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In this paper, we present finite element method simulations of top-emitting organic light-emitting diodes for designing optimized red, green, and blue full-color device structures. The OLED structures in the simulation are used to evaluate the device parameters, such as the outcoupling efficiency, electroluminescence spectra, and angular emission characteristics on organic layers with varying thickness and different cathodes. The numerical study also extracts these parameters for nano-structured devices. By observing the agreement between the simulated and measured data precisely, our simulations show capability of predicting the fabricated device results.
© 2016 Optical Society of America
1. Introduction
Organic light-emitting diodes (OLEDs) have attracted interest in recent years because they have a wide viewing angle, fast response time, high contrast ratio, and can be made to be flexible. They have been successfully applied in displays and solid-state lighting [1]. A vast number of both theoretical and device-oriented studies have revealed their fundamental working mechanisms. Top-emitting OLEDs (TEOLEDs), which emit through the semi-transparent top electrode, are a promising candidate for future display and lighting applications because they can provide a larger aperture ratio than that of the bottom-emitting devices, because of the incorporation of backplane thin-film transistors [2]. However, the amount of electrical power converted into emitted photons still needs to be improved for the current lighting and display industry. From an energy saving point of view, the device efficiency must be high. The total external quantum efficiency (EQE) is a critical device parameter and can be described by the product of the internal quantum efficiency and the outcoupling efficiency (ηout). An internal quantum efficiency of almost 100% was previously reached using phosphorescent materials [3]. However, designing highly efficient TEOLEDs is complicated because of complex micro-cavity effects [4]. Also, the layered stack and metal–organic interface of the TEOLEDs causes a ηout bottleneck because generated photons become trapped in wave-guided and surface plasmon polariton (SPP) modes [5]. Thus, repetitive fabrication trials to design an optimized TEOLED structure may be a time consuming and expensive experimental process and could waste materials. A deep understanding of the role of each layer is a prerequisite to successfully apply the extraction methods.
In this paper, we will show optical simulations with the aim of designing an optimized structure by employing FEM simulations for RGB full-color TEOLEDs [6, 7] and identifying the degree to which parameters must be controlled to obtain a high internal quantum yield. In particular, a numerical design of a top-emitting device can take into account complex microcavity effects, which are due to the highly reflective bottom and the partly reflective top electrodes used. Specifically, we wish to capture the fundamental optical physics of the TEOLED structure in a full-wave simulation and to understand the field distribution in the cavity between the top and bottom electrodes. The semi-transparent top electrode and the capping layer are taken into account in the TEOLED design. Photons from the light source are reflected multiple times and can be transmitted into the air in the radiating mode. The field distribution calculated for the whole device as well as the air regions was obtained using the well-known Maxwell’s equations. The proposed method can be applied to an OLED consisting of any number of layers because the development of our numerical algorithms is based on general electromagnetic theory. Study of the OLEDs must accommodate near field optics and the photonic mode density because of the use of thin organic and metal films [8]. The coherent fields reflected from the interfaces between the layers results in strong interference of a rapidly oscillating radiation pattern for a dipole source excited at a single emitting wavelength. The calculated radiation field is obtained by coherently considering the fields over the spectral range of our simulation. Also, TEOLEDs of the RGB full-color spectrum using a nano-textured layer [9] will be considered to confirm the enhancement of the light output of these devices. In this paper, the device fabrication and results are shown in section II. The simulation methods and related discussion are shown in section III including the design of the TEOLED using optical simulations. Finally, conclusions are drawn in section IV.
2. Experimental methods and results
2.1 NSTS formation
Green TEOLEDs using a nano-sized stochastic textured surface (NSTS) were studied in our previous report [9]. The NSTS investigated here is comprised of a stochastically corrugated structure in which Ag islands are embedded. First, Ag thin films of 8 nm and 12 nm were sputtered on a glass substrate in a home-made sputtering chamber. The Ag films were then exposed to 250 °C for 2 min using a rapid thermal annealing (RTA) system. This process formed stochastic nano-sized Ag islands, as shown in the atomic force microscope (AFM) image in Fig. 1(a). The power spectra of the grating pitch distribution were obtained using a fast Fourier transform (FFT). As shown in Fig. 1(b), the NSTS fabricated using 8 nm Ag thin films has a pitch from 150 nm to 600 nm and a peak intensity at 270 nm. The pitch distribution was 200 nm to 800 nm and peak intensity was at 410 nm for the 12 nm Ag films. The measured height distribution of the structures was 30–50 nm and 40–60 nm for the 8 nm and 12 nm Ag films, respectively.
2.2 Device fabrication and characterization
The glass substrates were pre-cleaned in acetone, methanol and deionized water. The RGB full-color TEOLEDs were fabricated using thermal evaporation. All of the metal and organic layers were deposited through shadow masks in a high vacuum chamber at a base pressure of 4 × 10−4 Pa. All devices had the structure Al anode (120 nm)/di-[4-(N,N-di-p-tolyl-amino)-phenyl]cyclohexane (TAPC):MoO3 (25%) and a TAPC hole transport layer (HTL)/emissive layer/1,3,5-tri[(3-pyridyl)-phen-3-yl]benzene (TmPyPB) as an electron transport layer (ETL). The blue emissive layer (EML) was a 3,5′-N,N′-dicarbazolebenzene (mCP) layer doped with 5 wt% iridium(III) bis[(4,6-difluorophenyl)-pyridinato-N,C2′] picolinate (FIrpic). The green EML was 8 wt % tris(2-phenylpyridine) iridium(III) (Ir(ppy)3) doped with 4,4′-bis(carbazol-9-yl)biphenyl (CBP). The red EML was a 15-nm-thick mCP layer doped with 8 wt% iridium (III)bis [2-methyldibenzo-(f,h) quinoxaline](acetylacetonate) (Ir(MDQ)2(acac)) and a 20-nm-thick 2,2′,2″(1,3,5-benzenetriyl)tris-(1-phenyl-1H-benzimidazole) (TPBi) layer doped with 8 wt% Ir(MDQ)2(acac). A 0.5-nm-thick LiF layer was used as the electron injection layer and 15 nm of Ag was used as the cathode. The TAPC layer above the Ag cathode was used as the capping layer (CPL). Figures 2(a) and 2(b) provide schematic illustrations of the conventional and NSTS embedded devices. The NSTS is positioned between the anode and glass substrate, and makes a corrugated structure in the overall device.
Fig. 2 A schematic illustration of the structure of the TEOLEDs with the NSTS. (a) Structure of the conventional device. (b) Structure of a NSTS embedded device.
The OLEDs were characterized by recording current-voltage characteristics as well as the electroluminescence (EL) spectra in the direction normal to the devices and as a function of the azimuthal angle. We used a programmable voltage source unit (Keithley, 236) to record the current-voltage characteristics of the OLEDs. The emission spectrum was recorded simultaneously with a spectroradiometer (Minolta, CS-1000) and the EL of the devices was measured using a calibrated Si photodiode (Hamamastu S5227-1010BQ). An optical fiber, a monochrometer combined with a photomultiplier tube, and a rotation stage were used to collect the angular emission characteristics by applying a current density of 10 mA/cm2. The active area of the devices was 2 × 2 mm.
2.3 Device results and discussion
To study the effect of the NSTS on the light output, devices with three different colors were fabricated on NSTS substrates to create red, green, and blue TEOLEDs. Figures 3(a) and 3(b) show the EQE and angular dependent emission characteristics of the devices with and without the NSTS for the blue and red devices, respectively. The EQE of TEOLEDs was calculated using the EL spectra measured at different viewing angles, as described in the Device Fabrication Section. We have not shown the results from the green device because we already demonstrated device efficiency enhancement by 33% in our previous work [9]. As shown in Figs. 3(a) and 3(b), insertion of the NSTS enhances the EQE of the devices. Interestingly, the NSTS-embedded devices exhibit wider angular dependent emission characteristics compared with planar devices. The reason for this phenomenon is that the broadband SPP mode extraction of stochastically distributed nano-structures. In blue devices, we obtain a 1.4-fold enhancement using the 8 nm Ag thin film when fabricating the NSTS. A greater enhancement of 1.6-fold was obtained using the 12 nm Ag thin film when fabricating the NSTS for the red devices. This means enhancement of the device efficiency for each color of the nano-structure embedded TEOLEDs depends on a different optimized pitch.
Fig. 3 The EQE of (a) the blue devices and (b) red devices. The normalized EL spectra as a function of observation angle: (c) blue-emitting device without NSTS; (d) blue-emitting device with the NSTS using an 8 nm Ag thin film; (e) blue-emitting device with the NSTS fabricated using 12 nm Ag thin film; (f) red-emitting device without the NSTS; (g) red-emitting device with the NSTS fabricated using an 8 nm Ag thin film; (h) red-emitting device with the NSTS fabricated using a 12 nm Ag thin film.
Figures 3(a) and 3(b) show that blue-emitting devices have an inherently lower efficiency compared with green- or red-emitting devices as blue light has a wider band gap that requires higher energy for effective blue emission [10]. Figures 3(c)–3(e) show the normalized electroluminescence spectra of blue-emitting devices as a function of observation angle. All of the blue-emitting devices with and without NSTS exhibit almost the same spectral shape over the emission wavelength range and have a deviation of the peak emission wavelength of only 2 nm. This means that although corrugation of the NSTS makes peaks and troughs in the devices, it does not significantly affect the resonance in microcavity, which determines the peak emission wavelength. Figures 3(f)–3(h) show the normalized EL spectra of the red-emitting devices as a function of observation angle. The red-emitting devices with and without the NSTS exhibit a deviation in the peak emission wavelength of only 3 nm. Although the peaks and valleys of the corrugated organic layer thickness can be locally changed between top and bottom electrodes, the effective overall cavity length is not changed significantly by observing the peak emission wavelengths between the reference and NSTS-based devices show only slight deviation of 2-3 nm. Moreover, the nanostructures in Fig. 1(b) exhibit broad pitch distribution arising broadly oriented wave vectors. Applying the stochastic nanostructure can enhance the emission intensity in the direction of the normal as well as widen the emission distribution in the all azimuthal direction. This phenomena is advantageous of our work unlike suffering from directional characteristics by using periodic nanostructure embedded OLEDs. This means that insertion of the NSTS does not affect the emission wavelength but enhances the device efficiency. Although we have not demonstrated the Commission Internationale de l´Éclairage (CIE) coordinates in this paper, we expect that there would be no apparent change with observation angle from the spectral results, which means that the corrugation of NSTS does not have a negative effect on the viewing characteristics of full-color TEOLEDs, which is important for applications in both display and lighting. The EL spectra of top-emitting OLEDs in Figs. 3(c)-3(h) show maximally 2-3 nm blueshift as increasing the viewing angles even the capping layer is used on the top semi-transparent metal electrode. There is a little degree of microcavity effect in the experimental results. This phenomena can be explained that the intrinsic full-width half maximum (FWHM) of most organic emitters including our one have FWHM over than 50 nm, which makes broad spectral margin for wavelength matching between the emitter and resonance condition of micro-cavity. Furthermore, the spectral blueshift with viewing angles can be largely suppressed in well-designed top-emitting devices, as shown in [11]. Thus, we will discuss the design procedure of top-emitting devices using full-wave simulation in Section 3.2.
3. Simulated results and discussion
3.1 Theoretical background
The TEOLED consists of a multi-stacked layer, as shown schematically in Fig. 2. The complex refractive indices of each layer at 520 nm are listed in Table 1. Because of the index mismatch among the organic, metal electrode, and air layers, a significant fraction of the generated photons are trapped in the device. According to classical ray optics, the EQE is approximately 1/2n2 for large n [12]. However, the multilayers of an OLED are not well represented by classical ray optics because of significant near-field effects, and the generation of SPP modes. Classical ray optics leads to an unrealistic result. Also, classical theory does not explain the dependence of the far-field emission pattern on the thin film of the organic layer. The behavior of radiating molecules in an optical cavity can be described by a dipole source to calculate the radiation characteristics of an OLED [13]. The simulations were performed using the FEM since complex geometries can be handled precisely [6–8]. The electromagnetic field distribution is represented by the space discretization of the wave equations that are derived from Maxwell’s equations. We first solved the governing equation for the electromagnetic fields using the following expressions
where is the dipole moment of the light source, and are the electric and magnetic fields, respectively, k is the wavenumber, ω is the angular frequency, j is the imaginary unit, ε0 is the permittivity of free-space and n is the complex refractive index. To obtain accurate simulations, we considered multiple reflections and transmissions, as shown schematically in Fig. 4.
Table 1. Complex refractive indices of the OLED layers used in the simulations
Using general electromagnetic theory in matrix form enables calculation of the effective reflection and transmission coefficients of each layer of the multilayered device. We can use the Fresnel equations to evaluate the downside reflection coefficient Г2 and transmission coefficient Τ2, and the upside reflection coefficient Г1 and transmission coefficient Τ1. We can determine relations of these factors as follows:
where neff and deff are the refractive index and the thickness of the middle layer, respectively. To realize radiating molecules in the simulation, we set 100 randomly oriented dipole sources to be embedded in the EML. The dipole sources oriented in the direction (θr, φr) are split into vertical and horizontal components to calculate the radiation separately. Here, the elevation direction parameter θr is uniformly distributed between 0 and π, and the azimuthal direction parameter φr is uniformly distributed between 0 and 2π. We employed a randomly oriented dipole source and calculate the incoherent summation of the radiation characteristics to obtain the output of the TEOLED. To calculate the RGB full-color spectrum, simulations were performed for wavelengths of 610 nm, 510 nm, and 450 nm since these are the peak wavelengths of the emission spectrum for each color. The multi-layered geometry in the simulation consisted of a glass substrate, NSTS, anode, organic layers, cathode, CPL, and the air. The 0.5 nm thick LiF layer below the cathode was ignored. The complex refractive indices illustrated in Table 1 come from values measured using spectroscopic ellipsometry. At the boundary of the system, outgoing waves were absorbed using a perfectly matched layer (PML). To establish enough space for the far-field condition, the entire simulation domain was 10.0 × 10.0 µm. When we simulated the NSTS, we used a periodic structure instead of applying the stochastic structure.3.2 Top-emitting device design
The purpose of this work is to demonstrate device efficiency enhancement using the stochastic outcoupling structure in RGB full colors. Our intention of this section is that the device efficiency enhancement is meaningful when the reference device is optimized since often efficiency enhancement is achieved in situations where the reference OLED is not optimized in terms of layer thickness. Once the reference OLED gets optimized, the enhancement factor is then lower or even below unity, but that is much more meaningful with outcoupling structure. Thus, we think it would imperative to investigate absolute device efficiency with different cavity thickness. Based on those work, we would illustrate meaningful nanostructure effects in next section. The main factors to consider for optimizing the OLEDs are the balance of the charge carriers and exciton confinement. Once those factors are satisfied, we can easily optimize the bottom-emitting device efficiency. However, TEOLEDs are more difficult to optimize because of a semi-transparent top metal electrode, which is highly conducting and has reasonable transmittance. The device is a microcavity resonator exhibiting different optical characteristics. The emission wavelengths of the radiating molecules and the resonance condition for a microcavity need to be matched when designing TEOLEDs. Fabry-Perot resonator theory can describe the optical characteristics of a microcavity with respect to cavity length, the position of the dipole source, and the reflectivities of the top and bottom electrodes [14]. The intensity I(λ, θ) of the light emitted from such a microcavity is given by
where λ is emission wavelength, θ is emission angle, I0 is the EL intensity of the radiating molecules, Rbot and Rtop are the reflectivities of the bottom and top electrodes, respectively, Ttop is the transmittance of the top electrode, φbot and φtop are the phase shifts upon reflection from the mirrors, L1 is the effective distance of the emitting dipoles from the highly reflective mirror and L is the total optical thickness of the cavity. All factors have to be chosen carefully to optimize the top-emitting devices. We optimized the device structure step by step and finally obtained devices with a markedly enhanced device efficiency. Rbot has a constant value of 0.95 since the bottom metal electrode is a reflective mirror, and Rtop and Ttop are controlled by the thickness of the top metal electrode. The remaining parameters L1, Rtop, and Ttop in Eq. (3) were determined through optimization of the parameters. We set [(2πL)/λ-(φbot + φtop)/2] in Eq. (3) to mπ to maximize the emission intensity, where m is an integer. According to Fabry-Perot resonator theory, the maximum emission intensity of the microcavity can be obtained at resonance, as follows:where λ is the intrinsic maximum emission wavelength of the emissive material, which is 510 nm, neff is the effective refractive index of the organic layers, which is about 1.9, and n is the resonance number, which is 2. Using Eq. (4), the whole cavity length, L, is calculated to be about 260 nm. The thickness of the CPL is chosen to minimize the microcavity effects by compensating the angular dependent phase shifts between the top and bottom electrodes [15]. Then, the rest of parameter values were simulated to determine the thickness of each layer to optimize the device efficiency for RGB full color. To achieve the optimized boundary conditions for maximizing the electron-hole recombination and photon emission, EML thicknesses of red, green, and blue colors were fixed at 35 nm, 30 nm, and 25 nm, respectively. After varying the thicknesses of the remaining layers according to Eq. (3), we can assign values to optimize the emission intensity while minimizing the microcavity effects. In our simulations, the emission intensities are calculated by integrating the Poynting vectors in the air and outgoing waves through the boundary at the air interface. Poynting vector integration over a surface is usually used for calculating the radiated power intensity [16]. The power intensity is as follows:Figures 5(a) and 5(b) show the emission intensities of the devices as a function of the thickness of the layers and the simulated spectra of the optimum red and blue devices. We choose optimized value of ETL, cathode, and CPL as a first peak point, and HTL as a second peak point satisfying second-order resonance condition of microcavity. The red-emitting device is thicker than the blue-emitting device since a longer cavity length is required. Figures 5(c) and 5(d) illustrate the optimized simulated emission spectra of red and blue-emitting devices. The simulated and fabricated planar devices have deviations of the maximum emission wavelengths of only 1 or 2 nm. The full width half maxima (FWHM) of measured results in Figs. 3(c)–3(g) are narrower than the simulated ones in Figs. 5(c) and 5(d) because the emissive materials in the fabricated devices determine the bandwidth of the EL emission, but have no influence on the simulated spectra. From these results, we can see that the simulations are accurate and useful for designing optimized top-emitting devices as a function of the whole cavity length and the thickness ratio of each layer.
Fig. 5 (a) The emission intensity of the blue-emitting device as a function of HTL, EML, ETL, cathode, and CPL thicknesses. (b) The emission intensity of the blue-emitting device as a function of HTL, EML, ETL, cathode, and CPL thicknesses. (c) The simulated spectrum of the optimized blue-emitting device. (d) The simulated spectrum of the optimized red-emitting device.
In TEOLEDs using two metal electrodes, SPP modes cause significant degradation of the outcoupling efficiency. A SPP mode is characterized by a coupled in-plane transverse electromagnetic mode at the metal-dielectric interface and its energy density decays by a factor of . Thus, investigation of the SPP effects in TEOLEDs is important. Properties of the SPP mode can be calculated using numerical solutions of Maxwell’s equations assuming perfect coupling between each metal-dielectric interface [16, 17]. Assuming a perpendicularly polarized electric field in the cavity, the surface plasmon electric field has the form
where x and z are the parallel and perpendicular dimensions at the metal/organic interface, kx and kz are the x- and z-dimensional wavenumbers, and t is the time. The microcavity sustains a number of SPP modes because it is a parallel-plate microcavity with metal surfaces. Since most power intensities of SPP modes are concentrated in the dominant mode, we plot the dominant SPP mode along a cross section of the cavity geometry in Fig. 6. The simulations were carried out for a planar green device. The field intensity was calculated to find the in-plane propagation vector for the guided mode inside the cavity and the radiating mode outside the cavity. In Fig. 6, the anode is located at 0 nm and the cathode is located at 250 nm. Between the anode and cathode, the fairly large bound SPP mode is oscillating and a relatively strong energy density is localized at the two metal-dielectric interfaces. As previously described, the bound SPP mode results in a loss of generated photons. For energies between the bound SPP and radiating air modes, the wave vector is determined by the surface plasmon relation, which can be described using the following equations [18]:where c is free-space wave velocity and ω is the angular frequency. Quasi-bound (QB) modes may provide transition regimes between SPP/QB modes to QB/radiating modes. Above the cathode, the radiating mode is observed. The field intensity decays along the direction perpendicular to the cathode/air interface, which demonstrates that the radiative mode originates from the SPP modes associated with the metal electrode interface [19]. These modes result in important physical effects of the plasmon processes, including plasmon decoherence by electron-hole pair generation and exciton-photon coupling.Fig. 6 Bound (SPP), radiative, and quasi-bound (QB) surface plasmon dispersion relations for the microcavity cross-section. Each mode is separated by dashed lines.
3.3 Nano-structure embedded TEOLED simulations
For TEOLEDs with NSTS, the dependence of the device efficiency enhancement on the NSTS parameters is calculated using the three-dimensional (3D) FEM method. Since stochastically distributed nano-structures are hard to realize in the simulations, we substituted periodically distributed nano-structures for the NSTS. The simulated device is composed of a glass substrate, NSTS, anode, HTL, EML, ETL, cathode, CPL, and the air. The 3D planar and nano-structured devices are shown in Figs. 7(a) and 7(b). The nano-structure is composed of a trapezoidal shape, which gives a similar effect to the hemisphere shape of the Ag islands in the NSTS. The ratio of the top and bottom lines of the trapezoid in the simulation is 1:2. The nanostructures on the PENS show hemisphere-like shape rather than trapezoidal-like one, as shown in Fig. 1(a). Thus, we have to use hemisphere-like shape in simulation. There is about 5% deviation of calculating results between the hemisphere- and trapezoidal-like shapes structure simulations when we apply 2D geometry. We don’t have problem for proceeding the 2D geometric simulation. However, when we perform the 3D geometric simulation by using hemisphere-like shape, it uses a large amount of computer resources resulting very long calculation time. In order to reduce the simulation time, we tried trapezoidal-shape in 3D geometric simulation since the straight line of trapezoidal-like shape needs smaller computer resources than curve line of hemisphere-like shape during simulation. Although we did not use exact shape of fabricated nanostructure in simulation study, it can still represent comparatively accurate effect of nanostructure to radiation intensity pattern tendencies. Dipole sources were chosen for the excitation source since they represent the electron-hole recombination well. Practically, exciton generation is distributed in the entire EML. Multiple dipole sources can be also distributed in the active layer during the 3D simulations. However, using multiple dipole sources or periodic boundary conditions is not appropriate because it will lead to undesirable interference. Therefore, dipole sources within a finite computational domain are located at one specific point. Also, inhomogeneous mesh sizes were used during the simulation. The unit mesh size for simulation is 2 nm to 20 nm which is in the range of 1/20 to 1/2 a wavelength. Mesh sizes near the nano-structures are relatively small compared with the air since the geometries of the nano-structures require complex calculations. Figures 7(c) and 7(d) exhibits a simulated 3D radiation pattern of planar and corrugated devices. As shown in the experimental radiation patterns, the nanostructure-embedded device shows widen angular distribution as well as enhanced emission intensity in the normal direction. Figure 7(e) shows the simulated two-dimensional (2D) radiation patterns of blue TEOLEDs with and without the nano-structure. We can observe in Figs. 7(c)-7(e) that applying the nano-structure can enhance the emission intensity in the direction of the normal as well as widen the emission distribution in the azimuthal direction. Figure 7(f) shows the simulated and measured radiation patterns of the planar blue emitting devices as a function of azimuthal angle. The simulated radiation pattern has a slightly wider distribution compared with the measured one, but both results are in reasonable agreement. This means our simulation can predict the radiation pattern of the TEOLEDs. We already showed the same trend using green TEOLEDs in our previous work [9], and red and blue emitting devices also show this trend, as shown in Figs. 3(a) and 3(b). All the radiation patterns in Figs. 7(c)-7(f) show forward directive characteristics rather than Lambertian distribution due to microcavity effect. Although the CPL and well-designed cavity can minimize the angular dependent microcavity effects in the TEOLEDs, forward directivity of the radiation pattern does not disappear completely [14, 15]. Hemispherical or trapezoidal shaped nano-structure embedded devices result in various photon propagation trajectories that were not shown in planar devices. Thus, the radiation pattern of the corrugated structure is enhanced and the emission characteristics were widened compared with the planar device.
Fig. 7 (a) Representation of a planar TEOLED and (b) representation of a trapezoidal-shaped nano-structure embedded TEOLED in the simulation. (c) Simulated 3D radiation pattern of a planar device. (d) Simulated 3D radiation pattern of a corrugated device. (e) Comparison of the simulated radiation patterns of planar and corrugated devices. (f) Comparison of the simulated and measured radiation patterns of planar blue-emitting devices.
Our simulation study ultimately resulted in the accurate calculation of stochastic nano-structure embedded devices. However, realization of a stochastic nano-structure embedded device in the simulation is very difficult because of the broadly distributed pitches. But if we know the distribution function of the outcoupling efficiency according to the size of the periodic nano-structure embedded devices, then we can obtain a statistical calculation of the outcoupling efficiency. This is described as follows [20]:
where t1 and t2 give the distribution range of the stochastic nano-structure, ak is the distribution intensity of j-th point, ηj is the outcoupling efficiency of j-th point, and ηeff is the total outcoupling efficiency.In Fig. 8(a), the distribution of the periodic, stochastic, and random nano-structures is plotted. All the pitch distributions of periodic, stochastic, and random nano-structures have same area below the curved lines. The distribution in pitch of the periodic nano-structure is centered at 350 nm, maximizing the efficiency of green devices, and exhibits a Dirac delta function. The pitch distribution of stochastic nano-structure is imported from data shown in Fig. 1(b) obtained from the fabricated NSTS using 8 nm thickness Ag thin films and exhibits a quasi-Gaussian dependence. The pitch distribution of the random nano-structure has the same range as that of a stochastic nano-structure, but the distribution intensities are fixed at a certain point that has the same area confined by the distribution curve lines. Figure 8(b) shows the outcoupling efficiency as a function of pitch distribution. In this study, a periodic nano-structure is applied to calculate the outcoupling efficiency for RGB full-color devices. The red, green, and blue devices had their own optimum pitch values of 410 nm, 350 nm, and 250 nm, respectively, for maximizing the device efficiency. A pitch of 0 nm means that the device is planar. As the emission wavelength was increased, the optimized pitch value also increased. This explains the difference in the enhancement factor when using a stochastic nano-structure fabricated with 8 nm Ag thin films or 12 nm Ag thin films according to emission color as shown in Figs. 3(a) and 3(b). However, the optimum pitch values of the simulated and measured results can differ since the surface smoothness and film continuity of the fabricated devices would be poor for a thin film at its interface, which limits the extraction of the SPP mode and changes the optimum pitch. From Figs. 8(a) and 8(b), we can obtain the all the parameters needed to solve Eq. (7) and the results can be calculated according to the types of nano-structure including the planar device case. In Fig. 8(c), the planar distribution has a low efficiency since the planar top-emitting device suffers from a trapped waveguide and SPP modes generation. The periodic nano-structure distribution gives the highest enhancement factor of 1.8-fold for the green-emitting device, but the outcoupling efficiency of the red and blue-emitting devices is low because the periodic nano-structure can affect the device efficiency at particular wavelengths, satisfying the Bragg condition [21]. Also, periodic nano-structure embedded OLEDs emit a directional radiation pattern, which is undesirable for display applications [22, 23]. A random nano-structure distribution gives about a 1.3-fold enhancement in RGB devices. A similar enhancement comes from the constant distribution of intensities over all ranges. In a stochastic distribution, enhancement factors of blue and green emitting devices are between the maximum enhancement factors of the periodic and random green-emitting devices. From these results, it can be seen that the stochastic nano-structure has the capability to exhibit a high enhancement factor at a particular wavelength and has a reasonable enhancement factor over a broad wavelength range. This means that stochastic nano-structure can be applied to specific colors of devices as well as a full-color device for enhancing the device efficiency. Compared with the radiation pattern of a periodic nano-structure embedded device, the stochastic nano-structure embedded device has smooth and wide angular dependent emission characteristics, as described in this report. Previously reported efficiency enhancement methods in OLEDs use periodic nano-structures that give directional emission characteristics. However, in our work, generated photons are emitted over all azimuthal directions because the peaks and troughs have broad periodicity, resulting in a quasi-Lambertian emission pattern. Investigation of the effect of a periodic nano-structure on the efficiency of the OLEDs using simulations has been attempted in several studies. To our knowledge, this is the first time that a statistical approach has been tried to calculate the effect of stochastic and randomly distributed nano-structures embedded in OLEDs on the device efficiency. We hope that this approach will lead to further refinements to understand the effect of a stochastically distributed nano-structure in OLEDs.
Fig. 8 (a) The distribution of the periodic, stochastic, and random nano-structures. (b) The outcoupling efficiency as a function of grating pitch for RGB emitting devices. The height is fixed at 50 nm. (c) The outcoupling efficiency as a function of the type of nano-structure.
4. Conclusion
We investigated the effect of the cavity length and nano-structure on the performance of microcavity phosphorescent red, green, and blue emitting TEOLEDs using a systematic study. By precisely designing the layer thicknesses, the device efficiency of the reference TEOLEDs was optimized. We demonstrated efficiency enhancement using a broadly distributed nano-structure as well as widening of the angular dependent emission characteristics in RGB full-color OLEDs. The resulting enhancement of the EQE is due to the radiation in the normal and azimuthal directions of the bound SPP mode. The proposed architecture is advantageous for high performance and full-color lighting and display applications, and can be applied easily to the fabrication of large sized OLEDs.
Acknowledgments
This work was supported by the Samsung Display Company. We were also supported by the Industrial Strategic Technology Development Program (no. 10042412) funded by the Ministry of Trade, Industry and Energy of Korea.
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