267 Original scientific paper  MIDEM Society Combined optical model for micro-structured organic light-emitting diodes Milan Kovačič1, Paul-Anton Will2, Benjamin Lipovšek1, Janez Krč1, Simone Lenk2, Sebastian Reineke2, and Marko Topič1 1University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia 2Technische Universität Dresden, Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Institute for Applied Physics, Dresden, Germany Abstract: Organic light-emitting diodes (OLEDs) with prospect of low cost, high efficiency and high quality lighting are a promising future light source. One of their limitations is poor light outcoupling, reaching only 20-30 % for conventional flat-plate lighting devices. Optical modelling and simulations are of great importance in optimizing the outcoupling efficiency. Complex structures of OLEDs, in which thin layers with emitting sources are combined with thick texturized substrate layers, require coupled optical modelling approach. We developed a combined optical model, comprising a thin layer stack where light is described as waves and thick texturized layers where light is described as rays. This combination enables simulation of OLEDs as complete devices with micro textures. We present the main considerations of the developed model. Finally, an OLED with laser structured sine textures is used to compare experimental results with simulation results obtained with the developed model. Keywords: OLED; organic light emitting diode; optical modeling; light outcoupling Združeni optični model za mikrostrukturirane organske svetleče diode Izvleček: Organske svetleče diode (OLED) predstavljajo obetajoč svetlobni vir, ki ga lahko uporabimo tudi pri razsvetljavi prostorov. Predvidena nizkocenovna proizvodnja visoko učinkovitih OLED omogoča izdelavo svetil z velikimi površinami. Ena izmed glavnih omejitev sodobnih OLED je nizka stopnja učinkovitosti izstopa svetlobe iz tankoplastne strukture elementa. Konvencionalne izvedbe OLED z gladkimi površinami dosegajo le 20-30 % stopnjo učinkovitosti izstopa svetlobe. Pomembno vlogo pri načrtovanju in optični optimizaciji struktur OLED igra optično modeliranje v povezavi z numeričnimi simulacijami. Strukture OLED združujejo tanke organske plasti v kombinaciji z debelejšimi plastmi (substrati), zato pri simulaciji potrebujemo poseben, združen optični model, ki omogoča koherentno in nekoherentno širjenje svetlobe. Razvili smo tridimenzionalni združeni optični model, kjer tanke plasti z optičnimi viri lahko obravnavamo skupaj z debelejšimi plastmi, ki hkrati vsebujejo teksture za izboljšanje učinkovitosti izstopa svetlobe. Ta kombinacija nam tako omogoča simulacije in optično optimizacijo celotnih OLED struktur, ki vsebujejo mikroteksturirane površine. V prispevku so predstavljene glavne lastnosti modela. Rezultate simulacij z razvitim modelom validiramo z izdelanimi vzorci, kjer smo teksture izdelali z laserskim graviranjem steklenega substrata. Ključne besede: OLED; organske svetleče diode; optično modeliranje; ekstrakcija svetlobe * Corresponding Author’s e-mail: milan.kovacic@fe.uni-lj.si Journal of Microelectronics, Electronic Components and Materials Vol. 46, No. 4(2016), 267 – 275 1 Introduction Over 20 % of the generated electrical power in the de- veloped countries and a considerable amount in the developing countries is used for lighting and the con- sumption will continue to grow [1]. Therefore, efficient lighting is one of the cornerstones of reducing the carbon footprint for achieving a greener future. One of the emerging lighting technologies called organic light-emitting diodes (OLEDs), offers high possibilities of becoming a future lighting source, since it is a thin film, large area (and not point source like their inor- ganic equivalents) lightweight device with a potential to provide low cost, highly efficient and high quality general lighting [2–4]. Similar to the limited conver- sion efficiency of photovoltaic devices or laser power converters [5, 6], OLEDs are also facing theoretical lim- its. One of the main obstacles for OLEDs to reach their full potential is poor light outcoupling, as for normal 268 devices only ~20-30 % of the generated light reaches the far field as useful light [7, 8], while the internal conversion efficiency from an injected electron to a generated photon is close to 100 % [9–11]. Intensive research has been done in the last years to reduce the optical losses in OLEDs, see for example [12–14], but a lot of room for improvement still remains. OLEDs are optically relatively complex devices, where even planar devices include combination of thin and thick layers, a microcavity effect, a different orientation of emitting dipoles – anisotropy, coupling of light to surface plas- mon polaritons (SPP), an arbitrary angular distribution of emitted light, absorption in layers and others. There- fore, optical modelling and simulations are an essential tool in design and optimization of these devices. In this article, we present an optical model that we developed for a three-dimensional (3D) simulation of OLED struc- tures including micro textures for efficient control of light. The model couples emitting sources (dipoles) in thin organic layers with thin-film optics of surrounding layers, ray tracing in thick incoherent layers and at mi- cro textured surfaces. The physics of the model will be presented, followed by selected examples of validation on realistic OLED structures. 2 Optical model 2.1 OLED structure and operation A conventional bottom-emitting p-i-n OLED structure is presented in Figure 1. It consists of a thin layer stack, containing light emission sources and a thick transpar- ent substrate, e.g. glass or transparent foil that can be non-structured or structured. Light is generated in thin emission layer (EML) by ra- diative recombination of electrons and holes. To en- sure good supply of both, optional electron- and hole- transport (ETL, HTL), injection (EIL, HIL) and blocking layers (EBL, HBL) are added and contacted with an opaque highly reflective silver cathode and a transpar- ent indium tin oxide (ITO) anode as shown in Figure 1. The thicknesses of thin layers are in the range of light wavelengths therefore the light has to be treated co- herently, in terms of electromagnetic waves. In thicker layers (e.g. the transparent substrate) the light has to be treated incoherently, in terms of rays. The overall OLED device efficiency, including optical and electrical performance, can be presented by the external quantum efficiency (EQE) [15, 16], which is the ratio between the number of photons reaching the far field as useful light to the number of injected charge carriers: ( ) ( ) ( )*el rad,e outEQE s d λ γ λ η λ η λ λ= ∫ (1) ( ) ( ) ( ) rad,e* rad,e rad,e rad,e1 F F η λ η λ η η λ = − + (2) ( ) ( )out U F λ η λ = (3) Where sel is a normalized luminescence spectrum of the emitting material ( ( )el 1s d λ λ λ =∫ ), γ is the electrical efficiency and η*rad,e is the effective radiative efficiency of the emitter. Its definition is given in Eq. (2), in which ηrad,e is the intrinsic radiative efficiency of the emitter and F(λ) is the total radiated power at the emitter lo- cation relative to the power radiated in an infinite ho- mogeneous medium (also called the Purcell factor). Finally ηout in Eq. (1) is the outcoupling efficiency that is defined in Eq. (3) as the ratio of the total radiated power outcoupled from the OLED structure to the far field (usually air), U(λ), to the total Purcell factor, F(λ). Looking back to Eqs. (1)-(3), we can see that the optical properties of EQE are fully defined by U(λ) and F(λ) pa- rameters. An optical model should therefore determine these two parameters (U(λ) and F(λ)), while also pro- vide an insight in optical behavior inside and outside the structure. nitrogen Ag cathode - EIL&ETL HBL EBL ITO - anode glass EML HIL&HTL 100 nm 70 nm 10 nm 20 nm 10 nm 50 nm 90 nm thick - 1.1 mm Emission Outcoupled light air + - Figure 1: Structure of a conventional p-i-n bottom- emitting red OLED deposited on a glass substrate and encapsulated under a nitrogen atmosphere. Texturiza- tion of the substrate (on light escaping side) is indicat- ed on the right hand side of the substrate. M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 269 2.2 Concept of the model Our model combines two sub-models: a thin-film opti- cal model with light sources and a ray-tracing model - Figure 2. The thin-film model is based on a transfer matrix model (TMM), in which we incorporate internal light sources, in form of dipoles (as commonly used to describe light generation in organic layers) or in any other arbitrary form of light sources. The ray-tracing model is a 3D model utilized in CROWM simulator [17]. The ray-tracing model of the simulator was upgraded with TMM to be able to include thin-layer stacks also outside the OLED device (e.g. on the front side of the device, in general). The TMM approach requires that the thin layers are locally flat and plane parallel. Ap- plied textures with micrometer dimensions (dimen- sions larger than light wavelengths of interest) still ful- fill this condition, thus our model enables us to include micro textures either on the surface or at internal inter- faces of OLED structures (see Figure 2). In the following sections, we present the main properties of the devel- oped simulation model with governing equations and main specifics. Figure 2: Combined OLED model, combining thin film layers containing dipole sources (locally flat TMM mod- el) with thick incoherent layers (CROWM). 2.3 TMM with internal light sources Organic layers and the thin film contacts in the OLED structure are stacks of locally flat plane parallel coher- ent layers. To describe the light behavior in these stacks without particular light sources at the first stage, TMM presents an efficient solution for the calculation of the optical properties inside and outside the stack. Most commonly, TMM is used for modelling of thin-film op- tical devices with an external light source (e.g. an illu- minated flat solar cell), while in the OLEDs, the light is generated inside the thin-film structure. Therefore, to incorporate such an internal light source, we modified the TMM formulation to properly describe the light generation and propagation in a thin layer stack. A similar approach has been presented in [18]. Following the TMM formalism from [19], a plane wave propagating obliquely through the thin-film stack un- der some angle iϑ can first be separated according to its polarization – we differentiate between the trans- verse-electric (TE) and the transverse-magnetic (TM) polarizations, based on the plane of incidence and the orientation of the electric and magnetic fields. Next, for each of the two polarizations, the waves are further distributed into two components: the transverse plane wave component that is travelling perpendicularly to the flat interfaces through the stack, and the compo- nent that is travelling in parallel along the interfaces. TMM formalism treats only the transverse components which interact (interfere) constructively or destruc- tively with each other, while information about the full wave is contained in the propagating angle. The electric field that belongs to the transverse wave com- ponent of emission source (incident light or internal source) is calculated separately for the TE and TM po- larization for emission as: T,TE TE emiE E= T,TM TM emi emicosE E ϑ= (4) where emiϑ is the incident angle of the total electric field incident on interfaces. In the following formulation, all the electric fields in the equations are considered to be the electric fields that belong to the transverse wave component, as denoted by the superscript T, and can originate from either the TE or the TM polarization, thus all further presented formulations need to be consid- ered separately for TE and TM polarizations as specified in TMM formulations [19]. A thin-film layer structure, that is described by the layer thicknesses and by the corresponding complex refrac- tive indices of the individual layers, can be defined by a TMM formalism using the product of propagation ma- trices P (propagation through layer) and matching ma- trices M (reflection and transmission at the interface) [19]. The matching matrices (M) are obtained by Fres- nel’s transverse reflection ( Tjr ) and transverse transmis- sion ( Tjt ) coefficients (separately for TE and TM) at j-th interface as: T T T T j,l j j,r j,r jT T T TT j,l j j,r j,rj 11 · · 1 E r E E M E r E Et + + + − − −          = =                 (5) where T j,l E ± and Tj,rE ± are electric fields on the left and right side of the j-th interface, respectively, propagat- ing in the positive (+) or the negative (–) direction. thin layers with light sources (coherent - modified TMM) thick texturized layer (incoherent, RT) medium in transmission (incoherent, RT) dipole sources Localy flat thin film structure with a dipole source M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 270 Propagation matrices (P) are obtained by propagating the above fields through the k-th layer as: [ ] k k T T T k,l k,r k,r kT T T k,l k,r k,r 0 · · 0 j j E E Ee P E E Ee δ δ + + + − − −−        = =              (6) Where dk contains the information about the phase change and the absorption inside the layer, via the layer thickness and the complex refractive index of the layer material. A more detailed explanation and deriva- tion of P and M matrices can be found in [19]. In the case of devices with internal sources (e.g. OLEDs), the initial electric field (presenting the emission source) is generated inside the thin film structure, namely in- side a specified layer. We assume the sources are locat- ed on a plane parallel to the interfaces. More detailed emission source definition for OLED sources (dipoles) is presented in the next subchapter. To incorporate the initial electric field of the source, we put a new virtual interface parallel to the existing interfaces inside the specified layer (m) at an arbitrary position. The position of this virtual interface is defined by the spatial posi- tion parameter p as shown in eq. (7). The interface splits the original (m-th) layer into two layers with their thick- nesses defined by p parameter (0 < p < 1) as: v,l m *d d p= ( )v,r m * 1d d p= − (7) Where dv,1 and dv,r are the thicknesses of the left and the right part of the m-th layer after the splitting, re- spectively. Figure 3: Schematic representation of a thin-film mul- tilayer stack with an additional virtual interface incor- porating an internal source in arbitrary layer m. New electric fields (equation (4)) are introduced at the new virtual interface “v”, their values are defined by par- ticular emitting sources. This initial source waves are propagating away of the interface, therefore we have on the left side of the interface a source wave in nega- tive direction ( TemiE − ) and on the right side in positive direction ( TemiE + ). Considering that the virtual interface is placed within the layer we can write the following relations: T T T v,r v,l emi E E E+ + += + T T T v,l v,r emi E E E− − −= + (8) To describe these new conditions at the virtual inter- face, we split the entire optical system into two parts, the first part describing the thin film environment on the left of the virtual interface, and second on the right. The thin film stack on the left of the virtual interface can thus be described as: [ ][ ][ ] [ ] T TT 11 12v,l v,r*1 1 2 2 m 1 mT T TT 1 21 22v,l v,r1 0 · · · · · · B BE EE M P M M P E B BE EE + ++ −− − −−          = = … =                  (9) and on the right of the virtual interface as: [ ][ ] [ ][ ] T T T 11 12v,r ** N N m m m 1 N 1 N 1T T 21 22v,r N · · · · · · 0 F FE E E P M P P M F FE E + + + + − −− −        = … =              (10) where *mP and ** m P − are modified propagation matri- ces due to the change of thicknesses due to introduc- ing a new virtual interface. Additionally, as the source is inside the thin film structure and no incident light from the outside is considered, the transversal electric fields representing the incoming light from the outside of the thin film structure ( T1E + and TNE − ) are set to 0. Using equations (8), (9) and (10), it is straightforward to calculate the new conditions ( ( ) T v,l r E ± ) at the virtual inter- face due to the introduced emission source ( TemiE ± ) in the entire thin film system. Here we present the final results for superimposed fields at the position of the virtual in- terface only (either for TE or TM polarisation): ( )T T T11v,r 11 emi 12 emi 11 11 12 21 * · · · · FE B E B E B F B F + + −= − + ( )T T T12 21v,r emi emi 11 11 12 21 · * · · B FE E E B F B F − − +−= + + (11) It is worth noting that due to dipole emission symme- try T Temi emiE E + −= , the presented formulations are never- theless applicable also to non-symmetric sources. Once we determine the fields at the virtual interface, that represent source fields ( ) T v,l r E ± , the electric fields at all other interfaces can be easily calculated using the standard TMM formulations [19]. In the final step we calculate the total ET and HT fields at each interface as: ( ) T T T i,t i,t i T TT i,t i,ti i 1 E E E E EH η + − + −  +   =   −     (12) where ηi is the material impedance connecting ET and HT field in the specific material. As ( ) T v,l r E ± are modified by 1 2 3 m N-1 N... ... d2 d3 dN-1 1 2 3 m N-2 N-1... ... ... ... ... ... Θ1 Θ2 Θ3 ΘN-1 ± 2 TE ±3 TE ΘN ... ... 1n̂ 2n̂ 3n̂ ± 1 TE ±1 T zE − ± 2 T NE − ± 1 T NE − ±TNE 1ˆNn − ˆNn ± , T v rE ± , T v lE dm·dc dm·(1-dc) m+1 ±T zE ˆmnˆmn Θm-1 Θm Θm ΘN-2 M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 271 forward and backward matrices (optical environment), all the results will be relative, to the modified source expressed with the conditions at the virtual layer (not to the original input emission source). Using ET and HT fields, we simply calculate the total power densities of the wave entering the i-th layer by using the Poynting vector as: ( ) ( )T T*i i i i1 / cos2P Re E H ϑ= × (13) Here, ( )icos ϑ is added to the classic Poynting vector formulation to obtain the power of the complete wave propagating under an oblique angle iϑ through the i-th layer. Finally, due to the modified source, expressed with the conditions at the virtual interface, all power densities must be normalized with respect to the total power density that exist on both sides of the virtual in- terface and corresponds to the total emission power of the source (Pemi,tot). By knowing the relative power en- tering each layer we can simply calculate the relative absorption (Ai) in each layer. And finally, the relative power of the light that exits the thin film stack at the left and the right side of the stack correspond to P1 and PN, respectively. 2.4 Definition of internal light sources In the case of OLEDs, the electroluminescent emission is considered as a dipole transition from an excited mo- lecular state to the ground state [20]. The sizes of the emitting sources in OLEDs do not exceed a few nanom- eters, being very small with respect to the wavelength, thus they can be approximated by point dipoles [20]. Point dipole emitters are in the model simulated as a classical, continuously oscillating dipole sources with predefined spectrum and angular intensity distribu- tion (AID). The AID of a dipole in infinite medium is presented in Figure 4. The 3D AID and the two cross- sections with the corresponding angular functions are presented for the vertically oriented dipole (see black arrow). From here on the dipole orientation (vertical, horizontal) is referred to with respect to the interface planes of the structure. If the dipole is rotated, its AID rotates accordingly. Once it is put inside a thin-film multilayer structure, interference effects with reflected waves have to be considered (included in TMM). As dipoles emit light as spherical waves, which is not very useful in TMM formulations, their emission is converted through Fourier decomposition into plane waves travelling under specified angles. These angles may be real or imaginary valued, according to Fourier decomposition [20]. The imaginary components repre- sent evanescent waves, which are also taken into ac- count in the TMM. Emitting sources (dipoles) are considered to be iso- tropically orientated in the plane of the layered system, thus only orientation with respect to the layered sys- tem normal has to be considered. Any arbitrary orient- ed dipole is decomposed into three orthogonal dipoles in the model, two parallel (horizontal) and one perpen- dicular (vertical) dipole, defined by their orientation to the interfaces of the planar system and the corre- sponding emission polarization. Special care has to be taken when defining the TE and TM components of the planar waves approaching the interfaces at different incident angles. While the magnetic field is always per- pendicular to the dipole orientation, the electric field lies in the plane which is defined by dipole orientation and the direction of wave propagation. Another condi- tion is that magnetic field, electric field and the propa- gation direction are perpendicular to each other. Based on these rules TE and TM components can be defined in the model. In the OLED, the emitting layer is combined from mul- tiple randomly oriented dipoles that can in general have some preferential orientation to the layered sys- tem normal, this can be a consequence of material properties or deposition methods (e.g. sputtering, spin coating). This preferential orientation of dipoles can be incorporated in anisotropy coefficient a, as a ratio be- tween the number of vertical dipoles to the number of all dipoles. In the case of random orientation of dipoles, Figure 4: Vertically (according to the xy plane) oriented dipole in homogeneous space, with cross-sectional projections showing polar (ϑ) and azimuth (Φ) angles. M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 272 a = 1/3, meaning that contributions from all three or- thogonal dipoles (two horizontal and one vertical as defined above) are considered equally. Incorporating anisotropy reduces the highly complex problem of de- scribing detailed dipole orientation to a rather simple problem of defining the fraction of parallel and per- pendicular dipole moments [20]. For complete optical description of emission source (dipole), TTM approach described in previous subchap- ter needs to be applied for all discretized Fourier plane waves defining the (dipole) source. The ratio of total emitted power in layered system and total emitted power of the same source in an infinitive medium is the Purcell factor for a given wavelength, F(λ), and is our first important optical parameter that can be defined by simulation. 2.5 Combining TMM model with the ray tracing simulator CROWM A simple flat structure with a single thick layer can be easily simulated using an expanded TMM formula- tion that also considers incoherent light propagation through the thick flat layer [21]. However, a problem occurs when we introduce more complicated struc- tures, e.g. such as structures with textured surfaces of the thick layer or with additional thin layers on top of the substrate. To overcome this problem, we combined our TMM model with the optical simulator CROWM [17] that enables complete optical simulation of advanced structures including thin and thick layers with or with- out textures. This way, it is possible to simulate arbi- trary complex LED devices with flat or micro-textured substrates as well as with additional thin-film stacks incorporated in the device, such as antireflection lay- ers etc. The simulation initiates by calculating the out- put of the developed TMM model with internal sources (relative powers P1 and PN, their angles of propagation and TE/TM decomposition), which are then taken as the input into the general CROWM simulation (com- bination of ray tracing and classical TMM). While the polar angles (ϑ) are defined with TMM formulations, the azimuth angles (Φ) are, due to assumed z-axis sym- metry and under the assumption of isotropically ori- ented dipoles in a planar layer, equally distributed over possible discrete values (0-360°). Each discrete part is then considered as a ray (separately for TE and TM) and traced through the rest of the structure until it is either extracted to air or reabsorbed in the structure. Addi- tionally, since sources are considered as point sources in a locally flat structure, a large number of sources dis- tributed across the entire area of the device (see Figure 2) are considered, and the final result is an average of all the contributions, ensuring realistic representation of the real device. 2.6 Model limitation and advantages The thin-film model with emission sources is con- sidered locally flat and anisotropic in parallel planes, which is true for most OLEDs. The emitting organic layer is considered to be non-absorbing as absorption can suppress spontaneous emission from radiating di- poles [22]. As absorption of emissive layers (at emissive wavelengths) is considerably small it can be neglected without affecting accuracy [15]. Multiple emitting layers (interfaces) with independ- ent anisotropy, independent emission locations, inde- pendent emission spectrum and independent distri- bution in emissive layer(s) can be simulated, this being very suitable for white (multi-color) devices. In many models [18, 23] only transmission to the exit medium (usually air) and total relative emission (Purcell factor) are presented, while in our model absorption of each individual layer can also be extracted. Due to the use of ray tracing in combination with TMM, multiple thick layers with thin-film stacks and various micro textures can be included in the simulations. Another important advantage of our model is the pos- sibility of simulating with restricted geometry in lateral dimensions. An entire device with independently limit- ed emission and limited texture area can be simulated. This is very useful especially in research, where smaller samples are usually produced with limited emission area and limited texture area, see Figure 5 where only small pixel area is active and emits light while the tex- ture is produced only above this pixel area. This can have immense effect on final results, thus limited area simulations are very beneficial for modeling realistic devices. 3 Experimental validation of the combined model In this contribution, we present an experimental vali- dation of the combined model on red bottom emitting p-i-n OLEDs (produced at TU Dresden) with flat and sine textured substrate / air interface. OLED structure with layer thicknesses is presented in Figure 1, while fi- nal device with visible laser structured sine texture can be seen in Figure 2. Sine textures were produced using laser structuring of the glass substrate – see Figure 5. Final textures are simple 1D sine textures with constant period P = 175 µm and three different heights h (2.5 µm, 6.5 µm and 15 µm). OLED production details can be found in [16, 24]. M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 273 Figure 5: A produced bottom-emitting red OLED (four dots as indicated by the contacts) with sine textures on glass / air interface. Red rectangle indicates limited tex- tured area of approx. 7x9 mm2. Additionally, profilom- eter measurements of the sine textures for selected example is also shown. Emitter material properties ( γ = 0.92, ηrad,e = 0.87, an- isotropy a = 0.256, sel – emission spectrum, emission positon) are taken from a previously published data [15] or gained from internal sources and were experi- mentally confirmed. The emission position was set at a single position in the emission layer with p = 1, the emission is still considered to be in emission layer, but infinitively close to the HBL (see Figure 1). Optical properties, in particular layer thicknesses and material refractive indices were supplied by TU Dresden and are within the anticipated error range. Here we present comparison between simulations and experimental results for the total radiant intensity, EQE and AID which are important performance parameters of OLEDs. Comparison between simulations and ex- periment for total radiant intensity for flat and textured (sine textures with P = 175 µm and h = 15 µm) devices can be seen in Figure 6. Good matching between simu- lations and experiment can be observed, especially for the flat device. Some deviations are due to limited tex- ture size in the experimental device (see Figure 5), as in simulations we simulated textured area as infinitive (this is justified for actual lightning applications since the emission and texture area are both large enough, more than 10x10 cm2). Figure 6: Comparison of total radiant intensity of a flat device and textured (sine textures with P = 175 µm and h = 15 µm) device for measurements and simulations. We also compare measured and simulated EQE. The EQE was gained from AID measurements assuming ro- tation symmetry as: ( ) ( )c e c 2 , sineEQE I I d d I hc ϑλ π λ ϑ λ ϑ ϑ λ= (14) Where Ie is radiand intensity, Ic is applied current, e is elementary charge, c is the speed of light in vacuum, h is Planck constant and ϑ is a polar angle. The EQE was calculated and simulated for a flat and a texturized OLED. The EQE of a flat OLED was taken as a reference and the gain (G) when using textures was defined as: texturized flat flat *100% EQE EQEG EQE − = (15) We present here simulation and experimental results for 3 texturized OLED devices, with different sine as- pect ratios (AR = h/P) of the textures. The results are presented in Table 1. Good matching was found again, minor deviations are due to limited texture size in ex- perimental device (see Figure 5). Length, l (µm) 0 100 200 300 400 500 He ig ht , h (µ m ) 0 2 4 6 8 10 12 14 16 Wavelength, λ (nm) 550 600 650 700 750 R ad ia nt in te ns ity , I e ( a. u. ) 0 1e-6 2e-6 3e-6 4e-6 5e-6 6e-6 Texturized - experiment Texturized - simulations Flat - experiment Flat - simulations M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 274 Table 1: Gain (G) comparison between experimental and simulation results for different AR of the sine tex- tures. Aspect ratio – AR (h (µm) / P (µm)) G (%) - experiment G (%) - simulations 0 (0 / -) 0 0 0.0143 (2.5 / 175) 7.0 9.0 0.0371 (6.5 / 175) 11.2 12.5 0.0857 (15 / 175) 19.7 20.6 Another important parameter in OLEDs is the AID. We compare the simulated AID for flat and textured devices. Results for OLED with flat and texturized de- vice (sine textures P = 175 µm, h = 15 µm) can be seen in Figure 7. Here we present an AID at emission peak wavelength of 610  nm. Comparing normalized simu- lated and experimental AID data from 0o to 60 o, devia- tions up to 2 % and up to 3 % can be found at individual angles for the flat and the textured device, respectively. While for angles over 60 o where limited texture size (as light travelling under high angles in substrate does not fall on the textured surface entirely) starts to influence the measurement results, thus the difference rises up to 7 % and 15 % for flat and textured device, respec- tively. Only small deviations between simulation and experimental AID is identified and very good matching for flat and textured device can be observed. Figure 7: Angular intensity distribution (AID) compari- son for flat and device with textured interface (sine tex- tures on interface substrate/air with P = 175 µm and h = 15 µm) vs. simulation results for corresponding structures. Additionally, ideal Lambertian distribution is added. 4 Conclusions A new combined optical model, based on TMM and ray-tracing approaches has been developed. De- tailed modification of TMM to incorporate internal dipole sources was presented. TMM model with inter- nal sources was combined with ray tracing simulator CROWM, to incorporate simulations of thick texturized layers. Dipoles as emission sources in OLEDs were ap- plied to TMM formulations. OLEDs optical performance parameters - outcoupling efficiency and Purcell factor were gained using developed optical model and used in further calculations where good matching with ex- perimental results was obtained. Additionally, simu- lated angular intensity distribution showed excellent matching with experimental results. The mismatch for angles up to 60o was under 3 %, for both flat and tex- tured devices. In the final part, validation of the devel- oped model was presented by comparison of simulat- ed results with experimental ones. Good matching was obtained for red bottom-emitting p-i-n OLED devices on glass with flat and micro-textured front surface. De- veloped optical model accurately predicts optical be- havior of flat and textured OLEDs and is appropriate for further simulations of advanced OLED devices. OLEDs with 1D front surface sine textures (textures were made by simple laser structuring of glass) outperform the flat counterpart in all performance parameters. 5 Acknowledgment The authors acknowledge the financial support from the Slovenian Research Agency (P2-0197). M. Kovačič personally acknowledges the Slovenian Research Agency for providing PhD funding. 6 References 1. Y.-L. Chang and Z.-H. Lu, “White Organic Light- Emitting Diodes for Solid-State Lighting,” J. Disp. Technol., vol. 9, no. 6, pp. 459–468, Jun. 2013. 2. “NEC Lighting announces OLED Device with 156 Lm/W efficiency.” [Online]. Available: http://www. osadirect.com/news/article/918/nec-lighting-an- nounces-oled-device-with-156-lmw-efficiency/. [Accessed: 06-Mar-2015]. 3. “Konica Minolta break their own record with world’s most efficient OLED panel (139 lm/W).” [Online]. Available: http://www.oled-info.com/ konica-minolta-break-their-own-record-worlds- most-efficient-oled-panel-139-lmw. [Accessed: 06-Mar-2015]. 0 30 60 90 0.0 0.2 0.4 0.6 0.8 1.0 Texturized OLED - experiment Flat OLED - experiment Texturized OLED - simulations Flat OLED - simulations Lambertian M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275 275 4. S. Reineke, M. Thomschke, B. Luessem, and K. Leo, “White organic light-emitting diodes: Status and perspective,” Rev. Mod. Phys., vol. 85, no. 3, pp. 1245–1293, Jul. 2013. 5. M. Jošt and M. Topič, “Efficiency limits in photo- voltaics: Case of single junction solar cells,” Facta Univ. - Ser. Electron. Energ., vol. 27, no. 4, pp. 631– 638, 2014. 6. R. Kimovec and M. Topič, “COMPARISON OF MEAS- URED PERFORMANCE AND THEORETICAL LIMITS OF GAAS LASER POWER CONVERTERS UNDER MONOCHROMATIC LIGHT,” Facta Univ. Ser. Elec- tron. Energ., vol. 30, no. 1, pp. 93–106, Aug. 2016. 7. S. r. Forrest, D. d. c. Bradley, and M. e. Thompson, “Measuring the Efficiency of Organic Light-Emit- ting Devices,” Adv. Mater., vol. 15, no. 13, pp. 1043– 1048, Jul. 2003. 8. J. Krc, B. Lipovsek, and M. Topic, “Design for high out-coupling efficiency of white OLED using CROWM - a combined geometric/wave optics model,” in Renewable Energy and the Environment (2013), paper JM3A.16, 2013, p. JM3A.16. 9. L. Xiao, S.-J. Su, Y. Agata, H. Lan, and J. Kido, “Nearly 100% Internal Quantum Efficiency in an Organic Blue-Light Electrophosphorescent Device Using a Weak Electron Transporting Material with a Wide Energy Gap,” Adv. Mater., vol. 21, no. 12, pp. 1271– 1274, Mar. 2009. 10. F. B. Dias et al., “Triplet Harvesting with 100% Ef- ficiency by Way of Thermally Activated Delayed Fluorescence in Charge Transfer OLED Emitters,” Adv. Mater., vol. 25, no. 27, pp. 3707–3714, Jul. 2013. 11. Q. Zhang et al., “Nearly 100% Internal Quantum Ef- ficiency in Undoped Electroluminescent Devices Employing Pure Organic Emitters,” Adv. Mater., vol. 27, no. 12, pp. 2096–2100, Mar. 2015. 12. K. Saxena, V. K. Jain, and D. S. Mehta, “A review on the light extraction techniques in organic elec- troluminescent devices,” Opt. Mater., vol. 32, no. 1, pp. 221–233, Nov. 2009. 13. W. Brütting, J. Frischeisen, T. D. Schmidt, B. J. Scholz, and C. Mayr, “Device efficiency of organic light-emitting diodes: Progress by improved light outcoupling,” Phys. Status Solidi A, vol. 210, no. 1, pp. 44–65, Jan. 2013. 14. M. C. Gather and S. Reineke, “Recent advances in light outcoupling from white organic light-emit- ting diodes,” J. Photonics Energy, vol. 5, p. 57607, May 2015. 15. M. Furno, R. Meerheim, S. Hofmann, B. Luessem, and K. Leo, “Efficiency and rate of spontaneous emission in organic electroluminescent devices,” Phys. Rev. B, vol. 85, no. 11, p. 115205, Mar. 2012. 16. R. Meerheim, M. Furno, S. Hofmann, B. Luessem, and K. Leo, “Quantification of energy loss mecha- nisms in organic light-emitting diodes,” Appl. Phys. Lett., vol. 97, no. 25, p. 253305, Dec. 2010. 17. B. Lipovšek, J. Krč, and M. Topič, “Optical model for thin-film photovoltaic devices with large surface textures at the front side,” Inf. Midem, vol. 41, no. 4, pp. 264–271, 2011. 18. K. A. Neyts, “Simulation of light emission from thin-film microcavities,” J. Opt. Soc. Am. -Opt. Im- age Sci. Vis., vol. 15, no. 4, pp. 962–971, Apr. 1998. 19. J. S. Orfanidis, Electromagnetic Waves and Anten- nas. Rutgers University, 2010. 20. A. Buckley, Ed., Organic Light-Emitting Diodes, 1 edition. Woodhead Publishing, 2013. 21. A. Čampa, Modelling and optimization of advanced optical concepts in thin-film solar cells Ljubljana: Založba FE in FRI, 2010. 22. M. S. Tomaš and Z. Lenac, “Decay of excited mol- ecules in absorbing planar cavities,” Phys. Rev. A, vol. 56, no. 5, pp. 4197–4206, Nov. 1997. 23. H. Benisty, R. Stanley, and M. Mayer, “Method of source terms for dipole emission modification in modes of arbitrary planar structures,” J. Opt. Soc. Am. -Opt. Image Sci. Vis., vol. 15, no. 5, pp. 1192– 1201, May 1998. 24. M. Kovačič et al., “Modelling of light outcoupling in OLEDs with sine textures,” in Conference pro- ceedings 2016, 52nd International Conference on Microelectronics, Devices and Materials and the Workshop on Biosensors and Microfluidics, An- karan, Slovenia, 2016, vol. 2016, pp. 153–157. Arrived: 20. 12. 2016 Accepted: 04. 01. 2017 M. Kovačič et al; Informacije Midem, Vol. 46, No. 4(2016), 267 – 275