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Computer simulation studies of absorption enhancement in a silicon (Si) substrate by nanoshell-related lo- calized surface plasmon resonance (LSPR) based on ...
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Light absorption enhancement in thin silicon film by embedded metallic nanoshells Oren Guilatt,1 Boris Apter,2 and Uzi Efron1,2,* 1

Department of Electro-Optical Engineering, Ben Gurion University, Beer-Sheva 84105, Israel 2 Department of Electrical Engineering, Holon Institute of Technology, Holon 58102, Israel *Corresponding author: [email protected]

Received November 18, 2009; revised February 3, 2010; accepted February 7, 2010; posted February 24, 2010 (Doc. ID 120208); published April 7, 2010 Computer simulation studies of absorption enhancement in a silicon (Si) substrate by nanoshell-related localized surface plasmon resonance (LSPR) based on a finite-difference time-domain analysis are presented. The results of these studies show significant enhancement of over 15⫻ in the near-bandgap spectral region of Si, using 40 nm diameter, two-dimensional silver (Ag) nanoshells, simulating cylindrical nanoshell structure. The studies also indicate a clear advantage of the cylindrical nanoshell structure over that of a completely filled Ag-nanocylinders. The enhancement was studied as a function of the metallic shell thickness. The results suggest that the main enhancement mechanism in this case of tubular nanoshells embedded in the Si substrate is that of field-enhanced absorption caused by the strong LSPR-enhanced electric field, extending into the silicon substrate. © 2010 Optical Society of America OCIS codes: 350.6050, 240.6680, 040.5350, 160.5140.

Solar cell technology is considered as one of the main approaches in satisfying the critical need for renewable nonfossil sources of energy. One of the key photovoltaic materials is the silicon, considered as one of the best candidates for large-scale photovoltaic conversion of sunlight [1]. However, the indirect bandgap of crystalline Si normally requires the use of thick layers of ⬃100 ␮m, in order to obtain sufficient absorption of the near-IR (NIR) radiation [2]. This in turn requires the use of pure materials with long minority carrier diffusion length, which increases the production costs. Hence, strategies for enhanced light absorption need to be explored to enable efficient light harvesting by thinner photoactive layers. One approach is to exploit the large optical cross sections associated with localized surface plasmon resonances (LSPRs) generated in metallic nanoparticle to enhance the electron-hole pair generation in the embedding silicon (Si) substrate [3]. Surface plasmons, or surface plasmon polaritons, are electron density fluctuations at the interface between a metal and a dielectric material. Such resonant modes can be excited at the surface of nanoparticles, by an incoming plane wave. These LSPR modes exhibit a marked tunable resonance [4]. The near-resonance optical cross sections of nanoparticles are much larger than their geometrical cross section. Furthermore, these resonances can be tuned to match the bandgap of silicon or other photosubstrates as required [3,5,6]. Most of the previous studies on absorption or photogeneration enhancement have focused on the use of nanoparticles deposited on the surface of the device, with the main enhancement mechanism related to enhanced light scattering and trapping [1,7–10]. In one of the few works describing the embedding of nanopaticles within a Si substrate, Kirkengen et al. [11] suggested that such nanoparticle embedding may enhance the photogeneration of electron-hole pairs in Si owing to the direct phononless photoabsorption process. Hu et al. [12] demon0146-9592/10/081139-3/$15.00

strated a theoretical enhancement of up to 50⫻ for near-bandgap radiation due to nanoparticles embedded in Si. There has been no significant effort in studying the photoabsorption or photogeneration enhancement by nanoshell structures. In a recent publication Le et al. [13] described the enhancement of NIR radiation using tightly packed clusters of nanoshells, in which the enhancement mechanism is related to the repulsion of the electric field from the tightly packed shells into the narrow intershell spacing. In this Letter, we have focused on the absorption enhancement in Si using metal nanoshells embedded in it, which—as pointed out above—has been scarcely researched hitherto. The particular focus of this research is on the use of nanoshell structures, rather than full metal nanotubes or nanospheres, for potentially reducing parasitic metal absorption and cutting cost. The study was conducted by numerically solving the Maxwell’s equations using commercially available finite-difference time-domain (FDTD) simulation software (FullWAVE by Rsoft). The simulation setup was based on a cell including a single silver (Ag) nanoshell embedded in a Si substrate, 80 nm wide and 50 nm high. To ensure that the results are qualitatively the same for the variations of the last two parameters, we sample tested structures with up to twice the indicated values. Figure 1 shows the basic setup for the simulation [Fig. 1(a)] and various two-dimensional cross-sectional shapes of tubular nanoshells simulated in our study [Fig. 1(b)]: circular, semicircular, circular arc, and brackets. All simulated nanoshells have silica 共SiO2兲 or Si cylindrical cores. The outer diameter of all shapes was 40 nm, and the diameter of SiO2 / Si core varied between 0 and 32 nm, depending on the Ag nanoshell thickness. The simulation was set with perfectly matching layer boundary condition in the z direction and periodic boundary conditions (with a period of 80 nm) in the x direction. The grid size used was ten times smaller © 2010 Optical Society of America

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Fig. 1. (Color online) (a) Geometry of simulated structure. Nanoshells are embedded in a 50 nm Si host film in a lattice with 80 nm pitch. (b) Cross-sectional shapes of the simulated nanoshells.

than the smallest feature in our setup, and the time step used was ⬃105 times smaller than the inverse simulation frequency. The optical constants of materials used for simulations were taken from the FullWAVE database. The absorption by Si was measured for the specified structures in the range of 300–1000 nm using transverse magnetically polarized source. Figure 2 shows the results of studying shellthickness variations for nanoshell with a closed circular cross section. Figure 2(a) shows the absorption for two representative shell thicknesses compared to the absorption in a 50-nm-thick bare Si film. The re-

Fig. 2. (Color online) Absorption by Si for 40 nm diameter circular shells with shell-thickness variation. (a) shows two representative results for 12 and 4 nm shell thicknesses compared to the absorption by bare Si. (b) Spectral dependence of absorption by Si for different nanoshell thicknesses.

sults can be divided into two regions: from 300 to 450 nm and from 450 to 1000 nm. The shorter wavelength region is characterized by an overall improvement that is only slightly dependent on the shell thickness. Conversely, the absorption at the longer wavelength region is highly dependent on the shell thickness, as detailed in Fig. 2(b). Figure 3 shows the result of the integrated absorption over three spectral regions: 300–1000 nm, 500–1000 nm, and the NIR region (750–1000 nm). The enhancement is sharply peaked at around 4–5 nm for the longer nearbandgap band of 750–1000 nm, while the wideband (300–1000 nm)-integrated enhancement shows weak dependence on the shell thickness. However, in all cases, the enhancement of nanoshells outperforms that of a completely filled nanotube (20-nm-thick shell). The longer wavelength band enhancement is even more pronounced when normalizing the Si absorption to the metal area (Fig. 3, open symbols), accentuating the enhancement efficiency of thin metallic shells in that spectral region. It can be seen that 800%–1000% in the absorption enhancement can be achieved for almost the entire spectrum between 500 and 1000 nm with a suitable combination of the shell thickness ranging from 4 to 8 nm. Since nanoshells in this range contain 1.5–2.7 times less the metalsurface area than a completely filled Ag disk (tube), they have a clear advantage over the use of completely filled nanotubes. Figure 4 shows the absorption by Si for 4-nm-thick nanoshells with the same outer radius—having different cross-sectional shapes and different core materials. The integrated absorption over the spectral range of 500–1000 nm [Fig. 4(b)] shows the advantage of SiO2 filled nanoshells, over Si-core, for solar cell applications.

Fig. 3. (Color online) Enhancement of Si absorption integrated over three spectral ranges. 0 nm shell thickness stands for bare Si, and 20 nm shell thickness stands for whole metal cylinders. The absorption enhancement relative to that of a 50 nm Si film in the same spectral range is shown on the left hand scale (solid curves). The same result normalized to metallic shell area is shown on the righthand scale (dashed curves).

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radii ratio, for the 4 and 12 nm shell thicknesses 共R 共−兲 = ␭4共−兲nm / ␭12 nm兲 is 1.55, which is in a reasonable agreement with our results of R = 850 nm/ 640 nm= 1.32. It should be noted that while these results were found to depend on the choice of the slab thickness in terms of the spectral location and relative intensities of the resonance peaks, the shell-thickness behavior was found to be qualitatively the same both in terms of the peak locations and the relative absorption enhancement. To conclude, the enhancement of absorption in the silicon substrate using the nanoshell-induced LSPR was studied using a FDTD-based simulation. The 40 nm tubular Ag nanoshells with shell thicknesses varying between 4 and 16 nm, as well as a completely filled Ag nanocylinder, were studied in the 300–1000 nm region. The study also included various crosssectional shapes of nanoshells as well as open shells. The results indicate a very strong nanoshell absorption enhancement of up to 15-fold in the nearbandgap region compared to that of a bare Si thin film, and over fourfold enhancement of the nanoshell structure compared to that of a filled Ag nanotube. The spectral enhancement was found to be highly dependent on the thickness of the shells as well as on the cross-sectional shape of the nanoshells and its core material. References

Fig. 4. (Color online) (a) Spectral absorption by Si, and (b) total absorption in the 500–1000 nm spectral range, for 4-nm-thick 40 nm diameter tubular nanoshells with different cross-sectional shapes and core materials.

The 270°-arc and brackets filled with SiO2 show higher total absorption, when normalized to the effective metal thickness, than the circular shapes, although they contain relatively less metal than the other structures. It should be noted that, contrary to expectations, SiO2-filled nanoshells produce significantly higher Si absorption than nanoshells filled with Si core, suggesting that the primary role of the core is in determining the plasmonic cavity’s quality factor rather than in providing the added Si absorption. Finally, for the assignment of the plasmonic resonance observed, we follow Prodan et al. [5] in identifying the two peaks observed for shell thicknesses of 4 and 12 nm, at the long wavelength region [Fig. 2(a)], as the low energy resonance 共␻1共−兲兲 shifted owing to their shell-thickness dependence. Using Prodan’s analysis ([5], Eq. 1, l = 1), we find that the expected ratio of the resonance wavelengths based on the shell

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