73 Original scientific paper Effect of Dipole Position and Orientation on Light Extraction for Red OLEDs on Periodically Corrugated Substrate - FEM Simulations Study Milan Kovačič University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia Abstract: One of the main efficiency-limiting factors for organic light-emitting diodes (OLEDs) is poor light extraction, which typically reaches only 20% (in best cases up to 30%) in flat standard devices. Optical modeling and simulations play an important role in improving light extraction and optimizing outcoupling efficiency. Using FEM modeling approach, the effect of dipole positions and orientations for red OLEDs on periodically corrugated substrate is evaluated and used to enhance the outcoupling efficiency. It is shown that with only 3 carefully selected dipole positions, the outcoupling efficiency over the whole area can be predicted with very reasonable accuracy, which greatly reduces the number of simulations required. The presented modelling approach is used for optimization of the sine texture as a substrate corrugation structure. OLEDs with optimized simulated texture show a relative improvement of light outcoupling from the thin film stack to the substrate by more than 25% compared to the flat plane devices. Keywords: OLED; outcoupling; finite element method; optical modelling Vpliv Pozicije in Orientacije Dipola na Izstop Svetlobe Rdečih OLED na Periodično Teksturiranem Substratu – FEM Simulacijska Obravnava Izvleček: Eden izmed glavnih dejavnikov, ki omejujejo učinkovitost organskih svetlečih diod (OLED), je nizka stopnja učinkovitosti izstopa svetlobe, ki pri standardnih napravah dosega le okoli 20% (v najboljših primerih pa do 30%). Optično modeliranje in simulacije igrajo pomembno vlogo pri izboljšanju izstopa svetlobe in optimizaciji optičnega izkoristka. Z uporabo FEM modeliranja se ovrednoti učinek položaja in usmeritve dipolov za rdečo OLED na periodično teksturiranem substratu, ki se uporablja za povečanje učinkovitosti izstopa svetlobe. Pokaže se, da je mogoče s samo 3 skrbno izbranimi položaji dipola, z dobro natančnostjo napovedati učinkovitost izstopa na celotnem območju, kar močno zmanjša število zahtevanih simulacij. Predstavljeni FEM pristop se uporabi za optimizacijo sinusne teksture kot strukture teksturiranega substrata. OLED z optimizirano simulirano teksturo kažejo relativno več kot 25% izboljšanje učinkovitosti izstopa svetlobe iz tankoplastne strukture v substrat v primerjavi s ploščatimi napravami. Ključne besede: OLED; izstop svetlobe; metoda končnih elementov; optično modeliranje * Corresponding Author’s e-mail: milan.kovacic@fe.uni-lj.si Journal of Microelectronics, Electronic Components and Materials Vol. 51, No. 1(2021), 73 – 84 https://doi.org/10.33180/InfMIDEM2021.105 1 Introduction Organic light-emitting diodes (OLEDs) have in recent years achieved a commercial widespread in display technology, especially in mobile and television dis- plays. OLEDs are also very promising for general indoor and outdoor lighting, due to low cost, high efficiency, and high color quality. OLEDs can be fabricated as a large area sources on rigid or flexible substrates, can be made transparent for application on windows, all of which is important in lighting and architecture design [1]–[5]. OLEDs based on phosphorescent [6] and more recently on thermally activated delayed fluorescence 74 M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 emitters [7], [8] have already achieved internal efficien- cies close to 100%. On the other hand, highest EQEs for typical flat plane devices reaches only 20-30%, which is due to high optical losses resulting in poor light out- coupling efficiency [9]. Optical losses in OLEDs can be divided into three main groups. First are substrate losses due to total internal reflection (TIR) on the substrate/air interface, where light gets captured inside the thick substrate. Second are waveguide losses, that happen due to TIR at or- ganic (transparent contact)/substrate interface, where light gets waveguided and eventually absorbed. Third part are losses due to coupling of light to surface plas- mon polaritons (SPP) at organic/metallic interfaces. Minor losses are also due to parasitic absorption in lay- ers [10]. There has been a lot of research and proposed solutions to improve the light outcoupling, see for ex- ample recent reviews [11], [12]. Especially on reducing the substrate losses, highly efficient solutions already exist, like attaching a half-sphere, different micro- texturing [13]–[17] and others [18], [19]. On the other hand, solutions to waveguide and SPP losses exists, like micro-lens arrays [20], introducing scattering par- ticles [21], corrugations [22], [23] and others [24], [25], but remain less researched and non-optimized. This is mainly because internal solutions are more challeng- ing to fabricate and to integrate with OLED thin film stack, without having negative impact on electrical ef- ficiency [26]. With this in mind, optical modelling and simulations play an important role in improving out- coupling efficiency, to predict optimal solutions prior to complicated fabrication process, to test only most promising ones. Simulations of light emission from thin film stacks with internal outcoupling solutions (e.g. tex- turization, corrugations, scattering particles) requires more advanced modelling approaches, compared to flat-plane devices. In this paper, finite element method (FEM [27]) opti- cal modelling is utilized to research effects of a corru- gated substrate, which introduces internal textures in the OLED device structure itself. The aim is improved outcoupling of light into the substrate. In particular the focus is on investigation of different positions and ori- entations of emitting dipoles on outcoupling efficiency for red OLED on periodically corrugated substrate. FEM modelling approach, describing main considerations when simulating OLEDs, is explained. Presented model is used to analyze how number and position of simu- lated dipoles affect the simulated outcoupling accu- racy. In addition, it is shown that in the analyzed cases already 3 specifically positioned dipoles in the simula- tion domain are sufficient to get good prediction of trends for outcoupling efficiency. Moreover, outcou- pling efficiency and outcoupling trends of differently oriented dipoles for different positions on corrugated substrate are evaluated. 2 OLED Modelling The outcoupling of light in OLEDs, which is the focus of this paper, can be presented by combined opto-electri- cal parameter called external quantum efficiency (EQE), which defines the ratio between the number of pho- tons reaching the far field as useful light to the num- ber of injected charge carriers. EQE is calculated using equation (1), where γ is electrical efficiency defined as ratio between the number of radiative recombination in emission layer and the number of injected charge carriers, () el s λ is normalized electroluminescent spec- trum of emission material, () out ηλ is outcoupling effi- ciency of generated light into far field and () * rad,e ηλ is effective radiative efficiency. () () () * el rad,e out λ d EQEs λ γη λη λλ = ∫ (1) where () () () rad,e * rad,e rad,er ad,e λ λ 1 λ F F η η ηη = −+ (2) () * rad,e ηλ determines the ratio between radiative and non-radiative recombination. rad,e η is the intrinsic ra- diative efficiency of the emitter and () λ F is the Purcell factor, defined as a ratio between total emitted light at the source location and total emitted light in infinitive homogeneous medium. Using optical simulations, also employed in this work, wavelength dependent outcou- pling efficiency of generated light () out ηλ and wave- length dependent Purcell factor () λ F are calculated, and with these and by using equations (1) and (2), EQE as a primary optical data can be calculated. 2.1 Modelling of light in thin film OLED stack In OLEDs light is generated in the emission layer (EML) inside a thin film structure (e.g., see thin film structure used in this paper – Figure 1(a)) by electrolumines- cence emission of emitter material molecules. As sizes of these molecules are much smaller (few nanometers) than emission light wavelength (visible light), these can be treated as differently oriented point dipole sources [28]. The dipoles have specific predefined emission spectrum (determined by the molecule type) and angular intensity distribution and polarization of light according to the orientation in the layered system. Dipoles can in general have any arbitrarily orientation 75 which can be represented by three perpendicular di- pole components, two horizontally (x-y) and one verti- cally (z) oriented according to the selected global coor- dinate system. In case of flat plane OLEDs, orientation of dipoles in the plane of layered system (x-y) plays no direct role on outcoupling efficiency itself (it can af- fect angular distribution of light) and is in most cases treated as isotopically oriented [29], thus only ratio be- tween vertical and horizontal dipoles is considered. To describe general orientation of all emitting dipoles in the system, an anisotropy coefficient a is introduced, which is defined as the ratio between the vertical di- pole component towards all three dipole components. Anisotropy coefficient a = 1/3 meaning isotropic ori- entation of dipoles, while a < 1/3 indicates preferential horizontal orientation of dipoles and a > 1/3, preferen- tial orientation of vertical dipoles. Simulation of flat plane devices can be quickly and effi- ciently done by decomposing the dipole emission into set of plane waves which are then transferred through the thin film stack by using transfer matrix method (TMM). In case of large external corrugations or other textures, TMM can be coupled with geometrical optics for complete device simulations [16], [17]. On the other hand, modelling and simulation of nano- textured, corrugated or by introducing other disrup- tion in horizontal directions (e.g., scattering particles) requires more advanced approach. For the modelling of nanostructured thin-film structure we use 3D optical simulator COMSOL Multiphysics [30], which is based on a finite element method. We choose FEM due to advantages over other methods (RCWA FDTD) due to possibility of better discretization with higher order approximation of field inside the element, fairly straightforward definition of material properties (dielectrics and metals) and boundary conditions (e.g. absorbing, symmetry), ability to handle complex 3-D geometry and especially delivery of steady-state so- lutions in frequency (wavelength) instead of time do- main (e.g. FDTD). Using FEM, an arbitrarily oriented dipole source can be placed anywhere inside the structure and its steady state can be simulated. As each dipole need to be treated as individual source in laterally large structure (incoherent relation between different dipoles), there is a problem how to set the boundary conditions of simulation domain to avoid coherent connections between different dipoles. This presents one of the main challenges in rigorous simulations of OLEDs, re- quiring special modelling approaches to be taken. For example, regular periodicity boundary conditions that significantly reduce the simulation domain to a single unit cell or less, cannot be used here, as imply coherent connections between sources in periodically repeated unit cells. One solution would be to put a single dipole source in a laterally large structure with dimensions large enough to take into account all effects taking place far away from the source with multiple simula- tions for each different dipole position and orientation [31]. Main drawback is the required size of the model, as propagation lengths can be very large, thus lateral sizes of at least 40 m m and more away from the source would be necessary to include majority of the effects. Such large models would require huge amount of com- putational power (especially limiting is the computer memory) and are thus not really feasible. Alternative method is the usage of the so-called Flo- quet transform method [32], [33] (FTM). FTM highly re- duces memory requirements as it enables simulations of a single period (geometry) with individual source anywhere in the basic cell by using the Floquet trans- form to decompose non-periodic dipole source to a linear superposition of Bloch periodic terms. Details on the method itself can be found in [32]. Drawback of this approach is that it requires large number of simula- tions for accurate results (many Bloch periodic terms). Numerous simulations are required due to application of different phases for in/out going waves at the edge of domain, required to cancel unwanted coherence be- tween dipoles from neighboring domains. With paral- lelization this can be tolerable and FTM is also used for simulations in this work. When constructing FEM model with FTM, we need to consider some specifics that we will describe in the fol- lowing. Simulation domain needs to contain at least one, but multiple (integer) periods can also be used. On top (vertical dimension) unbounded areas that are stretching to infinity (e.g. glass, air), need to be trun- cated using open boundaries, absorbing all incident light with zero reflectivity. Open boundaries like per- fectly matching layer (PML) or absorbing boundary conditions (ABC) are applied here. An important aspect is also the distance between open boundary and thin film stack. If the boundary is too close to the stack, pos- sible coupling of evanescent waves to the boundary can happen influencing the simulation accuracy, on the other hand if the boundary is too far away, this can result in larger domain, requiring more computational power, elongating the simulation time. Here a rule of thumb is applied that the minimal distance between boundary and thin film stack is around 1~1.5 * simu- lated wavelength. In lateral directions where perio- dicity is applied, 2 pairs of periodic Floquet boundary conditions are used. For periodic boundary conditions, special care needs to be taken when meshing, as mesh shape and size needs to be identical on both repeating M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 76 sides, otherwise large errors can happen. For the rest of the device, meshing of the structure with general rule of thumb can be used, with 8-10 elements per distance of effective wavelength. It needs to be mentioned that by using FTM (or other FEM method) angular intensity distribution (AID) of emitted light of OLED device in the far-field cannot be gained directly, only the total outcoupling efficiency and the Purcell factor can be calculated directly. For far field AID calculation, a reciprocity principle [34], [35] can be employed, that enables to calculate AID as a consequence of any single dipole (or continuous spa- tial emission by multiple dipoles) at any position in the OLED stack. For each plane wave entering from outside under specific angle of incidence, it can be recalculated (by knowing E field (simulations) at the dipole(s) loca- tion) how this dipole contributes to emission into this specific angle in the far field. Extending simulations to multiple incident angles (both zenith and azimuth), AID in the far field for all simulated incident angles can be gained. This approach can only access modes that reach the far field medium (glass, air), while all other modes are inaccessible, giving only partial data. For to- tal evaluation, reciprocity principle for calculating AID and FTM for calculating outcoupling efficiency and Pur- cell factor, could be used as complementary methods, enabling simulations of device with thin and optically thick layers as well as nano and micro-sized textures or other outcoupling solutions. 2.2 Corrugated OLED structure description and model In this contribution the focus is only on thin film stack and optical properties connected with it. In simulations glass substrate is treated as half infinitive, this is from ex- perimental point similarly as by attaching a large glass hemisphere on top of the substrate, that enables extrac- tion of almost all light that reaches the substrate. By this, losses due to TIR at substrate/air interface are excluded and additional back reflections into the thin film stack are neglected, thus only waveguide and SPP losses are included. Due to this, outcoupling efficiency through entire paper is considered for light reaching the sub- strate and consequently air by using a glass hemisphere (ignoring minimal losses at glass hemisphere/air inter- face). We focus on standard red bottom emitting OLED [10], [16], with high electrical efficiency γ = 1 and intrin- sic radiative efficiency rad,e η = 0.7. Simulated stack, with layer thicknesses marked, is presented in Figure 1(a). Emission layer (EML), where light is generated, is sand- wiched between two blocking layers (for electrons - EBL and holes - HBL), and two transport layers (for electrons - ETL and holes HTL), that ensure high recombination rate in EML. Contacts are realized by opaque Ag cathode and a transparent indium tin oxide (ITO) anode. In our simu- lation model, EBL, HBL and EML were joined into single EML layer, to avoid very thin layers that can be very prob- lematic to mesh and add unnecessary complexity to the device. This can be justified due to very similar optical properties of these layers so only minimal difference is expected. Emission dipoles are positioned at EML/HBL interface, as majority of recombination events occurs in vicinity of HBL, due to higher hole conductivity of EML. Entire thin film stack is deposited on top of a flat or sine textured substrate. A sinusoidal texture is selected as it is commonly used and can be experimentally fabricated on e.g. silicon or glass master by e-beam or other etch- ing techniques. Additionally, selected sine texture ex- hibits smooth morphology without any abrupt changes, minimizing possibility of introducing electrical defects. All results in this contribution are related to this texture shape. When layers are deposited on top of a textured sub- strate, they experience layer growth which is a combi- nation of conformal and isotropic growth [36]. In this case a more conformal growth (linear combination of both 0.3*isotropic + 0.7*conformal) was used, which is the most common growth ratio in many amorphous materials. Actual layer growth as used in model can be seen in Figure 1(b). h P ~ ~ Ag - 100 nm ETL - 70 nm HTL - 50 nm ITO - 90 nm Glass substrate - 1.1 mm ~ ~ EML - 40 nm h P ~ ~ Ag - 100 nm ETL - 70 nm HTL - 50 nm ITO - 90 nm Glass substrate - 1.1 mm ~ ~ EML - 40 nm x y z x y z a) b) Figure 1: a.) Thin film stack of a standard red bottom emitting OLED on a corrugated glass substrate. b) Po- sition of dipoles on a corrugated substrate (red dots shown on 1/8th of the period area only)– snapshot from Comsol simulator M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 77 In EML a continuous homogenous spatial emission in the emission layer is assumed, i.e. an uninterrupted distribution of dipoles across the entire emission layer. With laterally symmetrical textures, such as the 2D sine texture in this case – Figure 1 (b), an advantage of the symmetry of the structure can be taken and only di- poles on a smaller area can be simulated. In this case, this means that by considering dipoles on only 1/8 of the period (see Figure 1 (b) with red dots indicating di- pole positions), the coverage of emission sources over the entire period and thus structure can be described. On the other hand, for non-symmetrical textures (e.g. saw profile or random) all possible locations of dipoles need to be considered. In the case of the sine texture, 15 dipoles positioned at constant distances from each other within the 1/8 of the texture were used, with the aim to consider as many possible positions of the di- poles on the texture, including extreme positions (e.g. on top and bottom of the texture). The numbering of the dipoles starts with no. 1 at the bottom (minimum) of the texture and ends at the top (maximum) with no. 15. Other dipole positions and corresponding number markings can be read from Figure 2(a) (top view of the dipole area, which can be linked to Figure 1(b)). It must also be taken into account that not all dipole po- sitions, once extended to the whole period, make the same contribution to the total outcoupling efficiency, as some dipoles represent larger area than others - see Figure 2(a) (weighing factors for entire period marked with x-times) and Figure 2 (b-d). For example, area cor- responding to dipole at location 15 (also 1) when ex- tended to the whole period represent the same area as a dipole at location 7 (8 or 11) before extension, re- sulting in 8-times lower contribution for dipole at lo- cation 15 (or 1) than for dipole at location 7 (8 or 11). To compensate for this, an additional weighting factors are added to each simulated dipole according to the represented area in the whole structure - see weight- ing factors in brackets in Figure 2(a), next to the dipole number. The orientation of the dipole is defined by its dipole moment direction, which for horizontally oriented di- poles points in the x, y plane and for vertically oriented dipoles in ±z direction according to the globally de- fined coordinate system and not according to the tex- ture surface normal. For vertically oriented dipoles, this direction is uniquely defined in ±z direction. While for two horizontally oriented dipoles the orientation in the x, y plane is in general free, only with the requirement of 90 degrees between them. Due to introduced sym- metry in used model, the orientation is defined in the initial simulation domain (1/8 of the period), where two horizontally oriented dipoles are differentiated as hori- zontally oriented - 1, where dipole moment direction points in ±x-direction, and as horizontally oriented - 2, Figure 2: a.) Top view of dipole numbering on top of 1/8 of sine texture with weights factors in brackets. b-d.) Top view of sine textures, with marked dipole posi- tions (red dots shown on 1/8 th of the period area only) and arrows showing dipole orientations as defined and used in simulations. The three analyzed situations with respect to dipole orientations are denoted with horizontally – 1 (b), horizontally – 2 (c) and vertically (d) oriented dipoles. M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 123 4 5 6789 10 11 12 13 14 15 x x 1 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 8 ( ) x 8 ( ) x 8 ( ) x 2 ( ) x 1 ( ) y x y x y x y a) b) c) d) 123 4 5 6789 10 11 12 13 14 15 x x 1 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 8 ( ) x 8 ( ) x 8 ( ) x 2 ( ) x 1 ( ) y x y x y x y a) b) c) d) 123 4 5 6789 10 11 12 13 14 15 x x 1 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 8 ( ) x 8 ( ) x 8 ( ) x 2 ( ) x 1 ( ) y x y x y x y a) b) c) d) 123 4 5 6789 10 11 12 13 14 15 x x 1 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 4 ( ) x 8 ( ) x 8 ( ) x 8 ( ) x 2 ( ) x 1 ( ) y x y x y x y a) b) c) d) 78 where dipole moment direction points in ±y-direction- see Figure 2 (b-d). Looking at the symmetry, extension over the texture diagonal leads to a change of dipole moment direction by 90 degrees in a defined coordi- nate system. As our definition of dipole orientation is defined on the starting 1/8 of the structure, even though the dipole moment is rotated by 90 degrees, the orientation with respect to the structure remains the same and is still treated as the same orientation as defined in the original 1/8 of the period. For details on the orientation of dipoles over the entire period, see Figure 2 (b-d). 3 Results 3.1 Flat plane device To verify the presented FEM model, a simple device with a flat plane is simulated and results are compared (see Figure 3) with an internally developed TMM model which has been derived theoretically and verified ex- perimentally [16]. Two orientations of dipoles are considered separately in this case: horizontally oriented-1 (identical results have been obtained for the horizontally oriented-2 in case of flat device) and vertically oriented (along z axis). In Figure 3(a) simulation results are presented for the outcoupling efficiency - () out ηλ and in Figure 3(b) the Purcell factor - F(λ) (see definitions in Eq. 1). For both horizontally and vertically oriented dipoles very good agreement between the results can be observed, espe- cially for the outcoupling efficiency. On the other hand, some differences in the Purcell factor can be seen, but the deviations from the correct results are small and should even decrease with texturization due to multi- ple random scattering events, resulting in reduced un- wanted coherence between random scattering events resulting dipoles (boundary conditions). 3.2 OLED on corrugated substrate - effect of dipole location and orientation FEM model is used to analyze optical properties, with the focus on light outcoupling of the red OLED thin- film stack deposited on a sine textured substrate with a period P = 800 nm and different height ranging from 0 (flat) to 400 nm (see definition of P and h in Figure 1). The effect of dipole positions and heights on outcou- pling efficiency is analyzed. Results are presented for wavelength of 612 nm, that corresponds to the emis- sion spectrum peak presented in Figure 3(a). First, the focus is on how dipole positions and orienta- tions influence light outcoupling for different heights of the sine texture. For this, simulations of outcoupling ef- ficiency for each of 15 dipoles individually for all three orientations and with different heights (0-400 nm) of the texture were carried out. Results of the simulations are presented in Figure 4(a-c), where lines represent outcou- pling to substrate for each dipole individually and the crosses with dashed lines present weighted average of all 15 dipoles, which is actually the result corresponding to situation when all dipoles were included in calcula- tion at once. Since the dipoles are not coupled in a co- herent manner, such averaging can be carried out. First observation from the results plotted in Figure 4 (a- c) is a high spread of results depending on the position of the dipole, indicating high influence of dipole posi- tion on the outcoupling efficiency. It has to be noted that global orientation of dipoles in one orientation set (e.g., horizontally oriented -1) remains the same inde- pendent of the dipole position. Differences are increas- ing with increasing texture height. This is expected, as the differences in actual vertical positions of dipoles Figure 3: Comparison between two simulation mod- els of a flat plane OLED. Symbols and lines represent results obtained with the TMM method and the FEM model, respectively. a) Outcoupling efficiency (Light extraction to substrate), b) Purcell factor. a) b) M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 79 are larger for the textures with higher h. Differences in outcoupling efficiencies between specific dipole loca- tions can also be very high, especially for horizontal orientations, with absolute differences between mini- mum and maximum value above 10% for horizontal dipoles and even above 25% for vertical dipoles at tex- ture height of 400 nm. For a visual presentation of the effect of dipole loca- tion for the three different orientations, outcoupling efficiencies are compared again for OLED structure with the sine texture with P = 800, h = 250 (max. out- coupling with a = 0.24). The outcoupling efficiency ac- cording to the dipoles position on one quarter of the sine texture is shown in Figure 5. For both horizontal orientations, the highest outcoupling efficiency can be observed for the dipoles which are located on top of the texture, while outcoupling starts to decrease when moving towards the lower positions, again it slightly increases at the lower end. For horizontal-1, a high outcoupling at the ridge can be observed, while for horizontal-2 at the same position no such increase can be observed. With vertically oriented dipoles, in contrast to both horizontally oriented dipoles, a mini- mal outcoupling efficiency is achieved at the top end of the texture, which increases towards the middle of the texture, while outcoupling decreases again at the minimum. The outcoupling efficiency seems to follow the inclination on the texture. For horizontal dipoles a lower outcoupling at higher inclinations (separately in x or y direction for horizontal-1 and horizontal-2) is gained. While with vertical dipoles at higher inclina- tions a higher outcoupling efficiency is observed. This would indicate, as a highly simplified approximation, that textures with less steep features are required for an optimal outcoupling with horizontally oriented di- poles, while for vertically oriented dipoles exactly the opposite is required, i.e. textures with steeper features, indicating that the final outcoupling efficiency is a compromise between both scenarios. The optimal tex- ture would also change with the general orientation of the dipoles, since a different texture would be optimal if there would be more vertically oriented dipoles or more horizontally oriented dipoles. Ultimately, the out- coupling cannot only be related to the inclination of the texture, as there are a number of other effects, such as the actual texture shape, the emission wavelength, the thin-film structure, all of which are specific to each individual OLED design, but these findings can serve as guidelines for further research. In addition, the mixture of many optical effects, with a high dependency not only on the shape and size of the texture but also on the emitting dipole positions and orientations, shows the importance of optical modeling and simulations for the planning, optimization and analysis of optimal optical solutions for achieving the highest outcoupling of individual OLED design. Figure 4: Outcoupling efficiency (to glass substrate) for each individual dipole according to its position on texture for different heights of the texture. a) Horizontally - 1 oriented dipoles, b) Horizontally - 2 oriented dipoles and c) Verti- cally oriented dipoles. d), e), f ) - comparison between weighted average of all dipole positions taken into account and specifically selected ones. Added are maximum deviations for both higher and lower outcoupling efficiency. d) for horizontally - 1 oriented, e) horizontally - 2 oriented and f) vertically oriented dipoles. M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 Vertically oriented a) b) c) d) e) f) 80 3.3 Effect of number of dipoles used in simulations To evaluate how much each outcoupling efficiency at each dipole position differs from weighted average, in Figure 6 total relative deviation from weighted aver- age is presented, calculated as abs(( () out i η )- () out average η ) / () out average η ), where i is the number of the dipole (1-15), and summed over all texture heights. A high spread of deviations between all dipole posi- tions is observed. What can also be clearly observed is the difference in the deviations at the same positions but different orientations, which indicates that the de- viation is not only location-dependent but also strong- ly orientation-dependent. For example, dipoles at po- sition 3 show high deviations for horizontally-1 and vertically oriented dipoles, but very low deviations for horizontally – 2 oriented dipoles. Overall, the smallest deviations for all three orientations can be observed for dipoles at position 8 and 11. Investigation on what is the minimal number of dipoles and what are their locations to approach the results obtained in simulations using 15 dipole locations were done. The first choice would be to take a single dipole position, preferably the dipole at position 8, which gen- erally shows the least deviation from the averaged total data. On the other hand, a single dipole position would theoretically allow us to hit a special location where the results would differ significantly from all others (e.g., constructive or destructive coherence, etc.), so that mul- tiple dipole positions would be preferable. To compare the outcoupling trends, in Figure 4 (d, e, f) the outcou- pling for a single dipole at location 8 as the dipole with the smallest total deviation from the weighted average, the combination of the dipoles at locations 8 and 11 as two of the dipoles with the smallest deviation from the weighted average, special case of the combination of dipoles at the locations 7, 8, 11 as the combination of dipoles which are most represented on the geom- etry, and which are also at center locations, and at the end the combination of dipoles at the locations 6, 8, 13 which show the best agreement with the weighted av- erage over 15 dipole locations are shown. Interestingly, the most representative combination of dipoles was the combination of dipoles at locations 6, 8 and 13, which are also located at central locations but are more widely spread than the dipoles at sites 7, 8 and 11 – see Figure 2. This combination of dipole locations follows weighted data for 15 dipole locations very well. It should be noted that even by simulating a single dipole at location 8 or a combination of other dipole locations, as shown in Figure 4 (d, e, f), a good agreement with general trends 0.72 0.7 0.68 0.66 0.64 0.62 600 600 700 700 800 800 900 1000 900 1000 250 200 150 100 50 0 y  out x y z  out 0.72 0.7 0.68 0.66 0.64 0.62 600 600 700 700 800 800 900 1000 900 1000 250 200 150 100 50 0 x y z  out 0.54 0.5 0.46 0.42 0.38 600 600 700 700 800 800 900 1000 900 1000 250 200 150 100 50 0 a) b) c) M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 Figure 5: Outcoupling efficiency (color) for different dipole locations on top of a texture (P = 800, h = 250) for a) horizontally - 1, b) horizontally - 2 and c) vertically oriented dipoles. See Figure 2 for dipole orientation. Figure 6: Total relative deviation from weighted aver- age for each dipole and orientation. 81 is obtained, albeit with an over- or under- estimation of the actual outcoupling efficiency. These results show that even by simulating a smaller number of carefully se- lected dipole locations, it is possible to predict outcou- pling trends, which greatly reduces the simulation time, although for the most accurate data, as many dipole po- sitions as possible would have to be included in the sim- ulations. On the other hand, it must also be mentioned that not every dipole location or even the combination of two or three dipole locations with the wrong selec- tion (e.g. dipoles at extreme points, symmetry, e.g. no. 1, 5, 15) leads to good results. Not only can these results differ significantly from the actual data, they can also lead to false trends. In Figure 4(d, e, f), vertical lines rep- resenting the maximum and minimum output values at each texture height are added, showing high deviations from the actual weighted average, and also different trends for both horizontally oriented dipoles, with maxi- mum output at much higher heights (250 - 300 nm) of the texture than with weighted average (150 - 200 nm). Therefore, three carefully selected dipole positions, pref- erably in the middle and wide spread, are necessary for a good adaptation to several dipole positions. It should be noted that this study was performed for sine shaped textures, while for other texture shapes other combina- tions of dipole positions may be more suitable and need to be investigated separately. 3.4 Simulation improvements of outcoupling efficiency due to substrate corrugation So far only each individual dipole by position and ori- entation was evaluated, without commenting on the improvement of the outcoupling as a whole. From the presented results it can be observed that with increasing height of the texture outcoupling efficiency also increas- es and reaches a maximum for horizontally -1 oriented dipoles at the height of 150 nm and for horizontally - 2 oriented dipoles at 200 nm, whereas with even higher heights of the texture outcoupling starts to decrease. For vertically oriented dipoles, the outcoupling efficiency in- creases with increasing texture height and saturates at heights above 300 nm Thus, the optimal height depends on the actual orientation of the dipoles, with which the ratio between the individual contributions can be deter- mined, that will influence the final output. The actual ori- entation of the emitter material molecules on corrugat- ed substrates may also differ from that on flat substrates and must be determined and taken into account. The advantage of modelling, where outcoupling efficiency of light is calculated for each orientation separately, is the simple and straightforward possibility to recalcu- late the final outcoupling to the actual distribution of the dipole orientations without additional simulations by simply weighing each contribution. If we assume for this case that the general orientation of the dipoles does not change (a = 0.24) when deposited on corrugated substrates, the highest EQE ( 1, 0.7 eler ad ηη == ) for glass substrate (or for air by using a glass hemisphere) of 47.7% at a texture height of 250 nm can be found, which is more than 25% higher than for flat plane device with 37.6% EQE – see Figure 7(b), indicating a high potential of sine corrugated substrates for the outcoupling of light from the OLED thin film structure. Moreover, added is outcoupling efficiency as calculated by using only 3 di- pole locations (6, 8, 13), to show almost perfect match- ing with the simulation results for 15 locations used. In addition, the comparison of the Purcell factor between flat and textured structure (Figure 7(a)) displays only a minimal difference, indicating that texturing does not have a major impact on the microcavity in this case. It needs to be noted, that optimal texture height of h = 250 nm for P = 800 nm, was determined for a single wavelength at emission peak of 612 nm, while if wave- lengths over entire emission spectrum would be in- cluded in the optimization process, possibly different height would result in best outcoupling efficiency, thus further optimization would need to be employed. M. Kovačič.; Informacije Midem, Vol. 51, No. 1(2021), 73 – 84 a) b) Figure 7: Comparison of simulation results for flat plane OLED and OLED on textured substrate with P = 800 and h = 250 nm. Anisotropy of a = 0.24 is consid- ered for both cases. Added are simulations results for only 3 dipole positions (6, 8, 13). a) Purcell factor – aver- aged over multiple positions; b) outcoupling efficiency and EQE to glass substrate (to air by using a glass hemi- sphere) 82 4 Conclusions A modeling approach based on FEM was presented to research effects of dipole position and orientation on the outcoupling efficiency of red OLED devices with periodically corrugated substrates. High devia- tions from the averaged outcoupling efficiency for in- dividual positions and orientations of emitter dipoles were revealed, although it is shown that even with a smaller number (three) of carefully selected dipole po- sitions the outcoupling over the wide area of sinusoi- dal texture height with very reasonable accuracy can be predicted and the number of required simulations reduced by a factor of 5. For an optimal texture, out- coupling tendencies corresponding to texture inclina- tion are shown, with opposite effects for horizontally and vertically oriented dipoles. This shows how impor- tant it is to optimize the outcoupling solutions for each specific OLED design, especially for dipole orientation. Finally, a possible 25% improvement in EQE (improved outcoupling efficiency) is shown, over flat plane de- vices by using a sine textured substrate with a period of 800 nm and a height of 250 nm, with the possibility of additional improvements. Modeling and simulations show a high potential for further design and optimiza- tion of future outcoupling solutions. 5 Acknowledgments The author shows appreciation to M. Topič and J. Krč for their valuable suggestions, advices and support in writ- ing this paper. 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