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Efficient and Tunable Light Trapping Thin Films Feng Yu, Haining Wang, and Shengli Zou* Department of Chemistry, UniVersity of Central Florida, 4000 Central Florida BouleVard, Orlando, Florida 32816-2366 ReceiVed: October 18, 2009; ReVised Manuscript ReceiVed: December 17, 2009
Using the discrete dipole approximation method, we demonstrated enhanced absorption efficiencies, which are close to 100%, at tunable wavelengths in a two-layer silver thin film. The film is composed of a 100 nm thick perforated layer facing the incident light and a 100 nm thick solid layer. Resonance wavelengths are determined by the distances between perforated holes in the first layer as well as the separation between the two layers. The resonance wavelengths shift to the red with increasing separation distance between the two layers or the periodic distance of the hole arrays. Geometries of conical frustum shaped holes in the first layer are critical for the improved absorption efficiencies. When the hole bottom diameter equals the periodic distance and the upper diameter is about one-third of the bottom diameter, close to unit absorption efficiency can be obtained. The simulations provide a proof of concept example for designing ultrathin antireflection films. Introduction Thin films with reduced scattering and improved absorption efficiencies have applications in many fields such as solar cells. There are many different approaches in the design of films with reduced reflectivity,1–3 which include monolayer interference coating,3–6 coating with gradient dielectric constant.6–11 Monolayer interference coating requires the film thickness to be about a quarter of the incident wavelength. For the dielectric constant gradient approach, moth eye structures or porous films12–16 are utilized to reduce the effective index of refraction of the surface and minimize the surface scattering.10,11,17–21 The reflectivity of a smooth metal surface is high due to the extraordinarily high absorption coefficients of the metal such as silver or gold. Perfect absorbers using meta-materials were reported by many groups using nanostructured metal surfaces.22–36 Landy et al.22 reported near unit absorption at gigahertz frequencies using metallic split ring resonators and cut wire structures. Teperik et al.23 showed that unit absorption at all directions can be achieved using a nanostructured film composed of closely packed voids covered with a thin layer of gold. An optical black hole using core shell structures was presented by Narimonov and Kildishev.24 Wang and Zou37 found that extremely low scattering efficiencies can be obtained in a perforated silver film at tunable wavelengths. In this paper, using a two-layer silver film, we demonstrate unit absorption efficiencies at tunable wavelengths. The geometry and the periodic distance of the conical frustum shaped holes play an important role in the improved absorption efficiencies.
convergence of the calculations depends on the grid length of the polarizable cube. Exact results can be obtained when the grid length is small enough. The CPU time is linearly proportional to the cube number. The extinction and scattering cross sections of a target with N cubes can be calculated with equations N
Cext )
Csca )
k4 |E0 | 2
∑
4πk Im(E*inc,j · Pj) |E0 | 2 j)1
(1)
N
∫ dΩ| ∑ [Pj - nˆ(nˆ · Pj)]exp(-iknˆ · rj)|2 j)1
(2) where N is the number of cubes of the target, k represents the wave vector at incident wavelength λ, E0 is the amplitude of
Computational Method The discrete-dipole approximation (DDA) method38–42 is a popular method to calculate the optical spectra of films or particles with arbitrary shapes. In the DDA method, the target particle is divided into N small cubes, each of which is treated as a dipole. The polarization and local electric field at each cube position can be obtained by solving 3N linear equations. The * To whom correspondence should be addressed. E-mail: szou@ mail.ucf.edu. Telphone: 407-823-4123. Fax: 407-823-2252.
Figure 1. Schematic of the two-layer film. L refers to the distance between the two layers, t1 and t2 represent the thicknesses of the two layers, d1 and d2 are the bottom and upper diameters of the conical frustum shaped holes in the first layer and P denotes the periodic distance of the squarely arranged hole arrays.
10.1021/jp909974h 2010 American Chemical Society Published on Web 01/14/2010
Efficient and Tunable Light Trapping Thin Films
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Figure 2. (a) Scattering and (b) absorption spectra of a one-layer and two-layer silver films. The structure of the one-layer film is the same as that of the first layer of the two-layer film with a 100 nm thickness, d2 ) 115 nm and d1 ) 400 nm hole arrays, and periodic distance 400 nm. The distance between the two layers, L, in the two-layer film is 150 nm.
Figure 3. (a) Scattering and (b) absorption spectra of a two-layer silver film with 100 nm thicknesses for both layers (t1 and t2) and a 150 nm separation (L). The hole diameter, d1, and the periodic distance, P, are fixed at 400 nm, and d2 is varied from 20 to 210 nm.
the incident light, Einc,j indicates the incident electric field at cube j’s position, Pj is the induced electric dipole of cube j, nˆ represents the unit vector along the scattering direction, and rj refers to the coordinate vector of cube j. The absorption cross section Cabs can be calculated by Cext - Csca. The extinction, scattering, and absorption efficiencies are the ratios of the corresponding cross sections over the physical cross section of the film or particle. For the infinite films discussed in the manuscript, periodic boundary conditions are applied in the DDA program.42 Results and Discussion Wang and Zou37 showed that extremely low scattering efficiencies can be obtained using a perforated silver film. Enhanced absorption efficiencies were observed at wavelengths associated with the reduced scattering; however the enhancement is limited due to the enhanced transmission of the film.43–45 To improve the absorption efficiency of the film, we investigate the optical spectra of a two-layer film as shown in Figure 1. The film is arranged in the YZ plane. The incident light propagates along the X axis and the polarization direction is parallel to the Z axis. The film is composed of a perforated silver layer facing the incident wave and a solid layer with a separation L from the first layer. The dielectric constants of silver are taken from Palik’s handbook.46 The second layer is utilized to completely block the transmitted light and enhance film absorption efficiencies using the Fabry-Perot effect.47 The structure of the first layer is designed to minimize the scattering efficiency of the incident light and prohibit the escape of the trapped light between the two layers. The thicknesses of the two layers (t1 and t2) are fixed at 100 nm. The distance between the two layers, L, is varied from 150 to 250 nm. The perforated holes are arranged in a square lattice with a periodic distance,
P, ranging from 400 to 500 nm. The diameters of the conical frustum shaped holes d1 and d2 are also varied. In Figure 2, we compare the optical spectra of a one-layer perforated film with a two-layer film in which the first layer has the same configuration as that of the one-layer film. The thicknesses of both layers are fixed at 100 nm. The holes are arranged in a square lattice with a periodic distance of 400 nm, the diameters of the holes are d1 ) 400 nm and d2 ) 115 nm. There are two resonance dips in the scattering spectrum of the one-layer film. The dips are due to the coupling between holes, which has been observed in Wang and Zou’s report.37 The two resonance wavelengths shift from 444 and 570 nm to 460 and 582 nm, respectively, when the second solid layer, with a separation L of 150 nm from the first layer, is included. Interestingly, even though the scattering efficiencies at some wavelengths between 350 and 550 nm increase due to the reflection of the second layer, the scattering efficiencies are remarkably reduced to close to zero at the two resonance wavelengths of 460 and 582 nm. Figure 2b shows that the corresponding absorption efficiency is also improved from 85% in the one-layer film to 97% in the two-layer film at around 450 nm wavelength and from 59 to 99% at 580 nm wavelength. The effect of hole geometries on the optical properties of the two-layer films is explored. The thicknesses of the two layers are kept to be 100 nm, the periodic distance of the hole arrays in the first layer is 400 nm. The hole diameter d1 is fixed at 400 nm, which equals the periodic distance, P, and d2 is varied from 20 to 210 nm. Figure 3a shows that the scattering efficiency and resonance wavelength are changed only slightly for the resonance dips located at around 450 nm. The resonance wavelength at 498 nm is shifted to 626 nm when d2 is increased from 20 to 210 nm and the scattering efficiency also changes dramatically. The scattering efficiency at 498 nm wavelength
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Figure 4. (a) Scattering and (b) absorption spectra of a two-layer silver film with 100 nm thicknesses for both layers (t1 and t2) and a 150 nm separation (L). The periodic distance and the hole diameters (P, d1, and d2) are increased from (400, 400, and 115 nm) to (500, 500, and 180 nm).
Figure 5. (a) Scattering and absorption spectra of a two-layer silver film with different separations (L) ranging from 150 to 250 nm. The hole diameters d1 ) 400 nm and d2 ) 115 nm and the periodic distance is fixed at 400 nm.
is 17% when d1 is 20 nm. A close to zero scattering efficiency is observed at 582 nm wavelength when d2 is increased to 115 nm which is about one-third of d1. Increasing d2 from 20 to 115 nm allows more light penetrating through the first layer and subsequently leads to a reduced scattering efficiency of the film. When d2 is further increased to 210 nm, more reflected light from the second film may escape the film and the scattering efficiencies become larger. The scattering efficiency at 626 nm wavelength reaches 19% when d2 becomes 210 nm. Figure 3b shows that an absorption efficiency close to one can be observed at 582 nm wavelength associated with the zero scattering efficiency when d2 )115 nm. To further understand the mechanism leading to the improved absorption efficiencies and the variation of the resonance wavelength, we vary the periodic distance of the hole arrays and the separation between the two layers. Figure 4a,b shows the scattering and absorption spectra of films with different periodic distances. The separation between the two layers, L, is fixed at 150 nm, the thicknesses of the two layers are kept to be 100 nm. When the periodic distance is varied from 400 to 500 nm, the hole diameter d1 is kept to be the same as the periodic distance and d2 is taken to be about one-third of d1 which is optimal for the enhanced absorption efficiencies. Figure 4a,b shows that two resonance wavelengths at 460 and 582 nm shift monotonically red to 550 and 720 nm when the periodic distance is increased from 400 to 500 nm. The results indicate that both resonance wavelengths are sensitive to the periodic distance change and the longer resonance wavelength is more sensitive to the hole geometry change as shown in Figure 3. Figure 4 also shows that a higher order resonance at 440 nm wavelength appears when the periodic distance is increased to 500 nm. The dependence of the optical spectra of the film on the separation distance between the two layers, L, is examined by
varying L from 150 to 250 nm. In the calculations, the hole diameters d1 ) 400 nm and d2 ) 115 nm, the periodic distance is fixed at 400 nm. The thicknesses of the two layers are still kept to be 100 nm. Figure 5 shows that when L is increased from 150 to 250 nm, the resonance wavelength at 460 nm shifts slightly to shorter wavelengths. The slight shift indicates that the resonance peak is dominantly determined by the periodic distance of hole arrays rather than the separation between the two layers. The resonance wavelength at 582 nm when L ) 150 nm is shifted to 596 nm when L ) 200 nm and further shifts to 648 nm when L ) 250 nm. The resonance wavelength is longer than twice the layer separation due to the skin depth of the silver, which allows light to penetrate several ten nanometers deep in the film. Please note that a small peak with an efficiency of 44% appears at 490 nm wavelength when L ) 200 nm and the peak efficiency grows to close to 100% and red shifts to 536 nm when L ) 250 nm. The resonance wavelengths of these peaks are about twice the layer separation indicating that the resonance is due to the Fabry-Perot effect. The change of the resonance peak at longer wavelengths versus the separation between the two layers is consistent with the previous conclusions by Yu et al.47 Conclusion Using a two-layer silver film composed of a perforated and a solid layer, we showed that unit absorption efficiencies could be obtained at tunable wavelengths. The absorption efficiency is determined by the geometries of the conical frustum shaped holes. Unit absorption efficiencies can be achieved when the upper diameter (d2) of the hole is about one-third of the bottom diameter (d1), which equals the periodic distance. The resonance wavelength may be tuned by varying the periodic distance of the squarely arranged holes and the separation distance between
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