The simulation results of absorption enhancement in an amorphous-Si (a-Si) solar cell by depositing metal nanoparticles (NPs) on the device top and embedding metal NPs in a layer above the Al back-reflector are demonstrated. The absorption increase results from the near-field constructive interference of electromagnetic waves in the forward direction such that an increased amount of sunlight energy is distributed in the a-Si absorption layer. Among the three used metals of Al, Ag, and Au, Al NPs show the most efficient absorption enhancement. Between the two used NP geometries, Al nanocylinder (NC) are more effective in absorption enhancement than Al nanosphere (NS). Also, a random distribution of isolated metal NCs can lead to higher absorption enhancement, when compared with the cases of periodical metal NC distributions. Meanwhile, the fabrication of both top and bottom Al NCs in a solar cell results in further absorption enhancement. Misalignments between the top and bottom Al NCs do not significantly reduce the enhancement percentage. With a structure of vertically aligned top and bottom Al NCs, solar cell absorption can be increased by 52%.
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In an amorphous Si (a-Si) solar cell, because of the low carrier mobility, a thinner semiconductor layer has the advantage of higher carrier harvest in generating photocurrent. Also, the degradation issue in an a-Si solar cell, known as the Staebler-Wronski effect , requires the minimization of the active layer thickness to avoid carrier loss. However, a thin semiconductor absorbing layer may result in inefficient absorption and low device efficiency. Therefore, it is important to use certain methods for maintaining efficient absorption under the condition of a limited semiconductor thickness such that high short-circuit current and high filling factor of such a device can be achieved. Various methods for enhancing the absorption of a thin a-Si solar cell have been proposed [2–6]. Among those methods, sunlight scattering by a nanostructure, which is deposited on the top surface of a solar cell, has shown to be an effective technique. In particular, using a surface metal nanostructure for inducing surface plasmon (SP) to enhance solar cell absorption has attracted research attention in various photovoltaic materials, including organic [7–15], dye [16,17], GaAs [18,19], InGaN , and Si [21–30]. In each of those implementations, the absorption efficiency in a certain spectral band or the overall solar cell efficiency was more or less enhanced. The possible mechanisms of absorption enhancement with surface metal nanostructures include: 1) energy transfer from excited SPs into electrons for contributing to photovoltaic current ; 2) increased optical path of incident light in the absorbing layer through SP scattering [19,30]; 3) increased interaction time of light with absorbing material through SP (from ~1 to ~10 fs) ; 4) enhanced absorption through intense SP field [20,21,30]; and 5) enhanced light incidence into the solar cell material through the forward scattering of the metal nanostructures on the surface [22,28]. Among various metal nanostructures for the aforementioned application, the use of metal nanoparticles (NPs) for inducing localized surface plasmon (LSP) resonance represents one of the most practical approaches because of fabrication simplicity. Experimental implementations [19,23,25,26] and numerical simulations [20,23,26,29,30] have demonstrated the effectiveness and practical feasibility of this approach. However, in the previous studies of the solar cells with Au or Ag NPs on the top surfaces, significant reductions of sunlight absorption were observed in the photon energy ranges higher than the corresponding LSP resonance energies, leading to small overall increases of sunlight absorption or solar cell efficiency [18,23,29,30]. The absorption reduction originates from the sign change of the polarizability of the used metal NP, which may cause a destructive interference between the incident light and NP-scattered light in the absorption layer of the solar cell. Although the use of dielectric NP on the device top surface can avoid the destructive interference in the forward direction, the overall scattering strength is weak due to the small polarizability of a dielectric NP . Therefore, searching an appropriate metal type for placing on the solar cell top surface to produce constructive interference in the forward direction and hence enhance sunlight absorption is an important issue for solar cell development. In choosing metal type for such application, one with a larger LSP resonance energy is preferred to maximize the forward constructive interference effect in the solar spectrum range. Meanwhile, since the geometry of the metal NP and its location can also effectively influence the scattering behaviors, these factors also deserve detailed investigation.
In this paper, we demonstrate the simulation results of absorption enhancement in an a-Si solar cell by depositing metal NPs on the device top and embedding metal NPs in a layer above the Al back-reflector (back-contact). From the evaluated phase distribution results, it is found that the absorption increase is mainly caused by the enhanced near-field constructive interference effect in the forward direction through the mixture of LSP resonance and Fabry-Perot oscillation. such that an increased amount of sunlight energy is distributed in the a-Si absorption layer. The comparisons between three used metals of Al, Ag, and Au, Al NPs show the most efficient absorption enhancement, which is also larger than that of using SiO2 NPs of the same geometry. Also, by arranging both top and bottom metal NPs in a solar cell, further absorption enhancement can be obtained. With a vertically aligned top and bottom Al nanocylinder (NC) structure, the solar cell absorption can be increased by 52%. In section 2 of this paper, the problem geometry and simulation method are described. The simulation results with periodical distributions of NPs on the top of a solar cell are discussed in section 3. Then, the comparisons between the cases of a periodical NP distribution and a single NP are presented in section 4. Next, the effects of adding a bottom metal NP distribution are reported in section 5. Finally, the conclusions are drawn in section 6.
2. Problem geometry and simulation method
Figures 1(a) and 1(b) show the solar cell structures used for simulation study. Except the NPs, the simulation problem geometries represent the standard structures of a-Si solar cells. Either device structure consists of (from the bottom) an Al layer as the back contact, a thin n-type a-Si layer, an intrinsic a-Si layer, a thin p-type a-Si layer, and an indium-tin-oxide (ITO) layer. The front Al contact is neglected in simulation. In the problem geometry of Fig. 1(a), which will be referred to as the case of “top NP”, a metal NP, either an NC or a nanosphere (NS), is placed at the center of the top surface in the shown simulation window. The simulation window stands for a period in the configuration of a periodical metal NP distribution in both the x and y directions. To demonstrate the LSP effect, the simulations of using SiO2 NC and NS are also performed for comparison. In the problem geometry of Fig. 1(b), which will be referred to as the case of “double NPs”, to embed the bottom metal NP, another ITO layer is deposited between the p-type a-Si layer and the Al back contact. The NP in the bottom ITO layer contacts the bottom Al layer. To show the location of the bottom metal NP, only one-half the simulation window is shown in Fig. 1(b). The sunlight is assumed to be normally incident upon the device from the top. Although the sunlight is un-polarized, without loss of generality, we will consider polarized sunlight with the polarization oriented in the x direction. When the NPs are periodically distributed on the device surface and such a periodical arrangement does not much affect the NP scattering behaviors, or when the NPs are randomly distributed, the simulation results based on polarized sunlight can be directly applied to the real case of un-polarized sunlight due to the two-dimensionally isotropic nature of our problem; otherwise, slight modifications are needed. In Fig. 1(a), the thicknesses of the ITO, p-type a-Si, intrinsic a-Si, and n-type a-Si layers are assumed to be 20, 10, 110, and 10 nm, respectively, which represent a widely used device structure of this kind [29,30]. Here, the Al back-contact or reflector is assumed to be infinitely thick. In Fig. 1(b), the thicknesses of the top ITO, p-type a-Si, intrinsic a-Si, n-type a-Si, and bottom ITO layers are 20, 10, 100, 10, and 60 nm, respectively. The change of the thickness of the intrinsic a-Si layer from 110 into 100 nm means to optimize the absorption efficiency of the solar cell when NPs are not applied to the device. The simulation window has a dimension of 250 nm in either x or y direction. In the simulations, various metal and SiO2 NCs and NSs of the same geometries are used. The NC has the height of 75 nm and cross-section diameter of 100 nm. The NS has the diameter of 100 nm.
The simulation computations are performed with the finite-element method (FEM). The perfectly matched layers (PMLs) are used in the + z and –z directions for simulating the infinitely extended air and Al layers. The periodic boundary conditions are imposed to the simulation window in the + x, -x, + y, and -y directions to model the problem periodicity. To investigate field scattering due to the NP, we use the well-known scattered-field formula for simulation, in which the total electromagnetic field is divided into an unperturbed part and a scattered part [31,32]. It is noted that the maximum optical intensity in the absorbing layer of the solar cell can be obtained when the unperturbed field and scattered field are in phase in the forward direction. The unperturbed field is the electromagnetic solution with the designated solar cell structure, but without the NP under the condition of an incident plane wave. It can be obtained from an explicit analytic expression. The scattering due to the NP is then described by the scattered field. In the situation with NP, the total field with the given unperturbed part in a non-PML region is governed by the two Maxwell’s source-free curl equations. Because a PML serves to absorb the scattered field, in a PML region, only the scattered part needs to be described. Note that the continuity of the tangential component of the scattered field is required at the interface between a PML region and a non-PML region. Rigorously, the numerical treatment in the FEM is implemented by using the corresponding variational description . In numerical computations, a commercial software (COMSOL) was used. It has provided us with a reliable framework of the aforementioned scattered-field formulation. The accuracy of our numerical results was verified through the convergence test. The minimum division mesh size was 2 nm at the metal/dielectric interface. The maximum mesh size of an individual dielectric region is set to be one tenth the shortest wavelength in material of our concern (300 nm in free space). The dielectric constant of a-Si is obtained from the measurement data in  except that the absorption coefficient near the band edge is corrected based on the Forouhi-Bloomer model . The used refractive index and absorption coefficient as functions of wavelength for simulations are shown in Fig. 2 . The dielectric constants of various metals are obtained from . Fixed refractive indices of 1.46 and 1.7 are used for SiO2 and ITO, respectively.
3. Simulation results with a periodic NP distribution on the top
Figure 3 shows the photon absorption rates as functions of wavelength with Al, Ag, Au, and SiO2 NCs on the top of solar cells (see Fig. 1(a)). For comparison, the reference case, in which no NP is used, and the photon flux of AM 1.5G are also demonstrated. The results shown in Fig. 3 are obtained under the condition of periodical NP distributions with the period of 250 nm in both x and y directions. Here, one can see the oscillatory behavior of the reference curve due to the Fabry-Perot effect in the vertical direction. When an Au or Ag NC is placed on the top, the photon absorption in the UV-blue-green range is essentially reduced. However, on the long-wavelength side, absorption is enhanced except in the range between 690 and 800 nm, in which a Fabry-Perot peak in the reference case becomes weakened when a metal NC is used. As a result, the integrated photon absorption rate in the case of Au (Ag) NC is reduced (enhanced) by 9 (10) %, when compared with the reference case. The integrated photon absorption rates under various conditions are listed in Table 1 . In Fig. 3, one can also see that when an Al NC is placed on the device top, the photon absorption rate is always enhanced in the whole concerned spectral range except that between 690 and 800 nm, leading to the increase of integrated photon absorption rate by 39%. For comparison, a SiO2 NC of the same geometry is also used for evaluating the photon absorption rate. In this situation, the photon absorption rate is also significantly increased (by 16%), as compared with the reference case.
Because the absorption layer of the solar cell is below the NP by 20-150 nm, the absorption enhancement is supposed to be due to the enhanced near-field constructive interference effect of sunlight in the absorption layer. The interference behavior is controlled by the relative phase between the aforementioned unperturbed and scattered fields. The phase differences between the unperturbed and scattered fields at the location right below the NP center with a depth of 65 nm from the top surface of the p-type a-Si layer as functions of wavelength for the four kinds of NP are shown in Fig. 4 . Here, one can see that among the metal NPs, the phase difference of the Al case is generally smaller than those of the Au and Ag cases. However, the phase difference of the SiO2 case is generally the smallest among the four cases. The non-zero phase difference in the SiO2 case is mainly due to the layered structure of the solar cell. The deviations of the phase difference curves from the SiO2 case in using metal NPs are strongly related to LSP resonances. According to the Mie theory , the phase distribution of the perturbed field behind a metal NP is usually significantly altered. However, because of the complex solar cell structure, the spectral distributions of phase difference become complicated even though the extinction spectral peaks of the Al, Ag, and Au NP cases can be identified to be at 420, 570, and 640 nm, respectively. These wavelengths are marked by the vertical arrows in Fig. 4. It is noted that all the four curves in Fig. 4 have peaks around 660 nm. Also, the three metal curves have a common dip around 720 nm, which is shifted to ~740 nm in the SiO2 curve. The peaks and dips correspond to Fabry-Perot resonance and anti-resonance spectral positions, respectively, which have been influenced by the NP. Here, the common Fabry-Perot behaviors lead to the similar spectral features beyond 630 nm in wavelength. It is noted that by using a SiO2 NP, although the optical intensity in the forward direction can be relatively stronger when compared with those in other directions, its overall scattering is not as strong as that of an Al NP, which has the LSP resonance effects, such that its absorption enhancement is smaller than that of the Al NP case.
The results in Figs. 3 and 4 show the superiority of using Al NC for increasing absorption through the enhancement of the constructive interference effect in the forward direction. To understand the effects of NP geometry, we repeat the simulation for Fig. 3 by replacing NCs by NSs. The results similar to Fig. 3 are shown in Fig. 5 . Here, one can see that SiO2 NS also significantly enhances photon absorption rate (also by 16% when compared with the reference case, as shown in Table 1). Al NS still leads to the largest absorption enhancement. By using Al (Ag) NSs, the photon absorption rate can be increased by 31 (22) %, when compared with the reference case (see Table 1). Also, Au NS results in slight absorption enhancement (by 3%). In the Ag and Au cases, the use of NS results in increased enhancements; however, in the Al case, the use of NS leads to reduced enhancement, when compared with the individual cases of NC. Figure 6 shows the phase difference data similar to those in Fig. 4 for the cases of NS. Here, one can see the similar behaviors to those shown in Fig. 4. The SiO2 case has generally the smallest phase difference between the unperturbed and scattered light, followed by the Al case. The three wavelengths for the maximum extinctions (LSP resonances) at 310, 415, and 550 nm of the Al, Ag, and Au cases, respectively, are also marked by vertical arrows in Fig. 6. The significantly shorter wavelengths for LSP resonances in the cases of NS are attributed to the much smaller contact area of an NS with the device surface. The LSP resonances in the NC cases are strongly influenced by the contacting ITO layer. It is noted that both SiO2 curves in Figs. 4 and 6 show a common peak near 480 nm, around which the curves of metal NCs and NSs also show local maxima. This feature can be caused by the interference behavior of the multi-layer solar cell structure and is common in all cases. In the Al case, because of the end-facet contact of an NC with the top ITO of 1.7 in refractive index, the resonance wavelength of the dominant substrate LSP mode  is located at 420 nm (see Fig. 4). At this wavelength, the LSP-induced absorption enhancement is more prominent due to stronger sunlight intensity, when compared with the case of Al NS, in which the surrounding air results in the LSP resonance wavelength around 310 nm (see Fig. 6) of weak sunlight intensity. Therefore, an Al NC leads to a higher absorption enhancement than an Al NS. On the other hand, in the cases of Ag and Au, the LSP resonances with both NC and NS are located in the spectral range of high sunlight intensity. However, because of the sharp metal edges, which cause higher Ohmic loss, in the NC geometry, the relatively higher dissipation in Ag and Au (compared with Al) results in higher loss in the NC geometry, when compared with the NS geometry. Hence, the absorption enhancements in the Ag and Au NC cases become lower than those in the corresponding NS cases.
To further understand the enhanced constructive interference effect in the forward direction, the distributions of electrical intensity enhancement ratios with respect to the reference case for the total field within the a-Si regions in the x-z plane are shown in Fig. 7 . Here, x = 0 corresponds to the center of the NP. Also, z = 0 corresponds to the bottom of the n-type a-Si layer. The two horizontal white dashed lines represent the boundaries between the p-type and intrinsic a-Si layers and between the intrinsic and n-type layers. Figures 7(a)-7(h) correspond to the cases of Al NC at 525 nm (enhanced), Ag NC at 600 nm (enhanced), Ag NC at 405 nm (suppressed), SiO2 NC at 525 nm (enhanced), Al NS at 525 nm (enhanced), Ag NS at 525 nm (enhanced), Ag NS at 405 nm (suppressed), and SiO2 NS at 525 nm (enhanced), respectively. Here, one can see from Figs. 7(c) and 7(g) that the reduction trend of the constructive interference effect significantly decreases sunlight absorption of the whole a-Si layer. The formation of the two bright spots in the situations of strong constructive interference effect is attributed to Fabry-Perot oscillation. It is noted that the color coding scales are different among different cases in Fig. 7. By comparing the group of Figs. 7(a) and 7(e) with the group of Figs. 7(d) and 7(h), one can see that the scattering strength of a SiO2 NP is indeed lower than that of an Al NP, leading to the relatively smaller absorption enhancement in the case of SiO2 NP.
4. Simulation results with a single NP on the top
The results given above correspond to the condition of periodic NP distribution on the device top. In this section, we show the solar cell absorption behaviors when a single metal NP is used. Figure 8 shows the comparisons of photon absorption rate as a function of wavelength between the cases of single NC and periodic NC distributions of Al, Ag, and Au. Again, the curves of reference and AM 1.5G are also depicted for comparison. To obtain the data in Fig. 8, we assume that the effective absorption region, which is defined for evaluating the total photon absorption rate, is a circular area of 282 nm in diameter. The assumption of this diameter value means to make the effective absorption area the same as that (250 nm x 250 nm) in the cases of periodical NP distributions. Here, one can see that the spectral oscillation patterns of photon absorption rate are different between the cases of single NC and periodic NC distribution. The periodic distribution of NC leads to certain diffraction effects and changes the local Fabry-Perot behaviors. Also, the LSP interaction between neighboring NPs may also cause the changes of spectral patterns. One can observe alternative variations of enhancement and suppression with wavelength in comparing the cases of single NC and periodic NC distribution. The integrated photon absorption rates and their ratios with respect to the reference level are listed in Table 2 . Here, one can see the slight increase of photon absorption rate by using a single NP of any concerned metal, when compared with the condition of periodical NP distribution.
Figures 9(a) and 9(b) show the distributions of electric intensity enhancement ratios over that of the reference case at 500 nm in wavelength in the x-y plane at the depth of 65 nm from the top surface of the p-a-Si layer with the circles centered at the centers an Al NC (a) and an Ag NC (b) of 100 nm in diameter on the device top. The values of D in nm indicate the diameters of the white dashed circular curves. Here, one can see the enhanced and reduced intensity distributions right below the Al and Ag NC, respectively. The total photon absorption rates shown in Fig. 8 depend on the definition of the effective absorption area. Figure 10 shows the enhancement ratios of photon absorption as functions of the effective absorption diameter. The enhancement ratio is defined as the ratio of the integrated photon absorption rate in the case with NC over that without NC (the reference). Therefore, in Fig. 10, when the effective absorption diameter approaches infinity, the enhancement ratio will asymptotically approach one. Here, one can see that by using an Au NC, when the effective absorption diameter is between 200 and 500 nm, the enhancement ratio is always smaller than unity, implying that in this situation the incident sunlight is either absorbed by the Au NP, backscattered into air, or scattered in a manner that the photon energy is pushed away from the designated effective absorption region. On the other hand, by using an Al or Ag NC, the enhancement ratio decreases monotonically with effective absorption diameter. In particular, the use of an Ag NC leads to a faster decay into unity, implying that the effect of Ag NC scattering is limited to a smaller region around the metal NP when compared with that of Al NC scattering. By using an Al or Ag NC, the metal NP can “attract” sunlight energy into the designated effective absorption region from outside.
5. Comparison between the cases of top, bottom, and double NPs
The results above show the enhanced constructive interference effects in the forward direction by placing metal and dielectric NPs on the front (top) side of a solar cell. In this section, we demonstrate the effects of enhanced backscattering by depositing metal NPs on the backside (bottom side) of the solar cell. For this purpose, we consider the device structure shown in Fig. 1(b). To embed a metal NP between the Al back-contact and the n-a-Si layer, an ITO layer is inserted in between. Here, we assume that an Al NC is embedded in this ITO layer. For our simulations, we also assume that the bottom Al NC has a diameter of 100 nm and a height of 60 nm (smaller than that of the top metal NC at 75 nm). This NC height is the same as the thickness of the bottom ITO layer such that the bottom metal NC contacts with both the n-a-Si layer above and the Al back-contact below. In this solar cell, the thickness of the i-a-Si layer is reduced from 110 nm to 100 nm to optimize the Fabry-Perot oscillation for maximizing the absorption in the reference case. Figure 11 shows the photon absorption rates as functions of wavelength in the cases of periodical top Al NC distribution (top), periodical bottom Al NC distribution (bottom), and both top and bottom Al NC distributions (double). In the case of double NCs, the top and bottom Al NCs are vertically aligned (the same x-y coordinates). The curves of the reference case (no metal NP) and AM 1.5G are also shown for comparison. Here, one can see that without the top Al NC, the use of the bottom Al NC suppresses the absorption near its peak around 525 nm. However, two absorption peaks are formed around 675 and 750 nm by using the bottom Al NC for enhancing the integrated absorption. These two peaks correspond to the LSP resonances of the bottom Al NC. However, the formation of these peaks results in only 10% increase of integrated absorption, which is significantly lower than the 39% absorption enhancement in the case of top Al NC only, as shown in Table 3 . Nevertheless, the combination of the vertically aligned top and bottom Al NCs can lead to an integrated absorption enhancement of 52%. Compared with the case of top Al NC only, the addition of the bottom Al NC results in a significant absorption increase on the long-wavelength side even though that around the peak is slightly reduced. In this situation, the integrated absorption is significantly enhanced. Figures 12(a) -12(i) show the distributions of electrical intensity enhancement ratios (over that of the reference case) in the x-z plane of the cases in Fig. 11 with (a)-(c) for the cases of top NC, (d)-(f) for the cases of bottom NC, and (g)-(i) for the cases of double NCs. The corresponding wavelengths are 525 nm in (a), (d), and (g), 600 nm in (b), (e), and (h), and 675 nm in (c), (f), and (i). The two horizontal white dashed lines represent the boundaries between the p-type and intrinsic a-Si layers and between the intrinsic and n-type layers. Here, one can see that at each wavelength, the intensity enhancement patterns are similar among the cases of top NC, bottom NC, and double NCs, except that in Fig. 12(c). However, the levels of enhancement are quite different. The significantly higher enhancement levels in the case of double NCs can be clearly seen.
In Figs. 11 and 12, we demonstrate the absorption enhancement when the top and bottom Al NCs are vertically aligned. In Figs. 13 and 14 , we compare the results of different misalignments between the top and bottom Al NCs. Figure 13 shows the photon absorption rates as functions of wavelength in various cases of double Al NCs with the vertical alignment shifted horizontally by one-quarter (Λ/4 shift) and one-half (Λ/2 shift) the period, Λ, in the x- and y directions. The incident sunlight is assumed to be x-polarized. The curves of no shift, reference, and AM 1.5G are also shown for comparison. Here, one can see that the misalignments cause minor modifications of the absorption curves. Clear changes are observed at the kinks around 600 nm. This feature can be due to the Fabry-Perot effect between the top and bottom NCs when they are vertically aligned. As the two NCs become misaligned, this kink becomes less prominent. The integrated photon absorption rates and their ratios with respect to the reference level of various cases are shown in Table 3. Here, one can see that with even up to one-half period misalignments, the integrated photon absorption rates are only slightly reduced (by up to 6%). Therefore, the vertical alignment of the top and bottom NCs is not critical for enhancing absorption under the assumed condition of periodical NC distributions at the top and bottom. Figures 14(a)-14(l) show the distributions of electrical intensity enhancement ratios (over that of the reference case) in the x-z plane of the cases in Fig. 13 with (a)-(c) for the case of Λ/4 shift-x, (d)-(f) for the case of Λ/2 shift-x, (g)-(i) for the case of Λ/4 shift-y, and (j)-(l) for the case of Λ/2 shift-y. The corresponding wavelengths are 525 nm in (a), (d), (g), and (j), 600 nm in (b), (e), (h), and (k), and 675 nm in (c), (f), (i), and (l). The two horizontal white dashed lines represent the boundaries between the p-type and intrinsic a-Si layers and between the intrinsic and n-type layers. It is noted that Figs. 14(g)-14(l), which demonstrate the intensity enhancement ratio distributions in the x-z plane by shifting the alignments in the y direction, look similar to Figs. 12(g)-12(i). Because of the symmetrical NC arrangements between the x and y axes, the misalignments in the y direction does not seem to affect much the electrical intensity distributions. However, it is worth mentioning that the slight changes, particularly in Fig. 14(j), can be attributed to the misalignment in the other direction and the oriented incident polarization (in the x direction). Regarding the results in Figs. 14(a)-14(f), we can first notice the horizontal shifts of the bright spots in Figs. 14(c) and 14(f) (at 675 nm in wavelength) from the center, as the cases shown in Figs. 14(i) and 14(l), by 62.5 and 125 nm, which correspond to Λ/4 and Λ/2 shifts, respectively. As mentioned earlier, the feature around 675 nm in Figs. 11 and 13 is due to the LSP resonance of the bottom Al NC. The location of resonance field distribution shifts with the NC position. The bright spots in Figs. 14(b) and 14(e) (at 600 nm in wavelength) also show horizontal shifts with respect to those in Figs. 14(h) and 14(k). However, the shift ranges are significantly smaller than the corresponding misalignment ranges, Λ/4 and Λ/2, respectively. As pointed out earlier, the feature around 600 nm is related to the Fabry-Perot effect between the top and bottom Al NCs. Therefore, although they are separated by Λ/4 or Λ/2, the maximum intensity locations (the bright spots) in between do not shift that much in the x direction. Then, at 525 nm in wavelength, such interactions between the top and bottom Al NCs are stronger such that the horizontal shift ranges of the lower bright spots become even smaller, as shown in Figs. 14(a) and 14(d), when compared with those in Figs. 14(g) and 14(j). The detailed interactions between the top and bottom metal NPs, including the Fabry-Perot effect and the possible LSP coupling, deserve further investigation.
In summary, we have demonstrated the simulation results of absorption enhancement in an a-Si solar cell by depositing metal NPs on the device top and embedding metal NPs in a layer above the Al back-reflector. The absorption increase resulted from the near-field constructive interference of optical fields in the forward direction such that an increased amount of sunlight energy was distributed in the a-Si absorption layer. Among the three used metals of Al, Ag, and Au, Al NP showed the most efficient absorption enhancement. Between the two used NP geometries, Al NCs were more effective in absorption enhancement than Al NSs. Also, a random distribution of isolated NCs could lead to higher absorption enhancement, when compared with the cases of periodical NC distributions. Meanwhile, the fabrications of both top and bottom Al NCs in a solar cell resulted in further absorption enhancement. Misalignments between the top and bottom Al NCs did not significantly reduce the enhancement percentage. With a vertically aligned top and bottom Al NC structure, the solar cell absorption could be increased by 52%.
This research was supported by National Science Council of Taiwan (NSCT), under grants of NSC 97-2120-M-002-005, NSC 98-2622-E-002-002-CC1, NSC 96-2628-E-002-044-MY3, NSC 98-2221-E-002-033, and by the United States Air Force Office of Scientific Research (USAFOSR) under contracts AOARD-07-4010 and AOARD-09-4117.
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