Large-scale self-assembled nanophotonic scintillators for x-ray imaging
Patent Information
- Application Number
- PCT/US2026/019365
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2025-03-27
- Filing Date
- 2026-03-16
- Publication Date
- 2026-10-01
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Figure US2026019365_01102026_PF_FP_ABST
Abstract
Description
[0001] Large-scale self-assembled nanophotonic scintillators for X-ray imaging
[0002] This application claims priority of U. S . Provisional Patent Application Serial No . 63 / 778, 698, filed March 27, 2025, the disclosure of which is incorporated herein by reference in its entirety .
[0003] Statement of Government Support
[0004] This invention was made with government support under W911NF-18-2-0048 awarded by the U. S . Army Research Office, HR0011-22-9-0005 awarded by the Defense Advanced Research Projects Agency, FA9550-21-1-0299 and FA9550-20-1-0115 awarded by the Air Force Office of Scientific Research, and DGE2141064 awarded by the National Science Foundation. The government has certain rights in the invention.
[0005] Field
[0006] This disclosure describes large scale nanophotonic scintillators and other emitting medium for X-ray and other types of imaging and the associated fabrication processes .
[0007] Background
[0008] Scintillation, the process by which materials emit light upon exposure to high-energy particles such as X-rays, is paramount to numerous technologies . Its role is particularly prominent in X-ray imaging and characterization, where scintillators are crucialfor converting X-ray energy into visible light, which can then be detected and analyzed. Advances in bulk scintillator processing have been key to their widespread adoption in X-ray imaging applications . Techniques like the Czochralski and Bridgman methods are highly scalable and have been adapted to produce large, high quality scintillator crystals in bulk. Other established techniques such as thermal evaporation and sol-gel methods have also been successfully tailored for large-area polycrystalline scintillator manufacturing.
[0009] An emerging approach in scintillator research - coined "nanophotonic scintillators" - includes structuring scintillator materials at the scale of their emission wavelength to control their emission properties, such as their light yield, emission, directionality detection efficiency, and timing. Such enhancements open up new possibilities for more precise and efficient X-ray imaging technologies . Such nanophotonic scintillators are not limited to scintillator materials for X-rays but may also extend to semiconductor-based electroluminescent materials used in light emitting diodes (LEDs) .
[0010] Despite these promising results, the widespread adoption of nanophotonic scintillators is hindered by challenges in scalable fabrication techniques . Current top-down fabrication methods, which rely on sophisticated lithographic techniques, offer nanometer-scale resolution and repeatability but are often complex, costly, difficult to scale to large areas, and not transferable to "unconventional" substrate materials such as scintillator crystals . On the other hand, bottom-up approaches such as laser printing, chemical or self-assembly methods, and topographical control of particle positioning have been exploredas alternatives . However, these methods come with their own set of limitations, including throughput constraints, surface defects, roughness, and restricted material choices, which also hinder their practical application.
[0011] To maximize the technological impact of nanophotonic scintillators, it would be beneficial to develop fabrication techniques that are scalable to industry-standard detector dimensions (~ cm) , while preserving enhancements obtained from nanophotonic patterning.
[0012] Summary
[0013] A large-area nanophotonic scintillator and associated fabrication methods are disclosed. In some embodiments, a nanophotonic extraction layer comprising discrete high refractive index scattering structures is formed on a scintillating substrate using scalable processes including nanoimprinting, templated selfassembly, and thermally induced reflow or dewetting of a deposited high refractive index material . The high refractive index scattering structures may have subwavelength or near-wavelength periodicity selected relative to the emission wavelength and effective medium index to enhance optical outcoupling.
[0014] The disclosed fabrication method enables formation of nanophotonic scintillators over centimeter-scale and larger areas compatible with industrial X-ray imaging formats . Compared to an unpatterned scintillator, the nanophotonic coating increases extracted photon flux by improving coupling of internally generated optical modes to radiative modes and reducing photontrapping within the high-index substrate . Because the fabrication approach relies on master mold replication and self-organized formation of discrete scattering structures, it provides high repeatability, substrate agnosticism, and scalability to large-area devices .
[0015] While demonstrated using cerium-doped yttrium aluminum garnet (Ce :YAG) scintillators, the disclosure is applicable to other scintillators and light-emitting media, including rare-earth-doped crystals, halide scintillators, perovskites, and electroluminescent semiconductors, where analogous nanophotonic structuring may enhance light extraction, emission directionality, and overall photon conversion efficiency.
[0016] According to one embodiment, a method of manufacturing an enhanced light emitting medium is disclosed. The method comprises forming a textured template layer on a light emitting medium; and forming, on the textured template layer, a plurality of discrete high refractive index scattering structures arranged according to the textured template layer, wherein forming the plurality of discrete high refractive index scattering structures comprises depositing a high refractive index material and thermally processing the high refractive index material to form the plurality of discrete high refractive index scattering structures .
[0017] In some embodiments, the textured template layer comprises an imprintable layer. In certain embodiments, the imprintable layer comprises a heat activated polymer, a heat activated thermoplastic, a photo activated polymer curable with UV, or an inorganic organic hybrid sol gel material .In certain embodiments, forming the textured template layer comprises nanoimprinting the imprintable layer . In certain embodiments, nanoimprinting the imprintable layer comprises pressing a stamp onto the imprintable layer . In certain embodiments, the stamp is replicated from a master mold. In certain embodiments, the master mold is formed by lithography. In certain embodiments, the lithography comprises interference lithography or electron beam lithography.
[0018] In some embodiments, the high refractive index material is deposited using physical vapor deposition, chemical vapor deposition, sputtering, atomic layer deposition, or solution processing .
[0019] In some embodiments, thermally processing the high refractive index material induces breakup, reflow, agglomeration, or Rayleigh type instability to form the plurality of discrete high refractive index scattering structures . In some embodiments, forming the plurality of discrete high refractive index scattering structures comprises patterned deposition, lift off, or etching. In some embodiments, forming the plurality of discrete high refractive index scattering structures comprises angled deposition or multi angle deposition with substrate rotation. In some embodiments, forming the plurality of discrete high refractive index scattering structures comprises solution deposition and consolidation of nanoparticles .
[0020] In some embodiments, the high refractive index material comprises an optical glass . In certain embodiments, the optical glass comprises a chalcogenide glass . In some embodiments, thehigh refractive index material comprises one or more of TiO2, Ta2Os, HfO2, ZrO2, SiO2, A12O3, SiNx, or Si .
[0021] In some embodiments, a cladding layer is formed over the plurality of discrete high refractive index scattering structures . In certain embodiments, the cladding layer comprises SiO2.
[0022] In some embodiments, the textured template layer defines a period selected based on an emission wavelength of the light emitting medium. In certain embodiments, the period is within 50 percent above or below the emission wavelength.
[0023] In some embodiments, a thickness of the imprintable layer is selected such that a surface of the light emitting medium in closest proximity with an imprinted pattern is located at an optically close distance from the plurality of discrete high refractive index scattering structures . In certain embodiments, the optically close distance is between 0 and 10 times A / n eff, wherein A is an emission wavelength of the light emitting medium; and n eff is an effective medium refractive index at a light emitting medium / coating interface .
[0024] In some embodiments, the light emitting medium comprises a scintillator . In certain embodiments, the scintillator comprises a rare earth doped oxide scintillator, halide scintillator, oxide and silicate based scintillator, plastic and organic scintillator, or perovskite and hybrid scintillator .
[0025] According to another embodiment, a scintillator is disclosed. The scintillator comprises a scintillating material; a textured template layer disposed on one surface of the scintillatingmaterial; and a plurality of discrete high refractive index scattering structures disposed on the textured template layer and arranged according to the textured template layer . In some embodiments, the textured template layer comprises an imprintable layer. In some embodiments, the textured template layer comprises a grid pattern. In certain embodiments, the grid pattern comprises a rectangular lattice, a hexagonal lattice, or an inverse-designed non trivial lattice .
[0026] In some embodiments, the plurality of discrete high refractive index scattering structures comprise nanospheroids, domes, caps, cones, or pillars .
[0027] In some embodiments, the scintillating material has an emission wavelength, and wherein a period of the textured template layer is within 50 percent above or below the emission wavelength.
[0028] In some embodiments, the scintillator comprises an enhancement of 2.6 or more as compared to the scintillating material without the textured template layer and the plurality of discrete high refractive index scattering structures .
[0029] In some embodiments, the scintillating material has dimensions of at least 40 mm x 40 mm. In some embodiments, the scintillating material has dimensions of at least 1 mm x 1 mm.
[0030] According to another embodiment, a light emitter is disclosed. The light emitter comprises a light emitting material; a textured template layer disposed on one surface of the light emitting material; and a plurality of discrete high refractive index scattering structures disposed on the textured templatelayer and arranged according to the textured template layer. In some embodiments, the light emitting material comprises an electroluminescent semiconductor material . In certain embodiments, the electroluminescent semiconductor material comprises gallium nitride (GaN) or indium gallium nitride ( InGaN) .
[0031] In some embodiments, the light emitting material has an emission wavelength, and wherein a period of the textured template layer is within 50 percent above or below the emission wavelength.
[0032] In some embodiments, the plurality of discrete high refractive index scattering structures comprise nanospheroids, domes, caps, cones, or pillars .
[0033] Brief Description of the Drawings
[0034] For a better understanding of the present disclosure, reference is made to the accompanying drawings, in which like elements are referenced with like numerals, and in which:
[0035] FIGs . 1A-1C show the fabrication process of the selfassembled nanophotonic scintillator;
[0036] FIG. 2 shows a cross-section of the self-assembled nanophotonic created using the fabrication process;
[0037] FIG. 3A is a photograph of large scale sample after fabrication of nanostructured layer on a 0.5 mm-thick YAG: Ce scintillator substrate ( IL sample) ;
[0038] FIG. 3B is a top view scanning electron micrograph of the dewetted nano-array (IL sample) ;
[0039] FIG. 3C is a zoomed-in top view (IL sample) ;FIG . 3D is a cross-sectional view of a single nanoparticle . From bottom to top, the cross-section shows the imprintable layer, a single chalcogenide nanoparticle, and air;
[0040] FIG . 4A is an intensity line scan (EL sample with tl = 1 mm) under X-ray exposure across unpatterned, coated, and patterned areas of the sample . The coating refers to the imprintable layer and silica cladding depicted in FIGs . 1A-1C and 2 , without chalcogenide . The pattern refers to the imprintable layer, chalcogenide nanoparticle and silica cladding;
[0041] FIG . 4B is the corresponding theoretical predictions for the unpatterned and patterned scintillators of FIG . 4A. Data is normalized to the mean signal value from the unpatterned signal ;
[0042] FIG . 4C is an intensity line scan ( IL sample with t2 = 0 . 5 mm) under X-ray exposure across unpatterned, coated, and patterned areas of the sample . The coating refers to the imprintable layer and silica cladding depicted in FIGs . 1A-1C and 2 , without chalcogenide . The pattern refers to the imprintable layer, chalcogenide nanoparticle and silica cladding;
[0043] FIG . 4D is the corresponding theoretical predictions for the unpatterned and patterned scintillators of FIG . 4C . Data is normalized to the mean signal value from the unpatterned signal ;
[0044] FIG . 4E is a Large-area nanophotonic scintillator benchmark : comparing light yield enhancement and patterned area for all comparable devices reported in the literature . The dot shading corresponds to the ratio of wavelength A to photonic crystal periodicity P . Subwavelength designs correspond to X / P > 1 .
[0045] FIGs . 5A-5F show X-ray imaging with large-area nanophotonic scintillators . FIGs . 5A and 5F are photographs of different obj ects to be imaged . The squares denote enlarged fields of view . FIGs . 5B, 5D and 5G are the corresponding raw X-ray images , whileFIGs . 5C, 5E and 5H are the corresponding flat-field corrected and contrast-adjusted X-ray images; and
[0046] FIGs . 6A-6F demonstrate controlling spatial resolution with disorder in photonic crystal scintillators . FIG. 6A shows the experimental setup for X-ray imaging with large-area nanophotonic scintillators . FIG. 6B shows the transfer function of the disordered photonic crystal modeled as a convolution between that of an ordered photonic crystal (PhC) and that of a disordered height map. FIG. 6C shows an atomic force micrographs (AFM) for EL samples . FIG. 6D shows an atomic force micrograph (AFM) for IL samples . FIGs . 6E-6F show the corresponding spatial resolution measurements in the presence of a razor blade to block part of the incoming X-rays . FIG. 6G shows the relative decrease in spatial resolution (increase in blur) as a function of the disorder root mean square (RMS) . Full lines are calculated for fields propagating through the whole scintillator (thickness t) , dashed lines for its effective thickness teff taking into account X-ray absorption. The dots represent measurements for the two samples (1 and 2 ) described herein .
[0047] Detailed Description
[0048] Definitions
[0049] For purposes of the present disclosure, the following terms are defined. These definitions are intended to clarify the description and are not intended to limit the scope of the disclosure unless expressly stated otherwise .
[0050] "Light emitting medium" refers to any material that emits electromagnetic radiation in response to excitation. Non limitingexamples include scintillators, phosphors, photoluminescent materials, electroluminescent materials, LEDs, OLEDs, quantum dot materials, and perovskite emitters . In some embodiments, the light emitting medium emits optical radiation in the visible or near visible range .
[0051] "Scintillator" refers to a material configured to emit optical photons responsive to incident high energy radiation, including X rays, gamma rays, and high energy particles . A scintillator may be a bulk scintillator, a thin film scintillator, a scintillator ceramic, or a composite scintillator .
[0052] "Nanophotonic scintillator" refers to a scintillator comprising a nanostructured extraction layer, coating, or surface modification configured to increase extracted photon flux from the scintillator relative to a corresponding scintillator without the nanostructure .
[0053] "Coating" refers to one or more layers disposed on a substrate, and may include one or more of an imprintable layer, a high refractive index layer, discrete nanostructures formed from a deposited film, or a cladding layer .
[0054] "Imprintable layer" refers to a layer configured to be textured by a stamp or mold. The imprintable layer may comprise a polymer, thermoplastic, photo activated polymer (for example UV curable) , heat activated polymer, or inorganic organic hybrid material including sol gel derived materials . The imprintable layer may serve as a template for subsequent formation or placement of a scattering array."Texturing" refers to formation of surface relief features on a layer or substrate, including recesses and / or protrusions . Texturing may be performed by imprinting, embossing, replication molding, interference lithography, electron beam lithography, photolithography, etching, laser based texturing, or combinations thereof . In some embodiments, the term "texturing" includes formation of a two dimensional array of features used as a template .
[0055] "Stamp" refers to a tool used to texture an imprintable layer . A stamp may comprise a polymeric stamp, an elastomeric stamp, or another tool replicated from a master mold. A stamp may be transparent to UV radiation. In some embodiments, stamps are prepared by drop casting a polymer on a silicon mold to create a s t amp .
[0056] "Master mold" refers to an original mold defining a surface pattern used directly or indirectly to form one or more stamps or secondary molds . The master mold may be formed using lithography, including electron beam lithography and or interference lithography.
[0057] "Photonic crystal" or "PhC" refers to a structured optical extraction layer comprising a periodic or guasi periodic modulation of refractive index or surface relief with a characteristic length scale comparable to an emission wavelength. As used herein, "photonic crystal" includes structures having controlled disorder and structures that are not perfectly periodic but retain extraction enhancement functionality.
[0058] "Grid pattern" refers to any two dimensional lattice defining textured regions and interstitial regions, which may be a singleor a multilayer. A grid pattern may include rectangular lattices, hexagonal lattices, and inverse designed non-trivial lattice types .
[0059] "Pyramids" refers to recesses, wells, or interstitial regions between grid lines in a textured template . The recesses need not be literal pyramids and may include tapered wells, rounded wells, or other textures .
[0060] "Period" or "pitch (P) " refers to a repeating length scale of a patterned array, including a center to center distance between adjacent features, a repeat distance of a lattice, or an average repeat distance in the case of quasi periodic patterns .
[0061] "Subwavelength" refers to a structure having a period P selected relative to an emission wavelength X. In some embodiments, the period P is within 50 percent above or below the emission wavelength X.
[0062] "High refractive index" refers to a refractive index greater than that of the surrounding medium at an emission wavelength of the light emitting medium. In some embodiments, high refractive index refers to n > 1.7. In some embodiments, n > 2.0. In some embodiments, n > 2.2. Chalcogenide glasses are examples of high refractive index materials .
[0063] "Optical glass" refers to an inorganic material capable of transmitting light in at least a portion of the visible and or near infrared spectrum and having a glass transition temperature . "Optical glass" may include oxide glasses, fluoride glasses, chalcogenide glasses, and hybrid organic inorganic sol gel derivedglasses . In some embodiments, the optical glass is a chalcogenide glass deposited as a thin film and subj ected to annealing.
[0064] "Templated dewetting" refers to a process in which a deposited layer rearranges during thermal processing to form discrete structures, where the arrangement or placement of such structures is influenced by an underlying textured template . In some embodiments, templated dewetting includes one or more of thin film breakup, capillary driven reflow, agglomeration, spinodal dewetting, or Rayleigh type instability, resulting in discrete features guided by the textured template .
[0065] "Nanoparticle array" refers to a plurality of discrete features formed from a deposited high index layer . The "nanoparticles" need not be separately synthesized particles . The term includes features formed by dewetting or reflow of a thin film to form nanospheroids, domes, caps, or similar geometries .
[0066] "Nanospheroid" refers to a discrete feature having a generally rounded or partially rounded geometry. Nanospheroids may include spherical cap like structures, hemispherical structures, ellipsoidal structures, and rounded dome structures . The nanospheroids may be formed by annealing above a glass transition temperature to induce rearrangement of a thin film into highly ordered features .
[0067] "Cladding layer" refers to a protective layer disposed over a nanoparticle array or other surface structures . In some embodiments, the cladding layer comprises SiO2deposited to reduce oxidation or environmental degradation of the nanoparticle array."Optically close distance" refers to a distance between (i) a region of the scintillator surface producing or guiding optical radiation and (ii) a scattering array or textured interface, where the distance is sufficiently small to couple optical fields to the scattering array. In some embodiments, an optically close distance is defined to be between 0 and 10 times X / n eff, where X is the emission wavelength and n_eff is the effective medium refractive index at the scintillator / coating interface .
[0068] "Effective medium index" or "n_eff" refers to an effective refractive index associated with a composite interface region, including contributions of the scintillator substrate, imprintable layer, nanoparticle array, and surrounding medium.
[0069] "Disorder" refers to deviations from ideal periodicity in a patterned array, including variations in feature placement, feature height, feature diameter, feature shape, missing features, and line edge roughness . In some embodiments, disorder is characterized by height maps obtained from atomic force microscopy and extracted using Fourier analysis .
[0070] "Controlled disorder" refers to disorder that is intentionally selected or engineered, for example to tune an extraction and spatial resolution tradeoff .
[0071] "Spatial resolution" refers to the ability of an imaging system to resolve spatial features . In some embodiments herein, spatial resolution is characterized by imaging a sharp edge (for example a razor blade) and extracting a line spread function and full width at half maximum (FWHM) . A relative decrease in resolution may be defined as a ratio of FWHMs (disordered photonic crystal vs flatreference) , wherein values greater than 1 correspond to greater blur .
[0072] "EL sample" refers to a device or sample fabricated using electron beam lithography derived molds . "IL sample" refers to a device or sample fabricated using interference lithography derived molds . These terms are used as example embodiments and are not limiting.
[0073] "Large area" refers to a patterned area larger than about 1 cm2. In some embodiments, large area refers to at least 10 cm2. In some embodiments, at least 100 cm2.
[0074] The fabrication methods described herein may be used to form a nanophotonic coating (including a photonic crystal or photonic crystal like scattering layer) on a scintillating substrate or, more generally, on any light emitting medium. In some embodiments, the nanophotonic coating comprises a plurality of discrete high refractive index scattering structures ( for example spheroids, domes, caps, cones, pillars, or other features) disposed on a textured template layer .
[0075] (i) Materials
[0076] The scattering structures may comprise an optical material selected to provide a refractive index higher than that of the surrounding medium at an emission wavelength and sufficiently low optical loss over the relevant spectral band. Non-limiting examples of suitable materials include optical glasses (including heavy metal oxide glasses, phosphate glasses, fluorophosphate glasses, tellurite glasses, high index silicate glasses,lanthanide containing glasses, specialty fluoride glasses, and hybrid organic inorganic sol gel derived glasses) , chalcogenide glasses, and high refractive index inorganic dielectrics or semiconductors (including TiO2, Ta2O5, HfO2, ZrO2, SiO2, A12O3, SiNx, Si, or combinations thereof) .
[0077] Further, while a Ce :YAG bulk scintillator was used in the testing, other scintillators may be used, including but not limited to rare earth doped oxide scintillators, halide scintillators, oxide and silicate based scintillators, plastic and organic scintillators, and perovskite and hybrid scintillators . Non limiting examples include : (i) rare earth doped oxide scintillators, including cerium doped yttrium aluminium garnet (Ce :YAG) , LYSO (Lui . 8Y0 . 2SiO5 (Ce) ) , LSO (Lu2SiO5) , YAP (YA103 : Ce) , LuAG (Lu3A15O12 : Ce) , Gd2SiO5 (GSO: Ce) , YV04 : Eu, and Gd2O2S (GOS : Ce) ; (ii) halide scintillators, including CsI (Tl) , CsI (Na) , Nal (Tl) , BaF2, LaBr3 (Ce) , CeBr3, SrI2 (Eu) , and Lil (Eu) ; (iii) oxide and silicate based scintillators, including BGO (Bi4Ge3O12 ) , PbWO4 (PWO) , ZnW04, CdWO4, and CaWO4 ; (iv) plastic and organic scintillators, including polyvinyl toluene (PVT) , BCF 10, BCF 12, BC 408, commercial plastic scintillators (Saint Gobain, Elj en Technology, etc . ) , anthracene, and liquid scintillators (EJ 301, BC 501A) ; and (v) perovskite and hybrid scintillators, including MAPbBr3 and CsPbBr3.
[0078] (ii) Example Fabrication Process
[0079] This process begins with the fabrication of a silicon master mold by traditional lithographic techniques . Both interference lithography and electron beam lithography may be used to make distinct molds, enabling different trade-offs between patternedarea and resolution. The sample prepared with electron beam lithography (EL) extends over an area 4 mm * 4 mm, while the sample prepared with interference lithography ( IL) extends over a much larger area of 4 cm x 4 cm. Note, however, that much larger dimensions are also possible .
[0080] Specifically, as noted above, a first mold (Mold 1 ) is prepared by electron beam lithography over an area of 4 mm x 4 mm. Note that other areas, such as 1 mm x 1 mm or larger, are also possible . Following oxygen plasma cleaning and HMDS monolayer deposition, a negative electron beam resist (maN 2403, MicroResist Technology GmbH, Germany) is spun at 3000 rpm on a silicon wafer covered with a 30nm native oxide . The resist is soft baked at 90 °C for 2 min. An inverted grid pattern is written using an electron beam having a suitable voltage and current .
[0081] This grid may be any suitable lattice types, including rectangular, hexagonal, and inverse-designed non trivial lattice types . The areas between the grid lines may be referred to as pyramids . Furthermore, the period of the grid may be within 50% (above or below) of the emission wavelength, which may significantly enhance scattering. In one specific embodiment, a rectangular grid with a period of 450 nm was used. The resist is developed using a TMAH-based developer (AZ-726, MicroChemicals GmbH, Germany) for 2 min. The native oxide is selectively etched using ICP reactive ion etching (RIE 230iP, Samco, Japan) with fluorine chemistry.
[0082] A second mold (Mold 2 ) is prepared by interference lithography over an area of 40mm * 40mm. Note that larger molds may be madeusing this method. A HeCd laser source (A = 325nm) is directed at a pinhole placed approximately 60 cm away from a Lloyd' s mirror setup. An antiref lective coating layer is spun at 3500 rpm onto a silicon wafer with a 30nm native oxide (AZ Barli II 90, iMicroMaterials, Germany) , and baked at 180 °C for 1 min. A layer of positive photoresist (AZ 3312, iMicroMaterials, Germany) is spun at 5000 rpm over the antiref lective coating, followed by a soft bake at 110 °C for 1 min. The second mold is exposed with an MLA 150 Advanced Maskless Aligner (Heidelberg Instruments, Germany) at 135 pC / cm2, followed by a post-exposure bake at 110 °C for 2 min. The photoresist is developed in AZ 726 for 2 min. The native oxide and antiref lective coating are etched using ICP reactive ion etching (RIE 2301P, Samco, Japan) with fluorine chemistry .
[0083] While interference lithography is described above, alternate direct writing techniques may be used, including focused ion beam lithography, two photon polymerization, scanning probe lithography and proj ection maskless lithography.
[0084] Both resulting molds are then stripped with an oxygen plasma cleaning step (e3511 Plasma Asher, ESI, USA) . The resulting silicon wafer is placed in a 251KOH solution at 60 °C for anisotropic silicon etching for 2 min. The native oxide hard mask is stripped with a 1 min dip in diluted HF 10 : 1. Alternative microfabrication techniques that rely on other wet or dry etching processes to transfer the lithographic pattern to the substrate are also possible .
[0085] In some embodiments, the resulting molds may be fabricated to optimize performance . Specifically, as noted above, theperiodicity of the grids (which is defined as the width plus the spacing of the grids) may be within 50% of the wavelength emitted by the scintillator . The width of the grids may be minimized as a percentage of overall pitch size . For a pitch of 450 nm, the grid linewidth may be approximately 50 nm or less . The depth of the pyramids in the grid may be between 0.1 and 5 times the period.
[0086] In the next process step, nanoimprint lithography may be leveraged to reproduce the master texture onto the bulk scintillator or other light emitting medium. Specifically, in one embodiment, the resulting silicon mold is treated with an antisticking layer ( Trichloro ( 1H, 1H, 2H, 2Hperf luorooctyl ) silane, Millipore Sigma, USA) in a vacuum desiccator following a short oxygen plasma surface activation. A (poly) dimethylsiloxane layer (PDMS Sylgard 184, Corning, USA) is drop-casted on the silanized mold and cured at 80 °C for 2 h. Upon curing, the PDMS layer is peeled off from the mold. This PDMS layer may be referred to as the PDMS stamp . This stamp may or may not be etched. In other embodiments, a different material may be used to make the stamp . These materials include other polymers or materials that are capable of transferring the pattern from the silicon mold, such as a fluorinated UV curable polymer, nickel and others .
[0087] This stamp, replicated from a silicon master mold, is then pressed onto a UV-curable imprintable layer 20 which is disposed directly on the scintillator substrate 10 and exposed to ultraviolet light, as shown in FIG. 1A. Specifically, in one embodiment, a thin layer of a diluted UV-Curable polymer (Ormocer, MicroResist Technology, Germany) is spun onto the Ce :YAG bulk scintillator . Note that other polymers may be used. For example, UV-Curable Polymers, such as mr-UVCur (MicroResist TechnologyGmbH) , OrmoComp and OrmoStamp (microresist technology GmbH) , NOA Series (e . g. , NOA 61, NOA 65) (Norland Products) , UVP Series (Nissan Chemical) , SU-8 UV Resin (MicroChem Corp . ) , PETS (Polyethylene Glycol Diacrylate or Dimethacrylate) , and hybrid UV-Curable Materials (Organic-Inorganic) may be used. In other embodiments, hybrid UV-Curable Materials (Organic-Inorganic) , such as Zirconium-Silicon Based Hybrid Materials, Hybrid Sol-Gel Materials, and customizable / research-based polymers, such as pHEMA ( Poly ( 2-Hydroxyethyl Methacrylate) ) , PMMA-Based UV-Curable Variants, and Polyurethane Acrylates (PUA) may also be used as the imprintable layer.
[0088] The stamp is then pressed directly onto the imprintable layer 20. The thickness of the imprintable layer 20 may be selected such that the scintillator surface in closest proximity with the imprinted pattern may be located at an optically close distance from the actual scattering array. An optically close distance is defined to be between 0 and 10 times the distance defined by X / n eff wherein n eff is the effective medium index at the scintillator / coating interface .
[0089] A UV light source (X = 375 nm) is shone through the stamp to cure the imprintable layer 20, with a dose > 1500mJ / cm2. The stamp is then removed.
[0090] In a final process step, physical vapor deposition and dewetting is used to obtain a high-index nanoparticle array. In other embodiments, chemical vapor deposition or atomic layer deposition may be used. In another embodiment, solution processing may be used wherein a suspension of nanoparticles is used and thesolution film recedes from the pattern, leaving behind nanospheroids in the pyramids .
[0091] A thin layer of a high refractive index material, such as optical glass 30, is deposited using thermal evaporation, as shown in FIG. IB . Specifically, in one embodiment, a sub-lOOnm thin chalcogenide layer is deposited by thermal evaporation (PVD Products, USA) directly onto the patterned imprintable layer 20. The high refractive index material is thermally processed, such as by annealing above its glass transition temperature to dewet according to the underlying texture . The chalcogenide glass may be made using S-, Se- , or Ge- based chalcogens . As noted above, different optical glasses may also be used.
[0092] A final glass annealing step above its glass transition temperature induces the re-arrangement of the high refractive index material into a plurality of discrete high refractive index scattering structures 40. In some embodiments, the thermal processing induces breakup of the deposited film and capillary driven reflow and agglomeration of the high refractive index material into discrete features . In some embodiments, the breakup mechanism includes a Rayleigh type instability and or a spinodal dewetting mechanism, resulting in formation of nanospheroids, domes, or caps localized by the textured template . This plurality of discrete high refractive index scattering structures may be an array of highly ordered nanospheroids, as seen in FIG. 1C. The size of the nanospheroids may be selected to enhance spontaneous emission rates, and increase light extraction; maximize forward scattering and minimize backward scattering; and improve index matching between the scintillator material, the effective index ofthe coating (imprintable layer + nanoarray) and external medium (air or optical glue that makes connection with X ray detector) .
[0093] A cross-sectional view of the completed nanoscintillator is shown in FIG. 2. A cladding layer 50 may be formed on top of the plurality of discrete high refractive index scattering structures 40 to avoid future oxidation. In some embodiments, this cladding layer may be silica (SiO2) . This cladding layer 50 may be 15 nm, for example .
[0094] Precise process control may enable achieving defect-free nanostructures, as exemplified in FIG. 3A, which is a photograph of large scale sample after fabrication of nanostructured layer on a 0.5 mm-thick YAG: Ce scintillator substrate (IL sample) . The photonic crystals exhibits a subwavelength period of 450 nm, covering a total patterned area of 4 cm x 4 cm, therefore resulting around 10 billion nanoscale spheroids on the chip . FIG. 3B is a top view scanning electron micrograph of the dewetted nano-array ( IL sample) , while FIG. 3C shows a zoomed-in top view ( IL sample) . FIG. 3D is a cross-sectional view of a single discrete high refractive index scattering structure . From bottom to top, the cross-section shows the imprintable layer 20, and a single discrete high refractive index scattering structure 40.
[0095] (iii) Alternative fabrication processes
[0096] In other embodiments, the textured template layer and / or the plurality of high refractive index scattering structures may be formed using other manufacturing techniques . For example, the textured template layer may be produced by other variants ofnanoimprinting, including but not limited to step and repeat imprinting, roll to roll imprinting, thermal embossing, inj ection replication. In one embodiment, the stamp-based step may happen either before or after deposition of the layer of high refractive index material . The high refractive index material may be deposited using physical vapor deposition, chemical vapor deposition, sputtering, atomic layer deposition, solution processing, or combinations thereof, including deposition at non normal incidence angles (angled deposition) and or multi angle deposition with substrate rotation to tune feature shape and directionality. In some embodiments, the scattering structures are formed directly ( for example without dewetting) by patterned deposition, deposition through a patterned template, etching of a deposited high refractive index layer, and / or nanoparticle consolidation within the textured template . These implementations are nonlimiting, and the present disclosure is not restricted to a particular patterning mechanism, deposition method, or scattering feature formation route .
[0097] For example, in some embodiments, the plurality of discrete high refractive index scattering structures is formed by patterned deposition of the high refractive index material . A patterned resist layer may be formed on the textured template layer or on a substantially planar surface using photolithography, electron beam lithography, interference lithography, nanoimprint lithography, or a shadow mask. The high refractive index material may then be deposited by physical vapor deposition, sputtering, chemical vapor deposition, or atomic layer deposition. In embodiments using lift off, the patterned resist is removed after deposition to lift off excess material and leave behind discrete high refractive index scattering structures . In embodiments using etching, the highrefractive index material is first deposited as a continuous film and subsequently patterned by a dry etch or wet etch to define discrete scattering structures, followed by removal of any remaining resist or hard mask.
[0098] Scintillation Enhancement
[0099] Using a recent framework to model scintillation emission in nanophotonic structures, an enhancement in nanophotonic scintillation by amplifying light yield may be provided due to better in / out-coupling of light (which maps to an enhancement in non-equilibrium optical absorption in the scintillator layer, via Lorentz reciprocity) , as experimentally observed in FIGs . 4A and 4C . Taking the bare scintillator as a reference (no coating nor pattern) , in some embodiments, simulations suggest an increase in scintillation light yield of 3.48-fold (EL) and 6.96-fold (IL) . These enhancement values are confirmed experimentally, with Xray line scans showed in FIGs . 4A-4D: 3.00 ± 0.21 (EL) and 6. 62 ± 1. 6 ( IL) . FIG. 4A is an intensity line scan for the EL sample under X-ray exposure across unpatterned, coated, and patterned areas of the sample . FIG. 4B is the corresponding theoretical predictions for the unpatterned and patterned scintillators of FIG. 4A. Line 100 shows the normalized signal for the unpatterned area, while line 101 shows the normalized signal for the patterned area . Note that the patterned area of the EL sample shows an enhancement of 2. 6 as compared to an unpatented scintillating material . FIG. 4C is an intensity line scan for the IL sample under X-ray exposure across unpatterned, coated, and patterned areas of the sample . FIG. 4D is the corresponding theoretical predictions for the unpatterned and patterned scintillators of FIG. 4C . Data for FIGs .
[0100] 4B and 4D is normalized to the mean signal value from theunpatterned signal . Line 102 shows the normalized signal for the unpatterned area, while line 103 shows the normalized signal for the patterned area . Note that the patterned area of the IL sample shows an enhancement of 6.0 as compared to an unpatented scintillating material .
[0101] Since the fabricated structures are spheroids, these numerical simulations include a multi-step process that combines finite element methods and rigorous coupled wave analysis . Specifically, the nanophotonic scintillation enhancement is modeled using a three-step approach. The large thickness (in mm) of the scintillator and the complex geometry of the nanophotonic structure make it challenging to use a single computational tool with high efficiency and low computational cost . Therefore, a combination of finite element (FE) and rigorous coupled wave analysis (RCWA) methods is employed. The simulated nanophotonic scintillator includes a chalcogenide spheroid with a diameter of about 395 nm, a subwavelength period of 450 nm, an imprintable layer of 450 nm thickness, and scintillator substrate . The refractive index of SiO2is obtained from literature, while that of the Ormocer polymer (1.5) and YAG: Ce are given by the suppliers . The refractive index of chalcogenide is obtained from in-house ellipsometry measurements . All calculations were carried out in the wavelength range of 540 to 560 nm, with the YAG: Ce emission peak centered at 550 nm. A commercially available FE solver, COMSOL Multiphysics®, was used to model the electromagnetic response of the spheroid nanophotonic structure . Initially, the superstrate was simulated without YAG: Ce (polymer coating and chalcogenide Spheroid) . It was then combined with a thinner ( 1 pm) YAG: Ce scintillator to optimize the geometry. Next, the spheroids were replaced with multiple stacked cylinders that approximate theelectromagnetic response (transmission and reflection) of the full spheroid structure calculated in the first step (still with an FE solver) . This makes it possible to transition from FE simulations, where simulating a thick substrate would be difficult to model, to RCWA simulations, where the approximated structure and a thick substrate can be used since it is a semianalytical method. In the third step, an automatically dif erentiable RCWA solver was used to simulate the approximate geometry with the thick substrate . The absorption / emission (via reciprocity) within / from the volume of the scintillator is calculated for both polarizations (transverse electric (TE) and transverse magnetic (TM) ) and averaged to mimic unpolarized light . Finally, the enhancement factor was calculated as the ratio of the spectrally integrated emission of the patterned scintillator to the unpatterned scintillator.
[0102] The difference in nanophotonic scintillation enhancement between the two samples may be attributed to several factors . First, in simulations, it was found that thicker scintillators generally exhibit less nanophotonic enhancement, which is consistent with an analysis based on density of states (the samples' thickness are tl = 1 mm and t2 = 0.5 mm) . Second, the influence of different dewetting schemes and mold guality was experimentally observed.
[0103] Compared to previous works that aimed at realizing large area micro or nanostructures on scintillators, the present disclosure realizes almost a six-fold nanophotonic enhancement over a patterned area of >1, 600 mm2(which is only limited by the size of the available scintillators) . An overview of the state of the art is shown in FIG. 4E . Previous work with comparably large patterned areas realized enhancements of ~ 1.3.This five-fold improvement over the state of the art is attributed to the use of subwavelength nanophotonic structures . Periodic nanophotonic structures of period P such that X / P > 1 are known to be optimal in terms of density of states enhancement . The fact that the present disclosure is compatible with patterning of high index, subwavelength structures is therefore key in scaling up nanophotonic scintillator technology to areas required for X-ray imaging applications .
[0104] Large Area X-Ray Imaging
[0105] Using the larger area IL sample ( 4 cm * 4 cm) in the Xray imaging setup shown in FIG . 6A, X-ray scans of inorganic and organic specimens were taken . The X-ray 70 strikes the surface of the scintillator 80 opposite the side with the nanospheroids 81 . Light is emitted from the side with the nanospheroids 81 and passes through an obj ective lens 90 and onto a light detector, such as a CCD detector 95. Each X-ray scan is taken in conj unction with an X-ray flat field image used for post-processing, and the final brightness and contrast are digitally adj usted ( as would be done in a commercial X-ray scanner for industrial or medical applications ) .
[0106] First, parts of a chicken foot ( tarsometatarsus and digits ) , shown in FIGs . 5A-5E, were imaged. FIG . 5A is a photograph of the chicken foot . Several phalanges separated by interphalangeal j oints are clearly visible : two proximal and middle phalanges in FIGS . 5B-5C (which are enlarged views of Box 120 ) , and two intermediate and distal phalanges in FIG . 5D-5E (which are enlarged views of Box 121 ) . FIGs . 5B and 5D show the corresponding raw X-ray images, while FIGs . 5C and 5E are the corresponding flat-field corrected and contrast-adjusted X-ray images . A USB stick was imaged, and the results are shown in FIG. 5F-5H. FIG. 5F is a photograph of the USB stick. FIG. 5G shows the corresponding raw X-ray image, while FIG. 5H is the corresponding flat-field corrected and contrast-ad usted X-ray image (which are enlarged views of Box 122 ) . Multiple levels of printed circuits overlayed on top of each other may be clearly distinguished. These images demonstrate the potential of the disclosed scintillators to realize X-ray scans of centimeter-large objects with nanophotonic enhancement .
[0107] All experiments, including imaging and measurements of scintillation enhancement and spatial resolution, were done using a custom-built experimental setup inside of a ZEISS Xradia Versa 620 micro-CT . Images were captured using a Hamamatsu ORCA- Fusion C14440-20UP CMOS camera along with a wide-f ield-of-view camera lens (Edmund Optics 33-304) . A narrow bandpass filter centered at 550 nm (AVR Optics, 15 nm bandwidth) was placed in front of the camera lens to minimize unwanted background from other wavelengths . In all experiments, the source was ds = 150 mm away from the scintillator, while the obj ect distance (do) depended on the desired geometric magnification of each image, defined as Mg = ds / do .
[0108] FIGs . 5B and 5D were captured under the following conditions : X-ray energy and power of 30 kVp and 2 W, exposure time of 10 s, binning of 4, and subarray of 144 x 144, and geometric magnification of 1.2. Finally, FIG. 5G was captured under the following conditions : X-ray energy and power of 60 kVp and 6.5 W, exposure time of 7 s, binning of 1, subarray of 576 x 576, andgeometric magnification of 2. Post-processing included flat-field correction and digitally adjusting brightness and contrast (see FIGs . 50, 5E and 5H) . The flat-fields were captured by simply removing the obj ects without changing any of the aforementioned parameters .
[0109] CONTROLLING SPATIAL RESOLUTION WITH DISORDER IN PHOTONIC CRYSTAL SCINTILLATORS
[0110] Next, the influence of fabrication disorder on the spatial resolution of nanophotonic scintillators was studied. When comparing atomic force microscopy (ARM, shown in FIGs . 6C-6D) images of the two samples, various levels of disorder are observed which may be attributed to the different lithography methods used to realize the nanoimprinting mold. A disorder distribution is extracted for both samples using Fourier analysis (see FIG. 6B) . Each sample' s spatial resolution was experimentally characterized by X-ray imaging the sharp edge of a razor blade (with a setup shown in FIG. 6A) .
[0111] Generally, a correlation is observed between greater amounts of nanof brication disorder and a decrease in the scintillator' s spatial resolution (blur increase) . Specifically, the nanofabricated pattern on the EL sample (see FIG. 6E) has no significant influence on its spatial resolution (with a slight relative decrease within experimental uncertainty) . However, the IL sample (see FIG. 6F) exhibits a decrease in relative spatial resolution by a factor of 2.48 + 0.10.
[0112] To account for the influence of disorder on spatial resolution, a framework of stochastic surface transfer functionswas adapted to X-ray scintillation imaging. The disorder distribution from AFM measurements is modeled as a Gaussian-distributed surface transfer function that blurs optical waves incident from within the scintillator. The relative decrease in spatial resolution for both samples was calculated (corresponding to an increase in optical blur, shown in FIG. 6G) , with scintillation emission happening on the front facet of the scintillator (propagation through thickness t) and at the mean X-ray absorption position (propagation through thickness teff) • The relative decrease in resolution is defined as the ratio of full widths at half maxima of the line spread functions ( for a disordered photonic crystal vs . a flat scintillator surface) - a value > 1 corresponding to a decrease in resolution, greater blur, and coarser features of the X-ray scan. These ab initio disorder simulations agree within 7% (comparing data from the EL sample and simulations for tl, eff ) and 15% (comparing data from the IL sample and simulations for t2 ) . The remaining discrepancy originates from the uncertainty in the depth at which the imaging obj ective is focused .
[0113] The methods are also applicable to other light-emitting media including electroluminescent semiconductors (e . g. , GaN / InGaN LEDs) , where analogous nanophotonic structuring can improve light extraction and directionality.
[0114] The system described above has many advantages . This disclosure describes a platform for nanophotonic scintillation that may combine the following features :
[0115] ( 1 ) compatibility with > centimeter-scale fabrication methods, to enable large-area X-ray imaging;(2 ) subwavelength feature sizes, to maximize nanophotonic outcoupling;
[0116] (3) absence of residual layer, which may enhance nanophotonic outcoupling by reducing parasitic guided modes, scattering losses, and spectral and angular sensitivity;
[0117] (4 ) low-loss high-index (n > 2 ) nanostructures, ; and
[0118] (5) high repeatability since a master mold can be used to generate thousands or tens of thousands of large-area nanophotonic scintillators .
[0119] The combination of these features enables scintillation enhancement over scales commensurable with that of commercial X-ray flat panel detectors and provides a path towards their mass production. Additionally, a clear correlation has been established between nanofabrication disorder and spatial resolution decrease . Improvements in mold quality realized with interference lithography lead to lower amounts of nanofabrication disorder and little to no decrease in the scintillator' s spatial resolution, while improving scintillation light yield six-fold compared to the bare scintillator.
[0120] The present disclosure is not to be limited in scope by the specific embodiments described herein . Indeed, other various embodiments of and modifications to the present disclosure, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings . Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure . Further, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those ofordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes . Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.
Claims
What is claimed is :
1. A method of manufacturing an enhanced light emitting medium, comprising:forming a textured template layer on a light emitting medium; andforming, on the textured template layer, a plurality of discrete high refractive index scattering structures arranged according to the textured template layer,wherein forming the plurality of discrete high refractive index scattering structures comprises depositing a high refractive index material and thermally processing the high refractive index material to form the plurality of discrete high refractive index scattering structures .
2. The method of claim 1, wherein the textured template layer comprises an imprintable layer .
3. The method of claim 2, wherein the imprintable layer comprises a heat activated polymer, a heat activated thermoplastic, a photo activated polymer curable with UV, or an inorganic organic hybrid sol gel material .
4. The method of claim 2, wherein forming the textured template layer comprises nanoimprinting the imprintable layer .
5. The method of claim 4, wherein nanoimprinting the imprintable layer comprises pressing a stamp onto the imprintable layer.
6. The method of claim 5, wherein the stamp is replicated from a master mold.
7. The method of claim 6, wherein the master mold is formed by lithography.
8. The method of claim 7, wherein the lithography comprises interference lithography or electron beam lithography.
9. The method of claim 1, wherein the high refractive index material is deposited using physical vapor deposition, chemical vapor deposition, sputtering, atomic layer deposition, or solution processing.
10. The method of claim 1, wherein thermally processing the high refractive index material induces breakup, reflow, agglomeration, or Rayleigh type instability to form the plurality of discrete high refractive index scattering structures .
11. The method of claim 1, wherein forming the plurality of discrete high refractive index scattering structures comprises patterned deposition, lift off, or etching.
12. The method of claim 1, wherein forming the plurality of discrete high refractive index scattering structures comprises angled deposition or multi angle deposition with substrate rotation.
13. The method of claim 1, wherein forming the plurality of discrete high refractive index scattering structures comprises solution deposition and consolidation of nanoparticles .
14. The method of claim 1, wherein the high refractive index material comprises an optical glass .
15. The method of claim 14, wherein the optical glass comprises a chalcogenide glass .
16. The method of claim 1, wherein the high refractive index material comprises one or more of TiO2, Ta2O5, HfO2, ZrO , SiO2, A12O3, SiNx, or Si .
17. The method of claim 1, further comprising forming a cladding layer over the plurality of discrete high refractive index scattering structures .
18. The method of claim 17, wherein the cladding layer comprises SiO2.
19. The method of claim 1, wherein the textured template layer defines a period selected based on an emission wavelength of the light emitting medium.
20. The method of claim 19, wherein the period is within 50 percent above or below the emission wavelength.
21. The method of claim 2, wherein a thickness of the imprintable layer is selected such that a surface of the light emitting medium in closest proximity with an imprinted pattern is located at an optically close distance from the plurality of discrete high refractive index scattering structures .
22. The method of claim 21, wherein the optically close distance is between 0 and 10 times X / n_eff, wherein X is an emission wavelength of the light emitting medium; andn_eff is an effective medium refractive index at a light emitting medium / coating interface .
23. The method of claim 1, wherein the light emitting medium comprises a scintillator .
24. The method of claim 23, wherein the scintillator comprises a rare earth doped oxide scintillator, halide scintillator, oxide and silicate based scintillator, plastic and organic scintillator, or perovskite and hybrid scintillator .
25. A scintillator, comprising:a scintillating material;a textured template layer disposed on one surface of the scintillating material; anda plurality of discrete high refractive index scattering structures disposed on the textured template layer and arranged according to the textured template layer .
26. The scintillator of claim 25, wherein the textured template layer comprises an imprintable layer.
27. The scintillator of claim 25, wherein the textured template layer comprises a grid pattern.
28. The scintillator of claim 27, wherein the grid pattern comprises a rectangular lattice, a hexagonal lattice, or an inverse-designed non trivial lattice .
29. The scintillator of claim 25, wherein the plurality of discrete high refractive index scattering structures comprise nanospheroids, domes, caps, cones, or pillars .
30. The scintillator of claim 25, wherein the scintillating material has an emission wavelength, and wherein a period of the textured template layer is within 50 percent above or below the emission wavelength.
31. The scintillator of claim 25, wherein the scintillator comprises an enhancement of 2. 6 or more as compared to the scintillating material without the textured template layer and the plurality of discrete high refractive index scattering structures .
32. The scintillator of claim 25, wherein the scintillating material has dimensions of at least 40 mm x 40 mm.
33. The scintillator of claim 25, wherein the scintillating material has dimensions of at least 1 mm * 1 mm.
34. A light emitter, comprising:a light emitting material;a textured template layer disposed on one surface of the light emitting material; anda plurality of discrete high refractive index scattering structures disposed on the textured template layer and arranged according to the textured template layer .
35. The light emitter of claim 34, wherein the light emitting material comprises an electroluminescent semiconductor material .
36. The light emitter of claim 35, wherein the electroluminescent semiconductor material comprises gallium nitride (GaN) or indium gallium nitride ( InGaN) .
37. The light emitter of claim 34, wherein the light emitting material has an emission wavelength, and wherein a period of the textured template layer is within 50 percent above or below the emission wavelength.
38. The light emitter of claim 34, wherein the plurality of discrete high refractive index scattering structures comprise nanospheroids, domes, caps, cones, or pillars .