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The nonlinear dependence between the duty-cycle of semiconductor nanorod array and its surface reflectance minimization is demonstrated. The duty-cycle control on thin-SiO2 covered Si nanorod array is performed by O2- plasma pre-etching the self-assembled polystyrene nanosphere array mask with area density of 4 × 108 rod/cm−2. The 120-nm high SiO2 covered Si nanorod array is obtained after subsequent CF4/O2 plasma etching for 160 sec. This results in a tunable nanorod diameter from 445 to 285 nm after etching from 30 to 80 sec, corresponding to a varying nanorod duty-cycle from 89% to 57%. The TM-mode reflection analysis shows a diminishing Brewster angle shifted from 71° to 54° with increasing nanorod duty-cycle from 57% to 89% at 532 nm. The greatly reduced small-angle reflectance reveals a nonlinear trend with enlarging duty-cycle, leading to a minimum surface reflectance at nanorod duty-cycle of 85%. Both the simulation and experiment indicate that such a surface reflectance minimum is even lower than that of a uniformly SiO2 covered Si substrate on account of its periodical nanorod array architecture with tuned duty-cycle.
©2011 Optical Society of America
1. Introduction
During the past decades, both the roughened and ordered topographic geometries of low-k dielectric materials have been comprehensively investigated as an alternative key to manipulate the surface reflection and transmittance [1–4]. In application, these low-dimensional nanostructures have been used to construct numerous optical devices such as surface roughened light-emitting diodes, high-efficiency field emitters, and photovoltaic cells, etc. Up to now, versatile low-dimensional nanostructure arrays with extremely low reflectance are extensively utilized to replace the traditional multi-layered coating with excellent anti-reflection (AR) ability for improving the performance of aforementioned devices. One of these intriguing geometries is the silicon-based nanostructure array reported by Kanamori et al. [5,6]. By utilizing the electron-beam lithography and dry-etching, the sub-wavelength Si nanorod arrays with broadband AR feature was successfully demonstrated. Not long ago, Boden et al. [7] has also applied the state-of-the-art e-beam lithography for obtaining a broadband AR silicon surface with sub-wavelength-scale nanopillar array based on the moth-eye principle. Most investigations focused on establishing the sub-wavelength structure on various substrates by using the same specific technique with strict parameters and complex processing steps in order to obtain optimal optical properties [7,8]. For mass-productive application, these procedures are impractical for broad-area fabrication due to an extremely low fabricating speed in large-scale pattering.
Recently, the colloidal lithography has emerged as a low-cost and simplified technology which employs a two-dimensional self-aligned monolayer colloidal nanosphere array as a dry-etching mask for large-scale nanorod array formation [9,10]. Nevertheless, few experimental or modeling works were emphasized on the manipulation of the structural morphology and period for minimizing or tuning the surface reflectance spectrum [11].-Chen et al. have demonstrated a colloidal lithography method by using a sub-wavelength-scale monolayer polystyrene sphere mask for fabricating the optimized pyramid-shape AR structure with a one-step reactive ion etching process [10]. They introduced the rigorous coupled-wave analysis to explain the observed low reflectance of 2-3% from the 500-nm pyramid surface, whereas the surface of cylindrical pillars with same period and height fails to reduce its reflectance to <10%. Either the modeling or experimental works were emphasized on tuning the surface reflectance by changing period, however, the dependence between surface reflectance and the lattice constant (distance between neighboring spheres) as well as the duty-cycle has never been discussed in most of previous works. Neither the nonlinear correlation nor the optimization on the duty-cycle dependent nanorod surface reflectance was reported previously. With the motivation to develop the periodically aligned large-scale nanostructure array with topographic geometry dependent broadband AR spectrum, this work aims to minimize the surface reflectance of the Si nanorod array by tuning the polystyrene nanosphere size after forming the self-aligned array mask on Si substrate. By employing a dual-step etching procedure after monolayer colloidal lithography, we initially tune the size and duty-cycle (defined as the ratio of nanostructure size to its spacing) of the periodically aligned polystyrene nanosphere array via the oxygen ion-beam sculpturing, and then the size-tuned nanosphere array functions as the etching mask for cutting the thin silicon-dioxide (SiO2) film covered periodical Si nanorod array with tunable topographic morphology. The ultra-low surface reflection spectrum in visible and near-infrared (VIS-NIR) wavelength region and the diminishing Brewster angle characteristic of such nanorod arrays are investigated. The modeling and characterization on different duty-cycles of the Si nanorod arrays etched by controlling the diameter and interval spacing of the polystyrene nanosphere array are demonstrated. In particular, a nonlinear dependence between the minimized surface reflectance and the duty-cycle of the Si nanorod arrays are shown and elucidated via the theoretical simulation. The manipulative minimum reflectance as a nonlinear function of the Si nanorod duty-cycle is confirmed by employing a coupled refractive-index nanorod structure during computation.
2. Experimental setup
In experiment, the duty-cycle controlled nonlinear surface reflectance minimum was investigated by taking Si nanorod array as an example. First of all, the standard RCA cleaning process (developed formerly by the company of Radio Corporation of America, RCA) is employed to clean the native oxide of a p-type (111)-oriented Si substrate. The Si substrate with an area of 6.25 cm2 was initially immersed in H2SO4 aqueous solution at 67 wt.% and then in buffered oxide etchant (BOE) to decompose the organic compounds and to remove the residual oxide layer, respectively. After pre-treatment, a new SiO2 buffer with film thickness of 45 ± 2 nm covered Si substrate was prepared by immersing the Si substrate in a mixed H2O2/NH4OH solution with equivalent weight percentage ratio at 27.5°C following with a rinse in copious deionized water. This process is employed to transfer the Si substrate turns from hydrophobicity to hydrophilicity by coating a 45-nm thick SiO2 layer, since the self-assembly of monolayer polystyrene nanosphere array usually require a hydrophilic substrate. In order to fabricate the regular nanorod arrays, the polystyrene nanospheres (manufactured by Sigma-Aldrich Co.) with a mean diameter of 500 nm in aqueous suspension with a solid concentration of 2.5 wt% were used to spin-coat the Si substrate as an etching mask for Si nanorod formation. Since the regularity of the monolayer polystyrene nanosphere array based etching mask is essential to affect the periodicity of Si nanorod, the self-alignment process were performed on SiO2 covered Si substrate with area density of 4 × 108 rod/cm−2 by decreasing the spin-coating rate to 1250 rpm. Note that the centrifugal force is required to be larger than the adhesion force to enhance the array regularity during self-alignment. Similar works have been demonstrated previously [12–14]. It was found that monolayer polystyrene nanosphere array prepared with spin-coating method can hardly be obtained without high-speed rotation over 3500 rpm for 60 sec [12]. Such a strict parameter and time-consuming step results from strong aggregation between nanospheres. This problem has been solved in our case by improving dispersion of polystyrene nanospheres aqueous suspension to reach a relatively low spin rate. Jiang et al. also demonstrated a simple spin-coating technique for rapidly fabricating polymeric nanocomposite with wafer-scale process (4-inch wafer scale) [13]. The maximum achievable uniform scale for such kind of mask is greater than present work; however, the proposed recipe is unusual and difficult for reproduction. After dispersion the polystyrene nanospheres via a nonionic detergent in our case, the monolayer colloidal nanosphere alignment procedure is easily achieved at extremely low spin rate. Although the maximum achievable uniform size (6.25 cm2) of the mask reported in this work is slightly smaller than that reported in literature (4-inch wafer scale) [14], the tightly assembled polystyrene nanosphere array is formatted at 1250 rpm for 17 sec with an area density of 4 × 108 rod/cm−2. The schematics of the preferential etching procedure for the polystyrene nanosphere array masked SiO2/Si substrate are shown in Fig. 1 .
During the sculpturing of polystyrene nanosphere for duty-cycle tuning, the pure oxygen plasma (O2 -) with various etching time is used to tune (or shrink) the polystyrene nanosphere diameter in a RIE chamber, while the nanosphere distance (defined as the distance between the centers of adjacent nanospheres) remain unchanged to keep the constant periodicity within all masked area. To compare, the polystyrene nanosphere with diameters of 445, 365, and 285 nm were obtained by lengthening the oxygen plasma etching time to 30, 60, and 80 sec, respectively, at working chamber pressure of 0.15 Torr and RF plasma power of 55 W. With the reshaped polystyrene nanospheres patterned mask, the SiO2 covered Si nanorod array was in situ dry-etched by using a CF4 and O2 plasma mixture with CF4/O2 fluence ratio of 4 at same working pressure. Note that the small amount precursor gases of O2 can increases radicals and ions environmentally to improve the side-wall slope of the cylindrical-like SiO2-covered Si nanorod array [15]. In more detail, the plasma acted onto the nanosphere surface is nondirectional, and the entire sphere surface was exposed to plasma except for the area contacting with the SiO2. Thus, the nanosphere size can be systematically controlled, and the final product remains nearly a spherical form [16,17]. During reaction, the generated COx, H2O and OH molecules during the interaction of pure O2- plasma with organic polystyrene can be desorbed and then pumped away from the nanosphere surface. It is an important issue to concurrently control the reflectance and wettability of the nano-roughened surface. Both the previous work [18] and our experiment show that the Si nanorod array becomes super hydrophobic with a water contact angles beyond 150° when the nanorod exceeding a critical height 120 nm. Since a hydrophilic surface is required for the self-assembly of the polystyrene sphere monolayer (hence the need for an oxide layer), we have to make our Si substrate hydrophilic by coating thin SiO2 film in the beginning. However, the ultimate goal of our nanorod sample is to be a hydrophobic substrate with self-cleaning function. Hence, we need to transfer the SiO2 covered Si substrate into a low-reflective and hydrophobic surface by etching nanorods with height up to 120 nm. After removing the residual polystyrene nanosphere mask layer in an ultrasonic cleaner, the field-emission scanning electronic microscopy (FE-SEM, Hitachi S-4800) was employed to scale the nanorod array prepared with different experimental parameters. A transmission electron microscopy and X-ray energy-dispersive spectrometer (TEM-XEDS, HORIBA EMAX) mapping by using an electron-beam line scan technique were employed to realize the morphology and depth profile of the silicon and oxygen distribution in nanorod. The angular dependent reflectance spectra of nanorod surface with different duty-cycles were determined with a double-beam spectrophotometer (JASCO ARN-733). Subsequently, the refractive index of the SiO2 covered Si nanorod substrate mixed structure at Brewster angle incidence is simulated by combining the effective medium theory. The reflectance of nanorod samples was measured by using commercial laser ellipsometer (J. A. Woollam Co., VASE, 190-900 nm) covering UV-NIR wavelengths. In addition, a full-field rigorous electromagnetic couple-wave analysis (RCWA, using the diffraction mode calculation package of the R-Soft software) is employed to accurately and precisely simulate reflection properties in two-dimensional microstructures.
3. Results and Discussion
3.1 Duty-cycle and composition analyses of tunable nanorods
Figure 2 shows the size and distance of nanosphere array as a function of etching time. The original size of the polystyrene spheres prior to the pure O2- plasma etching is 500 nm. The SEM images clearly reveals that each Si nanorod array sample dry-etched under different recipe exhibits uniform size and spacing.
Both the size and distance show a slower change with shorter etching duration but increase their variation slope by extending plasma etching times to 40 sec or larger. The dual-stage variation on the etched polystyrene nanosphere size with the etching time is mainly attributed to the initial reaction time required for the oxygen plasma to decompose the polystyrene surface. The size of polystyrene nanospheres is reduced to 285 nm with the etching time lengthening to 80 sec, while the distance between the centers of adjacent spheres remain as constant determined by the initial nanosphere size. The etching rate of pure O2- plasma is faster (1.4 nm/sec) than those ever reported (0.16 nm/sec) in previous work [17], which greatly shortens the etching duration by nearly one order of magnitude. With the data shown in Fig. 2, the decreasing duty-cycle from 89% to 57% can also be obtained when reducing the size of polystyrene nanospheres from 445 nm to 285 nm. After the second-stage dry-etching with a mixed CF4 and O2 plasma etching rates of 0.8 nm/s, the FE-SEM of the cylindrical-like nanorod arrays with height about 120 ± 3 nm are shown in Figs. 3(a) –3(c). Note that the oblique mode (or call bird's-eye-view mode) SEM image obtained by collecting the backscattered electrons is usually employed to accurately and precisely present the topography of such kind of insulating surface. The backscattered electrons are beam electrons reflected from sample surface by elastic scattering, which are more energetic than the secondary electrons and are free of the surface charging effect. The backscattered electron based SEM topography can thus provide a high-contrast surface image for the insulating materials. The reactive-ion interaction within sufficiently short etching time is not a detrimental factor in degrading the smoothness of the SiO2/Si nanorod surface [19]. Note that the weak-oxygen assistant plasma induces a non-directional etching to cause a slight deformation of the nanorod.
Fig. 3 (a), (b), and (c) the FE-SEM image of SiO2/Si nanorod arrays with duty-cycle of 85%, 73%, and 57%, respectively; (d) A cross-sectional TEM micrograph of SiO2/Si nanorod; (e) Depth profile mapping of SiO2/Si nanorod measured by electron-beam scanning.
To further investigate the invasive effect during the CF4/O2 plasma etching process, the sample was in situ cut by using a dual-beam focused-ion-beam system (FEI DualBeam-1255) for TEM-XEDS diagnosis. The cross-sectional TEM image presents the a bi-layer structure for a single cylindrical-like SiO2/Si nanorod with a reducing side-wall slope due to the slightly anisotropic plasma etching process, as shown in Fig. 3(d). The top and bottom layers clearly reveal the image of amorphous SiO2 and Si with significant contrast, where the TEM-XEDS scanning mapping also provides the deviated depth profiles of O and Si composition, as shown in Fig. 3(e). As evidence, the O/Si ratio of XEDS data at nanorod surface region approaches nearly 2 to corroborate the SiO2 as a principal component in the top-amorphous layer, whereas the O content greatly attenuates to reflect the existence of pure Si nanorod structure at a depth beyond 50 nm. In addition, some fluorine atoms with composition ratio of 7% are incorporated into our SiO2 covered Si nanorod array samples. These results elucidate that utilizing the CF4/O2 plasma for dry-etching the thin-SiO2 covered Si substrate could form a fluorinated SiO2 structure.
3.2 Duty-cycle dependent reflectance and Brewster angle of SiO2/Si nanorod array
The TM polarized optical reflection diagnosis at 532 nm is performed to realize the duty-cycle dependent AR property and Brewster angle deviation of the nanorod arrays with different duty-cycles, SiO2/Si and Si substrates, as shown in Fig. 4 . After sculpturing the SiO2 covered Si substrate into nanorod array with duty-cycle of 57%, the TM mode reflectance at small incident angles is reduced from 0.31 to 0.21. The TM mode reflectance further decreases to 0.086 with the duty-cycle of Si nanorod array increasing to 89%. Without processing, the Brewster angle of TM mode reflection of bulk Si and SiO2/Si samples locates at 76° and 57°, respectively. With the formation of Si nanorod array, the Brewster angle shifts from 71° to 54° as the duty-cycle of nanorod array enlarges from 57% to 89%, which is mainly contributed by the combining effects of surface oxidization and roughening (see inset of Fig. 4(a)). Concurrently, the phenomenon of reflectance dip induced by TM-mode reflection related Brewster angle gradually diminishes while enlarging the duty-cycle of nanorod array. The contrast ratio of reflectance at Brewster angle to that at lower angles is greatly reduced to 2.9 when comparing with that of bulk Si sample (>500), which is independent of the nanorod duty-cycle. However, most of the Si nanorod array samples exhibit larger surface reflectance than that of bulk Si at incident angle larger than 60-65°. The periodically aligned Si nanorod array also exhibits lower reflectance covering a broadband spectrum than the bulk Si and SiO2 thin film, since both the air-gap and rod-size is smaller than that visible light wavelength to minimize Mie and Rayleigh scattering [20]. The wavelength dependent reflectance spectra of Si nanorod array samples in Fig. 4(b) shows a lowest reflectance of <3.5% at nanorod duty-cycle up to 89%, and such a low-reflectance extends broadly from UV to VIS wavelength region (with R<6% between 350 and 600 nm). In particular, it is observed that the reflectance enlarges from 6% to 19% at VIS-NIR region but becomes flattened from UV to NIR region when decreasing the duty-cycle from 89% to 57% or less, elucidating that the disappearance of reflectance fringe pattern from SiO2 covered Si surface can easily be achieved by fabricating small duty-cycle nanorod array.
Fig. 4 (a) Incident angle dependent reflectance spectra of nanorod arrays with duty-cycle of 89%, 73%, 57%, and Si substrate measured under the TM polarized incident light at 532 nm; Inset: The Brewster angle as a function of the duty-cycle. Note that the scattered data points are the measured data points and the curve is the fitting curve. (b) Surface reflectance of nanorod arrays with duty-cycle of 89%, 73%, 57%, and Si substrate measured at incident angle of 35 degree.
In comparison with previous work [7], the moth-eye type nanostructure can also approach the AR function mainly due to a gradual change in effective refractive index caused by its tapered features. In contrast, our proposed structure aims to understand the nonlinear dependence between the duty-cycle and the surface reflectance of the Si nanorod array, which offers an alternative approach as compared to the aforementioned structure. The AR characteristic can be optimized by varying the duty-cycle as well as the nanorod diameter without changing the lattice constant. It was found that the reflection of the textured (especially large-period) structure increases dramatically with respect to the diffraction order [10]. Our nanorod array sample with extremely high duty-cycle behaves like a SiO2 coated Si substrate, whereas it behaves like a Si substrate covered with sub-wavelength SiO2/Si nanorods by greatly decreasing the duty-cycle of nanorod. It is thus expectable that the sub-wavelength nano-structure would eliminate the diffraction-order light when reducing the nano-sphere size to 250 nm by shortening the duty-cycle to 50%. Alternatively, we observe only one relatively weak ring diffraction pattern. Furthermore, the greatly reduced reflectance of nanorod array with duty-cycle of 89% at lower incident angles serves as another evidence to support the ultra-low refractive index, which has already been comparable with the ultralow single-layer reflectance ever obtained from a fluorinated SiO2 film [21]. Note that our nanorod area density is reduced by one order of magnitude as compared with that ever reported [5,6]. According to the literature reported by Boden et al. [7], it was indicated that the reduction on surface reflectance in VIS region relies strictly on increasing the density of nanorod array. It inevitably raises the processing difficulty when approaching extremely low reflectance via the formation of high-density nanorod with very small size with currently available lithographic mask. Even though, our observation offers an alternative solution that the nanorod array with area density as low as 4 × 108 rod/cm−2 can also provide broadband AR performance only by tuning its duty-cycle.
3.3 Nonlinear trend of surface reflectance versus duty-cycle of SiO2/Si nanorod array
To elucidate the deviation on duty-cycles-dependent reflectance of nanorod array with varying diameter, we employ an effective refractive index for the nanorod/substrate mixed surface structure. The effective refractive index of nanorod/substrate mixed periodical structure with diameter/spacing of A/B is assumed as ((n2 rod) × (A/period)2 + (n2 substrate) × (B/period)2)0.5 at low incident angles, and the shrinkage on duty-cycle oppositely increases the nanorod spacing under constant period (or lattice constant), the effective refractive index for the Si nanorod array is described as
where S denotes the nano diameter and P the array period (rod-to-rod distance). That is, our experiments start with tuning nanorod diameter at same lattice constant, since the polystyrene nanosphere with same diameter is used for all samples. Otherwise, the variation of nanosphere size as well as the lattice constant concurrently changes the area density of the nanorods, which inevitably results in two geometrical parameters at same time. In our case, the refractive index of the SiO2 covered Si nanorod substrate mixed structure at Brewster angle incidence is estimated through the relation of tan−1 n = θ Brewster angle at 532 nm, which is found to reduce from 2.35 to 1.32 by increasing the duty-cycle of the SiO2/Si nanorod from 57% to 85%, as shown in Fig. 5 (square dotted). The nonlinear trend of the Si nanorod surface reflectance with enlarging duty-cycle leads to a minimum at nanorod duty-cycle of 85%. The simulation curve using Eq. (1) for duty-cycle ranging from 57% to 85% shown in Fig. 6 with nsubstrate/nrod = 3.56 at 532 nm also indicates a good agreement with the experimental data. The simulation clarifies that the gradually decreasing refractive index formed via increasing duty-cycle is not attributed to a material response but to an effective refractive index of the SiO2/Si nanorod/substrate mixed morphology. Subsequently, we wish to obtain the simulated broadband reflectance spectra of the SiO2 covered Si nanorod array. Instead of using effective refractive method, we simulate the reflectance spectrum with a full-field RCWA (using the diffraction mode calculation package from R-Soft software). The effective refractive index was not taken into the RCWA simulation.Fig. 6 Simulation results of nanorod array with (a) different mixed structure and (b) different duty-cycle in linear scale by Rsoft Diffraction Mode.
The RCWA approach can be used without modeling the nanorod array as a thin film with an effective refractive index, as shown in Figs. 6(a) and 6(b). First of all, we observe the phenomenon of interference fringes in reflection spectra as the refractive index of the nanorod approximates that of Si substrate (see case C in Fig. 6(a)). Obviously, the interfered reflection fringes diminish to result in a lower surface reflectance when the effective refractive index of the SiO2/Si mixed nanorod approximates the refractive index of air, as shown in case B of Fig. 6(a). In particular, the interference period greatly enhances to give a reflectance minimum at visible wavelengths but leaving higher value at UV and IR regions. Even though the SiO2/Si nanorod with precipitous side-wall exhibits a nearly constant refractive index due to the invariant aspect and compositional ratio of the Si/air mixed structure, it is mandatory to realize the effect of Si nanorod duty-cycle on the reflectance spectra of periodic nanorod arrays via theoretical modeling, whereas it reveals an extraordinarily nonlinear trend of the minimum reflectance and effective refractive index by changing the duty-cycle of the SiO2 nanorod/Si hybrid surface structure. In previous work, the reflectance spectrum of Si nanorod as a function of height/wavelength (L/λ) shows a less distinct multi-layer interference effect [22]. In our case, the reflectance of the duty-cycle changed SiO2/Si nanorod surface behaves more like a function linearly proportional to L/λ and cannot be well fitted by simply using the graded refractive index model.
During simulation, we also employ another set of fitting parameters by varying the nanorod spacing with constant nanorod diameter, which inevitably enlarge the period (or lattice constant) and dilute the area density of the nanorod array. Nevertheless, the simulated reflectance spectra of the nanorod array with varying duty-cycle and constant nanorod diameter also exhibits very similar trend on reflectance spectra and reveals a nonlinear relationship between its surface reflectance and duty-cycle. As shown in Fig. 7 , it is found that the curve of nanorod with duty cycle of 89% is well coincident with the simulated results. However, a significant deviation between the simulated and experimental spectra at short wavelength region for the nanorod sample with low duty-cycle is observed, which is mainly attributed to the anomalous dispersion contributed by the Si substrate. This originates from the lack of current simulation program, in which the dispersive substrate effect cannot be taken into consideration. Nonetheless, this work aim to emphasize the observation on the optimization of nanosphere duty-cycle for minimizing the nanorod surface reflectance. It is also found that the TM-mode surface reflectance increases when the periodic nanorod array structure disappears at higher duty-cycle >85% or approaches a purely SiO2/Si thin film. Without the periodical array, only the interference of reflections from the top and bottom of the SiO2 layer causes the maxima and minima [7]. In contrast, the surface reflectance of nanorod array also shows an increasing trend with decreasing duty-cycle (from 80% to 10%), indicating the diminishing influence of the nanorod array structure at smaller duty-cycles.
Fig. 7 Experimental and simulated reflectance of nanorod arrays as a function of duty-cycle of 60% (left) and 89% (right).
It is important to note that such a surface reflectance minimum is even lower than that of a uniformly SiO2 nanorods on account of its periodical nanorod array architecture. This result interprets that the nanorod surface reflectance eventually approach that of a SiO2 coated Si substrate at relatively high duty-cycles, whereas the reflectance of the low duty-cycle nanorod array is dominant by Si substrate.
4. Conclusion
A self-assembled of polystyrene nanospheres on the SiO2 covered Si substrate as an etching mask for periodic nanorod arrays formation is successfully demonstrated. The minimum density of closely packed polystyrene nanosphere arrays formatted under the optimum spin rate condition of 1250 rpm for 17 sec is 4 × 108 rod/cm−2. After utilizing O2- plasma and tuning etching times between 30, 60, and 80 sec, it is found a linear-like variation of the etched sizes with the etching time, indicating that the size of polystyrene nanospheres is effectively shrunk between 445, 365 and 285 nm, corresponding to the duty-cycle of 89%, 73%, and 57%. By CF4/O2 plasma etching for 160 sec, the obtained height of SiO2 covered Si nanorod arrays is 120 ± 3 nm. The TM polarized optical reflection diagnosis at 532 nm indicated the Brewster angle shifts from 71° to 54° as duty-cycle of the nanorod increased 57% form to 89%. The reflection related Brewster angle phenomenon gradually diminishes while leaving a reduced reflectance at small incident angles for the nanorod duty-cycle of close to 85%. Both the simulation and experiment indicate that such a surface reflectance minimum is even lower than that of a uniformly multi-layer thin-film coating on account of its periodical array architecture. In particular, the SiO2 covered Si nanorod arrays with duty-cycle about 85% causes a reflectance much lower than that of a uniformly SiO2 covered Si substrate, leading to a low reflectance and refractive index of <6% and 1.32, respectively, at VIS-NIR region. The simulation clarifies that the gradually decreasing refractive index formed via increasing duty-cycle is not attributed to a material response but to an effective refractive index of mixed index structure. For broadband AR application, such a duty-cycle tuning nanorod array with relative low surface nanorod density is relatively easy to be designed and fabricated for obtaining minimized reflectance.
Acknowledgment
This work was supported by the National Science Council of the Republic of China, Taiwan, R.O.C., under grants NSC98-2218-E-002-022 and NSC98-2623-E-002-002-ET.
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