Reflectivity of a glass thin film with different

Invited Paper

Reflectivity of a glass thin film with different nanostructures Haining Wang and Shengli Zou Department of Chemistry, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL, 32816-2366 ABSTRACT We investigate the reflectivity of glass thin films with different nanostructures using electromagnetic theory. The Discrete Dipole Approximation (DDA) method is used in the calculations. The thickness of the film is varied from 50 to 200 nm. Films composed of semi-ellipsoid, cylinder, and prism particle arrays are examined in order to understand the structure dependence of the thin film reflectivity at nanoscale level. When the film thickness is 50 nm, films with effective dielectric constant gradient exhibit lower reflectivity than those with the uniform dielectric constant. At short wavelengths, the thin film nanostructure has a significant influence to its reflectivity. For longer ones, especially when the wavelength is much larger than the film thickness, the effect of the nanostructure becomes less important and the volume of the film evolves to be an important factor. We also explore the reflectivity of glass films including a 100 nm thick solid substrate layer and nanostructures of different heights. For a film with semi-ellipsoid arrays of the same thickness, its reflectivity drops with the increase of the semi-ellipsoid diameter. The simulation results can be of help in the design of thin film solar cell coating for the enhancement of solar energy conversion efficiency. Keywords: reflectivity, DDA, semi-ellipsoid, thin film, nanostructure

1. INTRODUCTION Advancements in the nanotechnology have been challenging conventional scientific communities with new discoveries and properties for materials at nanoscale level. One of the thriving examples is the optical properties of nano-structured materials. When light passes through an interface between different media, the incident light will be reflected and refracted. The relations between the angles of reflection, refraction, and the incident light rays obey the law of reflection and Snell’s law1. The intensity of reflection (reflectivity) could be calculated by Fresnel equation2. Films with extremely low reflectivity3 are desirable in many applications, such as lens4, 5, solar cell6, 7 and optical recording8. There have been extensive investigations in the design of films with less reflectivity 9-15. For a monolayer coating, the reduced reflectivity can be achieved with interference technique16 by controlling the coating thickness close to the quarter of the incident wavelength, or gradient dielectric constant (square of the index of refraction) strategy17. In the gradient dielectric constant approach, the refractive index of a monolayer antireflection coating needs to be nc = n1n2 to achieve the minimized reflectivity, where nc, n1, and n2 are the refractive indices of antireflection coating, ambient and substrate media, respectively. However, materials with desirable index of refraction can hardly be found in nature. For example, the refractive index of the suitable coating between air (n1=1.0) and glass (n2=1.52) should be 1.23 which is much lower than the indexes of refraction of most natural materials. To prepare films with low index of refraction, researchers have been taking advantage of porous materials18. By fabricating TiO2 and SiO2 films with oblique angle deposition method, Schubert et al.18 obtained films with index of refraction as low as 1.05. When coatings of multilayers with dielectric constant gradient are utilized, the reflectivity of the film can be dramatically reduced. Southwell et al. 17 showed that the quintic or modified-quintic refractive index profiles could provide excellent antireflection properties. By making inverted pyramid arrays in silicon film, Jiang et al.19 obtained low reflectivity of silicon films in a cheap and scalable approach. Koynov et al.20 demonstrated

Plasmonics: Nanoimaging, Nanofabrication, and Their Applications IV, edited by Satoshi Kawata, Vladimir M. Shalaev, Din Ping Tsai, Proc. of SPIE Vol. 7033, 70331S, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.793264

Proc. of SPIE Vol. 7033 70331S-1 2008 SPIE Digital Library -- Subscriber Archive Copy

almost nonreflecting silicon surface with a wet chemical etching technique to prepare silicon surfaces with nanoscale texture structures. Antireflection coating can be applied in the design of solar cells with improved energy conversion efficiency. With the reduction of solar energy loss due to surface scattering, the absorption efficiency of the device can be improved and its energy conversion efficiency can be enhanced subsequently. Tremendous papers can be found in the study of solar cells21 with different materials including Si22-25, CdInSe2 (CIS)26, 27, and CdTe28. Thin film solar cell29 is believed to be the second generation solar cell due to its reduced weight and cost. On the purpose of designing solar cells with improved energy conversion efficiency, we aim to understand the nanostructure dependence of the reflectivity for a glass thin film which can be coated on a solar cell surface to diminish its surface scattering. Novel discoveries in the experiments demand the development of new theories to explain the experimental observations and predict new functionalities with designed structures. After Mie’s pioneering work30 on solving the electromagnetic scattering of spherical particles, there have been many new methods31-33 for the calculations of the optical properties of materials with arbitrary shapes. Those new methods include Discrete Dipole Approximation (DDA), Finite Difference Time Domain (FDTD), and Extended Boundary Condition methods (EBCM) 34. Wriedt et al.34 compared these different methods and concluded that the DDA method demands less computer time and generates more accurate results. There are also numerous calculation codes for DDA method, such as DDSCAT, SIRRI, ZDD and ADDA35. Antti Penttila et al.35 compared those codes, listed the advantages and disadvantages of those codes. DDSCAT code was used in our previous work36 and is also applied in the current work. Using the DDA method, we investigate the reflectivity of glass films of different nanostructures. The thickness and the periodic unit length of the film are varied in the simulations. The studies are focused on the nanostructure dependence of the reflectivity of a thin film instead of searching for optimal structures with minimized reflectivity.

2. METHODOLOGY DDA method is an efficient method for the calculations of the optical properties of targets with arbitrary composites and shapes. The DDA method was first proposed by Purcell and Pennypacker37, and had been improved by other researchers, for example Draine38, 39 et al. who developed the popular computational code DDSCAT40. In the DDA method, the target particle of arbitrary shape is divided into an array of N cubes, each of which could be considered as a polarizable dipole. By solving a 3N linear equation, the excited dipole and local electric field of each cube can be obtained. Subsequently, the extinction, absorption, and scattering cross sections of the particle can be calculated. The dielectric constants (or refractive indexes) of the material at different wavelengths are required to calculate the optical properties of the target particle. The CPU time of the simulations is linearly proportional to the number of cubes. The detailed description of the DDA method can be found in Draine’s paper38, we only show the equation for the calculations of the scattering cross section of an arbitrary target Csca =

k4 E0

N

2

2

∫ dΩ ∑[ Pj − nˆ (nˆ ⋅ Pj )] exp(−iknˆ ⋅ rj ) , j =1

where E0 is the magnitude of the incident electric field, k=2π/λ is the wave vector at wavelength λ, nˆ is the unit vector along the scattering direction, Pj is the induced dipole at the cube j position, rj denotes the coordinate of the cube j, and Ω is the integration angle in the space. Only scattering in the backward direction is considered in the reflectivity calculations.

Proc. of SPIE Vol. 7033 70331S-2

3. RESULTS In the simulations, the incident light is parallel to the X axis; the glass film is arranged in the YZ plane. The grid length (length of the unit cube) in the calculations is 5 nm. The refractive index of the glass is taken to be 1.52. The schematic representations of the glass film are displayed in Fig. 1

(A)

(B)

Fig. 1. Schematic representation of glass films with different nanostructures. (A) Film without a solid substrate layer; (B) Film with a solid substrate layer. 3.1 Reflectivity of glass films with different nanostructures and no solid substrate layer. We start with simulations for glass films with no solid substrate layer as shown in Fig. 1(A). Films with a semi-ellipsoid nanostructure are modeled. The symmetry axis of the semi-ellipsoid is along the X axis, the incident wave vector direction. The semi-ellipsoids are arranged in a square lattice with an edge to edge distance of zero. We compare the reflectivity of the films with semi-ellipsoid arrays and arrays of cylinder with the same bottom area and height as those of semi-ellipsoid. In the calculations, the bottom diameters of the semi-ellipsoid and cylinder are both taken to be 200 nm, and the heights are 50 nm. The results are shown in Fig. 2(A). Fig 2(A) shows that the glass film with semi-ellipsoid arrays has less reflectivity than that of cylinder arrays. The reflectivities of both films are less than that of a solid glass film with the same height. The reflectivity of the 50 nm thick solid glass film decreases from 0.16 to 0.038 when the incident wavelength is varied from 300 to 1000 nm. For the cylinder arrays, the reflectivity is dropped from 0.147 to 0.027. The reflectivity for the film with semi-ellipsoid arrays declines from 0.092 to 0.012. For a given wavelength, the reflectivity of a film with cylinder arrays is 70% of that for a solid film. The ratio of the reflectivity is close to but less than the percentage (78.5%) of the occupied area for a closely packed cylinder array arranged in a square lattice in a plane. The reflectivity of the film with semi-ellipsoid arrays glass is 30% of that of a solid film which is less than the volume ratio of 52% between the two films. 0.2

0.08

Reflectivity

Reflectivity

0.15

a b

0.1

c 0.05

0 300

0.06

a

0.04

b 0.02

400

500

600 700 800 Wavelength/nm

900

1000

0 300

400

500

(A)


900

1000

(B)

Fig. 2. Reflectivity spectra of glass films with different nanostructures. (A) Spectra of films with cylinder and semi-ellipsoid arrays with a 200 nm diameter and 50 nm height and a solid film with the same height. (a) Solid film; (b) cylinder; (c) semi-ellipsoid. (B) Spectra of glass films with tetrahedron and prism arrays with a bottom side length of 200 nm and height of 150 nm. (a) Prism; (b) tetrahedron.


Reflectivity

To investigate the influence of different 0.4 nanostructures to the reflectivity of the film, we calculate and compare the reflectivities of films 0.3 with tetrahedron arrays with those of prism arrays. For films with tetrahedron particle arrays, the 0.2 effective refractive index of the film varies linearly, b which is different from that of films with ellipsoidal c d particle arrays. The heights of the two particles are 0.1 e a also different. In the calculations, the side lengths of the tetrahedron and prism bottom are both 200 nm; 0 the heights for both prism and tetrahedron are 150 300 400 600 700 800 900 1000 500 Wavelength/nm nm. The results are shown in Fig. 2(B). Due to the Fig. 3. Reflectivity spectra of glass films with interference of light in a monolayer film, there is a semi-ellipsoid arrays of the same height (50 nm) dip at 400 nm wavelength for prism arrays. No and different bottom diameters (D). (a) D=200 nm; similar dip at the same wavelength is found for (b) D=300 nm; (c) D=400 nm; (d) D=500 nm; (e) films with tetrahedron arrays. When the incident D=600 nm wavelength is longer than 700 nm, the reflectivity of the tetrahedron array is about 20% of that with prism arrays, which is less than the volume ratio of 33% between the two films. The comparison between the results from Fig. 2(a) and (b) indicates that the volume rather than the shape of the nanostructure plays a more important role in the reflectivity of the thin film. We further explore the influence of the bottom diameter of semi-ellipsoid to the film reflectivity. In the simulations, the height of the semi-ellipsoid is fixed at 50 nm; the bottom diameters are changed from 200, 300, 400, 500, to 600 nm. The reflectivity spectra are shown in Fig. 3. Fig. 3 shows that when the bottom diameter of the semi-ellipsoid is varied, the reflectivity of the film changes only slightly when the incident wavelength is larger than 700 nm. When the incident wavelength is less than 700 nm, dramatic change in the spectrum due to the periodicity difference of the film is observed. We are cautious about those strong peaks and dips in the reflectivity spectra due to the periodicity of the nanostructure, further investigations will be pursued in the future. 3.2 Reflectivity of glass films with semi-ellipsoid arrays and a solid substrate layer.

0.2

a

0.15

Reflectivity

In the following simulations, we include a solid substrate layer in the glass film with semi-ellipsoid arrays. The schematic representation of the structure is sketched in Fig. 1(B). The substrate layer is also a glass film with a 100 nm thickness and the same index of refraction as that of the nanostructure. We initially keep the height of the semiellipsoid particle to be 50 nm, and change the bottom diameter from 200, 300, to 500 nm. The reflectivity spectra of these films are shown in Fig. 4. Fig. 4 shows that by adding a semi-ellipsoid particle array (50 nm height) on a solid glass film (100 nm thickness), the minimum reflectivity (interference minimum) wavelength is shifted from 300 nm to about 400 nm due to the increase of the film

c d b

0.1

0.05

0 300

400

500


900

1000

Fig. 4. Reflectivity spectra of a solid film (100 nm thickness), films with a 100 nm thick solid substrate layer and semi-ellipsoid arrays of the same height (50 nm) and different bottom diameter (D). (a) Solid film; (b) D=200 nm; (c) D=300 nm; (d) D=500 nm.


thickness. When the incident wavelength is at about 400 nm, films with semi-ellipsoid of larger diameters generate less reflectivity. When the incident wavelength is larger than 950 nm, the reflectivity of the film is not very sensitive to its nanostructure variation as displayed in Fig. 4.

0.2

0.15

Reflectivity

We also investigate the effect of the semiellipsoid height to the film reflectivity. In the simulations, the bottom diameter of the semiellipsoid is fixed at 300 nm and the height is changed from 50 to 200 nm. The solid substrate film with a 100 nm thickness is included in the simulations. The results are shown in Fig. 5. In Fig. 5, we may find that when the height of the semi-ellipsoid particle is increased from 50 to 200 nm, the reflectivity decreases when the wavelength is longer than 530 nm. The minimum reflectivity due to the interference for the film with 200 nm high semi-ellipsoid particles is larger than the one with 50 nm height. The simulations indicate that the reflectivity minimization due to the monolayer interference of a thin film may be damaged by its nanostructures.

a 0.1

b 0.05

0 400

500

600 Wavelength/nm

700

800

Fig. 5. Reflectivity spectra of films with semiellipsoid arrays of the same bottom diameter (300 nm) and different heights (H). (a) H=50 nm; (b) H=200 nm.

4. CONCLUSION We investigate the reflectivity of glass films with different nanostructures using discrete dipole approximation method. Films with semi-ellipsoid, cylinder, tetrahedron, and prism arrays are explored. The simulations show that nanostructures have a significant influence to the reflectivity of the film when the height of the nanostructure is close to the incident wavelength. The volume of the film is more important than its nanostructure when the film thickness is much less than the incident wavelength. The simulations also indicate that the reflectivity of the thin film decreases with the increase of the nanostructure height at longer wavelengths, however, the reflectivity minimization of the thin film due to monolayer interference effect can be damaged by the nanostructure of the film.

ACKNOWLEDGEMENTS We acknowledge the support of the startup fund from the University of Central Florida and the ACS PRF fund No. 48268-G6 for this research.

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