1. Introduction

OLEDs usually suffer from low light-extraction efficiency or coupling efficiency (CE) around 20% [1]. This deficiency is primarily caused by three factors: (1) Waveguiding – the total internal reflection (TIR) that occurs at the interfaces of substrate (n = 1.52 for glass)/air and organic layers (n = 1.7 ~ 1.9)/substrate; (2) Absorption – the plasmonic dissipation of optical power to the metal cathode or other material with nonzero extinction coefficient; (3) Fresnel loss – the refractive indexes mismatch between interfaces and thus causing reflection loss.

Absorption and Fresnel loss are somehow inevitable or difficult to avoid without sacrificing other device properties. Thus, the waveguiding loss is most likely to be lessened. As a result, we focus on eliminating this effect. To solve this problem, one can optimize the layer thickness of the OLED itself by electromagnetic theory [2]. To apply this theory, we would set the total optical cavity length to be integer times half of the desired wavelength, and the distance of dipole location to the reflective electrode to be integer times one-fourth of the desired wavelength [3]. In addition, devices with capping layers form stronger microcavity and have enhanced spontaneous emission [4].

An alternative method, geometric optics, is to optimize the characteristics of the micro-structured films attached to a specified OLED, which dictates that microlenses should be fabricated with a high fill factor, a large height ratio and a small diameter [5]. Furthermore, other techniques, such as micropyramid-array films [6], the insertion of aerogel layer [7] and photonic-crystal structures [8] were also reported.

However, according to the electromagnetic or geometrical optics theories, the OLED stack itself and the characteristics of microstructured films cannot be optimized at the same time by either approach. Because the performance of the coherent OLED stack whose thickness of each layer is around desired wavelength cannot be calculated by geometric optics. On the other hand, the incoherent substrate and microstructures whose thickness is much larger than desired wavelength can cause difficulty as analyzed by electromagnetic theory. To deal with the deficiency of low light-extraction efficiency of the OLED, we aim to achieve higher normal-direction luminance for a display and higher luminous power for lighting by attaching MAFs to the OLEDs.

In previous studies, Peng [9] depicted the total out-coupling efficiency of the OLED can be constituted of two terms, i.e. the fraction of light from emitter to substrate multiplied by the fraction of light from substrate to air. Sun [10] suggested an isotropic emission from organic films and combined a 3D Monte Carlo based ray-tracing method to obtain the angular dependence of light intensity of the MAF attached OLED. Krummacher [11] claimed that the apparent light extraction enhancement is dependent on the OLED architecture itself. Besides, Greiner [12] said this enhancement depends very much on the angular distribution of the light emitted into the substrate and demonstrated the escape probability of a light ray from the substrate into the air as functions of the starting angles and the OLED’s reflectance for various out-coupling strictures.

However, among all the literatures mentioned above, they didn’t provide any clear relationship between the light extraction enhancement or angular luminance enhancement and the emitter apodization inside the OLED. In this paper, in order to find such relationship, we take the advantages of both classical electromagnetic and ray-tracing theories and evaluate them once at a time without losing either physical importance. At first, angular luminous intensity (lm/sr) into the substrate of the OLED is evaluated by the rigorous electromagnetic theory or Hertzian dipole antenna theory [13]. Then, we take this angular luminous intensity as a source apodization input of the Monte Carlo based ray-tracing software, and finally retrieve the far-field angular luminance in the air.

2. Simulation

2.1 Theory

Light extraction from an OLED can be divided into two stages: the first step is from the OLED stack into the substrate and the second step is from the substrate into the air. The most suitable thickness of each layer for desired source apodization can be carefully chosen by using electromagnetic theory. Moreover, the characteristic optimization of the MAF which was attached to the OLED can be done by using geometric optics theory.

The angular intensity distribution of the light propagation from the OLED stack into the substrate was first calculated. Since the OLED thickness is comparable with the wavelength, light interference in the OLED stack should be considered. For higher accuracy, the formulation used in analysis of the OLED structure is based on electromagnetic theory. The Hertzian dipole antenna theory [13] was introduced to generate the electric field radiation pattern of the OLED dipole source, i.e., the emitter apodization. These radiation patterns are then taken in the second step as the input for the calculation of light propagation and extraction in the substrate. For light emitted from the substrate to air, since the substrate thickness is much greater than the wavelength, we use a ray-tracing approach based on geometric optics. The commercial software LightTools was applied to calculate the far-field angular luminance of the OLED with and without the MAF. In this way, the electromagnetic and geometrical optics theories are combined in a physically correct manner.

2.2 Input parameters

The simulation parameters for ray-tracing throughout this paper were described as follows. First, the OLED has an emissive area of 8 × 8 mm². In addition, its structure applied in ray-tracing method was made of: reflective cathode of 90% reflection/organic emitter/anode/glass (0.7 mm). In section 3.2, angular luminance distributions will be shown for different organic emitter structures with various source apodizations calculated based on the electromagnetic theory described in section 2.1. The Fresnel loss by the interface reflection was considered throughout our ray-tracing simulation. Higher cathode reflection results in higher enhancement by the MAF, which agrees with the previous literature [12].

Second, the size and thickness of the attached MAF are 10 × 10 mm² and 50 μm, respectively. In addition, the microlenses of the MAF in ray-tracing program are 10 μm in diameter, 3.8 μm in height and rectangular-arranged with gaps of 2.5 μm and these parameters were confirmed by SEM measurements. The MAF was made of transparent PET (Polyethylene terephthalate) film covered with PMMA (Polymethyl methacrylate) microlenses [14]; the refractive index of PET and PMMA applied in the program were 1.5750 and 1.4893, respectively.

3. Results

3.1 Artificial light sources

In first part, two artificial OLEDs’ intensity distributions were chosen as source apodizations where angular distributions of different directivity for the Lambertian (the first order cosine function) emitter and the 63-th order one are shown in Fig. 1(a) . To quantify their directivity, those two sources were characterized by their powers of the cosine function with respect to viewing angle. Cosine functions of larger power represent higher source directivity. As can be seen in Fig. 1(b) and Table 1 , sharper angular intensity profile or smaller angular FWHM (full width at half maximum) or smaller ${\theta }_{\text{1/2}}$, where ${\theta }_{\text{1/2}}$ is defined as the off-axis angle where the luminous intensity is a half of the peak intensity, resulted in higher coupling efficiency out of the planar substrate, but less enhancement after adhesion of MAFs.

 

Fig. 1 (a) Two artificial source emitting patterns and (b) the geometrical optics calculations of relative luminance (all values were normalized to normal direction value of each reference device).

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Table 1. Coupling efficiency, luminous power ratio, and normal luminance ratio of the two artificial sources

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After MAF attachment, the normal direction luminous intensity of sample B even down to 64% of the device without the MAF due to the light trapping phenomenon by the microlens edge [14]. Besides, more portions of large viewing-angle rays were extracted by microlenses, thus caused sample A to reach higher luminous power ratio (LPR), which is the power in air with MAF over the power in air without MAF, and normal direction luminance ratio (NLR), which is similarly normalized to normal direction luminance without MAF. Considering ray-tracing method, coupling efficiency (CE) is defined as luminous power integral through total forward hemisphere divided by optical power generated inside the device without taking the plasmonic metal dissipation and organic/ITO modes into account, i.e. the power in air over the power into the substrate. As a consequence, CE ratio is proportional to LPR. To evaluate the out-coupling efficiency improvements that the MAF yields, we integrate the luminous intensity over all viewing angles. These results are summarized in Table 1.

3.2 Real devices with different Alq₃ thickness

In second part, to further apply the rules to the OLED model in electromagnetic approach, four devices of Al (100 nm)/Alq₃ (60, 90, 120 and 150 nm)/NPB (60 nm)/ITO (100 nm)/Glass (0.7 mm) were fabricated and simulated. The angular luminous intensity distributions from OLED emitters into substrate were first evaluated as shown in Fig. 2 (a) . Taking this result as the initial condition for ray-tracing program led to Fig. 2 (b). The angular luminance of the OLEDs with and without the MAF and the enhancement ratio were measured by a spectroradiometer Minolta CS-1000S and shown in Fig. 2 (c).

 

Fig. 2 (a) The simulated source apodization varying Alq₃ thickness from electromagnetic theory; (b) the simulated luminance from geometrical optics; (c) the validation of experimental results.

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With increasing angular FWHM, the CE decreases and the LPR and NLR increases; the angular FWHM from large to small are for Alq₃ thicknesses of 150, 120, 90 and 60 nm, thereby the resulted CE from large to small are for those of 60, 90, 120 and 150 nm; the NLR and LPR from large to small are for those of 150, 120, 90 and 60 nm both numerically and experimentally.

In Table 2 , the NLR and LPR of the four different OLED Alq₃ thicknesses with MAF attachment were shown. The ${\theta }_{\text{peak}}$ is defined as the viewing angle where the luminous intensity is the peak intensity. In addition, we can conclude from Table 2 that the OLED with Alq₃ thickness of 60 nm had the best CE due to its smallest angular FWHM and that of 150 nm had the best NLR and LPR because of its most broad emitter intensity distribution or the highest off-axis viewing-angle intensity into the substrate.

Table 2. Luminous power ratio and normal direction luminance gain of four devices of different Alq₃ thickness

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The experimental result of Alq₃ 150nm without the MAF also has the largest luminance in off-axis viewing angle in reference device and thus best NLR, and the simulation results were also validated. In summary, devices with broader apodization, which has high intensity in off-axis angle, have better power gain and normal-direction luminance gain.

3.3 Mode analyses

From section 3.1 & 3.2, methods of Hertzian dipole antenna theory and Monte Carlo ray-tracing theory were combined to enlighten us the relationship between the apodization profiles inside and the angular luminance outside. However, to estimate the efficiency enhancement limitation of the MAFs and to include the influences of surface plasmon metal dissipation and organic/ITO modes into calculation, a transfer-matrix method with embedded source in planar structures [15-16] was presented in this section. This method separated the optical power distributions into four modes, which were the air, substrate, organic/ITO and surface plasmon modes. The substrate texturing techniques can only extract the substrate mode into the air mode. Thus, the enhancement limitation of the MAFs can be evaluated. Moreover, with the help of ray-tracing approach, the extra air mode extracted from the textured substrate can be validated with the experimental external mode and substrate mode data [17]. Furthermore, the experimental results of section 3.2 are compared to the calculated results as shown in Fig. 3(b) and the relative experimental air mode ratio of Alq₃ 60 nm were set to align with the calculated ratio.

 

Fig. 3 Mode ratios calculated by transfer matrix method with embedded sources. The blank area of each bar represented the optical power ratio of the surface plasmonic mode; (b) the experimental mode ratios. The extra air mode was according to the air mode multiplied by (LPR - 1).

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From Fig. 3, the OLED with Alq₃ thickness of 60 nm had the best air mode ratio of 23.8% because 50-80 nm was corresponding to quarter-wave optical thickness (QWOT) from dipole emitters to the reflective cathode. But device with Alq₃ thickness of 90 nm attached by the MAF had the best air mode plus extracted substrate mode due to its slightly broader emitter apodization. Although device of Alq₃ thickness of 150 nm had the best LPR (for both Sim & Exp) in Table 2, it still had the lowest air mode after attaching the MAF owing to its lowest air mode ratio without the MAF. Furthermore, the blank area of each device in Fig. 3 represented the surface plasmonic mode. Therefore, the longer dipole distances or Alq₃ thickness to the cathode, the less plasmonic mode ratio was.

4. Conclusion

The OLED efficiency improvement by the MAF is greatly influenced by not only the characteristics of microstructures but also the emitter apodization. The combination model of electromagnetic and geometrical optics theories was shown to provide insight of device optimization. To design a large CE device, a small angular FWHM of emitter profile, i.e., a microcavity device can be chosen; conversely, a large LPR and NLR device needs an emitter with wide angular FWHM. Besides, mode analyses of the air mode plus extracted substrate mode ratio can reveal more information about the potential for efficiency improvement. From the real case studies, the best CE device without the MAF was that with Alq₃ thickness of 60 nm, which is the optimized QWOT of the spectral peak of Alq₃; while the best CE device with the MAF was that with Alq₃ thickness of 90 nm, which is slightly longer than the optimized QWOT. The latter one has broader emitter apodization and larger substrate mode ratio potentially to be coupled out, and hence more substrate mode can be extracted by the MAF.