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We numerically investigate the effect of the pixel boundary on the angular emission characteristics of top-emitting organic light-emitting diodes (OLEDs) using the finite element method. A three-dimensional OLED structure has the square pixel boundary, which is surrounded by the pixel definition layer. The angular emission characteristics based on the Poynting vectors are calculated in various positions of a Hertz dipole emitter within the pixel boundary. When the dipole emitter is located near the center of the square pixel, the angular emission characteristics have a symmetric forward-directed pattern, which is similar to the angular emission pattern calculated by the thin-film-based optical model. When the position of the dipole emitter is close to the pixel boundary, the angular emission pattern becomes asymmetric because the optical reflections from the pixel boundary in the horizontal direction affect the emission pattern of the dipole emitter. The total angular emission characteristics of the top-emitting OLED are obtained by summing the individual angular emission pattern of the whole dipole emitters, which are assumed to be uniformly distributed in the two-dimensional emission plane. The asymmetrical angular emission characteristics of the dipole emitters near the pixel boundary contribute to narrowing the total angular emission pattern.
© 2015 Optical Society of America
1. Introduction
Top-emitting organic light-emitting diodes (OLEDs) have been used as an efficient method to enhance the brightness and the resolution of active matrix OLED displays (AMOLEDs) [1–3]. However, there exists a trade-off between the light extraction enhancement and the angular emission characteristics. Moreover, micro-cavity effect plays an important role in light emission efficiency because top-emitting OLEDs consist of multiple thin films with the total thickness of less than hundreds of nanometer [2, 3]. Thus, it is important to optimize the optical performance of top-emitting OLEDs based on the appropriate optical modeling.
In the case of a white AMOLED with separate red, green, and blue pixels, each pixel with the area of hundreds of micrometer is surrounded by the pixel definition layer (PDL), which is made of polyimide [4]. Because the refractive index of the PDL is different from those of thin-film organic layers, the optical reflections and refractions at the pixel boundaries will affect the angular emission characteristics together with the light extraction efficiency. In the view of ray optics, the light extraction of top-emitting OLEDs can be described by means of light escape cone, where the light emission inside the escape cone angle can be extracted into the top surface without total internal reflection [5]. If we assume the average refractive index of the organic layer to be norg = 1.77, the light escape cone has a value of 34°. In Fig. 1(a), the effect of the pixel boundary on the light emission is observed in the blue region of the emission layer (EML), where light escape cone is overlapped with the boundary of the PDL. When the vertical distance between the dipole emitter and the top surface is about t = 0.2 μm [1], the light emission whose lateral distance between the dipole emitter and the PDL boundary is less than b = 0.14 μm can be affected by the PDL boundary.
Fig. 1 (a) Schematic diagram of the cross-sectional view of a top-emitting OLED with light escape cones. The effect of the pixel boundary on the light emission is observed in the blue region of the EML, where light escape cone is overlapped with the PDL boundary. (b) Ratio of the emission area affected by the optical reflections and refractions at the pixel boundaries (marked in sky-blue color) to the total pixel area as a function of the pixel size of a. We set b = 0.14 μm, which corresponds to the vertical distance between the dipole emitter and the top surface of t = 0.2 μm [1].
As the resolution of the AMOLED increases and the pixel size decreases, the change of the total light emission characteristics caused by the refractive-index discontinuity at the pixel boundaries will become more pronounced. Based on the equation shown in the inset of Fig. 1(b), the ratio of the lateral emission area affected by the pixel boundary can be estimated. The bar graph in Fig. 1(b) shows the calculation result of the ratio of the emission area influenced by the optical reflections and refractions at the pixel boundaries (marked in sky-blue color) as a function of the pixel size (a). As the pixel size is reduced for higher resolution, the effect of the boundary refraction/reflection becomes more significant. Thus, it is essential to consider the effect of the finite pixel boundary in the optical modeling and characterization of top-emitting OLEDs for ultra-high resolution applications. However, there has been no theoretical, numerical, or experimental study on the effect of the finite pixel boundary on the light emission characteristics of OLEDs.
A thin-film-based optical modeling based on the transfer matrix method has been widely used for the optical design of OLEDs [6–10]. However, this optical modeling is restricted to two-dimensional structures and not applicable to the finite pixel boundary because the thin-film-based optical modeling method assumes that the plane of each layer to be infinite. Numerical approaches such as the finite-difference time-domain (FDTD) method [11–14] and the finite element method (FEM) [15] have been used to calculate the optical emission characteristics in the three-dimensional structures of OLEDs. However, there has been no numerical simulation result to include the finite pixel boundary in the three-dimensional structure of OLEDs.
In this paper, we numerically investigate the effect of the finite pixel boundary on the optical characteristics of top-emitting OLEDs. The optical characteristics of a three-dimensional OLED structure with the square pixel boundary are numerically calculated based on the FEM. The angular emission characteristics are calculated in various positions of a Hertz point dipole source within the pixel boundary. We investigate how the optical reflections and refractions at the pixel boundary affect the angular emission characteristics of top-emitting OLEDs.
2. Simulation model
A three-dimensional structure of the top-emitting OLED used in the simulation model is shown in Fig. 2(a), which corresponds to one of the pixels of any OLED display panels shown in the inset. The red, green, and blue pixels are separated by the PDL, which is made of polyimide. Because of the limitation in the computer memory capacity, it is assumed that the pixel domain has a 5 μm × 5 μm square and is surrounded by a 2-μm-wide PDL in the lateral direction. Commercial software of the COMSOL multiphysics is used in the FEM simulation with the space resolution of 5 nm [16]. The perfect matched layer (PML) is widely used to eliminate unnecessary reflections at the simulation boundary. In this calculation, we apply the scattering boundary condition, which provides the same function as the PML with the reduced memory capacity. All the simulations are performed at the wavelength of λ = 520 nm and the light emission from an exciton is modeled as a Hertz electrical point dipole.
Fig. 2 (a) Three-dimensional structure of the top-emitting OLED used in the simulation model, which corresponds to one of the pixels of any OLED display panels shown in the inset. (Top vacuum layer covering the top-emitting OLED is left out to enhance the visibility.) (b) Cross-sectional view of the top-emitting OLED along with the corresponding layer thickness.
The cross-sectional view of the top-emitting OLED used in the simulation model is found in Fig. 2(b), where the corresponding layer thickness is also designated. The multilayer structure in the vertical direction consists of Al (aluminum) as a reflective bottom anode, Alq3 (tris-(8-hydroxyquinoline)aluminum) as an organic emission layer, and indium-tin oxide (ITO)/Ag (silver)/ITO as a semi-transparent top cathode. The values of the complex refractive index of the materials are summarized in Table 1. The vertical location of the dipole emitter is determined to be 208 nm from the reflective bottom anode based on thin-film-based optical modeling to maximize the light emission efficiency under micro-cavity effect [6]. The respective thickness of ITO/Ag/ITO is chosen to have the reflectivity of the semi-transparent top cathode be 30%.
Table 1. Complex refractive index of the materials used in the simulation
3. Simulation results based on a single dipole emitter
The orientation of the dipole emitter plays an important role in the light extraction of top-emitting OLEDs [9, 10]. Figure 3 shows the calculated time-average power on the top surface of the pixel with respect to the direction of the dipole emitter. The emitter is located at the center of the square pixel in the lateral direction. When the dipole emitter is aligned in parallel to the multilayer plane (Px and Py), the strong light emission at the top surface has an isotropic circular shape, whose emission pattern is similar to the escape cone in the light-emitting diode [5]. The circular profiles of the light emission at the top surface are nearly the same for Px and Py. The relatively weak light emission in the lateral surface results from the combination of the optical waveguide mode and the surface plasmon mode, which cannot be extracted into the air [15]. The propagation of the optical waveguide mode and the surface plasmon mode is perpendicular to the direction of the dipole emitter. On the other hand, the light emission at the top surface is very weak when the dipole emitter is perpendicularly aligned to the multilayer plane (Pz). Strong light emission in all the four lateral surfaces is observed because the vertically-aligned dipole emitter is strongly coupled to the optical waveguide mode and the surface plasmon mode [15]. If the pixel size becomes larger in the lateral direction, the amount of light emission in the four lateral surfaces will be dramatically reduced due to very high absorption coefficient of the optical waveguide mode and the surface plasmon mode. In general, the dipole direction is randomly oriented in small-molecule OLEDs so that the dipole direction can be considered to be equally distributed in the x, y, and z directions. In this FEM simulation, we consider only the dipole direction of Px because the spatial distribution of the light emission at the top surface is symmetric for Px and Py and the light emission from Pz is relatively negligible at the top surface.
Fig. 3 Calculated time-average power on the top surface of the pixel with respect to the direction of the dipole emitter. The pixel boundaries are marked in the white dash lines, which ranges from −2.5 to + 2.5 μm.
Figure 4 shows the calculated time-average power in the cross section of the center line at various positions of the dipole emitter within the pixel boundary. The red arrows at the top surface indicate the spatial distribution of the time-average Poynting vectors, which have information of the magnitude and the direction of the optical power flow. When the dipole emitter is located at the center of the pixel, the light emission is not affected by the pixel boundary such that the angular power flow through the top surface shows a symmetric pattern. As the dipole emitter moves toward the pixel boundary, the optical reflections from the pixel boundary cause the emission pattern of the dipole emitter to be asymmetric.
Fig. 4 Calculated time-average power in the cross section of the center line at various positions of the dipole emitter within the pixel boundary. The red arrows at the top surface indicate the spatial distribution of the time-average Poynting vectors.
The blue line in Fig. 5(a) shows the angular emission characteristics obtained from the time-average Poynting vectors at the surface when the dipole is located at the center of the pixel. The light intensity is normalized in reference to the magnitude of the Poynting vector at the viewing angle of 0°. Due to the relatively strong micro-cavity effect between the transparent electrode (ITO/Ag/ITO) and the reflective metal anode (Al), the angular emission characteristic has a symmetric forward-directed pattern [1]. The angular emission characteristics are also calculated at the same multilayer structure based on the two-dimensional thin-film-based optical model [6, 7]. The two calculation results are close to each other, which verifies the accuracy of the FEM-based calculation for the top-emitting OLED.
Fig. 5 (a) Calculated results of the angular emission characteristics when the dipole is located at the center of the pixel. To verify the accuracy of the FEM-based calculation, the angular emission characteristics are also calculated at the same multilayer structure based on the two-dimensional thin-film-based optical model. (b) Calculation results of the angular emission characteristics on the top surface at various positions of the dipole emitter shown in Fig. 4.
Figure 5(b) shows the calculation results of the angular emission characteristics on the top surface at various positions of the dipole emitter shown in Fig. 4. When the dipole emitter is located near the center of the pixel, the angular emission characteristics are symmetric. As the dipole emitter moves toward the pixel boundary, the angular emission pattern becomes asymmetric. Finally, the angular distribution of the light emission becomes narrowed and tilted in reference to the viewing angle of 0° when the dipole emitter is located near the pixel boundary.
4. Simulation results based on multiple dipole emitters
The total light emission characteristics of the top-emitting OLED should be determined from an array of point dipole emitters, which approximates planar light source. We assume that point dipole emitters are uniformly distributed within the pixel boundary, as shown in Fig. 6(a). The average spacing between the dipole emitters is 0.5 μm, which corresponds to a maximum spacing to show the convergent results of angular emission characteristics with respect to the average spacing of the point dipole emitters.
Fig. 6 (a) Spatial arrangement of an array of the point dipole emitters. The average spacing between the dipole emitters is 0.5 μm. (b) Calculated time-average optical power on the top surface from the array of the point dipole emitters with the spatial incoherency considered.
Because each dipole is a spatially incoherent source, the average flux from the emitter array was found from the summation over randomly-distributed initial phases and the calculation was repeated with different randomization factor until it converged [14]. Because the interference effect among the spatially incoherent point dipoles disappears in the end, the saturated average power profile over randomly-distributed initial phases of the point dipole array will be equal to the total sum over the separate optical power profile from the individual dipole emitter. In this calculation, we obtain the spatially-incoherent total light emission characteristics by summing one hundred spatial power profiles, each of which results from the individual dipole emitter at a different location.
Figure 6(b) shows the calculated time-average optical power from the array of point dipoles on the top surface. Strong light emission is observed near the center of the pixel boundary, but light emission becomes weaker near the edge of the pixel boundary, which is marked in white dash lines. The light emission outside the pixel boundary is caused by the dipole emission near the pixel boundary.
The blue line in Fig. 7(a) shows the calculation results of the total angular emission characteristics on the top surface, which is based on the time-average Poynting vectors obtained by an array of 100 point dipole emitters in Fig. 6(a). For comparison, the angular emission characteristics from one dipole emitter located at the center of the pixel is shown in the red line. The total angular emission pattern becomes narrower in comparison with that caused by the single dipole emitter at the center of the pixel, which can be understood by identifying the separate contribution of the angular emission patterns from the right and left edge boundaries. Figure 7(b) shows the calculation results of the angular emission patterns caused by two dipole emitters at the position of (−1.75 μm, 0) and (−2.25 μm, 0) close to the left edge boundary and ( + 1.75 μm, 0) and ( + 2.25 μm, 0) close to the right edge boundary. When the two angular dependences are averaged, the asymmetry of the light emission near the pixel boundaries disappears. Thus, the total angular dependence shows a symmetrical pattern. However, the asymmetrical angular emission characteristics obtained from the pixel boundaries contribute to narrowing the total angular emission pattern compared with that caused by the single dipole emitter located at the center of the pixel.
Fig. 7 (a) (Blue line) Calculated total angular emission characteristics on the top surface, which is based on the time-average Poynting vectors obtained by an array of 100 point dipole emitters. (Red line) Calculated angular emission characteristics from one dipole emitter located at the center of the pixel (0, 0). (b) Calculated angular emission patterns obtained by the summation of two dipole emitters at the position of (−1.75 μm, 0) and (−2.25 μm, 0) close to the left edge boundary and at the position of ( + 1.75 μm, 0) and ( + 2.25 μm, 0) close to the right edge boundary. When the two asymmetrical emission patterns are averaged, the total angular emission pattern becomes symmetrical and narrower compared with that emitted from one dipole emitter located at the center of the pixel (0, 0).
In Fig. 7(a), there is no big difference of the angular emission characteristics caused by the multiple uniformly-distributed dipoles and the single center-located dipole. This indicates that the effect of the optical refraction/reflection at pixel boundary is not so significant. As shown in Fig. 1(a), the amount of the optical refraction at the pixel boundary is determined by the vertical distance between the dipole emitter and the top surface. In this calculation, we use a simple structure of the top-emitting OLED to reduce the computation time and to concentrate the effect of the PDL boundary on the light emission characteristics. In Fig. 2(b), the vertical distance from the emitting dipole to the top surface is only t = 0.077 μm so that the dipole emitters covering only 4% of the pixel area can be affected by the boundary refraction. However, general top-emitting OLEDs have more complicated device structures, stacking more layers such as the electron injection and transport layer to increase the electrical efficiency [1–3]. In these structures, the vertical distance between the dipole emitter and the top surface ranges from t = 0.17 to 0.3 μm. Consequently, the ratio of the emission area influenced by the optical reflections and refractions at the pixel boundaries increases from 8% up to 15%. If the same FEM simulation is performed at these complicated structures of top-emitting OLEDs, the effect of the boundary refraction will be more pronounced such that the angular emission characteristic of the multiple dipoles will significantly differ from that of a single center-located dipole.
5. Conclusion
We present comprehensive numerical modeling of top-emitting OLEDs based on the FEM, focusing on the effect of the pixel boundary on the angular emission characteristics. The light emission characteristics are calculated in the three-dimensional OLED structure having the square pixel boundary. The angular emission characteristics are calculated in various positions of a point dipole source within the pixel boundary. The angular emission characteristics depend on the distance between the point dipole and the pixel boundary, which determines whether the optical reflections from the pixel boundary in the horizontal direction affect the emission pattern of the dipole emitter or not. As the position of the dipole emitter moves toward the pixel boundary, the angular emission profile shifts from a symmetric to an asymmetric pattern. The total angular emission characteristics of the top-emitting OLED are obtained by summing the individual angular emission characteristics of the whole dipole emitters. We show that the asymmetrical angular emission characteristics of the dipole emitters near the pixel boundary contribute to narrowing the total angular emission pattern.
Acknowledgment
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2013R1A1A2007034), and by the OLED research center funded by Samsung Display.
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