sharp depression, is observed. The weakly wavelength-dependent absorption enhancements around 500 nm in Fig. 2 are due to the broadband anti-reflection effect caused by the surface nanostructures in the grating solar cells.
Fig. 2 Photon absorption rates of the solar cells with 1-D gratings as functions of wavelength with h = 50, 70, 110, and 150 nm when TM-polarized sunlight is incident angle with θ = 0. The result of the reference solar cell of flat surface is also shown for comparison.
Fig. 3 Reflectivity as a function of wavelength from the 1-D grating solar cell with h = 110 nm, θ = 0, and TM-polarized incident sunlight. The similar result of the reference device of flat surface is also shown for comparison.
The interactions between the incident sunlight and the solar cells can also be understood from the electrical field amplitude distributions in the solar cells. Figures 4(a) -4(d) show the electrical field amplitude distributions (in log scale) at 500, 600, 695, and 740 nm in wavelength, respectively, in the solar cell of 1-D grating with h = 110 nm when TM-polarized light is normally incident (θ = 0). In Fig. 4(a) for the case of 500 nm in wavelength, the gradual change of field strength across the dome boundary clearly indicates the anti-reflection effect. Except those near the metal surface, the electrical field strength essentially decreases with depth in the Si layer, indicating the effective amorphous Si absorption. Around the two top corners of the Ag nanowall, one can see the strong electrical field distribution of the lightning rod effect. At 600 nm (see Fig. 4(b)), the lightning rod effect becomes stronger. Also, a layered structure of field distribution can be seen, indicating the significant Fabry-Perot resonance effect at this wavelength to form the peak in Fig. 2. Then, in Fig. 4(c) for 695 nm, one can see the strong field distribution on each facet of the metal surface. Such a field distribution illustrates the behavior of SP-enhanced solar cell absorption around this wavelength. The similar strong field distribution on the metal surface around 740 nm shown in Fig. 4(d) indicates the strong interaction of another SP mode. It is noted that in Fig. 4(d) the field is mainly distributed in the groove region of the metal grating that is quite different from the distribution in Fig. 4(c), implying that the two SP modes have quite different properties.
Fig. 4 Electrical field amplitude distributions (in log scale) at the wavelengths of 500 (a), 600 (b), 695 (c), and 740 (d) nm in the solar cell with a 1-D grating of h = 110 nm when TM-polarized sunlight is normally incident (θ = 0).
Figure 5 shows the results similar to those in Fig. 2; however, with the polarization of incident sunlight along the x axis (the TE polarization). The result of the same reference sample (denoted by “flat”) is also shown for comparison. Here, one can see that with the periodical Ag nanowall structures, in each case of the four h values, three major peaks can be seen in the spectral range of 560-760 nm. It is noted that because in such a solar cell, the grating groove is formed along the x axis, SPP cannot couple with the incident sunlight polarized in the x direction. Also, LSP cannot be generated with the polarization along the x axis. The aforementioned sharp peaks must be attributed to Fabry-Perot resonance, as to be verified by the electrical field amplitude distributions in Figs. 6(b) -6(d). In Figs. 6(a)-6(d), we show the electrical field amplitude distributions (in log scale) at 500, 600, 695, and 745 nm in wavelength, respectively, in the solar cell with 1-D grating and h = 110 nm when TE-polarized sunlight is normally incident (θ = 0). The field distribution at 500 nm, as shown in Fig. 6(a), is quite different from that of incident TM-polarized light (see Fig. 4(a)). In Fig. 6(a), the abrupt change of field strength across the dome boundary reveals the considerable device reflection at the wavelength of 500 nm. One can also see the significant reflection from the metal structure to form a quasi-layered field distribution. The incident sunlight can hardly reach the metal groove region. The aforementioned anti-reflection effect may still play a certain role under the illumination of TE-polarized light. However, it becomes weaker as confirmed by the smaller absorption enhancements of the grating solar cells around 500 nm (see Fig. 5), when compared with those of incident TM-polarized sunlight (see Fig. 2). In Figs. 6(b) and 6(c), one can see bended layered field distributions with the geometries following the shape of the Ag nanowall. Such bended layered field distributions imply that the corresponding absorption peaks shown in Fig. 5 are due to Fabry-Perot resonance. Then, at 745 nm (see Fig. 6(d)), the layered field distribution is split into two regions: the Ag nanowall and the metal groove. In this situation, because the metal has different heights in the two regions, two separate Fabry-Perot resonance patterns are formed. Among various samples of different h values, the Fabry-Perot resonance wavelengths vary with the height of the Ag nanowall.
Fig. 5 Photon absorption rates of the solar cells with 1-D gratings as functions of wavelength with h = 50, 70, 110, and 150 nm when TE-polarized sunlight is incident with θ = 0. The result of the reference solar cell of flat surface is also shown for comparison.
Fig. 6 Electrical field amplitude distributions (in log scale) at the wavelengths of 500 (a), 600 (b), 695 (c), and 745 (d) nm in the solar cell with a 1-D grating of h = 110 nm when TE-polarized sunlight is normally incident (θ = 0).
Figure 7 shows the photon absorption rates of the solar cells with 2-D gratings as functions of wavelength with h = 50, 70, 110, and 150 nm in an area of 280 nm x 280 nm (a periodical element) when the sunlight incident angle is θ = 0 and the incident polarization is in the y direction. Note that in this 2-D grating case, there is no difference between TM and TE polarizations for normal incidence. The reference sample of flat surface for comparison here is designed to also have the same total Si volume as that of the 2-D grating device with h = 110 nm. Its Si layer thickness is 153 nm. In the 2-D grating case, the photon absorption enhancement in the short-wavelength range (approximately < 530 nm) is partly due to the broadband anti-reflection effect by introducing the metal nanopillar structures. Those major or minor peaks beyond 530 nm in wavelength are attributed to either SP interaction, Fabry-Perot resonance, or their mixture. The electrical field amplitude distributions at the wavelength of 500 nm in the two device cross sections (the y-z and x-z planes) in the case of h = 110 nm are shown in Figs. 8(a) and 8(b). Similar field distributions at 625, 685, and 740 nm are shown in Figs. 8(c) through 8(h). The bended layered field distributions in Figs. 8(a) through 8(d) indicate that the contributions to the absorption enhancements at 500 and 625 nm (see Fig. 7) include the Fabry-Perot resonance effect. However, it is believed that the broadband anti-reflection effect also contributes to the absorption enhancement around 500 nm. The mixtures of the layered field distributions and the strong metal surface field distributions in Figs. 8(e) through 8(h) imply that the absorption peaks at 685 and 740 nm can be attributed to the mixed effects of Fabry-Perot resonance and SP interaction.
Fig. 7 Photon absorption rates of the solar cells with 2-D gratings as functions of wavelength with h = 50, 70, 110, and 150 nm when sunlight is incident with θ = 0.
Fig. 8 Electrical field amplitude distributions (in log scale) in the y-z and x-z planes at the wavelengths of 500 ((a) and (b)), 625 ((c) and (d)), 685 ((e) and (f)), and 740 ((g) and (h)) nm in the solar cell with a 2-D grating of h = 110 nm when sunlight is normally incident (θ = 0).
Although so far, we have only demonstrated the results of the cases of normal incidence (θ = 0), the absorption enhancements at different incident angles are also evaluated. In Table 1 , we show the integrated photon absorption rates (integrated over the spectral range from 320 through 800 nm) of 1-D grating solar cells for various cases of different Ag nanowall heights (h), different incident polarizations and their averages at θ = 0, 30, and 60 degrees. The numbers shown in the table (without parentheses) are the integrated photon absorption rates (after multiplying them by 107 in s−1) in a square area of p = 280 nm in dimension. As described earlier, the flat solar cell has a Si layer thickness of 163 nm. This Si thickness was chosen to make its total Si volume the same as that of the 1-D grating device with h = 110 nm. Because all other 1-D grating solar cells have the total Si volumes quite close to that of this flat device (within 5% in difference), this flat device is used as the reference solar cell for comparison to demonstrate the enhancements of the integrated photon absorption rate in all the 1-D grating solar cells. The numbers within the parentheses in terms of percentage (%) represent the enhancements of those 1-D grating devices with respect to the references solar cell. In Table 1, one can see that with the periodical metal nanowall structures, the integrated absorption of either TM or TE polarized sunlight is enhanced. However, the absorption of TM polarized sunlight is relatively more enhanced when the incident angle is small. At any incident angle, the integrated photon absorption rates of TM polarized light are always larger than those of TE polarized light. Nevertheless, the enhancement percentages are not necessarily larger, particularly when the height of the Ag nanowall becomes large. In either TM or TE polarization case, the absorption enhancement first increases with h then drops when h reaches 110 or 150 nm. This trend can be understood as that although the broadband anti-reflection effect becomes stronger when the Ag nanowall height is small and increased, the effect saturates and then becomes weaker when the Ag nanowall height is further increased. This trend is less significant in the case of TE polarization, when compared with that of TM polarization. In both cases of TM and TE polarizations, the effects of grating structures become weaker as the sunlight incident angle is increased. This trend is mainly due to the diminishing anti-reflection effect when the sunlight is obliquely incident.
Table 1. Integrated photon absorption rates and the enhancement percentages (within the parentheses) with respect to the reference device of flat surface in various cases of 1-D grating solar cell. The numbers of photon absorption rates must be multiplied by 107 in the unit of s−1.
Table 2 shows the results of integrated photon absorption rate of the 2-D grating solar cells, similar to those in Table 1. The integrated photon absorption rates come from a period of the 2-D grating structure, i.e., a square area of p = 280 nm in dimension. The result of the reference solar cell of flat surface comes from the corresponding curve in Fig. 7. Because of the similar total Si volumes of other 2-D grating solar cells (<5% in difference), this reference device will be used for evaluating the enhancement percentages in all 2-D grating cases. It is noted that due to the different conditions of Fabry-Perot resonance, the integrated photon absorption rate of the reference device for 2-D grating solar cells at a small sunlight incident angle is larger than that for 1-D grating solar cells even though the flat amorphous Si layer of the former is thinner than that of the latter. To more clearly demonstrate the absorption enhancement trends, in Figs. 9(a) and 9(b), we plot the average integrated photon absorption rates of 1-D and 2-D grating solar cells, respectively, as functions of Ag grating height (h) for different sunlight incident angles at θ = 0, 30, and 60 degrees. Here, h = 0 corresponds to the reference device of flat surface. Generally speaking, with a 2-D grating structure, photon absorption is more enhanced in terms of the absolute value and enhancement percentage, when compared with the 1-D grating case. The general trends of increasing the height of the Ag nanopillar and the sunlight incident angle, and changing the incident polarization are the same as those of the 1-D grating solar cells.
Table 2. Integrated photon absorption rates and the enhancement percentages (within the parentheses) with respect to the reference device of flat surface in various cases of 2-D grating solar cell. The numbers of photon absorption rates must be multiplied by 107 in the unit of s−1.
Fig. 9 Average integrated photon absorption rates of 1-D (a) and 2-D (b) grating solar cells as functions of Ag grating height (h) for different sunlight incident angles at θ = 0, 30, and 60 degrees.
4. Surface plasmon interaction
Several peaks of photon absorption rate on the long-wavelength sides in Figs. 2 and 7 are attributed to the interactions of the induced SP modes on the Ag nanostructures with incident sunlight. Because the periodical Ag nanowall or nanopillar structure can support both SPP and LSP, the SP-induced absorption peaks in Figs. 2 and 7 can be caused by SPP, LSP, or their mixture. The SPP interaction with incident sunlight relies on the metal grating structure of an appropriate period, which was chosen to be p = 280 nm in this study. The continuous (red) curve on the right in Fig. 10 represents the dispersion relation of the SPP on the flat interface between amorphous Si and Ag. Here, β denotes the complex wave vector along the interface, i.e., along the y direction. The continuous (blue) curve on the left is a duplicate of the dispersion relation horizontally left-shifted by 2π/p = 0.0224 nm−1, i.e., the new dispersion relation including the momentum compensation effect of the metal grating. In Fig. 10, the two dashed curves stand for the light lines of air and amorphous Si (a-Si), as labeled in the figure. The space between the air light line and the vertical axis passing the origin (the dotted line) corresponds to the condition, under which the incident sunlight in the air can interact with the SPP generated on the Ag grating structure. With normal sunlight incidence (β = 0), the operation points of the SPP interaction are located at the intersections of the left dispersion curve with the vertical dotted line. The SPP interaction wavelengths at the two operation points are about 685 and 450 nm. Therefore, we may expect to observe photon absorption peaks around these two wavelengths in Fig. 2 for 1-D grating solar cells. In Fig. 2, around 670 and 700 nm, photon absorption peaks or shoulders can be observed in each h value case. Due to their small spectral separations from 685 nm, the photon absorption peaks and shoulders around 670 and 700 nm can be caused by the SPP interaction or a mixed interaction of SPP and LSP. Because the broadband anti-reflection effect dominates the absorption enhancement in the short-wavelength range, the possible SPP interaction contribution to photon absorption enhancement around 450 nm is unclear even though minor absorption peaks can be observed near this wavelength.
Fig. 10 Dispersion relation (the continuous curve on the right) of the SPP on the flat interface between amorphous Si and Ag and a duplicate horizontally left-shifted by 2π/p = 0.0224 nm−1. β denotes the complex wave vector along the interface. The two dashed curves stand for the light lines of air and amorphous Si (a-Si).
Because the interaction between an SPP mode and incident sunlight relies on the grating structure, i.e., the periodical Ag nanowall or nanopillar structure, if we change the periodicity of the metal grating, the SPP contribution can be reduced. On the other hand, an LSP mode can be preserved if the grating groove structure is maintained while the grating periodicity is changed. To further understand the contribution of SPP interaction, we consider a solar cell structure depicted in the insert of Fig. 11 . Here, a pattern of two successive metal nanowalls plus a flat-surface section are used to form a unit cell of a 1-D periodical solar cell structure of r in period. Figure 11 shows the photon absorption rates as functions of wavelength in the region of the two successive metal nanowalls for the cases of r = 560, 1120, and 3360 nm when h is 50 nm and TM-polarized sunlight is normally incident. The case of r = 560 nm corresponds to a 1-D grating solar cell depicted in Figs. 1(a) and 1(b). Therefore, the photon absorption rate of the curve of r = 560 nm in Fig. 11 is just double that of the corresponding curve in Fig. 2. With r = 1120 and 3360 nm, the SPP dispersion curve is left-shifted by only one-quarter and one-twelfth, respectively, that shown in Fig. 10. In this situation, the left-shifted dispersion curve cannot intersect with the vertical dotted line for effective SPP interaction such that the contribution of SPP interaction to absorption enhancement is reduced. In Fig. 11, one can see that as r increases, the peak around 700 nm becomes significantly weaker (still existent) while the peak level around 670 nm is almost unchanged. Also, the level of another peak around 750 nm is only slightly varied as r is increased. Therefore, the absorption peak around 700 nm is caused by the interaction of a hybrid mode of SPP and LSP with incident sunlight. When r is increased, the SPP component is reduced. It is noted that in SP hybridization, the resonance wavelength of a hybrid mode is usually shifted away from those of the individual components. The SPP component may have the maximum interaction strength around 685 nm, as predicted in Fig. 10. However, when it hybridizes with an LSP component, the hybrid resonance is red-shifted to 700 nm. The absorption peaks around 670 and 750 nm are mainly caused by LSP interactions with incident sunlight.
Fig. 11 Photon absorption rates as functions of wavelength in the region of the two successive metal nanowalls for the cases of r = 560, 1120, and 3360 nm when h is 50 nm and TM-polarized sunlight is normally incident. The modified solar cell structure is depicted in the insert.
Figures 12(a) -12(c) show the electrical field amplitude distributions (in log scale) at the wavelength of 670 nm in the cases of r = 560, 1120, and 3360 nm, respectively, in the solar cell section of the two metal nanowalls. Figures 12(d)-12(f) (12(g)-12(i)) show the corresponding results at 700 (750) nm in wavelength. Here, one can see that the electrical field amplitude distributions in Figs. 12(a)-12(c) look almost the same except that the intensity is slightly changed, indicating that the LSP mode pattern is weakly affected by the periodicity variation of the solar cell structure. Those in Figs. 12(g)-12(i) also look alike. However, the electrical field distributions are quite different between the two groups. In Figs. 12(a)-12(c), the LSP energy is distributed around the nanowalls. Nevertheless, in Figs. 12(g)-12(i), a significant amount of LSP energy is distributed in the groove regions. The characteristics of the two LSP modes at 670 and 750 nm are quite different. On the other hand, in Figs. 12(d)-12(f), the field distributions in the regions outside the two nanowalls in the y direction change with r value. To clearly demonstrate the field strength variations along the y-axis near the two ends of the computation window in Figs. 12(d)-12(f), in Fig. 13 , we plot the line-scan field strength distributions along a horizontal line 50 nm above the bottom of metal grating (see the horizontal dashed lines in Figs. 12(d)-12(f)) for the cases of three r values. Here, one can see that in the y range either larger than 240 nm or smaller than −240 nm, the electrical field amplitude decreases with increasing r value. This decreasing trend can be regarded as the indication of diminishing SPP contribution in this SP interaction feature.
Fig. 12 Electrical field amplitude distributions (in log scale) at the wavelengths of 670 nm ((a)-(c)), 700 nm ((d)-(f)), and 750 nm ((g)-(i)) in the cases of r = 560 nm ((a), (d), and (g)), 1120 nm ((b), (e), and (h)), and 3360 nm ((c), (f), and (i)) in the solar cell section of the two metal nanowalls.
Fig. 13 Electrical field amplitude distributions along a horizontal line 50 nm above the bottom of metal grating (see the horizontal dashed lines in Figs. 12(d)-12(f)) for the cases of three r values.
5. Conclusions
In summary, we have numerically demonstrated the absorption enhancement of an amorphous Si solar cell with a periodical 1-D Ag nanowall or 2-D Ag nanopillar structure on the Ag back-reflector. With such an Ag nanostructure, a surface grating geometry in the solar cell was formed after Si deposition and ITO coating. In particular, the contributions of SP interactions to the absorption enhancement in such a grating solar cell structure were investigated. Absorption enhancement in most of the solar spectral range of amorphous Si absorption (320-800 nm) has been observed. In the short-wavelength range of high amorphous Si absorption, the weakly wavelength-dependent absorption enhancement is mainly caused by the broadband anti-reflection effect, which is produced through the surface nanostructures. In the long-wavelength range of diminishing amorphous Si absorption, the strongly wavelength-dependent absorption enhancement is mainly caused by Fabry-Perot resonance and SP interaction. The SP interaction includes the contributions of SPP and LSP.
Acknowledgment
This research was supported by National Science Council, The Republic of China, under the grants of NSC 99-2221-E-002-113 and NSC 99-2221-E-002-123-MY3, by the Excellent Research Projects of National Taiwan University (99R80203 and 99R80306), and by US Air Force Scientific Research Office under the contract of AOARD-10-4049.
References and links
1. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology 8(2), 53–56 (1997). [CrossRef]
2. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999). [CrossRef] [PubMed]
3. S. Walheim, E. Schaffer, J. Mlynek, and U. Steiner, “Nanophase-separated polymer films as high-performance antireflection coatings,” Science 283(5401), 520–522 (1999). [CrossRef] [PubMed]
4. J. Hiller, J. D. Mendelsohn, and M. F. Rubner, “Reversibly erasable nanoporous anti-reflection coatings from polyelectrolyte multilayers,” Nat. Mater. 1(1), 59–63 (2002). [CrossRef] [PubMed]
5. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). [CrossRef] [PubMed]
6. J.-Q. Xi, J. K. Kim, and E. F. Schubert, “Silica nanorod-array films with very low refractive indices,” Nano Lett. 5(7), 1385–1387 (2005). [CrossRef] [PubMed]
7. Y. B. Tang, Z. H. Chen, H. S. Song, C. S. Lee, H. T. Cong, H. M. Cheng, W. J. Zhang, I. Bello, and S. T. Lee, “Vertically aligned p-type single-crystalline GaN nanorod arrays on n-type Si for heterojunction photovoltaic cells,” Nano Lett. 8(12), 4191–4195 (2008). [CrossRef] [PubMed]
8. Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. P. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008). [CrossRef] [PubMed]
9. J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, “Nanodome solar cells with efficient light management and self-cleaning,” Nano Lett. 10(6), 1979–1984 (2010). [CrossRef] [PubMed]
10. L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006). [CrossRef]
11. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]
12. A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A 78(2), 023825 (2008). [CrossRef]
13. D. Zhou and R. Biswas, “Photonic crystal enhanced light-trapping in thin film solar cells,” J. Appl. Phys. 103(9), 093102 (2008). [CrossRef]
14. P. Matheu, S. H. Lim, D. Derkacs, C. McPheeters, and E. T. Yu, “Metal and dielectric nanoparticle scattering for improved optical absorption in photovoltaic devices,” Appl. Phys. Lett. 93(11), 113108 (2008). [CrossRef]
15. X. F. Li, Y. R. Chen, J. Miao, P. Zhou, Y. X. Zheng, L. Y. Chen, and Y. P. Lee, “High solar absorption of a multilayered thin film structure,” Opt. Express 15(4), 1907–1912 (2007). [CrossRef] [PubMed]
16. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]
17. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008). [CrossRef] [PubMed]
18. D. M. Schaadt, B. Feng, and E. T. Yu, “Enhanced semiconductor optical absorption via surface plasmon excitation in metal nanoparticles,” Appl. Phys. Lett. 86(6), 063106 (2005). [CrossRef]
19. S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007). [CrossRef]
20. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008). [CrossRef]
21. 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(9), 093103 (2006). [CrossRef]
22. F. J. Haug, T. Söderström, O. Cubero, V. Terrazzoni-Daudrix, and C. Ballif, “Plasmonic absorption in textured silver back reflectors of thin film solar cells,” J. Appl. Phys. 104(6), 064509 (2008). [CrossRef]
23. C. Rockstuhl, S. Fahr, and F. Lederer, “Absorption enhancement in solar cells by localized plasmon polaritons,” J. Appl. Phys. 104(12), 123102 (2008). [CrossRef]
24. C. Hägglund, M. Zäch, G. Petersson, and B. Kasemo, “Electromagnetic coupling of light into a silicon solar cell by nanodisk plasmons,” Appl. Phys. Lett. 92(5), 053110 (2008). [CrossRef]
25. M. Kirkengen, J. Bergli, and Y. M. Galperin, “Direct generation of charge carriers in c-Si solar cells due to embedded nanoparticles,” J. Appl. Phys. 102(9), 093713 (2007). [CrossRef]
26. F. J. Tsai, J. Y. Wang, J. J. Huang, Y. W. Kiang, and C. C. Yang, “Absorption enhancement of an amorphous Si solar cell through surface plasmon-induced scattering with metal nanoparticles,” Opt. Express 18(S2Suppl 2), A207–A220 (2010). [CrossRef] [PubMed]
27. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef] [PubMed]
28. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced l0ight absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008). [CrossRef]
29. T. Kume, S. Hayashi, and K. Yamamoto, “Enhancement of photoelectric conversion efficiency in copper phthalocyanine solar cell by surface plasmon excitation,” Jpn. J. Appl. Phys. 32(Part 1, No. 8), 3486–3492 (1993). [CrossRef]
30. T. Kume, S. Hayashi, H. Ohkuma, and K. Yamamoto, “Enhancement of photoelectric conversion efficiency in copper phthalocyanine solar cell: white light excitation of surface plasmon polaritons,” Jpn. J. Appl. Phys. 34(Part 1, No. 12A), 6448–6451 (1995). [CrossRef]
31. M. Westphalen, U. Kreibig, J. Rostalski, H. Lüth, and D. Meissner, “Metal cluster enhanced organic solar cells,” Sol. Energy Mater. Sol. Cells 61(1), 97–105 (2000). [CrossRef]
32. B. P. Rand, P. Peumans, and S. R. Forrest, “Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters,” J. Appl. Phys. 96(12), 7519–7526 (2004). [CrossRef]
33. J. K. Mapel, M. Singh, M. A. Baldo, and K. Celebi, “Plasmonic excitation of organic double heterostructure solar cells,” Appl. Phys. Lett. 90(12), 121102 (2007). [CrossRef]
34. T. D. Heidel, J. K. Mapel, M. Singh, K. Celebi, and M. A. Baldo, “Surface plasmon polariton mediated energy transfer in organic photovoltaic devices,” Appl. Phys. Lett. 91(9), 093506 (2007). [CrossRef]
35. K. Tvingstedt, N.-K. Persson, O. Inganäs, A. Rahachou, and I. V. Zozoulenko, “Surface plasmon increase absorption in polymer photovoltaic cells,” Appl. Phys. Lett. 91(11), 113514 (2007). [CrossRef]
36. 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(7), 073307 (2008). [CrossRef]
37. C. Hägglund, M. Zäch, and B. Kasemo, “Enhanced charge carrier generation in dye sensitized solar cells by nanoparticle plasmons,” Appl. Phys. Lett. 92(1), 013113 (2008). [CrossRef]
38. J. Y. Wang, F. J. Tsai, J. J. Huang, C. Y. Chen, N. Li, Y. W. Kiang, and C. C. Yang, “Enhancing InGaN-based solar cell efficiency through localized surface plasmon interaction by embedding Ag nanoparticles in the absorbing layer,” Opt. Express 18(3), 2682–2694 (2010). [CrossRef] [PubMed]
39. Y. A. Akimov, W. S. Koh, and K. Ostrikov, “Enhancement of optical absorption in thin-film solar cells through the excitation of higher-order nanoparticle plasmon modes,” Opt. Express 17(12), 10195–10205 (2009). [CrossRef] [PubMed]
40. V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express 18(S2Suppl 2), A237–A245 (2010). [CrossRef] [PubMed]
41. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
42. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
43. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Boston, 1991).
