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The highly transparent micro-grating structures (MGSs) of sapphire substrate with large diffuse light scattering were theoretically and experimentally studied. From the finite difference time domain simulation, it was found that the degree of diffuse light scattering is strongly dependent on the size of grating structures. For a highly transparent property, the sapphire MGSs were optimally designed by the theoretical calculations using the rigorous coupled wave analysis method. The order of taper, geometry (i.e., width and height), and pitch length of MGSs were optimized to maximize their average total transmittance over a wide wavelength range of 300-1800 nm. Additionally, the influence of the deposition of low-refractive index material such as SiO2 onto sapphire MGSs on the transmittance characteristics was investigated. To verify experimentally the feasibility, the sapphire MGSs were fabricated by the conventional lithography and dry etching processes. The SiO2 deposited sapphire MGS exhibited a further increase in the total transmittance due to its relatively more graded refractive index profile while maintaining a significantly enhanced diffuse light scattering. The experimental data were in a reasonable agreement with the theoretical results.
©2011 Optical Society of America
1. Introduction
Over the past decades, the patterned surface structures such as the grating structures [1–4], corrugated surface structures [5–7] and photonic crystals [8, 9] have allowed a modification in the property of light to travel between air and the substrate material. Particularly, subwavelength surface relief structures, i.e., a period smaller than wavelength of incident light, such as the parabola subwavelength grating structures (SGSs) or hemi-urchin shaped nanostructures, exhibited superior antireflective properties in the broadband and wide acceptance angle [10, 11]. These structures are promising alternatives to overcome some problems in the conventional multilayer antireflection coatings including the material selection, thickness mismatch, and thermal instability [12]. Generally, the SGS could suppress efficiently the Fresnel reflection at the interface between two different optical media (i.e., air and the substrate material) over a wide range of wavelengths because the incident light at the surface allows only the zeroth order diffraction [13,14]. Thus, the SGSs have been beneficently used to enhance the light coupling/absorption in many applications including optoelectronic devices, photovoltaic devices, and glass components [15–18]. The various fabrication methods such as photolithography, e-beam lithography, nanoimprint lithography, laser interference lithography and hybrid nano-pattering lithography have been also employed [14, 19–22].
Recently, the light scattering technique has attracted intensive research interest because it is one of the most important means for increasing the overall absorption in photodetecting devices by extending the effective optical path and promoting the transmitted diffuse light [23, 24]. However, the SGS surface of the transparent substrate does not sufficiently provide efficient light scattering because the transmitted light cannot be diffracted in higher orders except for the zeroth order. Instead, the micro-scale grating surface may provide the higher order diffuse light coupling. In fact, the higher order diffraction process can be closely related to the light scattering behavior [25, 26]. Meanwhile, among various transparent substrate materials, the sapphire is widely used in optoelectronic device applications because of its extraordinary mechanical hardness, thermal and chemical stabilities. In order to improve device efficiencies, the surface relief structure design on flat sapphire substrate is still required because it exhibits a relatively poor transparency due to its high refractive index. In various fields of optoelectronic and photovoltaic applications, a large amount of totally transmitted light is the most important consideration for transparent substrate [14, 27]. It is more desirable if the portion of diffuse transmittance component becomes larger while keeping high total transmitted light, i.e., both high total transmittance and high haze factor. Therefore, first of all, the total transmittance should be maximized. In this express, we theoretically and experimentally investigated and analyzed the highly transparent sapphire micro-grating structures (MGSs) with a large diffuse transmittance using the finite different time domain (FDTD) and rigorous coupled wave analysis (RCWA) simulations. To maximize the average total transmittance of sapphire MGSs, the geometric parameters (i.e., shape, width, height, pitch length) were optimized. Additionally, for further improving the optical characteristics, the effects of SiO2 layer onto sapphire MGSs were also studied.
2. Modeling and simulation of sapphire MGSs
Before designing and optimizing the geometry of sapphire MGSs for broadband and high total transmittance, the behaviors of light in the sapphire SGS and MGS need to be theoretically explored by FDTD simulations. In this work, the sapphire MGS with a size of 2 μm was chosen because the explored wavelength range of the incident is 300-1800 nm. Figure 1 shows the contour plots of the calculated electric field distributions for light propagating from air to the (a) sapphire SGS (width: 300 nm, height: 300 nm) and (b) sapphire MGS (width: 2 μm, height: 2 μm) with parabolic shapes. In FDTD simulations, the Ey, i.e., amplitude of y-polarized electric field, was calculated when the plane wave was launched from the air and then propagated in the z direction. Here, the incident plane wave with a Gaussian beam profile was normalized at λ = 600 nm. The refractive index of sapphire was used as ~1.76. For the sapphire SGS, the light was transmitted straightly in the z direction though there is a weak interference pattern at its surface, as shown in Fig. 1(a). This means that the zeroth order diffracted light dominantly passes through the sapphire SGS. When the light was propagated into the sapphire MGS, in contrast, it created such strong light interference patterns with a wide angular spread, which can be expected to get more chances to experience the multiple diffuse scattering. This also may increase the probability to generate higher order diffractions outside the escape cone for increasing the optical path length in device applications. It is noticeable that the grating structure with a period (Λ) larger than the wavelength (λ) of incident light provides higher order diffracted transmissions, resulting in the efficient diffuse light scattering. The transmitted light with higher order diffraction modes in periodic grating structures can be explained by satisfying the boundary condition of continuity of the tangential electric field at the surface of the periodic grating structure followed as [28, 29]
where is the incident horizontal wave number in air, m is the particular integer, and is the transmitted m th order horizontal wave number in the sapphire substrate. By using the relationship of and , the Eq. (1) can be expressed as a function of wavelength-to-period ratio (λ/Λ) given bywhere is the refractive index of sapphire substrate, is the incident angle and is the m th order angle of transmission. The geometry of sapphire MGSs should be optimized for efficient light scattering while keeping still high total transmittance because the wavelength-to-period ratio should be minimized to allow higher order diffraction modes in Eq. (2). Therefore, we designed and optimized the grating structure of sapphire substrate by maximizing the total transmittance, keeping its period larger than the wavelength of the incident light. For this, the geometry of sapphire MGSs was optimized by subsequently determining the shape, width, height, and pitch length of sapphire MGSs as the geometric parameters. To determine the shape of sapphire MGSs, at first, the order of taper (OT) can be defined as a parameter in the equation of the tapered cone as follows [11]:where r is the radius of circle in the xy plane of a Cartesian coordinate system, and and are the height and width of sapphire MGSs, respectively. By changing the OT, for various shapes of sapphire MGSs with a periodic hexagonal array, the total transmittance was calculated over a wide range of wavelength (λ = 300-1800 nm) by the RCWA simulations. Herein, the initial geometry of sapphire MGSs was considered as = 2 μm, = 2 μm, and P = 0.5 μm, where P is the distance between MGSs (i.e., pitch length).
Fig. 1 Calculated electric fields of light propagating from air to the (a) sapphire SGS (width: 300 nm, height: 300 nm) and (b) sapphire MGS (width: 2 μm, height: 2 μm) with parabolic shapes.
3. Results and discussion
3.1. Design optimization of sapphire MGSs
Figure 2 shows (a) the contour plot of the calculated total transmittance spectra as a function of OT for the sapphire MGS with = 2 μm, = 2 μm, and P = 0.5 μm and (b) the calculated average total transmittance as a function of OT at wavelengths of 300-1800 nm. The insets of Fig. 2(b) show the corresponding computational geometries of the sapphire MGSs with periodic hexagonal array for OT = 1 and 2.3. As shown in Fig. 2(a), the total transmittance was increased with increasing the OT from 0.5 to 2.5, but it was slightly decreased above 2.5 of OT. Particularly, for OT > 1.5, the high total transmittance region with values of > 92% extended into the wavelength ranges of 700-800 nm and 1650-1800 nm. It is clear that the total transmittance can be improved by enhancing the light coupling efficiency between air and the modified surface of sapphire MGSs because the shape of grating structure affects significantly the change of refractive index profile and provides an antireflective surface [14, 30, 31]. To determine the optimum value of OT, the calculated total transmittance was averaged over a wide wavelength range of 300-1800 nm. As shown in Fig. 2(b), the maximum average total transmittance of 89.36% was obtained at OT = 2.3. In comparison of the computational geometries at OT = 1 and 2.3, it is evident that the parabolic shape of sapphire MGSs provides the more efficient light coupling than the conical shape.
Fig. 2 (a) Contour plot of the calculated total transmittance spectra as a function of OT for the sapphire MGS with = 2 μm, = 2 μm, and P = 0.5 μm and (b) calculated average total transmittance as a function of OT. The insets of (b) show the corresponding computational geometries of the sapphire MGSs for OT = 1 and 2.3.
After determining the optimal shape of sapphire MGSs, the total transmittance as a function of was investigated. Figure 3 shows (a) the contour plot of the calculated total transmittance spectra as a function of for the sapphire MGS with = 2 μm, OT = 2.3, and P = 0.5 μm and (b) the calculated average total transmittance as a function of . The total transmittance was slightly increased at long wavelengths of 1600-1800 nm with the increase of , but it was not largely influenced by the change of . As shown in Fig. 3(b), the average total transmittance was increased only by 0.86% as the width was increased from 1.8 μm to 3 μm. This indicates that the width of micro-scale grating structures is not the dominant factor in affecting their total transmittance characteristics. Therefore, we determined the 2.5 μm of as a normal value.
Fig. 3 (a) Contour plot of the calculated total transmittance spectra as a function of for the sapphire MGS with = 2 μm, OT = 2.3, and P = 0.5 μm and (b) calculated average total transmittance as a function of .
The contour plot of the calculated total transmittance spectra as a function of with = 2.5 μm, OT = 2.3, and P = 0.5 μm is shown in Fig. 4(a) . Figure 4(b) shows the calculated average total transmittance as a function of . The insets of Fig. 4(b) show the corresponding computational geometries of the sapphire MGSs with periodic hexagonal array for = 2 μm, 5 μm, and 10 μm. In contrast with , the total transmittance was significantly modified by changing the . As the became higher, the low total transmittance region with values of < 88% could be efficiently reduced in the wide range of wavelengths. This is because the incident light experiences a long relaxation length by the change of refractive index due to the higher height which leads to the higher total transmittance characteristics. As can be seen in Fig. 4(b), the average total transmittance was rapidly increased with increasing the from 1 μm to 5 μm, and it was slowly increased at > 5 μm. However, the relatively higher height has technical problems including the patterning and deep dry etching processes in actual device applications. Therefore, the optimal value was determined as 5 μm (i.e., aspect ratio of 2).
Fig. 4 (a) Contour plot of the calculated total transmittance spectra as a function of for the sapphire MGS with = 2.5 μm, = 2 μm, and P = 0.5 μm and (b) calculated average total transmittance as a function of . The insets of (b) show the corresponding computational geometries of the sapphire MGSs for = 2 μm, 5 μm, and 10 μm.
Figure 5 shows (a) the contour plot of the calculated total transmittance spectra as a function of P for the sapphire MGS with OT = 2.3, = 2.5 μm, = 5 μm and (b) the calculated average total transmittance as a function of P. The P is defined by a schematic drawing in the inset of Fig. 5(a). When the sapphire MGS was arranged and packed more closely (i.e., shorter P), the total transmittance was increased. Especially, the total transmittance was significantly decreased with increasing the P from 1 μm to 2 μm, as shown in Fig. 5(a). It is noted that a somewhat loosely packed array exhibits the better light coupling between air and the micro patterned surface of substrate than that of the closely packed array [31]. The high total transmittance region with values of > 92% was distributed over a wide range of wavelengths for P < 0.5 μm. In comparison to the closely packed sapphire MGS (P = 0), the low total transmittance region with values of < 88% was reduced at long wavelengths of 1100-1500 nm. By considering the average total transmittance in Fig. 5(b), the optimal sapphire MGS with OT = 2.3, = 2.5 μm, = 5 μm, and P = 0.5 μm was determined, exhibiting a maximum average total transmittance of 90.8%.
Fig. 5 (a) Contour plot of the calculated total transmittance spectra as a function of P for the sapphire MGS with OT = 2.3, = 2.5 μm, and = 5 μm and (b) calculated average total transmittance as a function of P.
3.2. SiO2 layer on the sapphire MGS
In order to design the sapphire MGS for higher total transmittance, we used the geometries of SiO2 layer on the sapphire MGS. The enhanced light coupling efficiency can be expected because the SiO2/Sapphire MGS by the use of SiO2 layer provides a relatively more graded refractive index profile. Furthermore, the SiO2 film on the sapphire MGS provides better surface protection. There may be also an improvement in the light scattering property due to the rough surface of deposited SiO2 films on the sapphire MGS. For this reason, we investigated the influence of the SiO2 layer onto the sapphire MGS on the total transmittance characteristics. Figure 6 shows (a) the contour plot of the calculated total transmittance as a function of wavelength for different heights of SiO2 layer () in the SiO2/sapphire MGS with OT = 2.3, = 2.5 μm, = 5 μm, and P = 0.5 μm and (b) the calculated average total transmittance as a function of. The inset of Fig. 6(b) shows the refractive index profile of a cross-sectional view in the computational geometry. In the theoretical modeling of the geometries of SiO2 layer on the sapphire MGS, we assumed that the SiO2 are deposited uniformly along the vertical and lateral directions. As shown in Fig. 6(a), the total transmittance could be considerably increased with increasing the . The high total transmittance region with values of > 94% extended into the wavelength ranges of 700-1100 nm and 1500-1800 nm, and the low total transmittance region with values of < 89% was partially reduced at wavelengths of 1100-1500 nm. As shown in Fig. 6(b), the average total transmittance was increased efficiently with slight fluctuations. This can be explained by the fact that the SiO2 layer acts as the interference layer which reduces Fresnel reflections. The total transmittance of SiO2/sapphire MGS was enhanced by the more graded refractive index profile. The refractive index difference between air and the surface of sapphire MGSs could be relaxed by an intermediate refractive index of SiO2 layer, thus leading to the improved total transmittance characteristics.
Fig. 6 (a) Contour plot of the calculated total transmittance spectra as a function of for the SiO2/sapphire MGS with OT = 2.3, = 2.5 μm, = 5 μm, and P = 0.5 μm and (b) calculated average total transmittance as a function of . The inset of (b) shows the refractive index profile of a cross-sectional view in the computational geometry.
4. Fabrication and characterization
To test simply the experimental feasibility of the predicted concept by the theoretical calculation, we fabricated the sapphire MGSs and SiO2/sapphire MGSs. For fabricating the sapphire MGS, the double-side polished sapphire substrate of ~200 μm was used to pattern the arrays of microstructures by a conventional lithography process including the photoresist patterning followed by dry etching. By using the inductively coupled plasma (ICP) etching with BCl3/He mixture gases, the hexagonally arrayed sapphire MGS with 1.5 μm of height, 2.5 μm of width, and 0.55 μm of pitch length was prepared. For SiO2/sapphire MGSs, the SiO2 layer was deposited on the sapphire MGS by plasma enhanced chemical vapor deposition process with SiH4/N2O as precursors. In order to experimentally characterize the transmission properties, the total transmittance of the samples was measured by using UV-VIS-NIR spectrophotometer (Cary 5000, Varian, USA) with an integrating sphere to collect all scattered light in the wavelength range of 300-1800 nm. The specular transmittance (i.e., zeroth order transmittance) was measured by the light falling directly to the detector. In this system, the photomultiplier tube (PMT) for 300-800 nm and an InGaAs dectector for 800-1800 nm were used. The diffuse transmittance was obtained from the difference between the total transmittance and the specular transmittance [32].
Figure 7 shows the measured (solid lines) and calculated (dash lines) total transmittance spectra for sapphire, sapphire MGS, and 500 nm SiO2/sapphire MGS at normal incidence of 8° (i.e., near-normal incidence). The cross-sectional field emission scanning electron microscopy (FE-SEM) images of the sapphire MGS and 500 nm SiO2/sapphire MGS are shown in the inset. For calculating the total transmittance of the fabricated sapphire MGS, the computational geometry of OT = 1.7, = 2.5 μm, = 1.5 μm, and P = 0.55 μm, which was estimated from the SEM images, was used. For bare sapphire substrate, the poor total transmittance of < ~86% was observed over a wide wavelength range. However, the total transmittance was efficiently increased by modifying the surface of sapphire through the MGS. At the wavelength regions of 300-1100 nm and 1600-1800 nm, the increased total transmittance was clearly observed, indicating an average total transmittance of 90.1% in the visible wavelength range. For 500 nm SiO2/sapphire MGS, the total transmittance was further increased up to an average value of ~93% with slightly increased oscillations. This is caused by the use of SiO2 layer with the intermediate refractive index as mentioned above. In measured total transmittance spectra, slight fluctuations in the wavelength range of ~800-900 nm occurred while switching between the PMT and the InGaAs detector. The calculated transmittance data reasonably agreed with the experimental results.
Fig. 7 Measured (solid lines) and calculated (dash lines) total transmittance spectra for sapphire, sapphire MGS, and 500 nm SiO2/sapphire MGS. The insets show the cross-sectional SEM images of the sapphire MGS and 500 nm SiO2/sapphire MGS.
To estimate the portion of light that is scattered or diffused (i.e., diffuse transmittance) in the total transmittance, the diffuse transmittance was measured. Figure 8 shows the measured diffuse transmittance spectra of the sapphire MGS, and 500 nm SiO2/sapphire MGS at normal incidence. For comparison, the diffuse transmittance spectra of the sapphire substrate are also shown. The inset shows the photographic images of the sapphire and SiO2/sapphire MGS and the top-view SEM image of the SiO2/sapphire MGS. The bare sapphire substrate exhibited very low diffuse transmittance of < 7.5% in the wide range of wavelengths. Instead, for sapphire MGS, a significant increase in the diffuse transmittance was observed, indicating an average diffuse transmittance of 85.2% in the visible wavelength range. This can be reasonably confirmed by the results of FDTD simulation in Fig. 1. The 500 nm SiO2/sapphire MGS yielded a further increase in the diffuse transmittance, resulting from the more enhanced total transmittance as well as the rough surface of deposited SiO2 layer as can be seen in SEM image of SiO2/sapphire MGS. In comparison of the photographic image of SiO2/sapphire MGS with that of bare sapphire substrate as shown in the insets of Fig. 8, the considerable light scattering property can be also observed with the naked eye. The experimental results indicate that the sapphire MGSs provide the strong light scattering property as well as the highly transparent sapphire substrate.
Fig. 8 Measured diffuse transmittance spectra of the sapphire, sapphire MGS, and 500 nm SiO2/sapphire MGS at normal incidence. The inset shows the photographic images of the sapphire and SiO2 sapphire MGS and the top-view SEM image of the SiO2/sapphire MGS.
5. Conclusion
The improved total transmittance and high light scattering property of sapphire MGSs were theoretically and experimentally investigated. From FDTD simulations for analyzing the light behavior in sapphire MGSs, the light interference patterns with a wide angular spread were observed, thus providing more chances for efficient light scattering. The strong light scattering is closely related to higher order diffractions in MGSs with a larger period than the wavelength of incident light. By characterizing the total transmittance for various geometries of sapphire MGSs based on the RCWA calculations, an optimal geometry of the sapphire MGS with OT = 2.3, = 2.5 μm, = 5 μm, and P = 0.5 μm was determined, exhibiting a maximum average total transmittance of 90.8%. Also, the SiO2/sapphire MGS exhibited a further increase in the transparency (average total transmittance of ~93% in the visible range) and light scattering property (average diffuse transmittance of 86.5% in the visible range) due to the effect of the graded refractive index profile and the rough surface by the deposited SiO2 layer. The theoretical and experimental results gave a reasonable consistency. These results suggest that the sapphire MGS can be a very promising candidate for optoelectronic device applications.
Acknowledgements
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0025071).
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