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Quasi-ordered moth-eye arrays were fabricated in Si using a colloidal lithography method to achieve highly efficient, omni-directional transmission of mid and far infrared (IR) radiation. The effect of structure height and aspect ratio on transmittance and scattering was explored experimentally and modeled quantitatively using effective medium theory. The highest aspect ratio structures (AR = 9.4) achieved peak transmittance of 98%, with >85% transmission for λ = 7-30 μm. A detailed photon balance was constructed by measuring transmission, forward scattering, specular reflection and diffuse reflection to quantify optical losses due to near-field effects. In addition, angle-dependent transmission measurements showed that moth-eye structures provide superior anti-reflective properties compared to unstructured interfaces over a wide angular range (0-60° incidence). The colloidal lithography method presented here is scalable and substrate-independent, providing a general approach to realize moth-eye structures and anti-reflection in many IR-compatible material systems.
© 2014 Optical Society of America
1. Introduction
Anti-reflective coatings (ARCs) are technologically important in optical and energy applications involving infrared (IR) radiation such as low temperature astronomy [1,2], thermal imaging [3], night vision, IR sensors/lasers [4,5], and multi-junction solar cells [6]. Unfortunately, many of the materials used in these venues have high refractive indices (e.g., Si = 3.42, Ge = 4.2, and III-V semiconductors = 3.5-6) which lead to large reflection losses. For example, a Si or Ge window will reflect ~47% or 60% of the incident IR light at normal incidence, respectively, as predicted by the Fresnel equations [7]. Traditional ARCs based on multiple thin dielectric layers deposited on the interface of interest can achieve high transmission (>99%) over limited wavelength ranges. However, interference-based ARCs are often expensive and complex to make, they have relatively narrow bandwidths (e.g., transmission >98% from 3 to 5 μm with an attenuating effect at higher λ, frequently becoming worse than the native substrate itself), transmission is very angle dependent, and thermal stresses from standing waves within the dielectric film stack can delaminate or destroy the coating in high power situations [8,9].
An alternative method to reduce reflection is to make an interface effectively ‘disappear’ by creating a smooth variation in refractive index between two media (i.e., constructing a graded index interface). When the graded index profile is on the same length scale as the wavelength of light, Fresnel reflection can be suppressed [10]. In the eye of the moth [Fig. 1], this effect is achieved by tissue protuberances with a sinusoidal height profile that reduce reflection in the visible and NIR. In addition, the quasi-ordered nature of the protuberance array suppresses diffraction and camouflages the moth from predators [11]. The moth-eye (ME) principle, in theory, can be used with any material platform to achieve the same effect by scaling the pitch and size of protuberances for the wavelength range of interest. Because the optical response of ME arrays is not based on interference, they avoid the aforementioned issues associated with traditional ARCs; in addition, from a fundamental point of view, they are better suited for both broadband [12–14] and omni-directional (angle-independent) applications [13].
Fig. 1 SEM images of a moth-eye showing the hexagonally-packed, quasi-ordered sinusoidal protuberances that give the moth eye its anti-reflective behavior.
The optical response of ME structures involves light-matter interactions that span several length scales, from near-field contributions at small wavelengths, to an effective medium with bulk-like constitutive optical properties at larger wavelengths. As such, optical experiments that quantitatively measure contributions from both Fresnel and Lambertian transmission and reflection are crucial to determine and understand the optical behavior of ME structures. We have taken this approach here: all components of the ‘photon balance’ (i.e., direct transmission, direct reflectance, forward diffuse scattering and diffuse backscattering) have been quantitatively measured to understand the importance of different optical phenomena over various wavelength ranges [12].
Specifically, in this work, we demonstrate a facile and scalable method to realize moth eye-based anti-reflective films in Si which have highly efficient, broadband and omni-directional response in the mid- and far-IR spectral regions. The overall ‘photon balance’ was quantitatively evaluated to understand the importance of various near- and far-field scattering phenomena. The optical response of ME films were also quantitatively modeled using effective medium theory in the infinite wavelength limit. Ultimately, it was experimentally demonstrated that transmission and reflection at short wavelengths was governed by Lambertian (diffuse) scattering phenomena, while long wavelength optical behavior depended critically on ME feature height.
2. Experimental methods and theoretical calculations
2.1. Moth-eye fabrication
Moth-eye structures in Si were fabricated using a colloidal lithography method outlined elsewhere [12], and briefly summarized below. The method is general and can be easily adapted to other substrates such as Ge, ZnSe, and sapphire. Monodisperse silica colloids (320 nm) were functionalized with allyltrimethoxysilane (ATMS, Sigma-Aldrich, 97%) in the presence of acetic acid and water in ethanol (pH 5.5), washed 3x in ethanol, and re-dispersed in 4:1 ethanol:chloroform. The suspension was deposited on undoped Si (225 μm thick, 3000 Ω•m, University Wafer) via dip coating using a Langmuir-Blodgett trough with constant surface pressure of ~8 mN/m. Depending on the dip coating speed, surface coverage could be controlled with grain sizes ranging from 10 to 200μm2, which mimic the mosaic patterns on the moth eye seen in Fig. 1. The colloidal pattern was transferred into Si via a two step reactive ion etch (RIE) process: (1) Bosch-RIE (PlasmaTherm 770 DRIE) using SF6/C4F8/Ar (825W, 9W bias, 3-cycle etch) for high-aspect ratio anisotropic etching, followed by (2) a polish and tapering step using SF6/Ar (380W, 30W bias) in a home-built ICP-RIE. The samples were cleaned between etches in HF to remove the silica mask, and finally cleaned in Piranha and HF. Using this two-step approach, the total height and taper of the final ME structures could be controlled.
2.2. Optical characterization
Mid infrared (MIR: 2-20μm) measurements were done using a Bruker Equinox-55 FTIR with LN2-cooled HgCdTe (MCT) detector for transmission [Fig. 2, configuration #1] and a La-DTGS (La-doped deuterated triglycine sulfate) detector for reflection [Fig. 2, configuration #2, 8° from normal]. Far IR (FIR: 20-50μm) transmission measurements were taken using a Nicolet Magna 850 FTIR with DTGS detector. Diffuse reflectance and forward scattering were measured using a custom-built Au-coated integrating sphere fabricated for the Bruker FTIR [cf. Fig. 2, configurations #3 and #4, respectively], as outlined in a previous paper [12]. The specular and diffuse reflectance measurements were referenced to a 100 nm thick Au-coated Si wafer and 100 nm Au-coated 600 grit sandpaper, respectively [15]. Angular transmission data were collected using a custom-built rotary stage attachment on the Bruker FTIR [cf. Fig. 2, configuration #1]; a parabolic mirror with aperture stop focused light on the sample (8° solid angle), and transmitted light was collected with another parabolic mirror attached to an LN2-cooled MCT detector.
Fig. 2 Experimental configuration for transmission, reflection, and diffuse scattering measurements. Configuration 1: direct and angle-dependent transmission, 2: specular reflection at 8° from normal incidence, 3: diffuse reflectance, and 4: forward scattering. S = sample, MCT = HgCdTe detector, DTGS = La-doped deuterated triglycine sulfate detector, FM = flip mirror, PM = parabolic mirror, and AS = aperture stop. Schematic is not to scale.
Reflection and transmission of light at an abrupt interface is described by the Fresnel equations, which predict ~70% transmission of IR light at normal incidence for a single air-Si interface. Since an actual wafer has two interfaces, multiple (internal) reflections lower the overall transmission to ~53% at normal incidence. If an ARC or ME array is placed on one side of the wafer, the overall transmission increases, but ~30% reflection from the (unstructured) back surface of the wafer still occurs; in this ‘single-side limit’, the overall transmission of the two-sided real system will be ~70% (i.e., one perfect anti-reflective surface and one Si-air interface). In the following sections, transmission data for ME structures are presented on both an absolute and relative basis. For the latter, transmission data were normalized by the theoretical single-side limit of ~70%, which was calculated using the wavelength-dependent complex refractive index and the substrate thickness (225μm) to account for absorption [7,16]. Given this frame of reference, a double-sided, bare Si wafer will have a normalized transmittance of ~0.53/0.7 = ~76%.
2.3. Effective medium calculations
A 2D effective medium approximation (EMA) was used to calculate the optical behavior of ME arrays in the infinite wavelength limit (d, h << λ, where d = feature pitch and h = feature height; see Fig. 3(a) inset), as outlined elsewhere [12]. Briefly, an effective refractive index, neff(λ,h), is calculated for a given feature shape using the Bruggeman model [8–10]:
where is the shape factor for a sinusoidal height profile. neff(λ,h) is then discretized into N = 100 homogenous layers with different refractive indices and solved as a stack of dielectrics using the transfer matrix method [17]. In the model, hexagonal close packing of features was assumed (i.e., circular bases covering 90.7% of the surface). Since neff for each layer depends only on the overall feature shape (sinusoidal, cone, etc.) and layer height, EMA predictions are not explicitly affected by the pitch d. The substrate thickness (225 μm) and its absorption were taken into account in all EMA calculations by way of the wavelength-dependent complex refractive index [7,16].Fig. 3 (a) Relative transmission spectra of Si moth-eye arrays with different feature heights (h = 0.5 μm (purple), 1.5 μm (green) and 3.0 μm (red)), calculated with the effective medium approximation (EMA). The transmission increase in the mid- and far-IR is strongly dependent on the feature height. (b) Relative transmission spectra measured for Si moth-eye arrays fabricated with feature heights of 0.8 μm (purple, aspect ratio AR = 2.8), 1.7 μm (green, AR = 5.2) and 3.0 μm (red, AR = 9.4). The increase in transmission in the mid-IR qualitatively follows the trend predicted by the EMA. (insets) SEM images of the moth-eye arrays. Note: the black curve (Si*) in each panel is for an unstructured Si wafer surface, and data are normalized by the theoretical single-side transmission limit of 70%.
3. Results and analysis
3.1. Effect of structure height and aspect ratio
The EMA predicts that film transmission is strongly correlated with protuberance height in the infinite wavelength limit [Fig. 3(a)]. In practice, this situation requires that the colloid mask is small compared to the wavelength and that the aspect ratio of surface features be relatively large (AR > 1). Figure 3(b) shows experimental results for three ME structures with increasing aspect ratio (2.8→5.2→9.4), fabricated using a 320 nm colloidal mask.
As predicted by the EMA and seen experimentally, transmission increases with increasing feature height for λ > 6μm. The maximum measured (normalized) transmission was 86% (λ = 6.2 μm), 90% (λ = 12 μm), and >98% (λ = 13μm) for feature heights of 800 nm, 1.7 μm and 3 μm, respectively, whereas, the unstructured Si wafer is 76%. At longer wavelengths, the anti-reflective properties of the ME generally decay because the feature height becomes negligible compared to the wavelength. At short wavelengths, the transmission drops drastically because of the opposite effect: feature size is comparable to the wavelength and near-field interactions become important in the form of diffuse reflectance (DR) and forward scattering (FS). The onset of near-field losses is also strongly correlated with feature height; the three ME structures become more transmissive than bare Si at λ = 4, 5.4, and 6 μm, respectively, in order of increasing aspect ratio. It has also been previously shown that larger mask sizes significantly increase scattering in the NIR region [12], further suggesting that aspect ratio is the most important control parameter to maximize transmission and simultaneously mitigate scattering losses.
3.2. Optical characterization
As mentioned earlier, measuring the ‘photon balance’ of ME arrays is necessary to determine the optical efficiency of the anti-reflective treatment and understand the relative contributions of direct transmission, specular reflection, diffuse reflection (DR) and forward scattering (FS) phenomena in different wavelength ranges. These measurements were undertaken for the highest aspect ratio sample [Fig. 4, AR = 9.4], as detailed in Fig. 5(a).The transmission of this sample calculated using the EMA is shown in blue, along with the Fresnel prediction for a bare Si wafer (Si*, black); the peak at ~16 μm is due to absorption by phonons [18]. The EMA model predicts that there should be a transmission increase of 5-17% for the 2-30 μm range due to the moth-eye effect at the front interface. In addition, the EMA quantitatively describes ME transmission for λ >10 μm where the infinite wavelength assumption holds. In this range, contributions from scattering (DR and FS) are negligible. However, as λ→0, diffuse scattering phenomena become more pronounced and transmission eventually drops to 10% at λ = 2 μm.
Fig. 4 SEM image of aspect ratio 9.4 moth-eye structure in Si fabricated with a 320 nm mask. Feature height is approximately 3μm. Sidewall scalloping at the bases of the features is due to the Bosch etch process.
Fig. 5 (a) As-measured transmission (ME, red), diffuse reflectance (DR, purple), forward scattering (FS, green), and photon balance (PB, orange) for the high aspect ratio (AR = 9.4) Si moth-eye structures shown in Fig. 3. Calculated transmission of the Si moth-eye structure (EMA, blue) and a bare Si wafer (Si*, black) are also shown. The EMA quantitatively predicts ME transmittance when the infinite wavelength limit is valid (λ>10 μm). (b) As-measured specular reflectance (ME, red) and calculated reflectance (EMA, blue) of the ME structure. The single-side perfect anti-reflective coating (SS limit, teal) and bare Si wafer (Si*, black) are also shown. The extremely low specular reflectance of the ME is due to DR and FS scattering losses rather than inherent anti-reflectivity due to a graded index profile.
The measured specular reflection from the ME sample, along with the single-side anti-reflectance limit (SS), EMA for the ME, and Fresnel prediction for a bare Si wafer are shown in Fig. 5(b). The SS limit represents a perfect anti-reflective coating (T = 100%) on the front side of the wafer only (i.e., back side reflection still occurs). It is important to point out that the seemingly ‘excellent’ low reflectance behavior of the ME below λ = 13 μm - lower than a perfect single-side coating - is due to diffuse scattering (DR and FS) rather than inherent anti-reflectance due to a graded index profile. This data shows that every component of the photon balance must be measured to differentiate the moth-eye effect from other scattering phenomena. As seen earlier, the EMA quantitatively predicts ME behavior in spectral regions where the infinite wavelength assumption is valid (λ > 10 μm for the present case).
To compare the synthesized ME samples with traditional ARC technology, a commercial Si window with interference-based coating (λ = 3-5μm design spec., Edmund Optics) on one side was tested in the same experimental setup. Figure 6 shows a comparison between the commercial coating (c-AR) and the aspect ratio 9.4 ME sample. The coated window has a maximum measured transmittance of 95% at 4.5μm, and averages ~92% from 2 to 5μm. For λ > 8μm, the transmission is significantly lower than that of bare Si. This behavior is typical of interference-based coatings because constructive interference can occur at wavelengths far from the design range. In contrast, the ME sample has transmittance higher than bare Si for λ = 6-45 μm, T >90% for 7.5-23 μm, >95% for 9-18 μm, and >98% at 13 μm. In short, the ME sample has more broadband anti-reflective response and significantly higher peak transmittance compared to typical interference-based ARCs for Si.
Fig. 6 Relative transmission of high aspect ratio ME structures (red) and a commercial, interference-based anti-reflective coating on Si (C-AR, green) for 3-5μm. Calculated (Si*, black) and measured (Si, cyan) spectra for a bare Si wafer is also shown. The commercial ARC achieves a peak transmission of ~95%, while the ME structure has a peak transmission of ~98%. (inset) Cross-sectional SEM image of the moth-eye array.
3.3. Angular response of moth-eye structures
Different illumination geometries are sometimes encountered in IR detection and imaging applications; as such, surface coatings with omni-directional anti-reflectivity are very desirable. Figure 7(a) shows the as-measured (points) and calculated (lines) angular-dependent transmittance for high aspect ratio (AR = 9.4) moth-eye structures on Si at λ = 10 μm, along with experimental data for a bare Si wafer. For incident angles up to θ = 30°, the ME structure agrees with the perfect single-side anti-reflection limit to within 2%; moreover, the ME enhances transmission for all incident angles up to θ = 60° from normal. In addition, the omni-directional enhancement in transmission with the ME is largely wavelength independent, as demonstrated in Fig. 7(b).
Fig. 7 (a) Experimental angle-dependent direct transmission of high aspect ratio (AR = 9.4) moth-eye structures on Si at λ = 10 μm (ME, red) compared to a bare Si wafer (Si, black). The calculated single-side anti-reflective limit (SS limit, teal) is also shown. (b) Angle-dependent transmission of the moth-eye sample at different IR wavelengths (8, 10, 14 μm = blue pluses, black triangles and red squares, respectively). The incident angle is measured from the surface normal.
4. Conclusions
We have outlined a process to create efficient broadband, omni-directional anti-reflective moth-eye structures on Si for mid- to far-IR applications, quantitatively measured their optical performance (e.g., sorting out contributions from direct transmittance, specular reflection, diffuse reflection and forward scattering), and modeled their behavior using effective medium theory. High aspect ratio (9.4) ME structures created with a 320 nm colloidal crystal mask achieved high peak transmittance (T >98% of an ideal anti-reflective surface at λ = 13 μm), broadband anti-reflection (T >90% for λ = 7.5-23μm; less reflection compared to a bare surface from λ = 6-45μm), larger bandwidth and better performance compared to a typical commercial interference-based ARC, and omni-directional response (e.g., transmittance greater than bare Si for incident angles from 0 to 60° from normal). Optical response (transmission and reflection) of ME structures was quantitatively described with effective medium theory in the infinite wavelength limit, which showed that transmission at long wavelengths was governed by moth-eye feature height. The onset of near-field losses was seen to depend on both the mask size and feature height. As such, controlling the aspect ratio of moth-eye features is the key to achieving both high transmittance and low scattering losses.
The colloidal lithography method presented here to fabricate ME arrays in Si is scalable and extendable to other IR-compatible substrates such as Ge, SiGe, ZnSe, and sapphire. In addition, the mask size, aspect ratio and etch parameters can be adjusted to tune the wavelength-dependent response of the resulting structures. In theory, the moth-eye method can be used to create anti-reflective interfaces from the deep-UV to millimeter wave regions. We have also demonstrated that this method can achieve highly efficient ME structures using quasi-ordered colloidal crystal masks that are easy to deposit. Ultimately, the moth-eye method provides a facile and scalable way to produce ultra-broadband anti-reflective structures that are largely insensitive to the incident angle of light.
Acknowledgments
This research work was supported by the Institute for Collaborative Biotechnologies through Grant W911NF-09-0001 from the U.S. Army Research Office and leveraged equipment supported by an NSF CAREER Award No. CHE-0953441. The content of the information does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred.
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