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Abstract
The finite-difference time-domain method is employed to study the light extraction efficiency of white light emitters. The cone arrays designed on top of white light emitters eliminate the dependency of light extraction on the wavelength and the cavity thickness and that leads to significant enhancement in light extraction efficiency for whole visible light spectrum. The light extraction efficiency of 81% has been achieved. Most importantly, the high extraction efficiency is achieved for the whole visible spectrum from 400 nm to 700 nm. This work will provide guidelines for designing highly efficient white light emitters for general illumination and display purpose.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Solid-state lighting (SSL) technology is penetrating our daily life because of various advantages, such as high energy efficiency, long life span, and environmentally benign. Light-emitting diodes (LEDs) and organic light-emitting diodes (OLEDs) as the most promising light emitters for the next-generation SSL sources has been attracting tremendous attention in recent years [1,2]. The use of cost-effective approaches to achieving high-efficiency devices are instrumental in the widespread adoption of this technology. Both high internal quantum efficiency and light extraction efficiency are required to achieve high-efficiency of SSL. Nearly 100% internal quantum efficiency of these light emitters has been achieved in recent years. The low light extraction of conventional LED (~4%) and OLED (~20%) emitters is one of the obstacles to obtaining high-efficiency light emitters [3–5]. Improving the light extraction efficiency of light emitters has been listed as one of the suggested light emitter research priority task in “Solid-State Lighting 2017 R&D Plan: Suggested Research Topics” published by the Department of Energy (DOE) [6]. The enhancement of light extraction efficiency of light emitters has been reported by utilizing microsphere/microlens arrays, microdomes, photonic crystals, higher refractive index substrate, corrugated structures, the patterned sapphire substrate, nano-honeycomb structures, and the inverted pyramid [5,7–18].
Microcavity light emitters have attracted much attention in recent years due to its advantages over the conventional light emitters. It has been reported that the microcavity structure can be used to enhance the light extraction of light emitters by changing the light distribution within the device [11,19–22]. However, there is a significant difference in luminance enhancements in different microcavity light emitters [19,23–25]. Specifically, the luminance enhancements showed strong wavelength-dependent for different microcavity light emitter structures. In DOE’s research & development plans, realizing the “stable and efficient white devices” was emphasized. Therefore, herein, we are focusing on improving the light extraction efficiency of microcavity light emitters in a wide range of wavelengths from 400 nm to 700 nm.
In this work, the finite-difference time-domain (FDTD) method is employed to optimize the microcavity light-emitting device structure. The light extraction efficiency of planar microcavity light emitter is optimized by tuning the cavity thickness and then the planar light emitter is used as a reference device to investigate the effect of nanostructures on light extraction efficiency. The hexagonal close-packed cone arrays are designed on planar microcavity light emitters to improve the light extraction efficiency instead of the commonly used nanostructures, such as microsphere arrays [26–33], microlens arrays [34–49], and microdomes [16–18,50]. The structures designed on light emitters are employed as an intermediate medium to extract more light from devices. The light generated in the device coupled into the nanostructures (in-coupling) and then extracted out from the nanostructures (out-coupling). Both high in-coupling efficiency and high out-coupling efficiency are required to achieve high light extraction efficiency. For light emitters with microsphere arrays, the in-coupling process is achieved through evanescent wave coupling [27], hence the in-coupling efficiency is low. The microsphere arrays designed in the polystyrene layer to achieve higher in-coupling efficiency results in high light extraction efficiency [28]. However, the out-coupling efficiency strongly depends on the wavelength for microsphere arrays, microlens arrays, or micro dome arrays, which led to the high extraction efficiency only for narrow wavelengths. In this work, we demonstrate that the cone arrays designed on light emitters can simultaneously achieve both high in-coupling efficiency and high out-coupling efficiency. Our finding shows that broadband light extraction efficiency could be achieved by engineering the microcavity light emitter structures. This shed light on designing high-efficiency white light emitters.
2. FDTD analysis of light extraction efficiency
The schematic of microcavity white light emitters with nanocone arrays analyzed in this work is shown in Fig. 1(a). The light extraction is calculated employing the FDTD method as reported in our previous work [27,28,33,51–53]. The device structure investigated was treated as 3-dimensional (3D) structures solved by considering the appropriate boundary conditions. The refractive indices of light emitters and cones were set to 2. Dipole sources were chosen as the light sources in the active region as it has been proven that electron-hole pair recombination can be represented by a dipole [54]. One period was divided into 16 parts, and two dipoles were positioned in each part. One dipole was put at the center. In total, 33 dipoles were positionedin the organic active region within one period. Multiple dipole sources were intrinsically suited for the simulation of the active layer in the 3D FDTD method. However, the use of multiple dipole sources leads to non-physical interference patterns. In order to simulate an incoherent un-polarized dipole source, for each dipole, three separate simulations were performed, which corresponds to a dipole oriented along x, y, and z-axis, respectively. Therefore, 33 × 3 separate simulations were carried out. The un-polarized field was obtained by summing the results incoherently. The far-field electric field was obtained by performing the Fourier Transform on the near-field electric field as reported in our previous work [51]. The power extracted out from light emitters with nanocone arrays was obtained by integrating the average far-field intensity over solid angles. The light extraction efficiency for each wavelength was calculated by taking the ratio of power extracted out from OLEDs to that of dipole power. The average light extraction in the visible region was averaged from 400 nm-700 nm.
Fig. 1 (a) Schematic of light emitters with hexagonal close-packed cone arrays and (b) average light extraction efficiency over the wavelength range of 400 nm-700 nm as a function of cavity thickness.
3. Effect of cavity thickness on the light extraction efficiency of planar microcavity light emitters
The light extraction efficiency of planar light emitters is calculated for the wavelengths from 394 nm to 683 nm, which covers the visible light spectrum. In order to study the cavity effect, the light extraction efficiency of planar light emitters with various cavity thicknesses was calculated as shown in Fig. 1(b) and Fig. 2. The cavity thickness was varied from 180 nm to 300 nm. Figure 2 shows the extraction efficiency of light emitters changes with cavity thickness for the wavelength range of 394 nm to 684 nm. The extraction efficiency for each wavelengthstrongly depends on cavity thickness and it illustrates periodical changes with the cavity thickness. In addition, the extraction efficiency for each cavity thickness shows strong wavelength-dependent. The average extraction efficiency was calculated over the wavelengths ranging from 394 nm to 683 nm as shown in Fig. 1(b), which also changes with the cavity thickness, but overall the extraction efficiency is low. Our finding shows that for planar microcavity light emitters, the light extraction efficiency varies with cavity thickness as well as with the wavelength. This is not favorable for practical applications, especially for general illumination purpose.
4. Effect of semi-vertical angle on the light extraction
The low extraction efficiency of planar light emitters is attributed to Fresnel reflection and the small light escape cone caused by the large refractive index contrast between light emitters and free space. Therefore, enlarging the light escape cone as well as reducing the Fresnel reflection is the key to achieving high extraction efficiency. This can be accomplished by designing nanostructure on top of light emitters [5]. The light generated in the light emitters propagates through the nanostructures into the free space. The nanostructures serve as the intermediate medium to couple the light in and out of nanostructures. Therefore, high in-coupling efficiency and high out-coupling efficiency are required to achieve high light extraction efficiency. Microlens and microdomes can significantly improve the in-coupling efficiency [28,50,55,56], however, out-coupling efficiency shows strong wavelength-dependent as the high out-coupling efficiency can only be achieved by constructive interference. Compared to the microsphere arrays, the cone arrays can achieve much higher in-coupling efficiency which is determined by the packing density of the cone arrays. Our previous work showed that light extraction of LEDs with hexagonal close-packed structure is higher than that with square close-packed structure, which is attributed to higher packing density of hexagonal close-packed structure [33]. Therefore, in our calculation, hexagonal close-packed cone arrays were designed on top of light emitters, which maximized the in-coupling efficiency. The base diameter of the cone was set as 0.8 μm while varying the semi-vertical angle from 10° to 90°. The light beyond the light escape cone in the planar device goes into the cones and the propagation direction changes due to the slope formed by the cone and free space. The amount of light that can be redirected out from the light emitters depends onthe semi-vertical angle of the cones, which is confirmed by our far-field radiation calculation as shown in Fig. 3. The far-field radiation pattern for the light emitters with 90° semi-vertical angle cones shows only angular dependency and symmetrically azimuthal distribution (see Fig. 3(h)). The inner and outer radiation rings are attributed to the interference effect. The overall intensity is relatively lower compared to these light emitters with smaller semi-vertical angles. The far-field intensity increased with the decrease in the semi-vertical angle and the strongest intensity is observed for the cones with semi-vertical angles between 20°-40° (see Fig. 3(b)–3(d)). The intensity starts to decrease when the semi-vertical angle decreases to 10°.
Fig. 3 Far-field radiation patterns of cone array microcavity light emitters with various semi-vertical angles of: (a) 10°, (b) 20°, (c) 30°, (d) 40°, (e) 50°, (f) 60°, (g) 70°, and (h) 90° (planar light emitters).
The low far-field intensity in planar light emitters is due to total internal reflection at the interface between the light emitters and free space. The large refractive index contrast (n~2 for OLED and n~2.5 for LED) between light emitters and free space leads to a small critical angle, and a narrow light escape cone, Ω = (1 – cosθc)/2. For the light emitters with cone arrays, the light goes into the cones first and is then emitted out from the sidewalls (slanted side) of the cones. The cones designed on top of light emitters enlarge the light escape cone to different degrees based on the semi-vertical angle of cones. At larger semi-vertical angles, the light escape cone increases with the decrease in the semi-vertical angle. The light escape cone begins to decrease when the semi-vertical angle is decreased beyond the critical angle of the material. In other words, the large semi-vertical angled cones are too close to planar, causing a portion of the light being reflected off the cone-air interface. This is because the light entering the nanostructure is still reflected downwards and back into the light emitters instead of getting out of the light emitters.
To quantitatively investigate the effect of semi-vertical angle on the light extraction efficiency of light emitters, the average light extraction efficiency over the wavelength range of 400 nm-700 nm was calculated as a function of a semi-vertical angle as shown in Fig. 4. The light extraction efficiency of OLED with 10° semi-vertical angle cone was 73%. It increased to 79% when the semi-vertical angle increased to 20°. The maximum light extraction efficiency of 81% was obtained at the semi-vertical angle of 30° and it decreased to 77% when the semi-vertical angle increased to 40°. The light extraction gradually reduced to 70%, 63%, 53%, 42%, and 26% when the semi-vertical angle increased to 50°, 60°, 70°, 80°, and 90°, respectively. Thelight extraction efficiency increased with an increase in semi-vertical angle, then decreased as the semi-vertical angle lies above the critical angle of the cone material.
Fig. 4 The average light extraction efficiency of nanocone array light emitters over the wavelength range of 400 nm-700 nm with various semi-vertical angles.
The light extraction efficiency would be constant when the semi-vertical angle increased from 30° to 60° provided that the only light escape cone changes with the semi-vertical angle of cones. But, from the light extraction calculation, the maximum light extraction efficiency is only obtained at the semi-vertical angle of 30°. The extraction efficiency between the semi-vertical angle of 30° and 60° is not constant. This variable behavior arises through losses from the multiple reflections among higher-energy light as well as losses from the diffraction among the lower-energy light. As shown in Fig. 5(a), the critical angle (θc) of a planar light emitter is only 30° (for the refractive index of 2) and the calculated light extraction efficiency is 26% for the planar light emitter in this work. When the cone arrays with semi-vertical angle (α) larger than 90ο-θc were designed on top of the light emitter, the light escape cone increased allowing more of the light to be extracted out from the sidewalls of the cones, which increased the light extraction efficiency. The light that goes into region II will be extracted out as the angle of incidence is smaller than the critical angle, while the light goes into the region I will be reflected into the device and eventually trapped in the device. Therefore, the amount of light extracted out depends on how much light can get into region II. The amount of light going into the region II depends on the semi-vertical angle of cones, which determines the light escape cone and therefore the extraction efficiency. The results from the calculation showed that the light extraction efficiency of 42% is obtained for cone array white light emitters with the semi-vertical angle of 80°. The light extraction efficiency of 53% is obtained for cone array light emitters with the semi-vertical angle of 70°. When the semi-vertical angle decreases to 90ο-θc, the light escape cone increases and the corresponding light extraction efficiency increases to 63%. When we further decrease the semi-vertical angle, the light escape further increases and the light extraction efficiency further increases, because of the region of the cone corresponding to total internal reflection (region I) decreased in size. The light going into the region III experiences multi-reflection and interference inside the light cone and eventually extracted out from the nanostructure so long as it does not encounter spaces small enough to cause significant diffraction. The ratio of the light that goes into region III affects the light extraction efficiency because the width of the cone in the region III is so small that it is not able to contain a full harmonic of some of the photons that make it to the top of the light emitter. A significant amount of light is then lost to multiple reflections as well as effects resulting from diffraction through a circular aperture [33]. The diffraction patterns at the top of the nanocone cause photons to behave unusually and turn significantly, causing a small percentage of incoming light to experience total internal reflection and interference effects, but without ever contacting the nanostructure to air interface. This causes periodic behavior in the light extraction efficiencythat is dependent on the wavelength of the incident light along with the direct loss of efficiency in the region as shown in Fig. 5. Therefore, the light extraction efficiency increases with the decrease in the semi-vertical angle when the semi-vertical angle is θc < α < 90ο-θc. The maximum light extraction efficiency is obtained at a semi-vertical angle of θc. The light escape cone begins to decrease with a further decrease in the semi-vertical angle as shown in Fig. 5, which corresponds to the decrease in light extraction efficiency. This is illustrated by the light escape cone moving down the side of the nanostructure far enough that part of the escape cone moves into light emitters and thus light would start to be reflected into the light emitters instead of into the air. This indicates that the semi-vertical angle of cones has a significant effect on the light extraction efficiency. Therefore, any light that enters the cone in this configuration is either extracted directly or is reflected once to the other side of the cone and extracted out except for the light that diffracts near the top of the cone, causing some losses.
Fig. 5 The effect of semi-vertical angle on the light escape cone: the light escape cone (region II) initially increases with the semi-vertical angle and then decreases. Light in the region I is trapped in the light emitter devices, light in the region II is extracted out, and light in the region III experiences multiple reflection and inference and extracted out.
The wavelength-dependent light extraction efficiency with respect to the semi-vertical angle is plotted in Fig. 6. For the planar light emitters and light emitters with larger semi-vertical angles, a strong wavelength-dependent light extraction efficiency is observed. This dependence is a matter of interference induced by the cavity of the light emitter. The average efficiency of the nanostructure is also compromised as the large semi-vertical angle maintains a large total internal reflection region as depicted in Fig. 5. This accounts for the lower light extraction efficiency of the light emitter. As the semi-vertical angle becomes acuter, this effect erodes away to broadband extraction efficiency and overall higher light extraction efficiency because of the smaller total internal reflection regions shown in Fig. 5. As the angle becomes smaller than the critical angle of the material, however, the extraction efficiency begins to decrease again, and the wavelength dependency returns. This is attributed to the multi-reflection and interference effect of light into region III. As the semi-vertical angle becomes smaller, more light goes into region III, which results in the wavelength dependency light extraction efficiency. In summary, extremely high light extraction efficiency over the visible light spectrum has been achieved by tuning the semi-vertical angle of cones in microcavity white light emitters with cone arrays.
Fig. 6 The wavelength-dependent light extraction efficiency of cone array light emitters with various semi-vertical angles.
5. Effect of base diameter on the light extraction efficiency of cone array light emitters
In addition to the effect of the semi-vertical angle of cones on the light extraction of white light emitters, the effect of the base diameter of the nanocone arrays on the light extraction efficiency was also investigated to achieve the optimum light extraction of microcavity light emitters. In this study, hexagonal-close packed cone arrays with a constant semi-vertical angle of 30°, but various base diameters were designed on microcavity light emitters. The wavelength-dependent light extraction efficiency for cone array microcavity light emitters with various base diameters (0-1.2 μm, 0 μm diameter indicates the planar light emitters) are shown in Fig. 7(a). For the planar light emitter devices, the light extraction efficiency shows strongly wavelength-dependent and the overall light extraction is low. The wavelength dependency erodes away as the base diameter of cone increases and overall light extraction efficiency alsoincreases. The comparison of the far-field radiation patterns for the cone array microcavity light emitters with various diameters is presented in Fig. 7(b). Much higher far-field intensity is obtained for the emitters with cone arrays compared to that of the planar light emitters. The increase in the diameter of the cone has the effect of decreasing the periodicity of the extraction efficiency but has the effect of increasing the average extraction efficiency of the light emitters (see Fig. 7(c)) only up to a point. As we can see in Fig. 7(a), all diameters above 0.8 µm have a relatively stable extraction efficiency with a slight decrease in efficiency with larger diameters. This is not a property of the cones themselves but in actual a result of the geometric properties of making a cone array. The larger diameters correspond to larger gaps between the cones at their bases, meaning that a larger overall proportion of the emission surface is planar and the lower in-coupling efficiency. The overall increase in efficiency for larger cones up until 0.8 µm of diameter is a result of losses via non-geometric optics (diffraction) in the smaller ones. As the overall size of the cone increases, less of the light ends up in the very top of the cone as the area is more spread out, leading to fewer losses from circular aperture diffraction in the sub-wavelength of the cone.
Fig. 7 (a) Wavelength-dependent light extraction of cone arrays with different diameters of cones, (b) far-field radiation patterns of light emitters with various base diameters of cones, and (c) average light extraction efficiency of light emitters with cone arrays as a function of the diameter of cones.
6. Conclusion
The comprehensive study is carried out to optimize the microcavity light emitters. The FDTD method is employed to design the white light emitters with high light extraction efficiency. The results of our calculation show that light extraction efficiency of planar microcavity emitters strongly depends on the cavity thickness and it varies with wavelength. This is not favorable for practical applications. The use of nanostructures on the top white light emitter leads to significant enhancement in light extraction efficiency. Most importantly, these nanostructures eliminated the wavelength dependency and result in the extremely high light extraction efficiency over the whole visible spectrum. Specifically, the addition of cone arrays to the emission surface of microcavity light emitters can markedly increase the light extraction efficiency of the device through the elimination of total internal reflection at the emission surface. The base diameter, as well as the semi-vertical angle of the cone arrays, can be adjusted to maximize the light extraction efficiency of light emitters. Our finding shows that a broadband light extraction efficiency of 81% could be obtained, in contrast to 26% efficiency in planar light emitters, by using cones with a semi-vertical angle of 30° and a diameter of 0.8 µm. Thus, this work provides insight for designing white light emitters with high light extraction efficiency.
Funding
University of Tulsa through a faculty startup fund.
Acknowledgments
The authors would like to thank Professor Scott Holmstrom, Mr. Preston Vargas, and Mr. August Bont for helpful discussions.
Disclosures
The authors declare no conflicts of interest.
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