nanomaterials

Article Design and Modeling of Light Emitting Nano-Pixel Structure (LENS) for High Resolution Display (HRD) in a Visible Range

Tsion Eisenfeld 1 and Avi Karsenty 1,2,* 1 Advanced Laboratory of Electro-Optics (ALEO), Department of Applied Physics/Electro-Optics Engineering, Lev Academic Center, Jerusalem 9116001, Israel; [email protected] 2 Nanotechnology Center for Education and Research, Lev Academic Center, Jerusalem 9116001, Israel * Correspondence: [email protected]; Tel.: +972-2-675-1140



Received: 7 January 2020; Accepted: 24 January 2020; Published: 27 January 2020


Abstract: LENS (Light Emitting Nano-pixel Structure), a new nano-metric device, was designed, simulated, and modeled for feasibility analysis, with the challenge of combining high resolution and high brightness for display, essentially adapted for Augmented Reality (AR) and Virtual Reality. The device is made of two parts: The first one is a reflective nano-cone Light Emitting Device (LED) structure to reduce the Total Internal Reflection effects (TIR), and to enable improved light extraction efficiency. The second part is a Compound Parabolic Concentrator (CPC) above the nano-LED to narrow the outgoing light angular distribution so most of the light would be “accepted” by an imaging system. Such a way is drastically limiting any unnecessary light loss. Our simulations show that the total light intensity gain generated by each part of the pixel is at least 3800% when compared to a typical flat LED. It means that, for the same electrical power consumption, the battery life duration is increased by 38. Furthermore, this improvement significantly decreases the display thermal radiation by at least 300%. Since pixel resolution is critical to offer advanced applications, an extensive feasibility study was performed, using the LightTools software package for ray tracing optimization. In addition to the simulation results, an analytical model was developed. This new device holds the potential to change the efficiency for military, professional and consumer applications, and can serve as a game changer.

Keywords: nano pixel; light emitting diode (LED); enhanced efficiency; augmented reality (AR); virtual reality (VR); modeling

1. Introduction

1.1. The Need for a Nano-Display In the age of Full High Definition screens, the largest companies are engaged in hard technological battles in order to achieve ever larger image resolutions [1]. The sharper the image, the more it appears to be real, thus reaching the limits of the eye’s visual acuity, less than 1 arc minute per line pair [2]. As part of the candidate applications, one can find the living room’s and computer’s screens, but also smartphone’s screens and, more recently, headsets of virtual reality (oculus) and augmented reality (Lumus [3], Microsoft HoloLens [4]). There is a clear need for Nano-Display. If it is true that for the moment that the pixels are the size of about 50 to less than 10 microns [5] depending on the application, the day will come when the thirst for resolution will lead us to develop pixels smaller than a micrometer. Researchers will continue to push manufacturing limits even further. This is called nanotechnology. In fact, nanotechnology has been able to meet the highest requirements of transistor manufacturers (Intel, AMD, Qualcomm, ARM, Nvidia...)

Nanomaterials 2020, 10, 214; doi:10.3390/nano10020214 www.mdpi.com/journal/nanomaterials Nanomaterials 2020, 10, 214 2 of 23 by allowing component manufacturing of a few nanometers in width [6]. Nanotechnology has allowed to considerably increase the number of these small precious devices, and thus to constantly improve the computing power of our computers [7]. Today, Extreme UV photolithography manufacturing method has dramatically decreased the size of the transistors. Thus, applying to the world of display, nanotech has the potential to multiply the number of pixels on the same surface size as for transistors on a chip. However, for what reason would we want to start this nano-pixel race? Is the resolution of displays not already sufficient? Is the quest at the highest resolution not vain and useless? What characterizes high technology is the ability to offer new products and open up new horizons that until now had no particular need. Who would have thought that we would need a mobile phone that can photograph, film, and visualize everything directly on a high-quality color screen and even share it with family without taking a step? The technological advance indisputably sets the pace for manufacturers and consumers by offering them the products that, in addition to entertaining, advance the well-being of the human race and create new tools that are constantly improving. Today, it is acceptable to forecast that the future applications, based on very high-resolution screens, will certainly be optical systems such as Augmented Reality (AR) glasses and Virtual Reality (VR) headsets, where a high pixel resolution is required in very small size displays. For example, nowadays, the Himax company manufactures micro-display specially designed for headsets and sharing a resolution of 1024 768 pixels in a display size of 0.45” [8]. × The AR/VR market is estimated to exceed $100 billion in the coming years [9]. Such AR glasses directly project into the eye large and versatile quantities of data, without having to look at a smartphone screen. In addition, 3D objects will sneak into our field of vision and will be an integral part of our environment [10]. However, in order to reach such a milestone, AR glasses developers will have to find a way to make their eyewear aesthetic, lightweight, and easy to wear. In addition, the image quality will be paramount to ensure the best possible experience for the user [11]. Several parameters are essential to maintain a reasonable Head Mounted Displays’ (HMD) form factor while maintaining a good image quality. The screen or micro-display must be of the smallest possible size while ensuring sufficient resolution. Today, consumers’ resolution requirements are Full High Definition (FHD) and more. How to fit such a quantity of pixels on a surface of a few millimeters? Obviously, nanotechnology could then give a solution as it does for electronic chips. Pixels, smaller than one micrometer, will keep the same number of pixels as for a high-resolution computer screen but on a much smaller surface. As a result, the optical system responsible for projecting the image into the user eye would see its size reduced, substantially making these glasses less cumbersome. Nano displays are a game changer which enables reaching higher image resolution while maintaining very compact display panel dimensions. This is critical to ensure a good image quality in an acceptable form factor. Generally, the more the pixel count grows, the more the screen size expands. To shrink display dimensions, pixels need to reduce its size. Sub-micron pixels, in the nano scale, are without a doubt the holy grail of compact displays. Some future technologies will be completely dependent on nano pixels such as augmented reality contact lenses. Nano displays will ensure a small enough form factor, very high pixel resolution aside, with minimum thermal radiation.

1.2. Augmented and Virtual Reality (AR/VR) Head Mounted Displays headsets and Augmented Reality glasses and even smart contact lenses will sooner or later become a new High-Tech revolution, as it happened with smartphones two decades ago. Such a new reality will change the way we communicate, drive, and look for useful information. The consumer will find himself in a hybrid world where three-dimensional objects and persons will be part of its real environment and background. The main challenge is that the created and projected artificial 3D objects and persons will be indistinguishable from real ones. Otherwise, the consumer immersion sensation will be compromised. Optical scientists and physicists are working hard to realize aesthetic Augmented Reality glasses and headsets with acceptable image quality. Today, AR optical engines have lower contrast ratio, colors purity, brightness, and less resolution than common TV and Nanomaterials 2020, 10, 214 3 of 23 computer screens. Furthermore, their large dimensions make them look ugly and displeasing to the common consumer, severely limiting their market applications. Moreover, a high illumination power requirement makes batteries endurance ephemeral, a couple of hours in the best case, and makes them look big. AR glasses or headsets will need to look the same or thinner than large sunglasses in order to be acceptable for the consumer market. In this research, we intend to address these requirements by developing a nano-display technology, gathering all the advantages and enabling a new kind of consumer experience. In other words, the challenging aim of this research is to develop a new designed display, sharing smaller dimensions while maintaining similar or better resolution, higher pixel extinction capability than Liquid Cristal based micro-displays, augmented light efficiency, and higher brightness than OLED based micro-displays. A first publication of such Super-High Intensity Nano-Emitting (SHINE) pixel only was recently presented [12].

1.3. LENS Proposed Solution Our innovation seeks to develop a new kind of display, essentially adapted for Augmented and Virtual Reality (AVR) application, where the pixel’s resolution is critical, in order to offer a valuable user-experience for military, industry and consumer applications. To be suitable, such a display requires a high resolution while maintaining small dimensions. The proposed monochromatic green Nano-LED is based on InGaN/GaN materials. Indeed, direct GaN-based green LED emits a narrower spectrum than the phosphor converted green LED. As a result, the direct GaN green has a higher purity green light [13]. Furthermore, the display brightness [14] and its power efficiency (Lumens/Watts) are two essential parameters allowing, or not, outdoor applications and long battery life. Since the thermal dissipation remains a complicate exercise in very compact systems, increasing the light efficiency enables reducing the display working temperature [15]. Our proposed solution to the power efficiency issue is twofold: First, a Reflective Nano Cone LED structure to reduce the Total Internal Reflection effects (TIR), and to enable improved light extraction efficiency—secondly, a Compound Parabolic Concentrator (CPC) above the Nano-LED to narrow the outgoing light angular distribution so most of the light would be “accepted” by an imaging system. Such a way is drastically limiting any unnecessary light loss. It was demonstrated in our simulations that, when combined, the cone Nano-LED and the CPC improve the power efficiency by around 3800% when compared to a conventional flat shape LED. The design of such a Reflective Cone Nano-LED is presented. As part of this research, the LightTools software package was used for the ray tracing optimization, and in addition to the numerical simulation results, an analytical model was developed, as presented below.

2. Device Concept and Structure

2.1. Existing Technologies in the Industry Before presenting our proposed solution, it is important to review the main four micro-display existing industrial technologies, as well as the recent progresses at the academy [16]:

1. The Liquid Crystal Display (LCD) [17] is a flat-panel display or other electronically modulated optical device which uses the light-modulating properties of liquid crystals. Liquid crystals do not emit light directly, instead using a backlight or reflector to produce images in color or monochrome. 2. The Liquid Crystal-On-Silicon (LCOS) [18] technology has been developed for many years for image and video display applications. This technology combines the unique light-modulating properties of Liquid Crystal (LC) materials and the advantages of high-performance silicon Complementary Metal Oxide Semiconductor (CMOS) technology through dedicated LCOS assembly processes. 3. The Organic Light-Emitting Diode (OLED) [19]: In organic light-emitting diodes, the electro luminescent material comprising the emissive layer of the diode is an organic compound. Nanomaterials 2020, 10, 214 4 of 23

Nanomaterials 2020, 10, 214 4 of 22 The organic material is electrically conductive due to the delocalization of electrons caused by conjugationby conjugation over all over or partall or of part the molecule,of the molecu andle, the and material the material therefore therefore functions functions as an organic as an semiconductor.organic semiconductor. Through electron–hole Through electron–hol recombination,e recombination, a high-energy a molecular high-energy state molecular is formed. Thisstate state is calledformed. exciton, This state behaves called like exciton, a single beha moleculeves like with a single high molecule energy, andwith generates high energy, light afterand an generates exciton lifetime light after period. an exciton lifetime period. 4. 4.The The Digital Digital Light Light Processing Processing (DLP) (DLP) [20 [20]:]: The The Digital Digital MirrorMirror DeviceDevice (DMD)(DMD) is a Micro Micro Electro Electro MechanicalMechanical System System (MEMS) (MEMS) device device invented invented in 1987. in 1987. The DMDThe DMD is designed is designed for projection for projection usage, whereusage, the tiltingwhere mirrorthe tilting pixels mirror reflect pixels the light reflect out ofthe the light projection out of lens.the projection Thus, the lens. DMD Thus, generates the a large,DMD bright generates and higha large, contrast bright image and inhigh comparison contrast image to other in displaycomparison technologies to other asdisplay LCOS, LCD,technologies or OLEDdisplays. as LCOS, LCD, or OLED displays.

2.2.2.2. Recent Recent Progress Progress in in Academy Academy TheseThese last last few few years, years, several several research research teams teams have have developed developed different different nano-pixels nano-pixels technologies: technologies: AA team team led led by by Oxford Oxford University University scientists scientists expl exploredored the the link link between between the the electrical electrical and and optical optical propertiesproperties of of phase phase change change materials materials (materials (materials that that can can change change from from an an amorphous amorphous to to a a crystalline crystalline state).state). They They found found that, that, by by sandwiching sandwiching a a seven-nanometer seven-nanometer thick thick layer layer of of a a phase phase change change material material betweenbetween two two layers layers of of a a transparent transparent electrode, electrode, they they could could use use a a tiny tiny current current to to ‘draw’ ‘draw’ images images within within thethe sandwichsandwich stackstack [21 [21].]. At McGillAt McGill University University and McMaster and McMaster University, University, multicolor multicolor single InGaN single/GaN InGaN/GaNdot-in-nanowire dot-in-nanowire Light Emitting Light Diodes Emitting (LEDs) Diodes were fabricated(LEDs) were on thefabricated same substrate on the same using substrate selective usingarea Epitaxy.selective Itarea is observed Epitaxy. thatIt is theobserved structural that andthe structural optical properties and optical of InGaNproperties/GaN of quantum InGaN/GaN dots quantumdepend criticallydots depend on nanowire critically on diameters nanowire [22 diameter]. A researchs [22]. teamA research from Illinoisteam from University Illinois University developed developeda hierarchical a hierarchical multicolor multicolor nano-pixel nano-pixel matrix formed matrix by formed coordinating by coordinating luminescent luminescent metal ions metal to a ionsconjugated to a conjugated poly (40-octyl-2 poly (40′,6-octyl-20-bispyrazoyl′,6′-bispyrazoyl pyridine) pyridine) film via film contact via printingcontact printing [23]. At the[23]. National At the NationalChiao Tung Chiao University Tung University in Taiwan, in aTaiwan, Nano-Ring a Na Light-Emittingno-Ring Light-Emitting Diodes (NRLEDs)Diodes (NRLEDs) with diff witherent differentwall width wall (120 width nm, 80(120 nm nm, and 80 40 nm nm) and were 40 nm) fabricated were byfabricated specialized by specialized nano-sphere nano-sphere lithography lithographytechnology [technology24]. [24].

2.3.2.3. LENS LENS Proposed Proposed Solution: Solution: Architecture, Architecture, Design Design and and Added Added Values Values TheThe LENS proposedproposed solution solution is madeis made of an of array an ofarray Green of Nano-LEDs Green Nano-LEDs with sub-micron with sub-micron dimensions, dimensions,660 nm diameter. 660 nm LENS diameter. itself is madeLENS of itself two parts:is made A reflectiveof two parts: conical Anano-pixel reflective structureconical nano-pixel and a light structurecondenser. and This a light reflective condenser. conical This structure reflective permits conical narrowing structure thepermits outgoing narrowing light angular the outgoing distribution light angularand thus distribution limits total and internal thus reflections limits total on internal the output reflections surface. on As the a result,output more surface. light As is alloweda result, tomore exit lightthe pixel is allowed as shown to exit in Figurethe pixel1. as shown in Figure 1.

FigureFigure 1. 1. PresentationPresentation of of aa cross cross section section of of an an array array of of two two adjacent adjacent LENS LENS devices. devices. The The design design includes includes aa Reflective Reflective Coned Coned Nano-Green Nano-Green LED LED with with a a Compound Compound Parabolic Parabolic Concentrator Concentrator (CPC). (CPC). The The figure figure is is voluntarilyvoluntarily not not to to scale scale in in orde orderr to to present present the the new new concept. concept.

Nanomaterials 2020, 10, 214 5 of 23 Nanomaterials 2020, 10, 214 5 of 22

AsAs part part of of future research, sub-wavelength dime dimensionsnsions green green LED LED will will be be investigated, investigated, with with a a 130130 nm diameter. Again, Again, a a reflective reflective conical conical nano-pix nano-pixelel structure structure to to allow allow a a better better Light Light Extraction efficiencyefficiency and and a a light light condenser will be considered as shown in Figure 2 2..

FigureFigure 2. 2. PresentationPresentation of of a a cross cross section section of of an an array array of of two two adjacent adjacent LENS LENS devices devices with with reduced reduced dimensions.dimensions. The The design design includes includes a a reflective reflective Co Conedned Nano-Green Nano-Green LED LED with with a a Compound Parabolic Parabolic ConcentratorConcentrator (CPC). (CPC).

ThereThere areare severalseveral bottlenecks bottlenecks that that the the present present study study aims aims to solve to solve or contribute or contribute for a better for solution:a better solution:Shrinking Shrinking the LED dimensionsthe LED dimensions avoids internal avoids light internal absorption, light essentiallyabsorption, from essentially the quantum from well.the quantumIn our study, well. a In proposed our study, 5 nm a proposed thickness 5 quantumnm thickness well quantum absorption well is asabsorption small as 0.5%.is as small Furthermore, as 0.5%. Furthermore,designing a conical designing shape a conical LED to shape recycle LED TIR trappedto recycle rays, TIR greatly trapped contributes rays, greatly in multiplying contributes thein multiplyingLight Extraction the Light Efficiency Extraction in comparison Efficiency to ain flat comparison shape LED. to Lambertiana flat shape light LED. angular Lambertian distribution light angularin a regular distribution LED results in a in regular unnecessary LED results light loss. in unnecessary Indeed, most light of the loss. light Indeed, shining most from of a the flat light LED shiningwon’t be from accepted a flat by LED an opticalwon’t be system accepted with by smaller an optical numerical system aperture. with smaller Thus, addingnumerical a Compound aperture. Thus,Parabolic adding Concentrator a Compound on theParabolic LED’s Concentrator top allows controlling on the LED’s accurately top allows the output controlling Light accurately beam angular the outputdistribution. Light beam This way, angular light distribution. is injected into This an way, optical light system is injected with littleinto oran nooptical light system loss. with little or no light loss. 3. Methods 3. Methods 3.1. Monte Carlo Ray Tracing Using LightTools Simulation Software

3.1. MonteAn optical Carlo condenserRay Tracing element Using LightTools has been designed Simulation in Software order to reduce the angular distribution of the Nano-LED pixel. In this case, the Monte Carlo ray tracing method is used to understand and determine An optical condenser element has been designed in order to reduce the angular distribution of a way to collect rays going out from the Nano-LED and to shape the outgoing beam with a reduced the Nano-LED pixel. In this case, the Monte Carlo ray tracing method is used to understand and numerical aperture. An optimization method is used to design the best condenser. determine a way to collect rays going out from the Nano-LED and to shape the outgoing beam with LightTools optical software has been selected to generate our Monte Carlo simulations. Built-in a reduced numerical aperture. An optimization method is used to design the best condenser. tools and modules have been used to optimize and analyze our investigated pixel. LightTools is a LightTools optical software has been selected to generate our Monte Carlo simulations. Built-in software especially adapted for non-sequential ray tracing, analysis, and optimization. Variables, tools and modules have been used to optimize and analyze our investigated pixel. LightTools is a constraints, and merit functions are set while proprietary algorithms within the LightTools optimization software especially adapted for non-sequential ray tracing, analysis, and optimization. Variables, engine will minimize the merit function by changing the defined variables and simultaneously satisfying constraints, and merit functions are set while proprietary algorithms within the LightTools the specified constraints. Different kinds of condensers were considered, for example conventional optimization engine will minimize the merit function by changing the defined variables and spherical lens, a-spherical lens, freeform shape, reflective walls, and total internal reflection lens. simultaneously satisfying the specified constraints. Different kinds of condensers were considered, Furthermore, Boolean operations can be done to make custom elements. This software allows us to for example conventional spherical lens, a-spherical lens, freeform shape, reflective walls, and total define any material with specific optical parameters from scientific literature: 1. Absorption Spectrum, internal reflection lens. Furthermore, Boolean operations can be done to make custom elements. This 2. Emission Spectra, 3. Intensity Distribution and other simulation parameters such as the number software allows us to define any material with specific optical parameters from scientific literature: of rays propagating from Nano-LED regions. Then, we will be able to realize a realistic model of 1. Absorption Spectrum, 2. Emission Spectra, 3. Intensity Distribution and other simulation parameters such as the number of rays propagating from Nano-LED regions. Then, we will be able to realize a realistic model of the LED and its material properties—in LightTools, when the

Nanomaterials 2020, 10, 214 6 of 23 the LED and its material properties—in LightTools, when the distribution from a light source can be simulated by tracing Monte Carlo rays. These rays are accumulated on receivers, and are used to compute illumination analysis metrics such as: Illuminance (spatial distribution of power), Intensity (Angular distribution of power), and Luminance (both angular and spatial components). When rays are collected on a receiver, the data are usually divided into rectangular grids to analyze ray data. Data can be displayed as numbers/color maps.

3.2. Physical Simualtions vs. Geometry Ray Tracing Monte Carlo ray tracing is a geometric approximation commonly used in optics. This method of light propagation ignores physical effect as wave effects, electrical behavior of the implicated materials, and more. When reducing the investigated element dimensions below the light wavelength scale, such approximations are useless. In the nano-scale, Maxwell equations are the ones able to simulate the light behavior. Furthermore, diode junction analysis cannot be simulated with a ray tracing software. As part of all the physical aspects of a light-emitting diode, we find the spectral spectrum of an active layer, the current–voltage curve, and the energy diagram. Thus, the necessity of complementing physical software, which are capable of running physical equations and algorithms, will become necessary in the future.

4. LightTools—Ray Tracing Results

4.1. Reflective Nano-Cone LED

4.1.1. Structure, Dimensions, and Light Path The first floor of the investigated pixel is a light-emitting diode which emits a green light by electron/hole recombination. The p-type/n-type (PN) junction is made of lnGaN/GaN material with a 525 nm wavelength spectral peak. The GaN refractive index equals 2.4, which is much higher than an amorphic optical material, typically with a refractive index equal to 1.5168 as for BK7 glass material [25]. The structure of the conical LED is presented in Figure3a. The emitting junction is a circular area located at a distance of 42 nm from the outgoing surface as shown in the same figure. The light emitting area is installed in a conical cavity with reflective outer surfaces allowing rays to be reflected out of the LED. The dimensions chosen for our simulations are presented in Figure3a where the conical base diameter is 664 nm, and the overall height 442 nm. This 3/2 structural ratio is the result of our optimization effort. The Merit function was built such that the maximum light power could exit the conical structure, which is to say in order to get the best light efficiency possible. The structure’s top is truncated in order to meet realistic manufacturing constraints since a perfect top is not realistic. Such a relatively small truncation has no significant performance repercussion. As Snell’s law describes it, when rays try to pass from an incident medium to another with a lower Refractive Index (RI), only a few portions of light will pass and the rest will be reflected back by what is call Total Internal Reflection (TIR). Rays with angles smaller than the material critical angle will manage to escape. Instead, rays having higher angles than the critical ones will experience a total internal reflection. We understand that the main challenge for a Light Emitting Diode (LED) is the light efficiency. Since the material used, lnGaN/GaN, has a high refractive index, only a relatively small angular range will manage to escape outside the LED as shown in Figure3b–d. Nanomaterials 2020,, 10,, 214 214 77 of of 22 23

(a) (b)

(b) (d)

Figure 3. 3. (a()a LENS) LENS pixel pixel Cone Cone LED LED structure; structure; (b) (ab )typical a typical ray path ray path inside inside a reflective a reflective conical conical LED obtainedLED obtained with LightTools with LightTools software; software; (c) inwards (c) inwards emission emission light path; light (d path;) outgoing (d) outgoing ray split ray by splitFresnel by reflection.Fresnel reflection.

4.1.2. Light Light Extraction Extraction Efficiency Efficiency (LEE) The Light ExtractionExtraction EEfficiencyfficiency (LEE) (LEE) is is a cruciala crucia parameter.l parameter. In orderIn order to enhance to enhance it, there it, there is a need is a needfor shrinking for shrinking the LED the dimensionsLED dimensions in order in toorder avoid to internalavoid internal light absorption light absorption and optimize and optimize the conical the conicalshape to shape recycle to recycle rays. This rays. greatly This greatly contributes contributes to multiplying to multiplying the Light the Extraction Light Extraction Efficiency. Efficiency. In such Ingeometry, such geometry, the light the is forced light tois forced exit the to LED. exit Ifthe it doesLED. not If it succeed does not at thesucceed first tentative,at the first the tentative, light will the be lightreflected will back be reflected and forth back again and and forth again again until and it finally again exits until the it structure. finally exits The the only structure. parameter The that only can parameteraffect the e ffithatciency can affect is the the reflective efficiency wall is and the internalreflective materials wall and absorption. internal materials This is whereabsorption. nano scaleThis iscomes where to shrinknano scale the distances comes to that shrink light travels,the distance avoidings that any light significant travels, absorption. avoiding any significant absorption.The total internal reflection constraint makes a GaN based LED light extraction very challenging. Indeed,The GaN’stotal internal RI is much reflection higher constraint than air’s makes Refractive a GaN index based reducing LED light significantly extraction very the criticalchallenging. angle Indeed,value. The GaN’s refractive RI is much indexes higher used than in this air’s research Refracti forve the index three reducing layers, are significantly respectively the 2.54 critical (Quantum angle 1 value.Well), 2.45The refractive (P-GaN), andindexes 2.42 used (N-GaN). in this The research corresponding for the three absorption layers, are coe respectivelyfficients are 2.54 1 µm (Quantum− for the Well),Quantum 2.45 Well,(P-GaN), and 0and for 2.42 the p-type(N-GaN). Gallium-Nitride The corresponding (P-GaN) absorption and n-type coefficients Gallium-Nitride are 1 µm (N-GaN)-1 for the Quantumlayers. Then, Well, the and theoretical 0 for the lightp-type extraction Gallium-Nitride efficiency (P-GaN) of a flat and LED n-type can be Gallium-Nitride given by the ratio (N-GaN) of the layers.solid angles Then, of the a conetheoretical with an light apex extraction of Ω = 2 efficiencyθc and a of sphere a flat solid LED angle can be of given 4π, as by shown the ratio in Figure of the4: × solid angles of a cone with an apex of Ω = 2 × θc and a sphere solid angle of 4π, as shown in Figure 4:

Nanomaterials 2020, 10, 214 8 of 23 Nanomaterials 2020, 10, 214 8 of 22

FigureFigure 4. 4.Projection Projection ofof a cone onto onto a asphere. sphere.

For a Lambertian angular distribution emitter: For a Lambertian angular distribution emitter: 𝟐 𝟐𝛑(𝟏𝐜𝐨𝐬 𝛉𝐜 ) (1) 𝐋𝐄𝐄 𝐥𝐚𝐦𝐛𝐞𝐫𝐭𝐢𝐚𝐧 𝐞𝐦𝐢𝐬𝐬𝐢𝐨𝐧= 𝟏𝟎𝟎 𝟒𝛑 2 2π(1 cos θc) LEE lambertian emission = − 100 (1) where Өc = 24.6° for a GaN material. Thus, the resulting theoretical4π light ×extraction efficiency is 8.66%. For a uniform angular distribution emitter: where Өc = 24.6◦ for a GaN material. Thus, the resulting𝟐𝛑(𝟏𝐜𝐨𝐬𝛉 theoretical𝐜 ) light extraction efficiency(2) is 8.66%. 𝐋𝐄𝐄 𝐮𝐧𝐢𝐟𝐨𝐫𝐦 𝐞𝐦𝐢𝐬𝐬𝐢𝐨𝐧= 𝟏𝟎𝟎 For a uniform angular distribution emitter: 𝟒𝛑 The resulting theoretical light extraction efficiency is 4.54%. 2π(1 cos θc) Furthermore, in orderLEE to elaborate uniform an emission accurate= theoretical− LEE model,100 Fresnel reflections should (2) be implemented to our equation. Indeed, rays coming out from4π the LED× are divided in two segments. TheOne resultingsegment exits theoretical the LED light and the extraction other one effi isciency reflected is 4.54%.back. The energy of the reflected segment and the transmitted one are a function of the Angle Of Incidence (AOI) and of the Refractive index Furthermore, in order to elaborate an accurate theoretical LEE model, Fresnel reflections should (RI) of both of the medium n1 and n2. The following are Fresnel reflections equations [26] as shown be implementedbelow: to our equation. Indeed, rays coming out from the LED are divided in two segments. One segment exits the LED and the other one𝐧 is𝟏𝐜𝐨𝐬𝛉 reflected𝐢 𝐧𝟐𝐜𝐨𝐬𝛉 back.𝐭 The energy of the reflected segment(3) 𝐫𝐬 = and the transmitted one are a function of the Angle𝐧𝟏𝐜𝐨𝐬𝛉 Of𝐢 +𝐧 Incidence𝟐𝐜𝐨𝐬𝛉𝐭 (AOI) and of the Refractive index (RI) of both of the medium n1 and n2. The following are𝟐𝐧 Fresnel𝟏𝐜𝐨𝐬𝛉𝐢 reflections equations [26] as shown(4) below: 𝐭𝐬 = 𝐧𝟏𝐜𝐨𝐬𝛉𝐢 +𝐧𝟐𝐜𝐨𝐬𝛉𝐭 n1 cos θi n2 cos θt rs = 𝐧𝟐𝐜𝐨𝐬𝛉−𝐢 𝐧𝟏𝐜𝐨𝐬𝛉𝐭 (5) (3) 𝐫𝐩 n=1 cos θi + n2 cos θt 𝐧𝟐𝐜𝐨𝐬𝛉𝐢 +𝐧𝟏𝐜𝐨𝐬𝛉𝐭

2n𝟐𝐧1 cos𝟏𝐜𝐨𝐬𝛉θi 𝐢 (6) ts =𝐭𝐩 = (4) n1 𝐧cos𝟐𝐜𝐨𝐬𝛉θi +𝐢 +𝐧n2 𝟏cos𝐜𝐨𝐬𝛉θt𝐭

where: rs is the light S polarization reflection,n2 rcosp forθ Pi polarization,n1 cos θt ts is the S polarization transmission, rp = − (5) and tp the P polarization one. The unpolarizedn2 cos transmθi +issionn1 cos forθt a specific AOI is then given by: 𝐭𝐮𝐧𝐩𝐨𝐥𝐚𝐫𝐢𝐳𝐞𝐝 =𝐭𝐬 +𝐭𝐩 (7) 2n1 cos θi tp = (6) Then, the unpolarized transmission forn2 acos rangeθi + ofn AOI1 cos isθ givent by: 𝛉𝐜 (8) where: rs is the light S polarization reflection, rp for𝐭𝐮𝐧𝐩𝐨𝐥𝐚𝐫𝐢𝐳𝐞𝐝 P polarization, ts is the S polarization transmission, 𝟎 and tp the P polarization one. The unpolarized transmission for a specific AOI is then given by: The updated LEE formula is for a Lambertian angular distribution emitter: 𝛉𝐜 tunpolarized = ts + tp (9) (7) 𝐋𝐄𝐄 𝐥𝐚𝐦𝐛𝐞𝐫𝐭𝐢𝐚𝐧′ =𝐭𝐮𝐧𝐩𝐨𝐥𝐚𝐫𝐢𝐳𝐞𝐝 𝟎 Then,The the expected unpolarized Light transmission Extraction efficiency for a range with ofFresnel AOI reflection is given by:took into account is then LEE

Lambertian = 6.9%. Simulation with LightToolsZ θc software have shown very similar results with LEE Lambertian = 8.6 % and LEE Lambertian = 6.85%. Side walls material absorption is also a critical tunpolarized (8) parameter influencing the real possible 0Light extraction efficiency. Two materials have been investigated, Silver and Aluminum. Silver has the highest possible reflection in the visible range, but The updated LEE formula is for a Lambertian angular distribution emitter:

Z θc LEE lambertian0 = tunpolarized (9) 0 Nanomaterials 2020, 10, 214 9 of 23

The expected Light Extraction efficiency with Fresnel reflection took into account is then LEE Lambertian = 6.9%. Simulation with LightTools software have shown very similar results with LEE Lambertian = 8.6 % and LEE Lambertian = 6.85%. Side walls material absorption is also a criticalNanomaterials parameter 2020, influencing10, 214 the real possible Light extraction efficiency. Two materials have9 of 22 been investigated,Nanomaterials Silver 2020 and, 10, 214 Aluminum. Silver has the highest possible reflection in the visible range,9 of 22 but it it is more expensive. However, Aluminum is a much cheaper material sharing a higher light is more expensive. However, Aluminum is a much cheaper material sharing a higher light absorption absorption As a result, it can be seen that LightTools simulation LEE results (Figure 5) are better for As a result,it is more it can expensive. be seen thatHowever, LightTools Aluminum simulation is a much LEE cheaper results (Figurematerial5 )sharing are better a higher for the light Silver the Silver material than for Aluminum. For Silver material, the cone has ~78% efficiency (Figure 5a), absorption As a result, it can be seen that LightTools simulation LEE results (Figure 5) are better for materialand for than Aluminum for Aluminum. material For~73% Silver (Figure material, 5b). This the is an cone improvement has ~78% of effi 900%ciency in comparison (Figure5a), to and a for the Silver material than for Aluminum. For Silver material, the cone has ~78% efficiency (Figure 5a), Aluminumflat LED. material ~73% (Figure5b). This is an improvement of 900% in comparison to a flat LED. and for Aluminum material ~73% (Figure 5b). This is an improvement of 900% in comparison to a flat LED.

(a) (b)

Figure 5. LightTools Light(a) Extraction Efficiency results. (a) results for Silver; (b)( resultsb) for Aluminum. Figure 5. LightTools Light Extraction Efficiency results. (a) results for Silver; (b) results for Aluminum. Figure 5. LightTools Light Extraction Efficiency results. (a) results for Silver; (b) results for Aluminum. 4.1.3.4.1.4. Emitter Emitter Position Position vs. vs. LEE LEE 4.1.4.As Emitter the layer Position is pushed vs. LEEaway from the exit, the LEE improves. This is explained by the fact that, As the layer is pushed away from the exit, the LEE improves. This is explained by the fact that, in these conditions, the number of reflections on the side walls is decreasing as a function of the layer in these conditions,As the layer the is numberpushed away of reflections from the exit, on thethe sideLEE wallsimproves. is decreasing This is explained as a function by the fact of thethat, layer location as shown in Figure 6. In the other hand, pushing back the emitting surface shrinks it because in these conditions, the number of reflections on the side walls is decreasing as a function of the layer locationof the as cone shown structure. in Figure As 6we. In reach the otherthe top hand, of the pushing cone, the back diameter the emittingsection decreases. surface shrinksThis way, it becausethe location as shown in Figure 6. In the other hand, pushing back the emitting surface shrinks it because of thetotal cone brightness structure. is much As wereduced. reach Then, the topa distance of the of cone, 42 nm the seems diameter to be an section acceptable decreases. solution, since This way, of the cone structure. As we reach the top of the cone, the diameter section decreases. This way, the the totalthe emitting brightness area isdecreases much reduced. much faster Then, than ath distancee efficiency of increases, 42 nm seems as shown to be in an Figure acceptable 7. solution, total brightness is much reduced. Then, a distance of 42 nm seems to be an acceptable solution, since since thethe emitting area area decreases decreases much much faster faster than than the efficiency the efficiency increases, increases, as shown as shownin Figure in 7. Figure 7.

Figure 6. Light Extraction Efficiency vs. Emitter Position. FigureFigure 6. Light 6. Light Extraction Extraction E Efficiencyfficiency vs.vs. Emitter Position. Position.

Nanomaterials 2020, 10, 214 10 of 23 Nanomaterials 2020, 10, 214 10 of 22

Nanomaterials 2020, 10, 214 10 of 22

Figure 7. Emitting area surface vs. area height. Figure 7. Emitting area surface vs. area height. 4.1.4.4.1.5. Outgoing Outgoing Light Light Angular Angular and and Spatial SpatialFigure Distribution 7. Distribution Emitting area surface vs. area height. In orderIn4.1.5. order to analyzeOutgoing to analyze the Light the light Angularlight distribution distribution and Spatial at at the Distributionthe conecone exit aperture, aperture, an an intensity intensity receiver receiver and andan an IlluminanceIlluminance receiver receiver were were placed placed after after the the exit, exit, in in ambient ambient air. air. Each Each receiver receiver displays displays its own its own results. results. The IlluminanceIn order information to analyze displays the light the distribution light power at asthe a cone function exit aperture,of the ray an incidence intensity location receiver on and an The Illuminance information displays the light power as a function of the ray incidence location on the the receiver.Illuminance Power receiver units are were in Lux.placed The after intensity the exit, receiver in ambient displays air. Eachthe power receiver of thedisplays rays incomingits own results. receiver.on the PowerThe receiver Illuminance units surface are in information Lux.as a function The intensity displays of their receiverthe angle light of displayspower incidence. as thea function The power resulting of of the the Illuminanceray rays incidence incoming spatial location on the on receiverdistribution surfacethe receiver. as is apresented function Power in ofunits Figure their are angle in8. UnitsLux. of The incidence.are intensityin Candela. The receiver resultingThe cross displays Illuminancesection the powershows spatial ofa batwing the rays distribution likeincoming is presenteddistributionon in the Figure wherereceiver8 .the Units surface power are as is in amore function Candela. concentrated of Thetheir cross angleat the section of edge incidence. of shows the aperture.The a batwing resulting A layout likeIlluminance distribution analysis spatial whereallows the powerdistribution us to visualize is more is presented the concentrated concerned in Figure rays at the 8.contributi Units edge are ofng in theto Candela. the aperture. central The area Across layoutand section to the analysis apertureshows allowsa batwingedges. us like to visualizeIn the the distributioncentral concerned area, rayswhere rays are contributingthe emitted power outward, is more to the then concentrated central reflected area backat and the by toedge TIR the and of aperture the reflected aperture. edges. outwards A Inlayout the again. centralanalysis allows us to visualize the concerned rays contributing to the central area and to the aperture edges. area, raysSome are rays emitted are reflected outward, by the then top of reflected the cone, back which by is TIR a plane and surface. reflected outwards again. Some rays In the central area, rays are emitted outward, then reflected back by TIR and reflected outwards again. are reflectedSome by the rays top are of reflected the cone, by whichthe top isof athe plane cone, surface. which is a plane surface.

(a) (b)

(a) (b)

Figure 8. Cont. Nanomaterials 2020, 10, 214 11 of 22 Nanomaterials 2020, 10, 214 11 of 23 Nanomaterials 2020, 10, 214 11 of 22

(c) (c) ((dd)) Figure 8. Outgoing Cone light spatial distribution obtained with LightTools software. (a) cone light; FigureFigure 8. OutgoingOutgoing Cone Cone light light spatial spatial distributi distributionon obtained obtained with with LightTools LightTools software. software. ( (aa)) cone cone light; light; (b) y-axis distribution; (c) x-axis distribution; (d) colors Legend in Lux units. ((bb)) yy-axis-axis distribution; distribution; ( (c)) x-axis-axis distribution; ( d) c colorsolors Legend in Lux units. 4.1.5. High4.1.6. Brightness High Brightness Conical Conical Emitter Emitter Layer Layer 4.1.6. High Brightness Conical Emitter Layer The usualThe brightness usual brightness in daylight in daylight is around is around 3000 3000 nits nits [14 [14].]. In In an an HMD, HMD, toto be visible in in daylight daylight The usual brightness in daylight is around 3000 nits [14]. In an HMD, to be visible in daylight conditions,conditions, the image the image should should be projected be projected with with a similar a similar brightness. brightness. To To ensure ensure the highest highest brightness brightness conditions,possible, the image the emitting should layer be projected area should with be as a largesimilar as possiblebrightness. in order To ensureto increase the the highest amount brightness of light possible, the emitting layer area should be as large as possible in order to increase the amount of light possible,emitted. the emitting The increased layer area emitting should area be asimproves large as the possible maximum in order brightness to increase by the the area amount enlargement of light emitted. The increased emitting area improves the maximum brightness by the area enlargement emitted.factor. The increased The idea is emittingto follow thearea conical improves structure the with maximum the emitting brightness layer in orderby the to areaspread enlargement it over the factor. The idea is to follow the conical structure with the emitting layer in order to spread it over factor. Thelargest idea area is to possible follow (Figure the conical 9a). This structure process with can bethe done emitting several layer times in to order increase to spreadthe emitting it over area the the largesteven area more possible (Figure (Figure9b). The9 LEEa). Thisis not process significantly can beaffected done by several this increased times to emitting increase area. the Still, emitting our largest area possible (Figure 9a). This process can be done several times to increase the emitting area area evenLightTools more (Figure simulations9b). The (Figure LEE is10) not show significantly a result of a79%ffected LEE, by very this similar increased to the emitting circular area.emitting Still, even more (Figure 9b). The LEE is not significantly affected by this increased emitting area. Still, our our LightToolslayer configuration simulations seen (Figure before. 10 The) show total again result in emitting of 79% LEE,surface very is the similar ration toof the circular circular surfaces emitting LightTools simulations (Figure 10) show a result of 79% LEE, very similar to the circular emitting layer configurationarea described seen earlier before. and of The the total conical gain one. in Considering emitting surface that the is thecone ration dimensions of the are circular as described surfaces layer configuration seen before. The total gain in emitting surface is the ration of the circular surfaces area describedearlier, the earlier resulting and ofemitting the conical surface one. gain Considering is: that the cone dimensions are as described area described earlier and of the conical one.πr Considering 41,59 that the 10 cone dimensions are as described (10) earlier, the resulting emitting surfaceGain = gain is: = =3.19 earlier, the resulting emitting surface gainπr (r is: + √h +r) 13.05 10 2 2 Then, the brightness also shouldπrπ rbe improved41,59 by41.59 ~300% 10 10 accordingly− to the updated LEE. The(10) GainGain == p == × ==3.193.19 (10) gain could be improved evenπr more (r + with√h additional2+r)2 13.05 conical13.05 emitting 10 102 sub-layers. πr (r + h + r ) × −

(a)

(a)

(b)

Figure 9. LED cone. (a) LED cone with internal conical emitting layer; (b) LED cone with multiple sub-cone emitting layers.

(b)

FigureFigure 9. LEDLED cone. cone. ( (aa)) LED LED cone cone with with internal internal conical conical emitting emitting layer; layer; ( (bb)) LED LED cone cone with with multiple multiple sub-conesub-cone emitting emitting layers. layers. NanomaterialsNanomaterials 20202020, 10,,10 214, 214 12 of12 22 of 23

FigureFigure 10. 10.LightToolsLightTools 3D 3DModel Model of an of anLED LED cone cone with with internal internal conical conical emitting emitting layer. layer.

4.2. CompoundThen, the Parabolic brightness Concentrator also should (CPC) be improved by ~300% accordingly to the updated LEE. The gain could be improved even more with additional conical emitting sub-layers. The Compound Parabolic Concentrator is the complementary part of the pixel. The first part is the4.2. light Compound emitting Parabolic diode Concentratorwith a conical (CPC) structure permitting to extract light more efficiently, as describedThe earlier. Compound The second Parabolic part Concentrator function is isto the narrow complementary the angular part distribution of the pixel. of Thethe firstlight part beam. is the Thislight is required emitting to diode ensure with that a conicalthe light structure emitted permittingfrom the pixel to extract fits the lightnumerical more eaperturefficiently, of as a describeddesired opticalearlier. system. The secondAn optical part system function has is an to acceptan narrow thece angle angular into distribution which lightof can the propagate light beam. through This is therequired optics. Any to ensure ray having that the an lightangle emitted of propagation from the higher pixel fitsthan the the numerical optical system aperture angle of aof desired acceptance, optical willsystem. not succeed An optical in propagating system has inside an acceptance the system angle and into will which be a loss. light If can the propagate outgoing throughCone LED the rays optics. could be shaped to have a narrower angular distribution, less rays will be lost reducing—then the Any ray having an angle of propagation higher than the optical system angle of acceptance, will not waste of power, the overheating of the display, and, as a result, the battery power consumption and succeed in propagating inside the system and will be a loss. If the outgoing Cone LED rays could its overheating as well. Inside the CPC, light is reflected by a parabolic shaped wall by total internal be shaped to have a narrower angular distribution, less rays will be lost reducing—then the waste reflection and eventually exits the structure. of power, the overheating of the display, and, as a result, the battery power consumption and its There are no secondary reflections on the CPC wall, each ray is reflected only once and then overheating as well. Inside the CPC, light is reflected by a parabolic shaped wall by total internal exits. If necessary, walls can be made from a reflective material such as Al and Nickel so rays would reflection and eventually exits the structure. not be reflected by TIR. This would allow for designing a CPC cavity into any relevant wafer material There are no secondary reflections on the CPC wall, each ray is reflected only once and then exits. like Sapphire or Silicon (Figure 11a,b). This possibility is more suitable for manufacturing but is less If necessary, walls can be made from a reflective material such as Al and Nickel so rays would not efficient since the reflecting performances would be affected by the material absorbance when TIR be reflected by TIR. This would allow for designing a CPC cavity into any relevant wafer material achieves a 100% reflection. Silver or Aluminum absorption is below 10%, making a coated CPC a like Sapphire or Silicon (Figure 11a,b). This possibility is more suitable for manufacturing but is less relevant configuration. efficient since the reflecting performances would be affected by the material absorbance when TIR achieves a 100% reflection. Silver or Aluminum absorption is below 10%, making a coated CPC a relevant configuration. The CPC dimensions are set according to an input angular distribution, an output dimension, and the desire output angular distribution. In our investigation, the CPC has an acceptance angle of 90 since it collects the light coming out from the Cone LED. The outgoing desired angular ± ◦ distribution, without considering physical diffraction effect, is about 30 . Then, the dimension and ± ◦ the parabolic profile are given by the set of equations below [27]. The equation of parabola is given by:

x2 Y = (11) 2b(1 + sin θc)

The full height of CPC is given by:

w 1 H = (1 + )cos θc (12) 2 sin θc

(a) (b)

Figure 11. Views of the CPC structure. (a) a reflective cavity into Ag or Al material; (b) a CPC with Ag or Al reflective wall inside a Si or Sapphire material.

Nanomaterials 2020, 10, 214 12 of 22

Figure 10. LightTools 3D Model of an LED cone with internal conical emitting layer.

4.2. Compound Parabolic Concentrator (CPC) The Compound Parabolic Concentrator is the complementary part of the pixel. The first part is the light emitting diode with a conical structure permitting to extract light more efficiently, as described earlier. The second part function is to narrow the angular distribution of the light beam. This is required to ensure that the light emitted from the pixel fits the numerical aperture of a desired optical system. An optical system has an acceptance angle into which light can propagate through the optics. Any ray having an angle of propagation higher than the optical system angle of acceptance, willNanomaterials not succeed2020, 10 in, 214 propagating inside the system and will be a loss. If the outgoing Cone LED13 rays of 23 could be shaped to have a narrower angular distribution, less rays will be lost reducing—then the waste of power, the overheating of the display, and, as a result, the battery power consumption and its overheatingThe point onas parabolawell. Inside C can the beCPC, expressed light is inreflected terms of by coordinates, a parabolic where:shaped wall by total internal reflection and eventually exits the structure. = θ There are no secondary reflections on theX CPCbcos wac ll, each ray is reflected only once and then(13) exits. If necessary, walls can be made from a reflective material such as Al and Nickel so rays would Y = b(1 sin θc)/2 (14) not be reflected by TIR. This would allow for designing− a CPC cavity into any relevant wafer material like SapphireHeight to or aperture Silicon ratio(Figure is given11a,b). by: This possibility is more suitable for manufacturing but is less efficient since the reflecting performances would be affected by the material absorbance when TIR H 1 1  achieves a 100% reflection. Silver or Aluminum= 1 + absorptioncos θis below 10%, making a coated CPC(15) a w 2 sin θ c relevant configuration. c Nanomaterials 2020, 10, 214 13 of 22

The CPC dimensions are set according to an input angular distribution, an output dimension, and the desire output angular distribution. In our investigation, the CPC has an acceptance angle of ±90° since it collects the light coming out from the Cone LED. The outgoing desired angular distribution, without considering physical diffraction effect, is about ±30°. Then, the dimension and the parabolic profile are given by the set of equations below [27]. The equation of parabola is given by: x (11) Y= 2b(1 + sinθ) The full height of CPC is given by: w 1 (12) H= 1 + cosθ 2 sinθ The point on parabola C can be expressed in terms of coordinates, where:

X = bcosθ (13)

(a) Y=b(1sinθ)/2 (b) (14) Height to aperture ratio is given by: Figure 11. Views ofof thethe CPCCPC structure. structure. ( a(a)) a a reflective reflective cavity cavity into into Ag Ag or or Al Al material; material; (b) ( ab) CPC a CPC with with Ag H 1 1 Agor Al or reflectiveAl reflective wall wall inside inside a Si a or Si Sapphire or Sapphire material. material. (15) = 1 + cosθ w 2 sinθ

AsAs a result, a result, the the dimensions dimensions are are presented presented in in next next in in Figure Figure 12. 12 .

FigureFigure 12. 12. CPCCPC dimensions dimensions obtained obtained with with LightTools LightTools software. software.

Z Zis isthe the length length and and Y Yis isthe the height height of of a discrete a discrete portion portion of of the the parabolic parabolic shape shape corresponding corresponding to to thethe CPC CPC width. width. The The resulting resulting CPC CPC profile profile is isas as in inFigure Figure 13. 13 .

Figure 13. The optimized CPC profile.

Nanomaterials 2020, 10, 214 13 of 22

The CPC dimensions are set according to an input angular distribution, an output dimension, and the desire output angular distribution. In our investigation, the CPC has an acceptance angle of ±90° since it collects the light coming out from the Cone LED. The outgoing desired angular distribution, without considering physical diffraction effect, is about ±30°. Then, the dimension and the parabolic profile are given by the set of equations below [27]. The equation of parabola is given by: x (11) Y= 2b(1 + sinθ) The full height of CPC is given by: w 1 (12) H= 1 + cosθ 2 sinθ The point on parabola C can be expressed in terms of coordinates, where:

X = bcosθ (13)

Y=b(1sinθ)/2 (14) Height to aperture ratio is given by: H 1 1 (15) = 1 + cosθ w 2 sinθ As a result, the dimensions are presented in next in Figure 12.

Figure 12. CPC dimensions obtained with LightTools software.

Nanomaterials 2020, 10, 214 14 of 23 Z is the length and Y is the height of a discrete portion of the parabolic shape corresponding to the CPC width. The resulting CPC profile is as in Figure 13.

Nanomaterials 2020, 10, 214 FigureFigure 13. The 13. optimizedThe optimized CPC CPCprofile. profile. 14 of 22

4.3.4.3. CPC CPC and and Conical Conical LED LED Assembly Assembly AfterAfter being being separately separately optimized, optimized, the the two two parts parts of of the the pixel pixel are are joined joined together together to to achieve achieve the the pixelpixel assembly. assembly. This This assembly assembly is is composed composed by by the the conical conical LED LED with with high high light light extraction extraction e ffiefficiencyciency andand on on its its top top by by the the Compound Compound Parabolic Parabolic Concentrator, Concentrator, whose whose function function is to is narrow to narrow the beam the beam to best to fitbest the fit numerical the numerical aperture aperture of an of optical an optical system. system The. assemblyThe assembly dimensions dimensions are presented are presented in Figure in Figure 14. The14. conicalThe conical LED LED outgoing outgoing surface surface area fitsarea the fits entrance the entrance area of area the of CPC the to CPC avoid to avoid any loss any of loss light. of Thislight. wayThis it way allows it manufacturingallows manufacturing the pixel the structure pixel structure as one single as one cavity single instead cavity of instead manufacturing of manufacturing each part ofeach the pixelpart of cavity the pixel in at cavity least twoin at steps. least two The steps. pixel depthThe pixel almost depth reaches almost a micronreaches anda micron could and be evencould deeperbe even since deeper this dimensionsince this dimension doesn’t aff ectdoesn’t the visible affect pixelthe visible top size, pixel which top couldsize, which remain could unchanged. remain Theunchanged. pixel depth The is pixel a degree depth of is freedom, a degree permitting of freedom, to permitting adapt and to optimize adapt and the optimize pixel shape, the dependingpixel shape, ondepending the desired on optical the desired system optical numerical system aperture. numerical aperture.

FigureFigure 14. 14.Assembly Assembly dimensions dimensions obtained obtained with with LightTools LightTools software. software. 4.3.1. Pixel Assembly Ray Path 4.3.1. Pixel Assembly Ray Path The pixel assembly is composed by the Light source, the Cone LED, and the concentrator, the CPC. The pixel assembly is composed by the Light source, the Cone LED, and the concentrator, the As predicted, when combined, light is first extracted from the bottom LED and then propagates to the CPC. As predicted, when combined, light is first extracted from the bottom LED and then propagates CPC to be concentrated before finally leaving the assembly. The following is a propagating typical ray to the CPC to be concentrated before finally leaving the assembly. The following is a propagating path (Figure 15), as described earlier. typical ray path (Figure 15), as described earlier.

Figure 15. Typical LENS pixel ray path obtained with LightTools software.

4.3.2. Outgoing Light Angular and Spatial Distribution The associated Lambertian Cone LED source with the adapted top CPC generates an output spatial distribution as described in Figures 16 and 17.

Figure 16. LENS Pixel ray trace with Illuminance pattern output obtained with LightTools software.

Nanomaterials 2020, 10, 214 14 of 22

4.3.Nanomaterials CPC and 2020Conical, 10, 214 LED Assembly 14 of 22

4.3. AfterCPC andbeing Conical separately LED Assembly optimized, the two parts of the pixel are joined together to achieve the pixel assembly. This assembly is composed by the conical LED with high light extraction efficiency and onAfter its top being by theseparately Compound optimized, Parabolic the Concentrtwo partsator, of the whose pixel function are joined is to together narrow to the achieve beam tothe bestpixel fit assembly.the numerical This aperture assembly of isan composed optical system by the. The co nicalassembly LED dimensionswith high light are presentedextraction in efficiency Figure 14.and The on conical its top LED by the outgoing Compound surface Parabolic area fits Concentrthe entranceator, area whose of the function CPC to is avoid to narrow any loss the of beam light. to Thisbest way fit the it allowsnumerical manufacturing aperture of anthe optical pixel structuresystem. The as assemblyone single dimensions cavity instead are presentedof manufacturing in Figure each14. Thepart conical of the pixel LED cavityoutgoing in atsurface least two area steps. fits the The en pixeltrance depth area ofalmost the CPC reaches to avoid a micron any loss and of could light. beThis even way deeper it allows since manufacturing this dimension the doesn’t pixel structure affect the as visible one single pixel cavity top size, instead which of manufacturingcould remain unchanged.each part of The the pixel pixel depth cavity is in a degreeat least oftwo freedom, steps. The permitting pixel depth to adapt almost and reaches optimize a micron the pixel and shape, could dependingbe even deeper on the sincedesired this optical dimension system doesn’t numerical affect aperture. the visible pixel top size, which could remain unchanged. The pixel depth is a degree of freedom, permitting to adapt and optimize the pixel shape, depending on the desired optical system numerical aperture.

Figure 14. Assembly dimensions obtained with LightTools software.

4.3.1. Pixel AssemblyFigure Ray Path 14. Assembly dimensions obtained with LightTools software.

4.3.1.The Pixel pixel Assembly assembly Ray is composedPath by the Light source, the Cone LED, and the concentrator, the CPC. As predicted, when combined, light is first extracted from the bottom LED and then propagates to the TheCPC pixel to be assembly concentrated is composed before finally by the leaving Light source, the assembly. the Cone The LED, following and the is concentrator, a propagating the typicalCPC. Asray predicted, path (Figure when 15), combined, as described light earlier. is first extracted from the bottom LED and then propagates toNanomaterials the CPC 2020to be, 10 ,concentrated 214 before finally leaving the assembly. The following is a 15propagating of 23 typical ray path (Figure 15), as described earlier.

Figure 15. Typical LENS pixel ray path obtained with LightTools software.

Figure 15. Typical LENS pixel ray path obtained with LightTools software. 4.3.2. Outgoing LightFigure Angular 15. Typical and LENSSpatial pixel Distribution ray path obtained with LightTools software. 4.3.2. Outgoing Light Angular and Spatial Distribution 4.3.2.The OutgoingThe associated associated Light Lambertian Lambertian Angular and Cone Spatial LEDLED sourceDistributionsource with with the the adapted adapted top top CPC CPC generates generates an output an output spatialspatial distribution distribution as as described described in FiguresFigures 16 16 and and 17 17.. The associated Lambertian Cone LED source with the adapted top CPC generates an output spatial distribution as described in Figures 16 and 17.

Nanomaterials 2020, 10, 214 15 of 22

Figure 16. LENS Pixel ray trace with Illuminance pattern output obtained with LightTools software. Figure 16. LENS Pixel ray trace with Illuminance pattern output obtained with LightTools software.

Figure 16. LENS Pixel ray trace with Illuminance pattern output obtained with LightTools software.

Figure Figure17. LENA 17. LENA pixel pixelIlluminance Illuminance spatial spatial distribution distribution output output obtained obtained with LightToolsLightTools software. software.

As theoretically predicted, the associated Lambertian Cone LED source with the adapted top CPC As theoretically predicted, the associated Lambertian Cone LED source with the adapted top generates an output angular distribution equal to 15 as described in Figures 18 and 19. CPC generates an output angular distribution equal± to +–◦ 15° as described in Figures 18 and 19.

Figure 18. LENS pixel Intensity angular distribution output obtained with LightTools software.

Figure 19. LENS Pixel angular distribution CPC narrowing, LightTools simulation.

Nanomaterials 2020, 10, 214 15 of 22

Nanomaterials 2020, 10, 214 15 of 22

Figure 17. LENA pixel Illuminance spatial distribution output obtained with LightTools software.

As theoretically predicted, the associated Lambertian Cone LED source with the adapted top Figure 17. LENA pixel Illuminance spatial distribution output obtained with LightTools software. CPC generates an output angular distribution equal to +– 15° as described in Figures 18 and 19. As theoretically predicted, the associated Lambertian Cone LED source with the adapted top Nanomaterials 2020, 10, 214 16 of 23 CPC generates an output angular distribution equal to +– 15° as described in Figures 18 and 19.

Figure 18. LENS pixel Intensity angular distribution output obtained with LightTools software. Figure 18. LENS pixel Intensity angular distribution output obtained with LightTools software.

Figure 18. LENS pixel Intensity angular distribution output obtained with LightTools software.

FigureFigure 19. 19.LENSLENS Pixel Pixel angular angular distribution distribution CPC narrowing,narrowing, LightTools LightTools simulation. simulation.

4.4. Complete LENS Pixel Assembly Efficiency Improvement

Figure 19. LENS Pixel angular distribution CPC narrowing, LightTools simulation. In comparison to a simple Flat LED, the LENA pixel is several times more efficient. The output efficiency is the result of the Cone LED LEE improvement conjugated to the narrowing effect of the CPC on the output light beam.

4.4.1. Cone LED LEE Improvement To evaluate the Cone LED light extraction efficiency improvement in comparison to a flat LED, an Aluminum material Cone configuration is chosen. On one hand, it is not the most efficient material, the best being Silver, but, on the other hand, Aluminum is more likely to suit a mass production and industrial manufacturing as its cost is relatively low compared to Silver. Then, the Cone LED Light extraction efficiency improvement relatively to a flat LED LEE is given by:

Aluminum Cone LED LEE LEE Improvement = (16) Flat LED LEE Replacing the obtained values, we get:

72% LEE Improvement = = 10.43 (17) 6.9% The improvement is ~10 times in comparison to a typical flat LED LEE! Nanomaterials 2020, 10, 214 17 of 23 Nanomaterials 2020, 10, 214 16 of 22

4.4. Complete LENS Pixel Assembly Efficiency Improvement 4.4.2. CPC Brightness Improvement In comparison to a simple Flat LED, the LENA pixel is several times more efficient. The output Improving the light brightness in an eventual optical system is now possible since the CPC adapts efficiency is the result of the Cone LED LEE improvement conjugated to the narrowing effect of the the Nano-LED numerical aperture to the optics acceptance angle. To evaluate the gain obtained by the CPC on the output light beam. CPC numerical aperture adaptation, we divide the initial Cone LED angular distribution surface area by the final output angular distribution surface area, and we get: 4.4.1. Cone LED LEE Improvement A To evaluate the Cone LED light extraction effici2 ency improvement in comparison to a flat LED,(18) an Aluminum material Cone configuration is chosA1 en. On one hand, it is not the most efficient material, the best being Silver, but, on the other hand, Aluminum is more likely to suit a mass where A1 is the output angular distribution area and A2 the Cone LED as shown in Figure 20. production and industrial manufacturing as its cost is relatively low compared to Silver. Then, the Cone LED Light extraction efficiency improvement relatively2 to a flat LED LEE is given by: A1 = πr1 (19) 𝐴𝑙𝑢𝑚𝑖𝑛𝑢𝑚 𝐶𝑜𝑛𝑒 𝐿𝐸𝐷𝐿𝐸𝐸 (16) 𝐿𝐸𝐸 𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡 = = 2 A2 πr2𝐹𝑙𝑎𝑡 𝐿𝐸𝐷 𝐿𝐸𝐸 (20) Replacing the obtained values, we get: A πr2 2 = 2 (21) 2 A1 πr 72% 𝐿𝐸𝐸 𝐼𝑚𝑝𝑟𝑜𝑣𝑒𝑚𝑒𝑛𝑡 =1 =10.43 (17) 6.9% Then, for a purely geometric light propagation, the CPC brightness improvement is: The improvement is ~10 times in comparison to a typical flat LED LEE! 902 = 36 (22) 4.4.2. CPC Brightness Improvement 152 ImprovingHowever, when the light considering brightness diff ractionin an eventual effect of theoptical aperture: system is now possible since the CPC adapts the Nano-LED numerical aperture to the optics acceptance angle. To evaluate the gain λ obtained by the CPC numerical apertureθ =adaptati1.22 on,( )we divide the initial Cone LED angular(23) distribution surface area by the final output angular× distributionD surface area, and we get: θ = 1.22 (0.525𝐴 µm/2.56 µm) (18)(24) × 𝐴 θ = 30◦ (25) where A1 is the output angular distribution area and A2 the Cone LED as shown in Figure 20.

2 1 FigureFigure 20. The 20. angularThe angular distribution distribution radius radius of the of Cone the Cone LED LED beam beam r and r2 and the theCPC CPC output output beam beam radius radius r . r1.

Then, the total angular distribution output is the sum of the diffraction angle and the CPC 𝐴 =𝜋𝑟 (19) geometrical angular distribution: = θ + θ r10 diff𝐴raction =𝜋𝑟 CPC(20) (26)

r0 = 30◦ + 15◦ = 45◦ (27) 1 𝐴 𝜋𝑟 (21) = In this case, the right improvement should𝐴 be: 𝜋𝑟 Then, for a purely geometric light propagation, the CPC brightness improvement is: 2 2 r 90 2 90= = 4(22) (28) r 2 45=362 10 15 However, when considering diffraction effect of the aperture:

Nanomaterials 2020, 10, 214 18 of 23

Furthermore, since the CPC walls are made from a reflective material such as Sliver or Aluminum, additional absorption needs to be deducted to evaluate to total light efficiency. At a wavelength of 525 nm, Silver absorption is α = 1.7% [28] and Aluminum α = 8.3% [29].

4.4.3. The Total LENA Pixel Efficiency After evaluating the improvement generated by each part of the pixel, we can proceed to the total pixel light efficiency improvement. The total pixel efficiency is given by the equation:

Cone LED LEE improvement CPC brightness improvement Alumium reflectance ∗ ∗ = 10.43 4 0.917 (29) × × = 38.26

The Total improvement is 38 times. Meaning that, for the same electrical power consumption, the battery life duration is increased by 38! Furthermore, this improvement significantly decreases the operating temperature. Since the Cone LED has an LEE equal to 72%, only 28% of the light is absorbed in the LED structure and transformed in thermal radiation. In comparison for a flat LED 93.1% of the light is absorbed and transformed in thermal radiation. The light absorption in the LED is decreased by a factor of: Flat LED light absorption 93.1% = = 3.325 (30) Cone LED light absoption 28% It means that the thermal radiation is decreased by the same factor of 3.325. Although by concentrating light in a useful manner to match an optical system numerical aperture, the battery consumption is lowered as explained earlier. This permits to further lower the thermal radiation by a factor of A2/A1, as seen before, by 4 in our study. The total pixel thermal radiation should be then lowered by a factor of 3.325 4 = 13.3. × 4.5. LightTools Parameters Summary Since a lot of results were obtained, and presented above, it was important to summarize in one place all the parameters which were used for the 2D simulations. They are presented in Table1.

Table 1. LENS parameters using LightTools software.

Parameters Parameters Definition Values Device parameters:

Dem Emitting layer distance from top LED surface 42 nm Rem Emitting layer Radius 287 nm 2 Aem Emitting layer Area 14.826 µm Dcbase Cone base diameter 45 nm Dctop Cone top surface diameter 664 nm OHc Cone overall height 442 nm np-GaN P-GaN refractive index 2.45 nn-GaN N-GaN refractive index 2.42 RAlum Aluminum reflectance at 525 nm 91.703% RSilver Silver reflectance at 525 nm 98.341% Ratio Cone LED dimension ratio 2:3 Dcpcbase CPC base diameter 664 nm Dcpctop CPC top surface diameter 2564 nm OLcpc Overall CPC length 6023 nm InA CPC Input Angle 90◦ OutA CPC Output Angle 15◦ Nanomaterials 2020, 10, 214 19 of 23

Table 1. Cont.

Parameters Parameters Definition Values LightTools setup parameters used: LUM Photometric Source flux 100 Lumen λ Wavelength LED emission 525 nm σθ Emitting layer Angular distribution Lambertian Measured parameters:

σ ConeLED Output Cone LED angular distribution Lambertian σ Output Assembly angular distribution 15 assembly ± ◦ Output Cone LED light power with Aluminum LAl 72.74 Lumen ConeLED reflective material Output Cone LED light power with Silver LSi 78.18 Lumen ConeLED reflective material Output Cone and CPC assembly light power L 76.88 Lumen assembly with Silver reflective material Output Cone and CPC assembly light power L 66.70 Lumen assembly with Al reflective material

5. Discussion

5.1. Simulation vs. Reality Ray tracing is a geometric tool allowing the rapid tracing of the light path for narrow collimated beams called rays. Rays are randomly generated with a Monte Carlo algorithm and their behavior is fixed by Fresnel Descartes equations. Each “beamlet” called ray propagates into a predefined structure and encounters different material and surfaces. The main advantage of ray tracing is that ray paths are not pre-determined by the user. This permits discovering unexpected artifact like stray light and ghosts in imaging systems. Ray tracing software relies on perfect surfaces, ideal shapes, and material quality. Furthermore, physical optics phenomenon like diffraction effects and interferences require wave theory solving and are not completely or not at all simulated in Zemax and LightTools ray tracing software. Several questions can be raised in light of the gap existing between simulations and reality. Real manufacturing implies tolerances and boundaries which are neither always well-known nor understood. Often, a deep investigation based on multiple tests and years of experience is necessary to know what parameters are more sensitive than others. As a result, any simulation made with theoretical assumptions is doomed to be not enough realistic and accurate. Then, it is hard to evaluate if the Cone and the CPC parabolic shapes can be manufactured as in our simulations, or if manufacture tolerances are reasonable. This should be eventually known and understood with manufacturing tests and experiences. Furthermore, the surface quality which is considered as ideal in simulations is obviously much more challenging in reality. Surfaces are naturally diffusing in a real word, where in theory we expect them to be specular. Controlling the surfaces roughness is another challenge to be taken into account in nano-metric and micro-metric scales. However, the main lack of consistence is regarding the edge’s diffractions of the pixel. As the pixel aperture is close to the wavelength, the light is scattered beyond the geometric specular distribution.

5.2. Rectangular vs. Circular Aperture Diffraction When transmitted through a slit, light diffracts due to an edge diffraction effect. The pixel aperture shape has a direct effect on the diffraction pattern generated by light propagating through it. Indeed, as predicted by Bessel function, a circular aperture will generate a circular diffraction pattern. Instead, a rectangular or square aperture generates a central rectangular spot and a crossed pattern of the overall diffraction [30]. Most of the light is concentrated in the first central disk or rectangle. Indeed, 86% of the total diffracted energy pattern is inside the first dark ring. We now understand what far field light distribution could generate a rectangular LED aperture in comparison to our circular aperture Nanomaterials 2020, 10, 214 20 of 23 shape. The central rectangular diffraction pattern has similar energy properties and could be a relevant shape to design a micro LED. The reason we chose to study a circular aperture is because its more conventional and symmetric shape properties. However, a rectangular shape could have its own advantages as a better fill factor of the pixel matrix. Indeed, filling a surface of little circles is much less efficient than with rectangles. This earlier shape could allow a much smaller spacing between two close pixels. The display resolution should then be increased. According to Joseph Louis Lagrange, the best method to pack circles in a Euclidean space is by arranging them in a hexagonal way. In this case, the packing intensity or fill factor equals ~0.9069 [31]. Still, a rectangular shape packing intensity equals 1 for obvious reasons. In ideal conditions, the pixel resolution gain is then ~9% for rectangular pixels micro LED.

5.3. Sub-Wavelength Aperture Our study explores a pixel for which the aperture is larger than the wavelength. Further investigation could be done by evaluating a pixel with an aperture smaller than a wavelength. When light propagates in a sub-wavelength slit geometric consideration is not relevant anymore, as well as far field propagation. Indeed, in such a small scale, light interacts with matter atoms. Light propagation through a sub-wavelength slit is dictated by a Maxwell electromagnetic equation in matter. Maxwell equations take into account the slit thickness as well as the slit matter permittivity. In such a way, the plasmons influence on the light electric field is quantified and allows an accurate propagation model. The light transmission efficiency will directly depend on the physical interaction between free electrons in the matter and photons. Such phenomenon is known as the “plasmonic effect” [32]. Sub-wavelength LED aperture exploration may require physical additional simulations, and this is why complementary investigations will be set in the very near future. In this article, we focused on Ray Tracing and Efficiency.

5.4. Enhancement of the LENS Pixel Wall Reflection As earlier described, the Pixel outer surface is reflective walls impeaching light to exit the pixel structure by the sides and redirecting rays to the top pixel output. In our simulation, we investigated mainly two different reflective materials, Aluminum and Silver. These two materials are commonly used in optics. However, these materials are not ideal and their reflectance is not perfect. As explained before, these materials absorb a small portion of the light decreasing the light efficiency in particular where multiple reflections are occurring. In order to decrease the light absorption from the reflective walls (Figure 21), two different solutions could be explored. The first solution should be to add a dielectric layer coating above the reflective material such as Aluminum. Such a configuration is known as “enhanced Aluminum” [33]. It improves the reflective property. The disadvantage would be that it requires a more complicated process by adding an additional step for the dielectric layer. The other solution could be to abandon metallic material and instead to design a dielectric mirror coating. Metallic material advantage is their high performances over broadbands and large angular ranges. Designing a dielectric mirror coating made of multiple layers is a relevant solution for narrow angular range and/or narrow spectrum [34]. Since our spectrum is limited to the narrow LED spectrum one, such a dielectric coating mirror could be considered. Dielectric mirror coating has the potential to exceed metallic material reflectivity. Nanomaterials 2020, 10, 214 20 of 22

5.4. Enhancement of the LENS Pixel Wall Reflection As earlier described, the Pixel outer surface is reflective walls impeaching light to exit the pixel structure by the sides and redirecting rays to the top pixel output. In our simulation, we investigated mainly two different reflective materials, Aluminum and Silver. These two materials are commonly used in optics. However, these materials are not ideal and their reflectance is not perfect. As explained before, these materials absorb a small portion of the light decreasing the light efficiency in particular where multiple reflections are occurring. In order to decrease the light absorption from the reflective walls (Figure 21), two different solutions could be explored. The first solution should be to add a dielectric layer coating above the reflective material such as Aluminum. Such a configuration is known as “enhanced Aluminum” [33]. It improves the reflective property. The disadvantage would be that it requires a more complicated process by adding an additional step for the dielectric layer. The other solution could be to abandon metallic material and instead to design a dielectric mirror coating. Metallic material advantage is their high performances over broadbands and large angular ranges. Designing a dielectric mirror coating made of multiple layers is a relevant solution for narrow angular range and/or narrow spectrum [34]. Since our spectrum is limited to the narrow LED spectrumNanomaterials one,2020 such, 10, 214 a dielectric coating mirror could be considered. Dielectric mirror coating has21 ofthe 23 potential to exceed metallic material reflectivity.

Figure 21 21.. LENSLENS pixel pixel reflective reflective walls.

6. Conclusions Conclusions Summarizing thethe main main achievements achievements of thisof this first first research, research, several several aspects aspects of a new of Lighta new Emitting Light EmittingNano-pixel Nano-pixel Structure (LENS) Structure were (LENS) proposed, were based proposed, on complementary based on studiescomplementary and novelties, studies including and novelties,concept, architecture, including concept, and analytical architecture, adapted and models.analytical A adapted new concept models. of aA self-emitting new concept pixelof a self- was emittinginvestigated. pixel The was pixel investigated. is a green light The Nanopixel LEDis a green with an light optimized Nano LED reflective with conical an optimized shape. This reflective shape conicalallows Lightshape. Extraction This shape E ffiallowsciency Light considerable Extraction improvement Efficiency considerable of 900% in comparisonimprovement to of a flat900% LED in comparisonshape. The Nanoto a flat LED LED aperture shape. dimensionThe Nano LED is larger aperture than adimension wavelength is larger and is than optimized a wavelength to fit a lightand iscondenser optimized element. to fit a Alight Compound condenser Parabolic element. Concentrator, A Compound usually Parabolic used Concentrator, to concentrate usually sun light used into to concentratesolar cells, is sun mounted light into on thesolar cone cells, LED is mounted to narrow on the the output cone LED light to angular narrow distribution. the output Thelight mounted angular distribution.CPC succeeded The in mounted controlling CPC the succeeded output Light in contro angularlling distribution. the output Light The resultingangular distribution. intensity gain The is resulting400%, aperture intensity diffraction gain is included. 400%, aperture When combined diffraction together, included. it was When demonstrated combined in together, our simulations it was demonstratedthat the cone Nano-LED in our simulations and the Compoundthat the cone Parabolic Nano-LED Concentrator and the Compound improve Parabolic the power Concentrator efficiency by improvearound 3800% the power compared efficiency to a flatby around shape LED. 3800% compared to a flat shape LED. Regarding thethe prospect prospect of furtherof further research research into thisinto topic, this furthertopic, additionalfurther additional steps can besteps considered can be consideredto our study. to Indeed, our study. only Indeed, the optical only aspect the optical was investigated aspect was andinvestigated no anode and cathodeno anode were and designed cathode wereto allow designed a necessary to allow electrons a necessary flux. electrons Such an flux. electronic Such an design electronic will design permit will considering permit considering a concrete adevelopment concrete development of the novel of pixel.the novel Thus, pixel. a manufacturing Thus, a manufacturing process flow process could flow be could created be to created ensure to a ensurefeasible a and feasible optimized and optimized fabrication. fabrication. Moreover, theMoreover, self-emitting the self-emitting pixel design pixel could design be modified could and be modifiedadapted to and manufacturing adapted to manufacturing machines capabilities machines and capabilities realistic processes. and realistic The optical processes. software The usedoptical in softwarethis thesis used is unable in this to thesis predict is the unable light to behavior predict in the sub-wavelength light behavior apertures. in sub-wavelength Smaller and apertures. smaller Smallerpixels are and of smaller obvious pixels interest are andof obvious physical interest software and would physical contribute software towould a better contribute understanding to a better of sub-wavelength pixel efficiency and far field distribution. To finish, an array of pixels with a dedicated addressing scheme is the road leading to the ultimate new generation of ultra-high efficiency and ultra-high-resolution display. Complementary research, including next steps like physical behavior analysis, which is complementary to the ray tracing method, manufacturing, and testing will follow for sure, and we are already there.

Author Contributions: Research structure conceptualization, A.K.; Investigation, T.E.; Methodology, A.K.; Project administration, A.K.; LightTools Software, T.E.; Supervision, A.K.; Visualization, T.E.; Writing—original draft, T.E.; Writing—review and editing, A.K. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Nanomaterials 2020, 10, 214 22 of 23

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