Self-assembled nanostructures for antireflection optical coatings

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1 Self-assembled nanostructures for antireflection optical coatings Yang Zhao 1, Guangzhao Mao 2, and Jinsong Wang 1 1. Deaprtment of Electrical and Computer Engineering 2. Departmentof Chemical Engineering and Materials Science Wayne State University Detroit, MI Abstract We report the first results of self-assembled nanostructures using colloids for antireflection optical coatings. Two-dimensional (2D) periodic nano-structures were made by using self-assembled 2D colloidal crystals on top of a transparent substrate. An atomic force microscope was used to evaluate the quality of the nanostructure. The feature size of the structures was around 105 nm. This sub-wavelength structure is equivalent to an artificial film on top of the substrate. The effective refractive index of the film is found to be around 1.3. Such a low-index materials is desired for anti-reflection coating to reduce Fresnal reflection. We have observed the reduced reflection from glass surfaces as well as enhanced transmission. Our calculated results agree well with experimental measurement.

2 1. Introduction One of the most important characteristics of an optical material is its refractive index. Many optical applications require optical materials with desired refractive index. For example, in designing antireflection coating, we require a thin film with low refractive indices for various substrates. Unfortunately, most optical glasses have a refractive index around 1.5, which limits the application of these materials. Recently, artificial optical materials with nanoscale composite structures have been created [1-3]. These materials typically consist of varying fraction of air and a base material and it is possible to control the refractive index. Such new materials can certainly give optical designer more choices for creating novel structure and devices. Indeed, subwavelength structured (SWS) surfaces have been used for antireflection coating on semiconductor substrates [4, 5]. While the composite nanoscale structures are elegant, the technologies used for creating them are complicated. Typical feature size of the structures is 130 nm or less for applications at visible wavelengths. This is far beyond the conventional photolithography capability. Electron beam lithography and fast atom beam etching have been used for creating nanoscale SWS surfaces. However it requires expensive equipment and is very time consuming. For example, it took more than ten hours to fabricate a surfaces area of 1.5 mm 2 [5]. Obviously, this method is not suitable for low-cost production over large areas. In this paper we report a simple and effective method for creating nanoscale optical composite materials by using self-assembled colloidal crystals on a substrate. Self-assembled two- (2D) and three-dimensional (3D) colloidal crystals have been used for various optical applications, including photonic bandgap structures [6], corrugated waveguides [7, 8], and wavelength demultiplexers [9]. Large size, high quality samples can be made using simple apparatus and material properties can be monitored during and after the fabrication of structures. In this work, a single layer of 2D colloidal crystal was deposited upon the surface of the structure by convective assembly. This layer is used as a thin film for the creation of antireflection coating. The reflectivity of the structure is measured using a spectrometer. A simplified theory is used for the calculation of the effective refractive index of the composite film. The reflectivity of the coated surface is calculated using the interference theory of a thin film on a substrate. The measured reflectivity of the sample agrees well with the calculated result. 2. Sample preparation The composite material structure used in this study is shown in Fig. 1. It consists of a single layer of nanoparticles (NP) on a substrate. The substrate is glass and the nanoparticles are deposited on the substrate using convective assembly. The procedure for making the samples are as follows.

3 Fig. 1 Anti-reflection coating using self-assembled polystyrene nanoparticles. 2.1 Substrate cleaning The glass substrates used in experiment are precleaned Gold Seal Rite-on Micro Slides (Cat. 3051, Gold Seal Products). The RCA process is used to clean the substrate, which includes the following steps: 1. Glass substrates are cleaned in a piranha solution (1:3 30% H 2O2 H 2SO4 ) at 80 O C for 30 min. Once cooled, rinse them with copious amounts of water. 2.Glass substrates are put in 5:1:1 H 2 O NH4OH 30% H2O2 and sonicated for 60 min. Then, they are rinsed repeatedly with water and dried. 2.2 Self-assembly of polystyrene NPs on a substrate 2D nano-structures are made by using self-assembled colloidal crystals on top of a transparent substrate using convective assembly [6, 10-12]. In this method, water evaporation from a suspension film increases the volume fraction occupied by the particles. When the liquid film thickness approaches the particles diameters, capillary forces become strong enough to force the nucleation and growth of the crystal. Reducing the amount of particles in the suspension and enlarging its spreading area, we can ensure that a monolayer of 2D crystals is deposited on the surface of the substrate. However, the initial concentration of particles in the suspension should not be too low; otherwise, it may not cover all the area and cause voids in the 2D crystals. The colloid was mono-dispersed polystyrene (PS) suspension (Interfacial Dynamic Corp.) with particles of 105 nm in diameter, refractive index of 1.59 at around 600 nm wavelength, and concentration diluted to 1%. The resulted film is very uniform and covers an area around 2 cm x 2 cm. 3 AFM imaging of nanostructures An atomic force micropcope (AFM) was used to image the surface of the composite material film. All AFM images were collected in air using a Dimension 3100 Digital InstrumentsNanoscope. Etched Si nanoprobe tips (NSG 10, Nanoscience Instruments) with force constants of approximately 11.5 N m -1 were used. These tips were conical in shape with a cone angle of 20 and an effective radius of curvature at the tip around 10nm. The images shown

4 here are the original height images collected in the tapping mode. Scan rate was 1 Hz. Integral and proportional gains are approximately 0.4 and 0.7 respectively. Fig. 2 shows an AFM image of 8µ m x 8µ m scan size. It shows that the NPs self-assembled into an ordered polycrystalline pattern over a very large area. Sectional height analysis (Fig. 3) demonstrated that the NPs were uniform in size and the film is a single layer of periodically arranged particles with very small variation in thickness. It should be noted that, for antireflection coating application, polycrystalline colloidal crystals work as well as single crystals, since the period of the structure is much less than optical wavelengths. Fig. 2 Self-assembled monolayer NPs with a polycrystalline pattern. Scan size is 8 µ m x 8 µm 4. Measurement The reflectivity of the coated surface was measured using a Perkin-Elmer

5 spectrophotometer. The incident light was un-polarized and the incident angle of the light beam was less than 6 o. Figure 4 shows the measured reflectivity as a function of the wavelength. It can be seen that the SWS surface reduces the reflection at wavelengths from 400 to 800 nm. In particular, the minimum reflection is less than 0.4% at 575 nm, which is more than 10 times less than 4.2% of a normal glass surface reflectivity. Fig. 3 Sectional height analysis shows the flatness of the nanoparticle thin film.

6 Fig. 4. Measured and calculated reflectivity In addition, we have also measured the transmittance of the sample. Fig. 5 shows that the transmittance of a sample with colloidal crystal coating is higher than that of the substrate.

7 Fig. 5. Measured transmission 5. Calculation The fabricated nanostructure is an ideal film for anti-reflection coating. By adjusting the particles size and density, we can control the thickness and refractive index of the film to achieve total cancellation of reflection at a certain wavelength. Using theory of interference [13], we can calculate reflection from single layer coating. The phase shift between the reflections at the two interfaces of the coating is Here, d is the film thickness, The reflection coefficient ρ is β = 2π n * d 2 / λ (1) * n 2 is the effective refraction index of the film. ρ ρ = e 23 iβ e iβ + ρ + ρ 12 ρ e iβ 12 iβ 23e In Eq. (2), the reflection coefficient of the dielectric interface between layer i and j at normal incidence ni n j ρ ij = (3) n + n where n i and n j are the refractive indices of layer i and j, respectively. The total reflectivity is R= ρ 2 Obviously, one important step is to find the effective refractive index of the film n* 2 i j (2) Effective refractive index of Polystyrene thin film Based on a simple model [1,3], the first order approximation of the effective refraction index of one-dimensional sub-wavelength grating structure for normal incidence is n = +, (4) * 2 2 1/ 2 2 [ n1 (1 F) n2f ] where n 1 is the refractive index of air, n 2 is refractive index of polystyrene, and F is the filling factor of polystyrene NPs. The filling factor F in Eq. (4) is the volume percentage of the polystyrene NPs. To get the value of F, image processing methods were used to calculate the particles number and to verify the mean diameter of the polystyrene NPs. In Fig. 6b and 6c we show the particle number counting results by using

8 the morphological operation and watershed region segmentation method in MatLab, respectively. The calculated value of F is Fig. 6. Polystyrene NPs counting results by using image processing methods. Dispersions of glass substrate and NPs Materials dispersions of glass and polystyrene are considered in the calculation. Using the results from Ref. 14 and the datasheet of the glass micro slides (from Schott Glass Tech. Inc.), we obtained the refraction index data at several points. By using the implantation method, we obtained dispersion properties n(λ) at

9 400~800 nm wavelength range. Fig. 7 shows the n (λ) curves for glass substrate, polystyrene, and effective refractive index of the polystyrene NP thin film. These results are used in the calculations. Fig. 7. Dispersion curves of glass substrate, polystyrene, and the polystyrene NP thin film. Calculation Results The calculation results of the reflectance and transmission of this structure are shown in Fig. 4. It can be seen that the calculated results agree well with experimental measurements. Maximum difference in reflectivity is around 0.2% at 800 nm. 6. Summary and conclusion We have demonstrated a simple yet effective method for fabricating subwavelength structures. Colloidal crystals are used as a composite material whose thickness and refractive index can be controlled by changing the size and chemical composition of the particles. To demonstrate the application of such a composite material in antireflection coating, a single layer of colloidal crystals was deposited on a glass substrate. It was shown that the reflectivity of the coated sample has been reduced to less than 0.5 %.

10 Theoretical calculation of reflection from the coated sample was performed using the thin film theory. The effective refractive index of the composite materials was found to be around 1.3. The calculated results agree well with the experimental measurements. References 1. P Lalanne, M. Hutley, Artificial Media Optical Properties Subwavelength Scale in Encyclopedia of Optical Engineering, PP , Dekker, New York, (2003) 2. E. B. Grann, M. G. Moharam, and D. A. Pommet, J. Opt. Soc. Am. A 12, 333 (1995). 3. Brundrett D L, Glytsis E N, Gaylord T K. Homogeneous layer models for high-spatial-frequency dielectric surface relief gratings: conical diffraction and antireflection designs. Applied Optics, 1994, 33 (13): P. Lalanne and G. M. Morris, Nanotechnology 8, 53 (1997). 5. Y. Kanamori, M. Sasaki, K. Hane, Opt. Lett., 24, 1422, (1999) 6. Y. Xia, B. Gates, Y. Yin, and Y. Lu, Adv. Mater. 12, 693 (2000) and reference therein 7. Y. Zhao, I. Avrutsky, Opt. Lett., 24, 817, (1999) 8. Y. Zhao, I. Avrutsky, and B. Li, Applied Physics Letters, 75, , 9. I. Avrutsky, and Y. Zhao, IEEE Photon. Tech. Lett., 12, 1647, (2000) 10. N. D. Denkov, O. D. Velev, P. A. Kralchevsky, I. B. Ivanov, H. Yoshimura, and K. Nagayama, Langmuir 8, 3138 (1992). 11. G. S. Lazarov, N. D. Denkov, O. D. Velev, P. A. Kralchevsky, and N. Nagayama, J. Chem. Soc. Faraday Trans. 90, 2077 (1994); 12. O. D. Velev, T. A. Jede, R. F. Lobo, and A. M. Lenhoff, Nature 389, 447 (1997). 13. For example, M. Klein, T. Furtak, Optics: 2 nd Ed., John Wiley & Sons, Inc., New York, Nikolov I D, Ivanov C D. Optical plastic refractive measurements in the visible and the near-infrared regions. Applied Optics, 2000, 39 (13):

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