Enhanced light trapping is an attractive technique for improving the efficiency of thin film silicon solar cells. In this paper, we use FDTD simulations to study the scattering properties of silicon nanostructures on a silicon substrate and their application as enhanced light trappers. We find that the scattered spectrum and angular scattering distribution strongly depend on the excitation direction, that is, from air to substrate or from substrate to air. At the dipole resonance wavelength the scattering angles tend to be very narrow compared to those of silicon nanostructures in the absence of a substrate. Based on these properties, we propose a new thin film silicon solar cell design incorporating silicon nanostructures on both the front and back surfaces for enhanced light trapping.
© 2013 OSA
The scattering properties of nanoparticles which arise from their ability to sustain Mie resonances hold tremendous technological importance. This is evident from the numerous types of nanoparticles that have been designed, fabricated, and, studied over the past decade. For example, nanoshells , nanocups , nanorice , fanoshells , plexcitonic nanoparticles [5, 6], etc. In most cases, the goal of nanoparticle design is to engineer and control their scattering properties. For instance, core (Ag) – shell (Si or GaAs) nanoparticles  designed such that they possess degenerate electric and magnetic dipole resonances resulting to preferential forward scattering and zero backward scattering . Nanoparticle scattering has found applications in many areas including optical antennas  and solar cell applications . Scattering properties of nanoparticles tend to be strongly modified when they are attached to a high index substrate like silicon . As such, a complete understanding of substrate effect on nanoparticle scattering is very important especially for solar cell applications given that in nanoparticle enhanced solar cells, the nanoparticles are either attached to the front or back surface of the cell . Previous studies have indicated that interaction of metallic nanoparticle and its image in a substrate can be so strong that it gives rise to hybridization or energy shifting of nanoparticle plasmonic modes [10,12]. These effects in turn will modify scattering properties of nanoparticles . Scattering properties also depend strongly on whether the nanoparticle is metallic or dielectric. For solar cell applications, dielectric nanoparticles tend to be more advantageous given that metallic nanoparticles have high optical loss in the visible due to heating. Extensive studies have been carried out to understand substrate effect on metallic nanoparticle scattering [10, 12–15], but not for dielectric nanoparticles. Here, we study the effects of silicon substrate on scattering properties of silicon nanostructures. We use these substrate-modified properties in the design of silicon solar cells having silicon nanostructures on both the front and backside for enhanced light trapping. The nanostructures on the front side act like antireflection coatings  while the nanostructures on the back side act like mirrors, scattering light back into the solar cell. The shape of the nanostructure is chosen such that the area of contact between substrate and nanostructure is very large to ensure strong interaction.
We study the scattering properties of silicon nanostructures on a silicon substrate using numerical methods, specifically Finite Difference Time Domain (FDTD). Commercial FDTD software from Lumerical  is used for the simulation. The silicon nanostructures studied are cylindrical in shape. Based on their dimensions, silicon nanostructures can possess strong electric and magnetic dipole resonances (Mie Resonances) which scatter light strongly in the infrared  and visible [19–21]. The nanostructure studied has a diameter of 240 nm and height of 240 nm. These dimensions are chosen such that the Mie resonances of these nanostructures cover the wavelength region of interest in solar energy applications.
Figure 1 shows a cross-section of the simulation set-up. The “total field scattered field” (TFSF) source is used. TFSF is a plane wave source designed for simulating nanoparticle scattering. This source appears as a 3-D box in which one side is used as the injection plane. For this study, the injection side (plane) will always be perpendicular to the z-axis and direction of excitation will be indicated by an arrow. The TFSF source divides the simulation space into two regions: the total-field region and the scattered-field region. The region enclosed by the TFSF source is the total-field region because it contains both the incident (source) field and the scattered signal (scattered by the nanostructures) while the region outside the TFSF box contains only the scattered signal and so it is referred to as the scattered-field region. We study the scattering properties of silicon nanostructures on a silicon substrate by measuring their scattered spectrum, angular distribution of scattered power, and also, intensity field distribution within the nanostructure. For these measurements we use power monitors which collect high accuracy power flow information in the frequency domain. These monitors can also output H and E field values at specific spatial locations for a given wavelength. To collect the scattered spectrum, we use six 2-D power monitors arranged to form a box (S2) around the nanostructure. Dimensions of the box are 480 nm, 480nm, and, 420 nm in the x, y, and, z directions, respectively. The normalized nanostructure scattering cross-section is obtained by dividing the scattered power transmitted through this box of monitors by the source intensity and the geometric cross-sectional area of the nanostructure. For angular distribution of scattered power and intensity field distribution we use two 2-D monitors (S1) arranged orthogonal to each other in the z-x and z-y planes, respectively. These monitors have dimensions 4.6 µm by 4.6 µm.
3. Results and discussions
Figure 2(a) shows 3 different scenarios. A: silicon nanostructure in a homogenous medium (air); B: silicon nanostructure on silicon substrate with excitation direction from air to silicon substrate; C: silicon nanostructure on silicon substrate with excitation direction from silicon substrate to air. We will simply use scenario A, scenario B and, scenario C in the remainder of the text when referring to each of the above cases. Scenario B could correspond to the case where light is incident normally from air to the front (top) surface of a solar cell with the silicon nanostructures acting as an AR coating . On the other hand, scenario C could depict the case where light within the silicon solar cell is propagating from the front (top) side towards the back (bottom) side of the solar cell with the silicon nanostructures functioning as a mirror scattering the light back into the solar cell.
Figure 2(b) show scattering spectra for all 3 scenarios. The spectra A, B, C are completely different from each other. The spectrum of scenario A show the first 2 Mie resonances [20, 21] at wavelengths of 800 nm and 1000 nm which corresponds to electric and magnetic dipole resonances, respectively. The magnetic dipole resonance occurs when the wavelength inside the silicon nanostructure is approximately equal to the dimension of the nanostructure in the direction of propagation. Wavelength inside silicon is given by wavelength in air divided by refractive index of silicon. The spectrum corresponding to scenario B indicates line-width broadening when compared to scenario A. This line-width broadening can be explained by the fact that the silicon substrate has introduced new loss channels for the silicon nanostructure (nano-resonator) . The spectrum for scenario C has a strong resonance peak at a wavelength of 900 nm and a weak shoulder at a wavelength of 1100 nm. Differences in scattering cross-section between scenario B and scenario C can be explained as resulting from a difference in electric field driving strength . The effective dielectric function of a nanoparticle on a substrate depends on the substrate dielectric, medium dielectric, and, the coupling strength between the nanoparticle and its image within the substrate . For scenarios B and C, the coupling strength between the Si nanoparticle and its image within the substrate depends on the nanoparticle dipole moment. The nanoparticle dipole moment is directly proportional to the electric field driving strength . Therefore, a difference in electric field driving strength between scenarios B and C implies a difference in coupling strength between Si nanoparticle and its image in both scenarios. As such, the effective dielectric function for Si nanoparticle in scenario B is different from that in scenario C.
Figure 3 shows the intensity field distribution inside the Si nanostructure together with the angular distribution of the scattered power at a resonance wavelength of 800 nm for scenarios A (Figs. 3(a)-3(c)) and B (Figs. 3(d)-3(f)), and also, at a resonance wavelength of 900 nm for scenario C (Figs. 3(g)-3(i)). Note that the source is polarized in the x-direction and the propagation direction is as indicated in Fig. 2(a). The angular and intensity field distributions correspond to plots of As mentioned above and also shown in Fig. 1, the two 2-D power monitors orthogonal to each other and located in Z-X and Z-Y planes are used to generate intensity field distributions inside the nanostructure and polar plots of scattered power. The polar plots in black are obtained from a monitor in the Z-X plane while the plots in red are from monitor in Z-Y plane. These polar plots are obtained by extracting the values of Ex, Ey and Ez for spatial locations x, y, z lying on the circumference of a circle of radius 1.5 µm. The center of the circle coincides with the center of the silicon nanostructure. Figures 3(a)-3(c) show intensity field and polar plots of the scattered power for scenario A at a wavelength of 800 nm, which clearly indicates electric dipole scattering characteristics . It is important to note that for scenarios B (wavelength at 800 nm) and C (wavelength at 900 nm), the resonances are hybrids of electric and magnetic dipole modes. They are not pure electric dipole modes as in scenario A. The presence of the silicon substrate induces an anti-symmetric electric dipole image which results to an induced magnetic dipole mode . The induced magnetic dipoles are shown in Fig. 3(e) (scenario B) and Fig. 3(h) (scenario C) as circular intensity field distributions . Associated to the circular field distribution is a displacement current loop resulting to the magnetic dipole. Another clear distinction between scattering for a silicon nanostructure in air (scenario A) and a silicon nanostructure on a silicon substrate (scenarios B and C) is evident in the angular distribution plots. Polar plots for scenarios B (Fig. 3(f)) and C (Fig. 3(i)) as compared to scenario A (Fig. 3(c)) show a very narrow angular distribution of scattered power and also preferential scattering into the silicon substrate. It has already been reported that particles on high index substrates like silicon will scatter preferentially into the substrate . We observe an additional effect being the drastic narrowing of the angular distribution of scattered power. This narrow scattering distribution is due to the existence of the electric and the induced magnetic dipole resonances at the same wavelength [7,25]. This is because the scattered light from the induced magnetic and electric dipoles interfere constructively.
Polar plots of scattered power and intensity field distribution profiles were also studied at wavelengths of 1000 nm for scenario A (Figs. 4(a) - 4(c)), 1050 nm for scenario B (Figs. 4(d)-4(f)) and also, 1100 nm for scenario C (Figs. 4(g)-4(i)). Figure 4(d) for scenario B shows intensity profile where both edges of the silicon nanostructure have an almost equal and identical field intensity distribution, while Fig. 4(g) for scenario C shows an uneven intensity field distribution. Such an uneven intensity distribution could give rise to weak electric dipole resonance.
4. Double sided solar cell design
At a wavelength of 800 nm (Fig. 3(f)) and 1050 nm (Fig. 4(f)), scenario B scatters preferentially into the silicon substrate. Likewise, scenario C scatters preferentially into silicon substrate at a wavelength of 900 nm (Fig. 3(i)). As such, we propose a very simple thin film silicon solar cell design that could incorporate silicon nanostructures as scatterers on both the front (top) and back (bottom) surfaces. It has already been shown that silicon nanostructures patterned on the front surface of solar cells can function as efficient AR coatings . Here, we show that by including silicon nanostructures on the back (bottom) side of a 2 µm thick solar cell structure, the scattered signal that escapes from the back surface can be reduced by approximately 80%.
As shown in Fig. 5, a 2-D power monitor (M2) is placed on the back (bottom) side of the cell and another 2-D power monitor (M1) is placed on the front (top) side of the cell. M1 measures any backscattered light while M2 measures any forward scattered light transmitted through the solar cell structure. On the back (bottom) side of the cell seven silicon nanostructures are arranged such that six form a hexagon with the seventh at the center of the hexagon. All silicon nanostructures have identical dimensions, i.e. diameter and height are 240 nm, respectively. The silicon nanostructures are all equidistant from each other with a center-to-center distance of 480 nm. These seven nanostructures are spread out over an area with diameter of 1200 nm. Note that silicon has a critical angle of approximately 16 degrees, so, for a 2 µm thick cell, scattered signals from a silicon nanoparticle located on the front side of the cell will escape from the back surface through an area with diameter of approximately 1140 nm. By choosing the center-to-center distance as 480 nm we ensure that the nanostructures do not couple with each other. Inter-particle coupling will modify the scattering properties. In a real device, the front and back surfaces will have many nanostructures with inter-particle distance of 480 nm so that coupling between particles is negligible. The arrow in the TFSF source indicates that excitation is in the positive z-axis direction. Note that silicon nanostructures on the front (top) surface depicts scenario B while silicon nanostructures on the back (bottom) side depict scenario C. Figure 5(b) corresponds to the spectrum measured by M2 (bottom) while the inset is measured by M1 (top). The spectrum in red is obtained when there are no silicon nanostructures on the back (bottom) side of the cell, while the spectrum in black corresponds to the case when nanostructures are present on the backside. The spectra indicate that when the back surface is patterned with silicon nanostructures, significantly less scattered power escapes from the back side of the cell for wavelengths from 700 nm to 1050 nm, while, more scattered power escapes at wavelengths greater than 1050 nm. This is consistent with the angular scattering plots which indicate that at a wavelength of 1100 nm scenario C scatters preferentially in the forward direction (Fig. 4(i)) while at 900 nm, it scatters preferentially in the backward direction (Fig. 3(i)).
Since we can generate the angular scattering distribution plots for silicon nanoparticles on a silicon substrate for all wavelengths, we use the technique developed by Goetzberger  to calculate the fraction of total scattered power (from silicon nanoparticle on the front side) that is trapped within the 2 µm thick silicon solar cell structure (structure in Fig. 5(a)). This technique  calculates total absorption efficiency for solar cell by summation of a geometric series. The black spectrum in Fig. 6 shows the fraction of total scattered power trapped within the double sided solar cell structure. For comparison, absorption within a 2 µm thick silicon layer (blue) and the Yablonovitch theoretical absorption limit  (red) for 2 µm thick silicon solar cell are also plotted. The calculated short circuit currents are 34.5 mA/cm2 for Yablonovitch limit case, 26.7 mA/cm2 for the double-sided cell and 14.1 mA/cm2 for a 2 µm thick silicon film. We assumed 100% internal quantum efficiency in the calculation of the short circuit currents.
We have shown that the scattering properties of silicon nanostructures are strongly modified by the presence of a silicon substrate. These modified scattering properties enable silicon nanostructures to be used for enhanced light trapping in silicon solar cells. The presence of the silicon substrate results to an induced magnetic dipole with resonance energy degenerate with that of the electric dipole. Narrowing of the angular distribution of the scattered light is also observed. The angular scattering distribution indicates that depending on wavelength and direction of excitation, the effect of the substrate on the silicon nanostructure can be such that the light is scattered away from the high index silicon substrate. We also showed that the light trapping efficiency of a thin film silicon solar cell can be significantly improved by using silicon nanostructures as scatterers on both the front and back side of the cell.
This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
References and links
1. S. J. Oldenburg, G. D. Hale, J. B. Jackson, and N. J. Halas, “Light scattering from dipole and quadrupole nanoshell antennas,” Appl. Phys. Lett. 75(8), 1063–1065 (1999). [CrossRef]
4. S. Mukherjee, H. Sobhani, J. B. Lassiter, R. Bardhan, P. Nordlander, and N. J. Halas, “Fanoshells: Nanoparticles with built-in Fano resonances,” Nano Lett. 10(7), 2694–2701 (2010). [CrossRef] [PubMed]
5. N. T. Fofang, N. K. Grady, Z. Y. Fan, A. O. Govorov, and N. J. Halas, “Plexciton dynamics: exciton-plasmon coupling in a J-aggregate-Au nanoshell complex provides a mechanism for nonlinearity,” Nano Lett. 11(4), 1556–1560 (2011). [CrossRef] [PubMed]
6. N. T. Fofang, T. H. Park, O. Neumann, N. A. Mirin, P. Nordlander, and N. J. Halas, “Plexcitonic nanoparticles: plasmon-exciton coupling in nanoshell-J-aggregate complexes,” Nano Lett. 8(10), 3481–3487 (2008). [CrossRef] [PubMed]
7. W. Liu, A. E. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Broadband unidirectional scattering by magneto-electric core-shell nanoparticles,” ACS Nano 6(6), 5489–5497 (2012). [CrossRef] [PubMed]
8. G. Pellegrini, P. Mazzoldi, and G. Mattei, “Asymmetric plasmonic nanoshells as subwavelength directional nanoantennas and color nanorouters: a multipole interference approach,” J. Phys. Chem. C 116(40), 21536–21546 (2012). [CrossRef]
9. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. 93(19), 191113 (2008). [CrossRef]
10. M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9(5), 2188–2192 (2009). [CrossRef] [PubMed]
11. S. Pillai, F. J. Beck, K. R. Catchpole, Z. Ouyang, and M. A. Green, “The effect of dielectric spacer thickness on surface plasmon enhanced solar cells for front and rear side depositions,” J. Appl. Phys. 109(7), 073105 (2011). [CrossRef]
12. K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010). [CrossRef] [PubMed]
13. H. J. Chen, T. Ming, S. R. Zhang, Z. Jin, B. C. Yang, and J. F. Wang, “Effect of the dielectric properties of substrates on the scattering patterns of gold nanorods,” ACS Nano 5(6), 4865–4877 (2011). [CrossRef] [PubMed]
14. H. J. Chen, L. Shao, T. Ming, K. C. Woo, Y. C. Man, J. F. Wang, and H. Q. Lin, “Observation of the Fano resonance in gold nanorods supported on high-dielectric-constant substrates,” ACS Nano 5(8), 6754–6763 (2011). [CrossRef] [PubMed]
15. Y. Wu and P. Nordlander, “Finite-difference time-domain modeling of the optical properties of nanoparticles near dielectric substrates,” J. Phys. Chem. C 114(16), 7302–7307 (2010). [CrossRef]
16. P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun.3,692 (2012).
17. Lumerical FDTD Solutions, www.lumerical.com.
18. J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012). [CrossRef] [PubMed]
20. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12(7), 3749–3755 (2012). [CrossRef] [PubMed]
21. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19(6), 4815–4826 (2011). [CrossRef] [PubMed]
22. F. J. Beck, S. Mokkapati, A. Polman, and K. R. Catchpole, “Asymmetry in photocurrent enhancement by plasmonic nanoparticle arrays located on the front or on the rear of solar cells,” Appl. Phys. Lett. 96(3), 033113 (2010). [CrossRef]
25. B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20(18), 20376–20386 (2012). [CrossRef] [PubMed]
26. A. Goetzberger, “Optical confinement in thin Si-solar cells by diffuse back reflectors,” 15th Photovoltaic Specialists Conference, (1981)
27. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]