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Abstract
Deep-ultraviolet (DUV) optoelectronics require innovative light collimation and extraction schemes for wall-plug efficiency improvements. In this work, we computationally survey material limitations and opportunities for intense, wavelength-tunable DUV reflection using AlN-based periodic hole and pillar arrays. Refractive-index limitations for underlayer materials supporting reflection were identified, and MgF2 was chosen as a suitable low-index underlayer for further study. Optical resonances giving rise to intense reflection were then analyzed in AlN/MgF2 nanostructures by varying film thickness, duty cycle, and illumination incidence angle, and were categorized by the emergence of Fano modes sustained by guided mode resonances (holes) or Mie-like dipole resonances (pillars). The phase-offset conditions between complementary modes that sustain high reflectance (%R) were related to a thickness-to-pitch ratio (TPR) parameter, which depended on the geometry-specific resonant mechanism involved (e.g., guided mode vs. Mie dipole resonances) and yielded nearly wavelength-invariant behavior. A rational design space was constructed by pointwise TPR optimization for the entire DUV range (200-320 nm). As a proof of concept, this optimized phase space was used to design reflectors for key DUV wavelengths and achieved corresponding maximum %R of 85% at λ = 211 nm to >97% at λ = 320 nm.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Efficient generation and collimation of deep ultraviolet (DUV) light (λ ≈ 200-320 nm) is of paramount importance for fundamental science and technology alike, enabling disinfection [1], waste remediation [2], spectroscopy [3,4], information technologies [5,6], and manufacturing [7,8]. Recent progress in solid-state AlGaN-based UV light-emitters promises to meet demands in power consumption and portability at increasingly shorter wavelengths, as recent improvements in material growth and light extraction have resulted in high-single and modest double-digit wall-plug efficiencies (WPEs) [9–11]. Unfortunately, the majority of incumbent device configurations use absorbing material layers for hole injection and current spreading (e.g., p-doped GaN) that reduce light extraction and ultimately limit performance [11]. Moreover, high-reflecting and low-absorbing optical elements are often comprised of non-ohmic contact metals that require protective coatings [12–14], thermally insulating dielectric-based reflectors [15], or epitaxially grown reflectors that are prone to cracking [16], all exacerbating efficiency loss and low device yield. As such, alternative materials are sought to reduce absorption losses, maximize light collimation/extraction, and improve thermal management to accelerate the commercialization and deployment of solid-state DUV technologies.
Nanostructured flat optics (metasurfaces) have partially delivered on the promise of efficient and lossless UV optics in a highly compact and wavelength-tunable form factor [6,17–20]. Reports of DUV reflectors [21], polarizers [22,23], metalenses [24,25], and high-harmonic generators [26,27] have shown recent success in achieving functional DUV metaoptics. In this work, we investigate the DUV reflectance behavior of 2D-periodic, high-index, nanostructured hole arrays and pillars (i.e., high contrast grating structures - HCGs) comprised of AlN thin films supported on low-index substrate materials, most prominently MgF2. Owing to the high refractive index contrast with their environment, both hole and pillar configurations were found to yield intense and wavelength-tunable reflection across the entire UV range, in line with reported high-contrast grating structures designed for visible and IR wavelengths [28–30]. The governing modal behaviors within each structure were found to arise from coupling between thin-film modes and discrete periodicity-induced guided-mode or Mie resonances, and their evolution with geometric parameters was explored and assigned. An approximate design rule for optimal wavelength-invariant reflectance was found in the thickness-to-pitch ratio (TPR) of structures, which ensured proper phase offset between complementary resonant modes within the high-index nanostructure and was found to be distinct for hole and pillar arrays. Extending this TPR-based optimization to feature spacing and duty cycle yielded a geometric design space with reflectance and DUV wavelength constraints for normal-incidence reflectors. This roadmap was then used to extract optimal geometric parameters for hole and pillar arrays exhibiting maximum reflectance at various DUV design wavelengths of interest.
2. Computational methods
Finite-difference time-domain simulations (Ansys Lumerical FDTD) were employed for all simulations in the study. As shown in Fig. 1, simulated structures were configured with a thin layer of hexagonally patterned AlN material (hole or pillar arrays) of thickness t, with circular feature pitch p, radius r, and duty cycle 2r/p. This layer was supported by a 500 nm thick solid or patterned low-index underlayer with refractive index n2, and a solid semi-infinite sapphire substrate. The FDTD region (rectangular region containing 2 hexagonal unit cells) was simulated with perfectly matched (absorbing) out-of-plane Z-boundaries and periodic in-plane X- & Y-boundaries. A TE-polarized broadband plane wave source (S) was placed 390 nm above the top surface of the HCG and injected normally incident light (λ = [180, 390] nm) downward onto the structure. A reflection monitor (M) was placed 195 nm above S. Pillars (Fig. 2(b) inset) were identically simulated with the exception that the radius, r, represents the radius of the cylindrical pillar (instead of hole), and the pitch, p, represents the center-to-center distance between pillars.
Fig. 1. 3D simulation schematic and configurations for nanostructured UV reflectors. (a) Finite-difference time domain (FDTD) simulation schematic, comprised of a hexagonally structured top high-index layer (refractive index n1, thickness t, feature pitch p, feature radius r; purple), a 500 nm thick low-index underlayer (refractive index n2; orange), and a generic semi-infinite substrate (grey). An electromagnetic field monitor (M) and downward-propagating broadband plane-wave source (S) are introduced near the top of the simulation region. (b,c) Configurations used for both hole array and pillar structures, wherein the underlayer was intact (b), or fully perforated (c) down to the substrate with the same structuring as the top layer.
Fig. 2. Simulated underlayer refractive index tolerances for high contrast UV reflective behavior based on AlN hole arrays and pillars, with underlayer modeled as an unpatterned, dispersionless and lossless material with real refractive index of n2. Real refractive index dispersions for SiO2, MgF2, and air (dashed line) are shown in white contours. Normal incidence reflectivity is shown in the color scale on the right.
Simulations varying underlayer index (Fig. 2) were configured with arrays of holes (AlN film thickness, t = 90 nm, DC = 0.7, and pitch p = 210 nm) and pillars (t = 90 nm, DC = 0.7, and p = 190nm) on top of a solid, unpatterned underlayer (as shown in Fig. 1(b) and the insets of Fig. 2). All further simulations transferred the top layer pattern into the underlayer, which decreased the underlayer effective index and increased its index contrast with the top AlN grating layer. The traditional, freely suspended HCG (i.e., with air gap below) was not considered here, as high UV reflectance for such structures requires very thin layers (t < 130 nm) that are not mechanically robust. Moreover, freely suspended HCGs have already been thoroughly considered in literature for IR and visible wavelengths [28,31,32].
3. Results and discussion
3.1 Material constraints on high DUV reflectivity in AlN films on low-index underlayers
The action of high-index, periodic nanostructures is subject to the refractive index profile of their surroundings. Accordingly, Fig. 2 shows the material limitations of the high-contrast effect leveraged to render intense normal-incidence DUV reflectivity. Optical simulations were conducted by illuminating an AlN hexagonal hole array (p = 210) supported by a solid, planar slab of varying refractive index n2 (cf. Figure 1(b)). The canonical case of a fully suspended high-contrast grating is featured at n2 = 1, showing a broad, intense reflection band centered at approximately 230 nm. This high-contrast interference effect begins to taper at n2 ∼1.25 and vanishes entirely for n2 > ∼1.4. The low value and abruptness of this refractive index cutoff tightly constrains the available set of solid underlayer materials, and even a marginally higher index (SiO2 vs. MgF2) largely spoils high reflectivity. These limits are slightly more relaxed for pillars, which sustain intense but narrow resonances up to n2 ∼1.6.
Given the tight constraints on refractive index to support high-contrast resonant effects, metal-fluorides are a logical choice for the underlayer because they have both low real and complex permittivities down to wavelengths of ∼100 nm. MgF2 (with nunderlayer ≈ 1.45 at 200 nm) is the lowest-index material in this family and is therefore a natural candidate. MgF2 is also moderately thermally conductive (∼30 W/m·K), chemically robust, and has a low-to-moderate thermal expansion mismatch with the nitrides (∼8 ppm/K); moreover, it can be deposited via several methods [33] or used as a single-crystal substrate. Building on results in Fig. 2, an additional increase in overall refractive index contrast can be achieved by transferring the pattern further into the underlayer; for this reason, all further simulations were performed with perforated underlayers.
3.2 Geometry-dependent modal assignment
Optical resonances supported by near-wavelength, high-index dielectric nanostructures are highly sensitive to the structures’ specific geometry. Here, the reflectance behavior of periodic, MgF2-supported AlN nanostructures was explored as a function of two geometric parameters: AlN layer thickness and duty cycle (DC), both of which affect the thin-film interference behavior present in the system, as well as incident illumination angle for a nominally high-R ‘test’ configuration. Figure 3 summarizes these results for holes (a,c,e) and pillars (b,d,f). Figure 3(a) clearly shows three thickness regimes that yield modally distinct behavior, owing to the number of guided modes that can couple to a low-order thin-film resonance. Starting from the lowest simulated ttop at 20 nm, there is a single, intense, narrowband Fano resonance (black dashed curve) that abruptly evolves into a broader, intense reflectance band between 60 and 100 nm, where a thin-film resonance straddles two oppositely polar Fano modes (white dashed curves) [34]. Thicker films support a multitude of neighboring high-order Fano resonances of similar polarity, which partitions light into uncoupled or weakly coupled channels and extinguishes the intense broadband reflectance. Evidently, the first two resonant regimes are desirable for our purposes, requiring that the AlN film thickness stays below ∼125 nm for a design wavelength of ∼230 nm.
Fig. 3. Structure- and angle-dependent resonant behavior of high-contrast periodic nanostructures, namely (a,c,e) hole arrays and (b,d,f) pillars of AlN supported on a MgF2 underlayer. (a,b) Thickness-dependent reflectance contours at p = 210 nm and DC = 0.7, delineating the interplay of thin-film interference with neighboring Fano (hole) and Mie (pillar) resonances. (c,d) Duty cycle (DC) variation (phole = 210 nm, ppillar = 190 nm, and t = 90 nm), showing the evolution from nearly perfect thin-films to collective array resonances, to near-unity transmission through a vanishing layer (DChole = 1, DCpillar = 0). Stars denote the optimal DC for broad, intense reflectance in each configuration, and used in (e,f). Insets in (d) show the cross-sectional electric field intensity distribution (black = low, yellow = high) of a single pillar at the electric and magnetic dipole wavelengths (λED and λMD, respectively). (e,f) Angle-dependent specular reflectance of structures illuminated with broadband, TE-polarized light (phole = 210, ppillar = 190, DChole = 0.85, DCpillar = 0.6, thole = 100 nm, & tpillar = 90 nm) showing the relatively higher tolerance of pillar array reflectance to incident illumination angle (measured from normal). Black and white dashed lines represent coupled/high-contrast grating modes and oppositely polarized Fano modes, respectively.
The operating principles underlying the pillar/disk array behavior in Fig. 3(b) and 3(d) are quite similar to those of hole arrays, in that there is a coupling between two resonance types: (i) thin-film resonances and (ii) resonances attributed to discrete, periodic structuring. However, the periodicity-induced modes here are instead attributed to Mie-like scattering, which arises in both individual and collective micro/nano-structures and primarily involves the action of electric (ED) and magnetic (MD) dipole resonances within each scattering unit (high-index disk in this case) [35,36]. Cross-sectional electric field maps of a single pillar at the resonant center wavelengths λED and λMD (Fig. 3(d) inset) show the characteristic high-intensity ED node and MD loop in a single AlN/MgF2 pillar [35]. These independent modes redshift with increasing thickness, with MD-based reflection dominating the behavior. Similar principles allow for highly anti-reflective and absorptive behavior in properly tuned material and geometric systems [37].
As the hole array DC varies from 0 to 1 (decreasing solid fraction) in Fig. 3(c), the reflective behavior evolves from that of a classical planar slab exhibiting solely thin-film interference, to an intensely resonant, wavelength-selective structure. The lowest-order thin-film etalon (centered at ∼265 nm at DC = 0) transforms into the high-reflecting band positioned near 225 ± 20 nm in the high-contrast regime (DC > 0.6, black dashed curve), flanked by the increasingly sharp bounding Fano resonances on either side of it (white dashed curves). The overall blueshift in all resonant features can be attributed to the rapidly decreasing effective index of the structure with decreasing solid fraction. Having defined increasing DC with an increasing solid fraction from 0 to 1 for pillars, we now see the evolution from a complete lack of any reflection (infinitesimally small disks), to intense, narrowband ED/MD resonances, to thin-film interference in a nearly planar slab. Optimal reflectance and bandwidth were found at DChole = 0.85 and DCpillar = 0.6, which are marked with yellow stars in panels Fig. 3(c) and 3(d).
Angle dependence is an important consideration for thin-film reflectors, as the spectral reflectance profile changes dramatically with angle, and the incoming light to be collimated can be diffuse and/or spatially incoherent, impacting efficiency. As such, the angle-dependent specular reflectance of TE-polarized light (0-45°) for hole and pillar arrays was explored (Fig. 3(e) and 3(f)), where one can discern distinct operating principles between the two configurations (TM-polarized data can be found in Supplement 1). Both maintain at least one relatively high-reflectance mode that redshifts as incident angle increases to 45°; however, pillar arrays show greater robustness in their response with a smaller initial modal redshift than hole arrays (<1 nm/deg compared to 2.5 nm/deg) and a broader, more intense (>90%R) reflectance peak throughout. The enhanced angle-dependent robustness of the pillars relative to hole arrays is presumably due to the collective action of individual scattering disks (pillars), unlike thin-film interference that is highly dependent on internal path length through the layer, and therefore more easily de-tuned with incidence angle.
3.3 High-reflectance optimization via thickness-pitch ratio
As mentioned previously, structure pitch governs the location of guided-mode resonances, and is therefore the main determinant of the center and endpoint wavelengths for broadband reflection. However, shifting the pitch without also adjusting thin-film interference (by varying t or DC) de-tunes the unique phase condition necessary for high reflectance [28,34]. As such, by isolating the thickness region that yields optimal reflectance for a single hole pitch, we introduce a thickness-to-pitch ratio (TPR) metric, which accounts for this de-tuning as a proxy for mode phase offset, irrespective of design wavelength. Figure 4 shows the result of continuously varying pitch with a constant, coarsely optimized TPR for both Fig. 4(a) hole (TPR = 0.39) and Fig. 4(c) pillar arrays (TPR = 0.47), as well as three representative reflectance curves across the DUV range (panels (b) and (d)). Sustained R > 85% is observed for the entire wavelength range of interest, and reaches >95% for wavelengths approaching and exceeding 300 nm.
Fig. 4. Reflectance contour maps and selected line plots of nanostructured AlN/MgF2 layers with (a,b) DChole = 0.85 and (c,d) DCpillar = 0.6, exhibiting high, sustained reflectivity over the deep ultraviolet wavelength range by varying lattice pitch. AlN features were initialized with constant thickness-to-pitch ratios (TPR) of 0.39 (holes) and 0.47 (pillars), which were obtained from thickness sweeps at a single feature pitch (phole = 210 nm, ppillar = 190 nm).
While our first attempt at identifying a constant, optimal TPR yielded reasonably intense and broad reflectance across the UV range, it is unlikely that optimal TPRs are invariant with the dispersive, multi-modal phase space spanned by duty cycle and pitch, and more importantly, are not necessarily tied to a particular design wavelength. Accordingly, a pointwise TPR diagram was constructed to aid in identifying maximum reflectance (Rmax) at a given design wavelength (λmax) and choosing the proper structure thickness for highest Rmax. Figure 5 shows the intersection of Rmax and λmax contours for both 5(a) hole and 5(b) pillar arrays, as well as Fig. 5(c) and 5(d) for the optimal TPR to choose given the target design wavelength. The TPR phase space for hole arrays is bi-modal, owing to the crossover from a single, high-intensity Fano resonance in thinner layers (TPR ∼0.21) to a broader, high-contrast grating effect sustained by a neighboring Fano pair (with TPR ∼0.43). The pillar TPR phase space is much more homogeneous (mean TPR = 0.57), likely owing to the uniformly dominant Rmax of the uncoupled MD resonance.
Fig. 5. Calculated phase space for maximized normal-incidence DUV reflectance (Rmax) in AlN/MgF2 nanostructures. (a,b) Rmax color map and associated, overlaid wavelength contours (λmax) for (a) holes and (b) pillars with varying duty cycle and pitch values. (c,d) TPR values for optimized Rmax and λmax for both patterns. The dashed line in (c) delineates two distinct resonance regimes in which the optimal TPR depends on the presence and/or relative intensity of distinct Fano resonances (single Fano resonance vs. high-contrast grating effect, requiring a Fano resonance pair) supported by the high-index layer.
Having explored the achievable Rmax landscape for our chosen material system, it becomes instructive to attempt designs for particularly useful DUV wavelengths. This can be done by (i) identifying the design wavelength of interest and following its contour line to the highest Rmax sustained, (ii) identifying the pitch and duty cycle at this point, and (iii) multiplying the corresponding TPR by the chosen pitch to obtain optimal layer thickness (see Supplement 1 for details). Tables 1 and 2 show optimized geometric parameters for hole and pillar structures at key design wavelengths; all optimized structures showed R >80%, with most well above 90%. The high-Rmax parameter space appears to be wider for pillars in this range, with all sampled geometries at or above 90%, but it is also red-shifted in the parameter space under study. Given that bandwidth is an important consideration when designing high reflectors, a cutoff reflectance was introduced, and a resulting bandwidth at this cutoff recorded. As expected, bandwidth shrinks with shorter design wavelengths as material absorbance decreases the absolute Rmax.
Table 1. Optimized high-reflectance AlN/MgF2 hole array designs
Table 2. Optimized high-reflectance AlN/MgF2 pillar array designs
The nanostructures presented here could feasibly find use in a variety of applications, such as optical filtering, output coupling in cavity devices, and photocatalysis. The developed design rules extend reasonably well to AlxGa1-xN-based grating layers, provided that the design wavelength is sufficiently far from the direct-gap absorption edge. As such, the most immediate benefits can be realized in the DUV LED space, where we envision several possible device configurations implementing this reflector design. Two of these are featured in Fig. 6, which shows (a) a monolithic, AlGaN-based device structure with an AlxGa1-xN grating supported by a porous low-index underlayer comprised of or adjacent to a tunnel junction, and (b) a thin-film flip-chip configuration wherein a MgF2/AlN/MgF2 back-reflecting trilayer stack is deposited on top of a current spreading layer (tunnel junction or transparent conducting oxide, e.g., MgZnO), that is addressed by a sparse gridwork of contact metal (see Supplement 1 for trilayer reflectance simulations). Quantifying the full extraction and collimation benefits of these designs requires integration of the near-field electromagnetic scattering response and the geometric ray optics governing the remaining interactions in the full LED package; future computational efforts may seek to perform such mixed-level simulations. One promising route is extracting bidirectional reflection/transmission distribution functions (BxDFs) from the full-wave FDTD results that can then be used as empirical inputs for Monte-Carlo ray-tracing.
Fig. 6. Several evisioned DUV LED configurations integrating nanostructured grating reflectors. (a) A fully AlxGa1-xN-based device structure featuring a monolithic grating layer supported by a low-index, porous spacer. (b) Thin-film flip-chip configuration featuring a nanostructured back-reflector, surrounded by low-index (e.g., MgF2) spacer layers, including an optional current spreading layer addressed with a sparse gridwork of contact metal.
4. Conclusion
We have explored the AlN/MgF2 system as a viable deep-UV wavelength metasurface platform for intense normal-incidence reflection, and elucidated the landscape of high-index, low-absorptivity reflective nanostructures using numerical simulations. The optical behavior governing reflection wavelength and intensity was identified, structure-property relationships in two relevant near-wavelength structures were presented, and an optimization scheme for choosing rational designs based on a thickness-pitch ratio was proposed and preliminarily validated. These structures could feasibly be formed on any substrate and have an extremely low footprint due to their compact form factor, which helps inform the design space and outlook for high-extraction device configurations and UV metaoptics.
Funding
Army Research Office (W911NF-19-2-0026, W911NF-19-D-0001).
Acknowledgements
This research leveraged high performance computing facilities supported by the Institute for Collaborative Biotechnologies (ICB) and the UCSB Center for Scientific Computing (CSC), funded by the National Science Foundation (CNS-1725797, DMR 1720256). PS and MJG thank the Szilagyi Family (IEE Energy Breakthrough Fellowship) and the UCSB Solid State Lighting and Energy Electronics Center for support. The content of the information herein does not necessarily reflect the position or the policy of the U.S. Government, and no official endorsement should be inferred.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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