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We propose a structure with the metallic and dielectric nanoparticles on the surface of the silicon material and study its optical transmission properties. The structure with the radiuses of the silver and silica nanoparticles as 50 nm and 100 nm, respectively, with the gap as 8 nm between silver and silica nanoparticles is found to have the largest optical transmission into the silicon material in our simulations. The largest field intensities are on the bottom of the silver nanoparticles and these can result strong field scattering into the silicon material. From the plotting of the average power densities around the gaps and the air regions between the silver and silica nanoparticles, the light power can go thorough these regions and flow downward to the silicon material. It is also found that the light energy rotates around the bottom of the silver nanoparticles due to the strong localized surface plasmons. The rectangular arrangement of the nanoparticle structures with mixing metallic and dielectric nanoparticles are studied, and the cases for the structures with only the metallic nanoparticles or only the dielectric nanoparticles are also simulated and compared. The rectangular or hexagonal structures with mixing metallic and dielectric nanoparticles on the surface of the silicon substrate can have better optical transmission than the cases of the rectangular arrangement with only metallic or dielectric nanoparticles.
©2011 Optical Society of America
1. Introduction
Solar energy is one of the most promising renewable energy resources for the sustainable environment because it is abundant, long-life, and available everywhere in the earth. Increasing the efficiency of solar cells is an important research in the solar energy applications. The antireflection layer can avoid the reflection and give more sun light transmittance to the solar cell materials. The inverted pyramid structures are used to increase the optical transmittance in the wafer based silicon solar cells [1]; however, the inverted pyramid structure is not suitable for thin-film solar cells because its size is much larger than the thin film thickness which is only one to few micrometers. The thin film solar cells are attracted because of its lower material cost and more flexibility [2], but it has lower efficiency due to low optical transmission into the thin film material. To increase the optical transmittance in the thin film solar cells, many methods are proposed to increase the light trapping or optical absorption in the materials, including the silver nanoparticles [3–9], gold nanoparticles [8,10–14], silica nanoparticles [10,14], embedded silica nanoparticles [15], silver nanoclusters [16], nanostructure layer [17–19] or graded refractive index techniques [20,21], and recent progress in plasmonic solar cells having been reported in [22,23]. Most of these works are related to nanoparticles, and the theoretical study demonstrates that the use of dielectric nanoparticles can give similar or higher optical enhancement than the metallic nanoparticles [24]. Most of these studies use either the metallic or dielectric nanoparticles. In our best understanding, there is no systematic study of the combinations of the metallic and dielectric nanoparticles for the solar cell antireflection applications. This gives us the motivation to study how the optical transmission is in the structure having the mixtures of the metallic and dielectric nanoparticles.
In this paper, we study the optical transmission for the combinations of metallic and dielectric nanoparticles atop the surface of the silicon substrate. Although it needs to consider the thickness of the silicon substrate for the thin film solar cells, it does not affect the physical concepts if the silicon substrate is considered as infinite thickness. Thus, to be easier for the comprehension of physics in our designs, we assume that the silicon substrate is infinite thickness instead of finite thickness as a few micrometers in this paper. We start our study from the close packed forms, which means that the metallic and dielectric nanoparticles are close to each other. We investigate the structures with different radiuses of metallic and dielectric nanoparticles and describe their physical mechanisms by studying the field distributions and optical energy flowing in the structures. We also consider the other cases when the metallic and dielectric nanoparticles are not close to each other, i.e., there are the gaps between the nanoparticles, and study their optical transmissions to the silicon substrate. For comparison of different arrangement of the nanoparticles, we also study the optical transmissions for the rectangular arrangement of the combinations of metallic and dielectric nanoparticles. To show the advantages of the combinations of the metallic and dielectric nanoparticle structures for antireflection applications, we also compare the results with the rectangular arrangement of the metallic nanoparticles or dielectric nanoparticles only. This study cannot only be useful in the designs of high efficiency plasmonic solar cells but also for the antireflection applications.
2. Structure and simulation setup
Figure 1 shows the structure of metallic and dielectric nanoparticles with the close packed forms atop the silicon substrate in our study. Because the scattering cross sections of metallic nanoparticles are often larger than the geometrical area [8], we consider the metallic nanoparticles are smaller than the dielectric nanoparticles in our designs. As shown in Fig. 1, we consider that there are six small metallic nanoparticles around one large dielectric nanoparticle and there are three large dielectric nanoparticles around one small metallic nanoparticle, i.e, there are double numbers of metallic nanoparicles as comparing to the amount of dielectric nanoparticles. For the thin film solar cells, the thickness of the absorption materials should be considered, such as the study in [15]. Our purpose is to design the proposed mixed nanoparticle structures with higher optical transmission and to study their physical mechanisms. Thus, for simplicity, we choose the silicon material as the absorption material of solar cells and assume the silicon material thick enough to absorb all light transmitting to the silicon material. To investigate the performance of different nanoparticle structures, the optical transmissions to the silicon material should be simulated.
Fig. 1 (a) The three-dimensional cartoon plotting of large and small nanoparticles which have the close packed forms atop the silicon substrate. The incident plane wave propagates from up to down in -z direction. The periodic boundary conditions are set in the side walls of computation domain, while the perfectly matched layers (PML) are set on the top and bottom surfaces. (b) The top view of the structure, where the symmetric and anti-symmetric boundary conditions are applied for x-polarization. The marked region is the computation domain.
The Lumerical FDTD Solutions software [25], a commercial electromagnetic solver based on the finite-difference time-domain method (FDTD), is used in our simulations to study the optical transmissions for different combinations of nanoparticles. Because the bandgap of silicon material is about near-infrared light and there are few light intensities for the wavelength shorter than visible light region in AM 1.5 solar spectrum, we assume that only the visible light region to the near-infrared light region, the wavelength from 400 nm to 1100 nm, are considered in our simulations. The nanoparticle structures are periodic and have the symmetries, so we can use the symmetric boundary conditions for x-axis and anti-symmetric boundary conditions for y-axis for the incident wave with x-polarization to divide the simulation domain to one fourth as shown in Fig. 1. For the incident wave with y-polarization, the anti-symmetric boundary conditions for x-axis and the symmetric boundary conditions for y-axis should be applied. The perfectly matched layers are applied on the top and bottom surfaces in our computation domain, where the top surface is for simulating the air region and the bottom surface is for simulating the silicon material with infinite thickness. The non-uniform meshes are applied in the entire simulation domain. The mesh size in the regions around the nanoparticles is Δx = Δy = Δz = 1 nm, the mesh size in the silicon region is Δx = Δy = 1 nm and Δz = 2 nm, and the mesh size in the air region is generated automatically from Δx = Δy = Δz = 1 nm to Δx = Δy = 1 nm and Δz = 2 nm. The incident plane wave propagates form up to down in -z direction. The transmission of optical energy is defined as the light power flowing into the substrate normalized by the incident light power. Because the solar light is un-polarized, we take the average of the simulation results for the incident plane waves with x-polarization and y-polarization. The silver (Ag) and gold (Au) are chosen for the metallic material in our study because these two kinds of metal have been used widely in the plasmonic research. The silica and titanium oxide (TiO2) are chosen for the dielectric material because these are the cheap and common materials used in optical thin film layers and easy for integration of silicon procedures. The dielectric constants of these metallic and dielectric materials can be found in [26]. Taking the optical transmission results from the simulations in consideration of the AM 1.5 solar spectrum, we can calculate the number of photons transmitting into the silicon material for different nanoparticle structures and study their physical mechanisms. We also study the cases with the gaps between silver and silica nanoparticles, and compare the simulation results with the cases of the close packed forms.
3. Results and discussions
To study the optical transmission properties of the close packed structures which mix the metallic and dielectric nanoparticles atop the silicon substrate as shown in Fig. 1, we change the sizes of metallic and dielectric nanoparticles in our simulations. For comparison, we study three combinations of metallic and dielectric nanoparticles, including silver and silica, silver and titanium dioxide, and gold and silica. Figure 2 shows the optical transmissions to the silicon material normalized to the incident light intensity for the cases of silica nanoparticles with radius from 60 nm to 120 nm, and silver nanoparticles with different radius. It is found that the maximum of total light transmitting into the silicon substrate is for the case with ratio of the radiuses of the silver and silica nanoparticles about 0.5. For the cases with higher ratio of the radiuses of the silver and silica nanoparticles, the total light transmission is even worse than only bare silicon without any nanoparticles for most regions of wavelength from 400 nm to 1100 nm. Figures 3 and 4 show the results for the case of silver and titanium dioxide and the case of gold and silica, respectively. Because the refractive index of titanium dioxide is more dispersive and higher than the refractive index of the silica in the wavelength region from 400 nm to 1100 nm, the transmission verse wavelength in Fig. 3 is more complicated than the results in Fig. 2. Because the gold has higher loss than the silver, it is generally that the smaller optical transmissions in Fig. 4 as comparing to the results in Fig. 2, especially in the shorter wavelength regions. By studying the field plotting for different wavelengths for different cases in Figs. 2, 3, and 4, the light transmission are due to the scattering of the metallic nanoparticles, the scattering of the dielectric nanoparticles, the transmission through the dielectric nanoparticles to the silicon substrate, or the field coupling by the combinations of the metallic and dielectric nanoparticles. These combinations of the physical mechanisms cause the peaks in some of the results shown in Figs. 2, 3, and 4. These peaks may be because the strong optical transmission effects dominated by one or several specific physical mechanisms.
Fig. 2 The optical transmission of the Ag and silica nanoparticle structures with the close packed form, where the radius of silica nanoparticles is fixed at 60 nm for (a), 80 nm for (b), 100 nm for (c), and 120 nm for (d), and the radius of the Ag nanoparticles is varied.
Fig. 3 The optical transmission of the Ag and TiO2 nanoparticle structures with the close packed form, where the radius of TiO2 nanoparticles is fixed at 60 nm for (a), 80 nm for (b), 100 nm for (c), and 120 nm for (d), and the radius of the Ag nanoparticles is varied.
Fig. 4 The optical transmission of the Au and silica nanoparticle structures with the close packed form, where the radius of silica nanoparticles is fixed at 60 nm for (a), 80 nm for (b), 100 nm for (c), and 120 nm for (d), and the radius of the Au nanoparticles is varied.
By taking the optical transmission results in Figs. 2, 3, and 4, and considering the AM 1.5 solar spectrum, the numbers of photons transmitting into the silicon material per second and per unit area for the cases in Figs. 2, 3, and 4, are shown in Fig. 5(a), (b), and (c) , respectively. Here, the ratio is defined as the ratio of the radius of metallic and dielectric nanoparticles. More photons transmitting into the silicon material, more light energy are absorbed in the silicon material. For the silver and silica nanoparticle structures shown in Fig. 5(a), the cases of the radius of silica as 60 nm, 80 nm, 100 nm, and 120 nm, it is found that the maximum of the photon number transmission can be obtained as the ratio of radius of silver and silica nanoparticles is 0.5. The photon number transmission gets smaller as the size of the silver nanoparticles is larger. This may be because that the scattering cross sections of metal nanoparticles are larger than the dielectric nanoparticles, so the smaller silver nanoparticles with larger silica nanoparticles can achieve better scattering with a reasonable absorption loss in the metallic nanoparticles. For the silver and titanium dioxide nanoparticle structure as shown in Fig. 5(b), it is found that the larger photon number transmission happens for smaller ratio of the radius of silver and titanium dioxide nanoparticles. This may be because the titanium dioxide has larger refractive index than silica. For the gold and silica nanoparticle structure as shown in Fig. 5(c), it is found that the larger photon number transmission happens for the ratio of the radius of gold and silica nanoparticles about 0.4. However, the best case in Fig. 5(c) is smaller than the best case in Fig. 5(b) because the gold has larger loss than silver in the optical region. These results can give the design guide how to increase the optical transmission by the metallic and dielectric nanoparticle structures.
Fig. 5 The total photon number transmitting into the silicon material per second and per unit area in consideration of the AM 1.5 solar spectrum for the nanoparticle structures with different sizes of nanoparticles and radius ratios, where (a) is for silver and silica nanoparticle structure, (b) is for silver and titanium oxide nanoparticle structure, and (c) is for gold and silica nanoparticle structure. The ratio is defined as the ratio of the radius of metallic nanoparticles and radius of the dielectric nanoparticles,
It should be noticed that the results in Fig. 5 are taken from the results in Figs. 2, 3, and 4, which are very complicated as described. Interestingly, the photon number transmissions verse ratios for these metal and dielectric nanoparticle structures in Fig. 5 have some trends. To show that the effect of the nanoparticle structures with same ratio but different sizes of metal and dielectric nanoparticles, we take the results with ratio 0.5 shown in Fig. 5(a) as the example. For different size of silica nanoparticles but the ratio being kept 0.5, the photon number transmissions are similar for these cases in Fig. 5(a). Figure 6 shows the optical transmissions verse wavelength for the silver and silica nanoparticle structures with ratio 0.5 and they are different by each other. As the particle size is larger, the optical transmission has red-shift, i.e., the optical transmission is larger for longer wavelength but smaller for shorter wavelength.
Fig. 6 The optical transmission of the nanoparticle structures with the same ratio 0.5 but different sizes of the silver and silica nanoparticles.
There are several methods to fabricate the close packed forms, for example, nanosphere lithography, spin coating, etc. It is possible that the metallic and dielectric nanoparticles are not close to each other or there are the gap sizes between the metallic and dielectric nanoparticles during the specific fabrication procedures. Because the largest light energy transmission for the close packed form in Fig. 5 is the case with radius of silver as 50 nm and radius of silica as 100 nm, we fix the size of silver and silica nanoparticles but vary the different gaps between silver and silica nanoparticles. The optical transmission verse wavelength for different gap sizes are calculated and shown in Fig. 7(a) . We found that the light transmissions are larger for the short wavelength and smaller for the long wavelength as comparing to the cases with gaps and the case with no gap. As the gaps exist, the periods of the nanoparticles are varied accordingly in Fig. 7(a). Thus, there may be specific selections of the gap sizes for different wavelength to have the larger light transmissions. In consideration of the AM 1.5 solar spectrum, the total photon number transmissions into the silicon material per second and per unit area for the cases in Fig. 7(a) are shown in Fig. 7(b) and they are 2.306 × 1021, 2.318 × 1021, 2.381 × 1021, 2.310 × 1021, 2.294 × 1021, and 2.276 × 1021 photons*s−1*m−2 for gap 0 nm, 5 nm, 8 nm, 10 nm, 15 nm, and 20 nm, respectively. Although the results in Fig. 7(b) have slightly different, the case with the gap 8 nm has the largest optical transmission energy and its total photon number transmission has additional 3% as comparing to the case without gap. It is not easy to control the fabrication of this kind of mixing nanoparticle structure. However, it is possible to use the nanosphere lithography to fabricate the mixing structure of large dielectric nanoparticles and small metallic nanoparticles. First, the large dielectric nanoparticles can be positioned on the surface of the silicon substrate by spin coating. By controlling the spin rate or using the nanosphere lithography technique, the large dielectric nanoparticles can be in hexagonal arrangement in closed pack form. Then, the metallic film is deposited. Next, the large dielectric nanoparticles can be taken away by lift off techniques, and the small metallic nanoparticles can be formed by annealing. This will form the hexagonal arrangement of metallic nanoparticles with distance between neighboring metallic nanoparticle. Again, the dielectric nanoparticles can be put into the spaces of metallic nanoparticles to form the close packed structure of dielectric and metallic nanoparticles. The gap can be got if the smaller dielectric nanoparticles are put into the spaces of metallic nanoparticles; however, the gap is not easy to control uniformly. Anyway, the photon number transmission is still high for a range of gap by the study of the results in Fig. 7(b). There is the other alternative method to fabricate the mixing structure. First, we spin the large dielectric nanoparticles on the surface of the silicon substrate by spin coating. This forms the hexagonal arrangement in closed pack form. Next, the dielectric nanoparticles can be gotten smaller and the space between the dielectric nanoparticles can be formed by using the reactive ion etching technique. Then, the smaller metallic nanoparticles can be positioned into the space between the dielectric nanoparticles by spin coating again. This alternative method needs fewer processing procedures than the first method; however, it needs the reactive ion etching technique which is not cost effective in massive production for solar cells.
Fig. 7 The optical transmissions for varying the gaps between the silver and silica nanoparticles while the radiuses of the silver and silica nanoparticles are fixed as 50 nm and 100 nm, respectively. The total photon number transmissions are 2.306 × 1021, 2.318 × 1021, 2.381 × 1021, 2.310 × 1021, 2.294 × 1021, and 2.276 × 1021 photons*s−1*m−2 for gap 0 nm, 5 nm, 8 nm, 10 nm, 15 nm, 20 nm, respectively.
To understand the physical mechanisms of optical transmission properties for the cases with the gaps in Fig. 7, the field intensities and the energy flow distributions are plotted. Because the case with the gap 8 nm in Fig. 7 is the largest light transmission energy in consideration of 1.5 AM solar spectrum, we take this case as the example. Figure 8 shows the logarithmic scale of the electric field amplitudes |E| normalized by the incident waves in y-z, x-z, and x-y planes for the incident light with wavelength 774 nm, where the radiuses of the silver and silica nanoparticles are 50 nm and 100 nm, respectively, with the gap 8 nm. There are strong field intensities around the gaps between the silver and silica nanoparticles which may be due to the localized surface plasmons around the gaps. The largest field intensities are on the bottom of the silver nanoparticles, and this phenomenon can help the field scattering into the silicon material. The electric field amplitudes in different z from the top to the bottom of the nanoparticle structures are shown in Fig. 8(c) (Media 1). To understand how the light energy transmits into the silicon material, we select the regions A, B, C, D, E, F, and G in Fig. 8(a) and region H in Fig. 8(b) and plot the average power densities in these regions as shown in Fig. 9 (a) to (h) respectively. The region A is the gap region between silver and silica nanoparticles, the region B is the region around silver nanoparticle and silicon material, the region C is the region between two neighboring silver nanoparticles, the region D is the top region of silica nanoparticles, the region E is above the middle region around silica nanoparticle, the region F is below the middle region around silica nanoparticle, the region G is the bottom region of silica nanoparticles, and the region H is the region between two neighboring silica nanoparticles. From the plotting of the average power densities around the gap as shown in Fig. 9(a), it is found that the light power can go into the gaps and flow downward. This is an important phenomenon, and this results more light power can go through into the silicon material. It is interesting but not surprised that the light energy rotates around the bottom of the silver nanoparticles in Fig. 9(b) because of the strong localized surface plasmons around these regions. Figure 9(c) shows the regions of two neighboring silver nanoparticles but it should be noticed that there are the other two silica nanoparticles on its front and back sides, which can be seen as shown in Fig. 1(a). The region shown in Fig. 9(d) is similar region as shown in Fig. 9(h) but in different cross sections. Figure 9(c) shows that the light energy can go into this region and flow downward to the silicon material. Figures 9(d) to (h) are different regions of silica nanoparticles, and they show that the light energy can go through the silica nanoparticle and then flow into the silicon material. Notice that the scale bar is Figs. 9(d)-(h) is smaller as comparing to Figs. 9(a)-(c) because the light energy is smaller in Figs. 9(d)-(h) but most of them are still larger than 1 or close to 1. The maximums of the average power densities shown in Figs. 9(a) to (h) are 3.44, 16.51, 2.99, 0.87, 1.04, 1.48, 0.82, and 1.38, respectively. Comparing to the optical transmission for the bare silicon without any nanoparticles on the silicon surface as shown in Fig. 2 which has lesser than 70% transmission in all wavelength region from 400 nm to 1100 nm, Figs. 9(d)-(h) show that there are more light energy flows into the silicon substrate for the case with gap. Because the refractive index of silica is between the refractive index of air and silicon material, the silica particle may have the graded refractive index effect to cause higher light transmission from the air to silica and then to the silicon substrate. However, it may be also influenced by the neighboring silver and silica nanoparticles. To be easier to understand how the light energy transmits from the air to the silicon substrate, a video is plotted in Fig. 8(c) (Media 1) which shows the electric field intensities from the top surface of the silica particles to the silicon material for this case. From the simulation results of field intensities and average power densities in Figs. 8 and 9, the physical mechanism can be described and it gives the explanations that our proposed structures with silver and silica nanoparticles and the gap between them can have higher optical transmissions.
Fig. 8 The electric field amplitudes |E| normalized by the incident waves in (a) y-z plane (x = 0), (b) x-z plane (y = 0), and (c) x-y plane (z = 0) (Media 1) for the incident light wavelength 774 nm, where the radiuses of the silver and silica nanoparticles are 50 nm and 100 nm, respectively, with the gap 8 nm. The origin of the coordinate is at the bottom of one silica nanoparticle. The zoom in of the field intensities and the average power densities in the regions A, B, C, D, E, F, and G in (a) and the region H in (b) are shown in Figs. 9(a)-(h). Notice that the color bar is in logarithmic scale.
Fig. 9 The average power densities normalized by the incident average power densities shown as the quivers and the electric field amplitudes |E| normalized by the incident waves shown as the colors, where (a) to (h) are the regions A, B, C, D, E, F, and G in Fig. 8(a) and region H in Fig. 8 (b). The scale bar shown in the figures means five times of the incident average power densities. The maximums of the average power densities shown in (a) to (h) are 3.44, 16.51, 2.99, 0.87, 1.04, 1.48, 0.82, and 1.38, respectively. The size of each region is 20 nm × 20 nm. Notice that the color bar for electric field amplitudes is in logarithmic scale, and the scale bar for the average power densities normalized by the incident average power densities are different for (a)-(c) and (d)-(h).
There is the other common structure which has the rectangular arrangements for nanoparticles. It is different structure as comparing to Fig. 1 which is the hexagonal arrangement of metallic and dielectric nanoparticles. For the rectangular arrangement structure for the metallic and dielectric nanoparticles with the close packed forms, there are identical numbers of metallic and dielectric nanoparticles. Figure 10 shows the simulation results of the total photon number transmitting into the silicon material per second and per unit area in consideration of the AM 1.5 solar spectrum for the nanoparticle structures with different sizes of silver and silica nanoparticles. The results in Fig. 10 for rectangular arrangement can be compared with the results in Fig. 5(a) for the hexagonal arrangement, and these cases are with the close packed forms. It shows that the large light transmission in Fig. 10 also happens as the ratio of the radius of the silver nanoparticle and the radius of the silica nanoparticle about 0.5. The maximum of the photon number transmission is 2.307×1021 photons*s−1*m−2 for the case with the radius of silver nanoparticle 40 nm and the radius of the silica nanoparticle 80 nm. It also shows that the light transmission does not go down so quickly for rectangular arrangement in Fig. 10 as comparing to the cases of hexagonal arrangement in Fig. 5(a).
Fig. 10 For the rectangular arrangement structures of silver and silica nanoparticles, the total photon number transmitting into the silicon material per second and per unit area in consideration of the AM 1.5 solar spectrum for the nanoparticle structures with different sizes of silver and silica nanoparticles. The maximum of the photon number transmission is 2.307 × 1021 photons*s−1*m−2 for the case with the radius of silver nanoparticle 40 nm and the radius of the silica nanoparticle 80 nm.
For comparison of our proposed structures to mix the metallic and dielectric nanoparticles, we also simulate the cases for the structures with the metallic nanoparticles or dielectric nanoparticles only. Figures 11(a), (b), and (c) show the simulation results of the total photon number transmitting into the silicon material per second and per unit area in consideration of the AM 1.5 solar spectrum for the rectangular arrangement nanoparticle structures with different sizes and periods of silver, gold, and silica nanoparticles, respectively. Here, the period means the distance between the neighboring nanoparticles. The results for the silver cases in Fig. 11(a) are better than the gold cases in Fig. 11(b) and the silica cases in Fig. 11(c). It is also interested that the maximum photon number transmissions for silica cases in Fig. 11(c) are the close pack forms, i.e., the period is the same as the double of the radius. To be easier to compare with different cases in our studies, we summarize the maximum photon number transmission for different cases in this paper in Table 1 . The maximum photon number transmission in Fig. 11 is 2.223 × 1021 photons*s−1*m−2, which is the case with the radius of silver 100 nm and the period 450 nm. And if we take this case as the basis, the results of the rectangular arrangement with closed pack form in Fig. 10 which is 2.307 × 1021 photons*s−1*m−2 can have additional 3.8% photon number transmission and the results of the hexagonal arrangement with closed pack form which is 2.306 × 1021 photons*s−1*m−2 or with 8 nm gap which is 2.381 × 1021 photons*s−1*m−2 in Fig. 7(b) can have additional 3.7% or 7.1% photon number transmission. These comparisons show that the rectangular or hexagonal structures with mixing metallic and dielectric nanoparticles on the surface of the silicon substrate can have better optical transmission for the solar cells applications as comparing to the rectangular arrangement with only metallic or dielectric nanoparticles.
Fig. 11 For the rectangular arrangement structures of (a) silver nanoparticles, (b) gold nanoparticles, and (c) silica nanoparticles, the total photon number transmitting into the silicon material per second and per unit area in consideration of the AM 1.5 solar spectrum for the nanoparticle structures with different sizes and periods of the nanoparticles. The maximum of the photon number transmission is 2.223 × 1021 photons*s−1*m−2 for the case with the radius of silver nanoparticle 100 nm and the period 450 nm in (a).
Table 1. The maximum photon number transmission for different cases in this paper
4. Conclusion
We have studied the optical transmission properties for the metallic and dielectric nanoparticle structures atop the silicon substrate, including silver and gold for metal materials and silica and titanium dioxide for dielectric materials. We found the nanoparticle structure with the proper parameters can achieve the better enhancement of optical energy transmission and increase the light absorption in the silicon material. Mixing metallic and dielectric nanoparticles with the suitable gaps between nanoparticles gives higher efficiency. For the silver metallic nanoparticles and silica dielectric nanoparticles, it is found that the structure with the radiuses of the silica and silver nanoparticles as 100 nm and 50 nm, respectively, with the gap size as 8 nm has the best enhancements in our simulations.
From the analysis of the field distributions and the average power densities in the nanoparticle structures, several effects give the enhancements of optical transmissions in mixing metallic and dielectric nanoparticle structures. It is found that the light energy rotates around the bottom of the silver nanoparticles due to the strong localized surface plasmons around these regions. The large field intensities on the bottom of the silver nanoparticles can result strong light scattering into the silicon material. From the plotting of the average power densities around the gaps and the air regions between silver and silica nanoparticles, it is found that the light power can flow into the gaps and the air regions. It is also found that the light can transmit directly from air through silica nanoparticles to the silicon material. These mechanisms give more light power to transmit into the silicon material.
For comparisons, we also study the rectangular arrangement of the nanoparticle structures with mixing metallic and dielectric nanoparticles. The cases for the structures with only the metallic nanoparticles or only the dielectric nanoparticles are also simulated. The comparisons in different cases which are studied in this paper show that the rectangular or hexagonal structures with mixing metallic and dielectric nanoparticles on the surface of the silicon substrate can have better optical transmission than the cases of the rectangular arrangement with only metallic or dielectric nanoparticles.
We have proposed and studied the metallic and dielectric nanoparticle structures to enhance the optical transmission through the silicon material, and we have taken different metallic and dielectric nanoparticles as the examples and found the parameters for the largest light transmissions. The physical mechanism described in this study can be also useful for the structures with the other materials to have larger optical transmissions for solar cells or other optical applications.
Acknowledgments
This work was supported by the National Science Council of Taiwan (NSC-96-2221-E-002-133-MY3, NSC-98-2120-M-002-004) and Tzong Jwo Jang Educational Foundation (97-S-A10).
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