A Vision toward Ultimate Optical Out‐Coupling for Organic Light‐Emitting Diode Displays: 3D Pixel Configuration

Abstract Despite stringent power consumption requirements in many applications, over years organic light‐emitting diode (OLED) displays still suffer unsatisfactory energy efficiency due to poor light extraction. Approaches have been reported for OLED light out‐coupling, but they in general are not applicable for OLED displays due to difficulties in display image quality and fabrication complexity and compatibility. Thus to date, an effective and feasible light extraction technique that can boost efficiencies and yet keep image quality is still lacking and remains a great challenge. Here, a highly effective and scalable extraction‐enhancing OLED display pixel structure is proposed based on embedding the OLED inside a three‐dimensional reflective concave structure covered with a patterned high‐index filler. It can couple as much internal emission as possible into the filler region and then redirect otherwise confined light for out‐coupling. Comprehensive multi‐scale optical simulation validates that ultimately high light extraction efficiency approaching ≈80% and excellent viewing characteristics are simultaneously achievable with optimized structures using highly transparent top electrodes. This scheme is scalable and wavelength insensitive, and generally applicable to all red, green, and blue pixels in high‐resolution full‐color displays. Results of this work are believed to shed light on the development of future generations of advanced OLED displays.


More details of optical simulation methods
Since the proposed OLED pixel contains structures of very different dimensional scales, i.e., nm-scale structures that are smaller than wavelengths (e.g., thicknesses of the OLED active layers) and mscale structures that are significantly larger than wavelengths (e.g., pixel size, bank height, filler thickness etc.), optical properties of the proposed structure are analyzed with a multi-scale optical simulation, as schematically illustrated in Figure S1. It combines the rigorous and analytical electromagnetic wave-and dipole-based power dissipation model that is good for dealing detailed emission properties from nm-scale layered structures [1][2][3][4][5] , with the geometric optics simulation based on Monte Carlo ray tracing that is good for dealing larger-scale structures [6][7][8][9][10] . The optical modeling/simulation for the proposed structures then contains three steps, as shown in the flow chart of Figure S2: (1)    Step 1: First of all, with the OLED layer stacking structure, and the intrinsic emission spectrum and the emitting dipole orientation of the EML as inputs, the analytical electromagnetic dipole model is used to calculate the coupling of the radiation generated in the OLED active region to the high-index filler region (by assuming it is semi-infinite) as a function of the wavelength , the polarization (s, p), and the initial internal angle  int in the filler. From such calculation, the light coupling efficiency from the OLED active region to the high-index filler (i.e., η filler ) and the s-polarization/p-polarization/total emission patterns in the filler are obtained. Such radiation intensity distributions in the filler I s (,  int ), I p (,  int ) as a function of the wavelength , the polarization (s, p), and the internal angle  int are then used to set up ray sources in the filler for performing the ray-tracing simulation in the larger-scale concave structure (step 3).
The analytical electromagnetic dipole model (the analytical model) used in step 1 for calculating coupling of radiation generated in the OLED active region to the high-index filler region or air (for conventional top-emitting OLED) adopts a classical approach based on the equivalence between the molecular emission through electronic dipole transitions and the electromagnetic radiation from a classical electrical dipole antenna [1][2][3][4][5] . Such a model can take into account coupling of OLED emission into SPP and waveguided modes and the loss due to the electrodes. Using the plane-wave expansion of the dipole radiation field, the full-vectorial electromagnetic fields generated by a radiation dipole embedded in a layered structure can be calculated, from which the distribution of the radiation power into different plane-wave modes and the far-field radiation (e.g., coupling of OLED internal radiation into the semi-infinite filler region in proposed OLED structures or into air for conventional top-emitting OLEDs) related to emission characteristics of the OLED stack can be obtained. In the plane-wave expansion calculation, each plane-wave mode can be characterized by an in-plane wave vector k t , where k t is the component of the wave vector parallel to the planar layer surface/interface. Emission characteristics of an OLED are calculated by assuming that the emitting layer (EML) contains an ensemble of mutually incoherent dipole radiators with distributions in dipole orientations (e.g., a random isotropic distribution or some anisotropic distributions of the emitting dipoles), locations, and frequencies (e.g., the full spectral distribution from the intrinsic emission spectra of emitting layers). The overall far-field radiation characteristics into the high-index filler region or into air can then be obtained by averaging the contributions over these distributions.
The stack of OLED active layers are assumed to have the general structure of thick Ag bottom reflective electrode (150 nm)/hole-transport layer-HTL (y nm)/emitting layer-EML (10 nm)/electrontransport layer-ETL (x nm)/(semi-)transparent top electrode (either 20 nm Ag or 100 nm ITO). Actual optical constants [n(), k()] of organic layers, Ag, and ITO were used in optical simulation [see Figure  S2(b) in supplementary information]. For simplicity of simulation, the optical properties (refractive index n) of the typical host material CBP (n~1.81 at 520 nm) are assumed for all the HTL, EML, ETL, and filler materials.
Step 2: The optical reflectance, R s (, AOI ) and R p (,  AOI ), and optical transmittance, T s (, AOI ), T p (, AOI ), seen from the high-index filler as a function of the polarization (s, p polarization), wavelength , and angle of incidence ( AOI ) for each surface (bottom surface, bank slope surface) of the concave structure, that are needed for ray-tracing simulation in Step 3, are also calculated with the analytical electromagnetic wave theory. Step 3: With setting up ray sources (with results of step 1), surface optical properties (with results of step 2) and the geometric structure of the concave structure, the 3-dimensional (3D) polarization Monte Carlo ray-tracing simulation with the LightTools TM software (Synopsys, Inc) is then conducted to calculate extraction of the light from the high-index filler region, taking into consideration the distribution of ray sources as a function of the wavelength , polarization (s, p polarization), and initial internal angle  int . Eventually the overall light extraction efficiency from the high-index filler to air (i.e., η air ) and the overall out-coupled far-field emission intensity in air [I(, )] as a function the wavelength  and the external viewing angle .
The polarization ray-tracing calculus is adopted in the ray-tracing simulation so that the evolution of the polarization state throughout the whole optical process can be traced and polarizationdependent optical effects (such as intensity distributions of light sources, optical reflectance and transmittance of surfaces, Fresnel loss etc.) can be well taken into account for more accurate simulation and results. In the polarization ray-tracing calculus, the global coordinate system (with specified x, y, z axes as shown in Figure S3(a)) are used to keep track of evolution of various vector directions (e.g., the ray propagation vector k, the electric field (polarization) vector E) throughout the whole optical process. Meanwhile the local coordinate system for each optical surface/interface, as illustrated in Figure S3(b), are used to unambiguously partition the polarization states (s or p) of the light ray incident onto that surface/interface and to treat the polarization-dependent processes (e.g., R s , R p , T s , and T p ) at that surface/interface separately. The local coordinate system consists of three orthogonal vectors: the propagation vector (k), the vector perpendicular to the incident plane (s polarization direction), and the vector parallel to the incident plane (p polarization direction). As shown in Figure S3(b), considering a linearly polarized ray with the propagation vector k and the electric field vector E incident on a surface, characteristics of reflected and transmitted rays can be determined by partitioning E into the s component E s, local and the p component E p, local relative to the local coordinate system, treating each component with the polarization-dependent reflectance (R s , R p ) and transmittance (T s , T p ) of that surface (calculated in step 2), and then combining them to get the electric field vector E' (polarization) of the reflected or transmitted ray (with the propagation vector k') in the global coordinate system that would propagate toward the next surface/interface and undergo another optical process. By repeatedly tracing rays with vector operations alternately in the local and global coordinates till they are out-coupled to the air or lost at some point, the polarization-dependent optical characteristics of the optical system are assessed.
The ray source used for the 3D polarization ray-tracing simulation in step 3 is set up based on calculated radiation intensity distributions I s (,  int ), I p (,  int ) coupled to the filler region, that are calculated in step 1 and contain the complete wavelength, angular and polarization dependence. In consideration of the singularity issue in the polarization ray-tracing calculus 9,10 , the ray source in this study is built by using a user-defined polarizer to ensure that the rays pass through it will have the same polarization characteristics calculated from the electromagnetic wave method in step 1.
Although the Monde Carlo ray-tracing method works efficiently with increasing the number of rays, consideration of the computation loading limits the initial ray quantity to 200 million in this study. Through the comprehensive 3D polarization ray-tracing simulation with complete consideration of angular, spectral, and polarization dependence of ray sources, the light extraction efficiency from the high-index filler to air (i.e., η air ) and the far-field emission pattern in air I(, ) can be obtained. The overall light extraction efficiency from the OLED active region to air (i.e., η ext ) can then be obtained by η ext =η filler  η air .

Polarization-resolved spectrally integrated emission patterns (p-and s-polarization components)
for device 1-3 emission coupled into the high-index filler, respectively. Table S1. Summary of optical mode distribution ratios for devices 1-3 in the 3D pixel structure.
[a] surface plasmon modes (SPP).             ext 's calculated by (i) the fully rigorous electromagnetic wave optics approach that deals the OLED stack and the filler overcoating as a whole by wave optics, and (ii) the wave optics+ray optics approach that first uses the wave optics to calculate coupling of OLED internal emission into the filler layer (assumed semi-infinite) and then uses the ray optics to further calculate out-coupling from the filler to air: (b) device 1 OLED stack, (b) device 2 OLED stack, and (c) device 3 OLED stack.  ext 's calculated by both methods agree well within 4.5%, 3.5%, and 1% deviation percentages for devices 1, 2, and 3, respectively (smallest for device 3 having ITO as transparent top electrode for the filler overcoating thickness of >1 m, indicating sufficient confidence in calculation of optical outcoupling efficiency in this work (which mainly deal with filler thicknesses of 1 m).