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Abstract
In this study, we propose a low-cost, simple and feasible post-processing approach to improve the light extraction efficiency (LEE) of LED packages. Amorphous photonic structures (APSs) with only short-range order are fabricated from anodic aluminum oxide (AAO) and transferred to intermediate polymer stamp (IPS) by nanoimprint technology. The IPS with APSs is directly mounted onto the surface of an LED package, where the LEE is achieved as 94.6%. The scanning electron microscope (SEM) images of AAO templates and imprinted IPS are analyzed by radial distribution function and diameter histogram. The far-field patterns of APS-mounted LED packages are measured in electroluminescence (EL). The three-dimensional finite-difference time-domain (3D-FDTD) calculations of transmittance of APSs confirm that they improve the light extraction above the critical angle. Two-dimensional Fourier power spectra from SEM images of APSs are also calculated. The LEE enhancement is attributed to that the APSs have short-range order on a length scale comparable to emission wavelength of LED. We provide novel multistage simulations in a simplified FDTD model for the LED package. Finally, we discuss the influence of the morphology of APSs on the LEE of the APS mounted LEDs.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is well known that the total internal reflection limits the light extraction efficiency (LEE) of GaN-based light emitting diodes (LEDs) because the refractive index of GaN is about 2.5 at a wavelength of 450 nm [1, 2]. The problem of light extraction from GaN chip will be resolved after the escape cone overlapping if the encapsulation resin has high refractive index above 1.80 [3]. However, the refractive index of commercial encapsulation resin is lower than 1.60 due to both reliability and adhesion performance. So many efforts are paid to the redirection and absorption of the light rays in semiconductors [3–8]. The LEE of commercial GaN-based LED is achieved as nearly 90% [9]. Under low current density operation, the low loss extraction structure designation for LED will obtain the LEE above 90% [3, 8]. The LEE enhancement of several percent becomes difficult when the original LEE approaches to 90% [8]. Using photonic crystals (PhCs) the LEE is achieved as 73% for un-encapsulated 700 nm-thick GaN-based LEDs [10], and it reaches to 94% after encapsulation [11]. The fabrications of large-scale PhCs and ultra-thin GaN based LEDs are difficult, which make the techniques not suitable in LED industry [10].
Besides of total internal reflection, the Fresnel reflection may also cause a large extraction loss at the optical interface with much refractive index mismatch. Interference and moth-eye are two different routes to eliminate the Fresnel loss [12–15]. The destructive interference from multiple reflections occurs at interfaces between dissimilar dielectric thin films (typically λ/4 thick). Compared to interference technique, the moth-eye one has several advantages: mechanically and thermally robust, broadband and omni-directional anti-reflectivity [14]. Kim et al. reported a bio-mimic nanostructured LED lens that showed a transmittance of 98.4% at 560 nm [16]. There are still large reflective losses at the LED-encapsulant interface. Moreover, the LEE may be dominated by leaky modes and absorption in the semiconductors. Shin et al. imprinted moth-eye mold onto the LED package [17]. They obtained 3.27% of LEE enhancement for moth-eye structured LED compared to that for LEDs with the conventional smooth lens. The wall plug efficiency is about 47.8% at 0.09 A, which is moderately high, compared to the currently commercial level [9, 17]. It is seldom reported that the moth-eye structure is fabricated on the LED with extremely high LEE about 90% to eliminate the Fresnel loss.
As to moth-eye structures, the effective refractive index theory can be applied to explain the high transmittance when the characteristic dimension (d) of the interfacial structure is far smaller than the wavelength (λ) [14]. However, for large d similar to λ, the diffraction and scattering will dominate the light extraction. The large size nanostructures are still named as moth-eye or moth-eye-like structures [16–20]. The effective refractive index theory is invalid in the regime of d∼ λ. Moreover, many of these moth-eye structures are the amorphous photonic structures (APSs) which show short-range order only. The guided mode coupling theory used in PhC structure is also not suitable to deal with these APSs [10]. Many living organisms have non-iridescent structural colors, such as non-iridescent blue or green colors in the caruncles or feathers of some birds [21, 22]. The non-iridescent structural colors in an APS come as a result of coherent scattering and the presence of short-range order is necessary. Another interesting phenomenon that can be observed in APSs is the Anderson localization of light, which is caused by interference between different paths arising from multiple scattering of light by disorder [23, 24]. Fourier analysis based on Benedek’s electromagnetic theory explains why corneas with APSs are transparent [25]. In our previous work, Fourier transferring rings from scanning electron microscopy (SEM) images of APSs were qualitatively assigned to change the incident wave vector to extract the light [26]. We also found in experiment that the APSs played more roles in the light extraction than the ordered photonic structures did. The numerical simulation, such as finite-difference time-domain (FDTD) is used to study the light extracting features with nano size [18, 26]. Due to the computation capacity, the simulation size is usually only several microns. The quantitatively Fourier analysis combined with FDTD simulation are not performed on the global APSs.
The moth-eye structures were fabricated by nanoimprinting, colloidal lithography, spontaneous nano phase separation, etc. on the emission surface [16–20, 26]. It is obvious that nanoimprinting is applicable in mass production. However, the hard stamp with nano size is very expensive, and the imprinting processes may affect the uniformity and reproductive. Lumileds Co. reported the Lumiramic technique, which surface-mounted the phosphor ceramic plate on the thin-film flip-chip (TFFC) LED chips [27]. The Lumiramic plate is prepared as a separate component, which can be measured by a certain blue light excitation before the final assembly. In this way the number of white LED bins can be reduced considerably. In this work, we proposed an easy and feasible method that nanoscale APS was transferred to the silicone surface of LED package to improve the LEE by surface-mounting the intermediate polymer stamp (IPS) with the APS. The APS was fabricated from anodic aluminum oxide (AAO) and then imprinted onto the surface of IPS by nanoimprint technology. AAO patterns can be determined by different kinds of acidic electrolytes and the anodization voltage [28–30]. By optimization of the arrangement order and diameter of AAO, LEE of APS surface mounted LED was achieved as 94.6%. Combined the Fourier analysis with FDTD simulation, the light extraction mechanism by the APSs was studied. The best LEE achieved by optimizing APSs in FDTD simulations is 95.4%. Our method has the potential to be used in the micro-LEDs. It is well known that sidewall defects from etching damages can cause a serious decrease in the luminescence efficiency of micro-LEDs [31, 32]. And fabricating nanostructures by etching may introduce additional defects. In addition, micro-LEDs are quite thin because of removing original substrates and quite small (about tens of microns). Microlens made using a thermal resist reflow technique has been proposed to improve the LEE of micro-LEDs [31]. Our proposed method of surface-mounting APSs is free of etching and can be an alternative of microlens.
2. Experiments
Commercial nanoporous AAO templates, which are the silicon replicas of the original AAO structures on aluminum sheets, were used as the nanoimprint stamps to fabricate APSs. Figure 1(a) shows the schematic diagram of APS transferring and surface-mounting process. First, APS of AAO was transferred to the surface of IPS by nanoimprint technology. The advantages of using IPS are ease of demolding, reduced risk of breaking templates and capable of fitting to curved surface due to its soft material properties [33]. The IPS hot embossing process was carried out under a pressure of 35 bar and heated at 155℃ for 2 min. After hot embossing process, the IPS was detached from the AAO template. Subsequently, PDMS (Sylgard184, Dow Corning 10:1 ratio with the curing agent) acting as adhesive coating was dropped onto the commercial LED package (length=5.6 mm, width=3.0 mm, height=0.77 mm, model: HV56301BSF06DC, from Hualian Electronics Corp., Ltd.) which surface was silicone with a small curvature of about 0.12 mm-1. The LED chip inside the package emitted light with wavelength around 450 nm. Finally, the IPS was placed onto the PDMS. The whole device was then heated for 30 min at 100 ℃ to cure the PDMS. The top-view photo of the completed device is shown in Fig. 1(b). The completed device was cut by low speed diamond wheel saw (South Bay Technology, Model 650) and the corresponding cross-sectional SEM image is shown in Fig. 1(c), from which it can be seen that the IPS conforms well with the surface of the LED package. There were two important reasons that IPS and PDMS were adopted in transfer process. One was that IPS and PDMS were almost transparent in visible light range. The other was that the differences in refractive index between IPS, PDMS and silicone were negligible. They all had the refractive index of about 1.41. As can be seen from Fig. 1(b) and Fig. 1(c), the conjoint ratio between APS and LED chip can be considered close to 100%, which is a result of small curvature of LED package’s surface (about 0.12 mm-1), soft IPS, adoption of intermediate glue and vaccum pumping process.
Fig. 1. (a) The schematic diagram of APS transferring and surface-mounting process; (b) the top-view photo of the completed device; (c) the cross-sectional SEM image of the completed device cut by low speed diamond wheel saw.
The surface morphology of AAO templates and the IPSs were examined by scanning electron microscope (SEM, Nova Nano SEM 430). The electroluminescence (EL) spectra of the LEDs with and without APSs were measured by Everfine HAAS-2000 high accuracy array spectroradiometer using an integrating sphere (Φ0.3m, Everfine). Three-dimensional FDTD simulations were carried out to study the effect of APSs on the light extraction using Lumerical software (FDTD Solutions v8.21, Vancouver, BC, Canada) [34].
3. Results and discussion
The top-view SEM images of the porous AAO templates used in nanoimprint are shown in Fig. 2. It can be seen that the nano-hole array is not strictly uniform, but basically satisfies the hexagonal close-packed arrangement. And the nano-hole array can be divided into many small highly ordered regions, which show short-range order. In the small regions, the distance between adjacent holes is around 450 nm for all images in Fig. 2. And the hole diameters of AAO templates in Figs. 2(a), 2(b) and 2(c) are around 200, 300 and 400 nm, respectively (called AAO200, AAO300 and AAO400).
Fig. 2. The top-view SEM images of porous AAO templates with hole diameters around (a) 200 nm, (b) 300 nm and (c) 400 nm. The hole spacing is around 450 nm for the three images.
The morphology and pattern size characterizations of IPSs imprinted by AAO templates are shown in Fig. 3. The results in Figs. 3(a, d, g, j), Figs. 3(b, e, h, k) and Figs. 3(c, f, i, l) correspond to three AAO templates shown in Fig. 2. Since IPSs are imprinted by AAO templates, the morphology of IPSs will be complementary to those of the corresponding AAO templates and the pattern size will be the same as those of the templates. The shapes of cross section of pillars in Fig. 3(a) are relatively irregular, which is probably because the pore-widening process of corresponding AAO template in Fig. 2(a) is too short and has not yet reached a steady state. The cross section of pillars in Fig. 3(c) is close to hexagonal because the corresponding AAO template in Fig. 2(c) underwent a long enough pore-widening process so that the hexagonal “skeleton” of each hole is exposed [28]. The tilt-view SEM images in Figs. 3(d-f) show that the pillar unit has a rounded tip, which is consistent with the fact that the shape of the holes in AAO templates is a U-shape [28].The pillar array here is similar to moth-eye structures reported [14], and the difference is that the pillar array has no strict periodicity and the characteristic dimensions of pillar array are on the order of the wavelength of light.
Fig. 3. The morphology and pattern size characterizations of IPSs imprinted by AAO templates. (a-c) Top-view SEM images; (d-f) tilt-view SEM images; (g-i) radial distribution function (RDF) of pillar array; (j-l) the histogram of pillars’ diameter distribution. The histogram is normalized so that the integral of the histogram is 1. The results in (a,d,g, j), (b, e, h, k) and (c, f, i, l) correspond to three AAO templates shown in Figs. 2(a), 2(b) and 2(c), respectively.
Figures 3(g-i) shows the radial distribution function (RDF) of pillar array in Figs. 3(a-c). The RDF is a means of measuring the correlation between pillars within a system or, more specifically, a measure of, the probability of finding a pillar at a distance (r) away from a given reference pillar [35]. Here, the RDF is calculated by the image processing program, ImageJ. An intensity of 1 corresponds to the average pillar density. The first peak of the RDF of IPS1 (IPS from AAO200) is at radius of 0.465 μm, and its full width at half maximum (FWHM) is 0.099 μm. The first peak and FWHM of the RDF of IPS2 (IPS from AAO300) are 0.458 μm and 0.070 μm, respectively. The first peak and FWHM of the RDF of IPS3 (IPS from AAO400) are 0.437 μm and 0.083 μm, respectively. There are apparent differences in the position of the first peak of these RDF curves. This is partly due to the difference in the preparation process of AAO templates, and partly due to the error of replacing a non-circular pillar with a central point in ImageJ’s RDF algorithm. Among these IPSs, the first peak of IPS1 has the largest FWHM, indicating that the distance distribution of the nearest pillar in IPS1 is more dispersed and the disorder degree of pillar arrangement is higher. On the contrary, the pillar arrangement of IPS2 has relative low disorder. From the first peak positions of the RDF curves, the mean center-to-center distance of pillar array in Figs. 3(a-c) can be determined to 465, 458 and 437 nm, in good agreement with the distance of around 450 nm between adjacent holes of the AAO templates in Fig. 2(a-c). As shown in Figs. 3(g-i), after three or four identifiable and obvious peaks, the RDF value tends to 1, which demonstrates that the pillar arrays have only short-range order but lack long-range order and they are APSs. The histogram of pillars’ diameter distribution is shown in Figs. 3(j-l). The histogram can be approximated and fitted by the Gaussian probability density function. In this way, the diameters of pillars in Fig. 3(a-c) are determined to be 232 ± 36, 334 ± 31 and 422 ± 25 nm, respectively, which are consistent with the results in Fig. 2. This result also indicates that the pillar dimension distribution of IPS1 has the largest disorder.
Current-voltage (I-V) and light output power-current (L-I) curves for normal LEDs and APSs surface-mounted LEDs are shown in Fig. 4. There is no difference in the I-V curves between normal LED and APSs ones, indicating that the surface-mounting process doesn’t affect the electrical performances of LEDs. The L-I characteristics show that the light output power (LOP) at 100 mA is enhanced by 1.3%, 2.0% and 2.9% for APS1 (APS from AAO200), APS2 (APS from AAO300) and APS3 (APS from AAO400) mounted LEDs compared to the normal LEDs. The external quantum efficiency (EQE) is calculated by the following formula [36]:
where ${P_{out}}$ is the LOP, $h\bar{\nu }$ is the average photon energy in the EL spectrum, I is the injection current, and q is the unit elementary charge. The EQE-I curves are shown in the insets of Fig. 4. The calculated LED efficiencies are summarized in Table 1. By the way, the internal quantum efficiency (IQE) is 83.6%, estimated by fitting based on the rate equation model proposed by Ryu et al. [37]. The IQE is confirmed by temperature-dependent photoluminescence experiments, which is one of the most popular methods for IQE measurement [36]. According to the relationship: EQE = IQE ×LEE, the highest LEEs achieved can be calculated to be 94.6% for the LED with APS3, which is 3.0% higher than the LEE of normal LED (91.8%). To eliminate the effect of error, the integrating sphere was carefully calibrated with a standard light source before each test. Besides, five samples with the same APS were prepared and three measurements under the same operating conditions were made for each sample.Fig. 4. Experimental I-V and L-I curves for normal LEDs and (a) APS1, (b) APS2, (c) and APS3 mounted LEDs. The insets show the corresponding EQE-I curves.
Table 1. Efficiencies and their enhancements of normal LEDs and APSs surface-mounted LEDs
It’s worth mentioning that the LEE of 94.6% is one of the largest LEE values ever reported. The wall-plug efficiency (WPE) is defined by the ratio of the optical power emitted into free space from the LED to the electrical power provided to the LED [36]. And the peak WPE we achieved in the LED with APS3 is calculated to be 82.6%. L.Y. Kruitzky et al. reported a simulated LEE of 94% and a measured WPE of 78.1% [8]. In contrast to us, they realized the high efficiency design by optimizing the chip and package without any nanostructure. However, the high efficiency design requires that LED devices operate at low current density. LEDs are limited to operate at low current density, so LEDs can be radically designed with smaller metal contacts, thinner current spreading layer, and a reduced or eliminated heat sink, etc. The approach we proposed doesn’t has this limitation and only requires the surface of LED packages to be suitable for transferring. For example, the curvature of the surface must be low enough to ensure good conjoint ratio. Besides, what we proposed is a post-processing approach, which won’t affect the LED chip design. This means that our approach can even be used in conjunction with the LED chip design they proposed. Matioli et al. also reported a LEE of 94% by embedding air-gap PhCs within LEDs [11]. However, there are two drawbacks to their approach. The first one, which has been mentioned in the introduction, is that the fabrication of large-scale PhCs is difficult and expensive. The second one is that the growth of the LED devices must be interrupted to fabricate embedded PhCs. In contrast, our approach of obtaining nanostructures from AAO and transferring nanostructures by nanoimprint technology and surface-mounting is easier and more cost-effective.
Figure 5 shows the far-field intensity distributions of normal LED and LEDs with APS1, APS2 and APS3. The intensity distribution of normal LEDs in Fig. 5(a) has good rotational symmetry with respect to azimuth angle, and the APSs have no preferential orientation in the arrangement, so the intensity distribution of LEDs with APSs (see Figs. 5(b-d)) also approximately satisfies azimuth symmetry. As shown in Figs. 5(a-d), the high-brightness area (red) of APS mounted LEDs are distributed in a wider range than that of normal LED. In other words, the far-field intensity of APS mounted LEDs decrease more slowly than that of normal LED as theta angle increases from 0°. In Fig. 5(e), it can be clearly seen that the light intensity of normal LED is the largest at the theta of 0°, and it reduces sharply above the theta of 30°. The light intensity of APS3 mounted LED is stronger in the theta range above 30° than those of the other LEDs. For example, when the theta is 50°, the light intensity of the LED with APS3 is enhanced by 70.0% in comparison to that of normal LED. From the results of intensity distribution and output power, it can be concluded that APS mounted LED has stronger light scattering ability than normal LED. Although the light intensity near the 0° is slightly reduced, it makes the area with high light intensity more widely distributed, and also significantly improves the light intensity above 30°, finally enabling more light to be extracted to the air.
Fig. 5. Far-field patterns of (a) normal LED, and LEDs with (b) APS1, (c) APS2 and (d) APS3; (e) polar plots of the far-field intensity distribution of normal LED and LEDs with APS1, APS2, and APS3. Theta angle is the angle between the emergent light and the normal direction of an LED’s surface.
It is worth mentioning that far-field patterns of APS mounted LEDs are significantly different from the reported emission patterns of the AAO patterned LED in our previous work [26]. In our previous work, the asymmetry was observed in the far-field pattern obtained in a photoluminescence (PL) microscope and some sharp lobes were obtained in the angular resolution photoluminescence (ARPL) for the AAO patterned LED. In contrast, the far-field patterns of APS mounted LEDs in Fig. 5 possess good azimuth symmetry and show no sharp lobes. The difference of far-field patterns in symmetry can be explained by the difference of luminous area. In our previous work, the laser spot in the PL microscope is several microns on the LED and the dimension of the luminous area is also several microns. In such a small area, the short-range order of AAO patterns cannot be ignored and the AAO patterns can be approximated as quasi-periodic PhC patterns. Therefore, the far-field pattern from such a small area possesses no azimuth symmetry. In contrast, the dimension of the luminous area of APS mounted LEDs is several millimeters. Due to the lack of long-range order, the APSs have no preferential orientation in the arrangement over such a large area. Therefore, the far-field patterns of APS mounted LEDs possess good azimuth symmetry. The difference of sharp lobes can be explained by the different device structures. In our previous work, the AAO patterned LED refers to a two-inch sapphire substrate on which the LED structure was grown and AAO pattern was transferred. Most of the light generated from the active region of the LED will be trapped in the LED due to the severe total internal reflection. The appearance of sharp lobes in ARPL spectrum of AAO patterned LED is attributed to the diffraction of some guided modes extracted from the LED in our previous work. In this work, APS mounted LED is based on the normal LED with commercial encapsulation. There are no guided modes appearing in our normal LED, which can be confirmed by the absence of lobes induced by Fabry-Perot resonances in the far-field pattern of normal LED [10]. Therefore, the reason why the far-field patterns of APS mounted LEDs show no sharp lobes is that there are still no guided modes in APS mounted LEDs after APS surface-mounting process.
When the characteristic dimensions of emission surface structures have different scales to λ, the study methods are different. For example, the mean period and the diameter of the pillar array in APS3 are both around 450 nm, which are similar to emission wavelength of 450 nm. Thus, the ray optics is not applicable for this case due to the phenomena of possible interference and diffraction. The effective medium theory adopted by many other literature [5,6], explains the optical phenomenon of moth-eye structure. However, when the characteristic dimension of emission surface structure is not far less than the wavelength of light or the structure is not periodic, as in the case of APS3, the effective medium theory fails because the surface structure can’t be treated as a homogeneous material with a “bulk-like” (effective) refractive index that varies with position when interference and diffraction should not be ignored [14]. In our case, optical phenomenon is dominated by scattering of APSs on the same scale with emission wavelength, which means that Maxwell’s equations should be solved directly.
Therefore, the 3D-FDTD method was used to study the optical behavior of the APSs. Firstly, the optical transmission properties of APSs were studied. The schematic diagram for the transmission simulation model is shown in Fig. 6(a). In the FDTD model, a plane wave acting as the light source propagates from the IPS through the APS into the air. The incident angle is defined as the θ angle between the propagation direction and normal direction. The wavelength of the plane wave is set as 450 nm. The refractive index of IPS and the air is set as 1.41 and 1, respectively. Due to the limited computer memory and computation capacity, the lateral dimensions of the computational domain are 6 μm×6 μm. The boundary condition for the top simulation area is set as a perfectly matched layer (PML) boundary condition, which absorbs electromagnetic energy incident upon it. The boundary conditions for the four lateral boundaries are set as periodic boundary condition. The transmittance is calculated in terms of the power gathered from the monitor in the air divided by the source power.
Fig. 6. (a) The schematic diagram for the transmission simulation model; (b) the calculated transmittance curves for flat surface, APS1, APS2 and APS3, respectively.
The transmittance of different fabricated APSs calculated by FDTD is shown in Fig. 6(b). Here, the curved surface of silicone with the curvature of about 0.12$\textrm{m}{\textrm{m}^{ - 1}}$ is simplified to be a flat surface because the height difference between the highest and lowest points of the curved surface is only 0.6 nm in the region of the FDTD model. The transmittance curves show that the APSs effectively enhance the light transmission above the critical angle. For example, the transmittance at the incident angle of 60° is 9.5% for APS3, when the light transmittance of flat surface above the critical angle is completely zero. At the incident angle below the critical angle, the light transmittance of APSs is slightly lower than that of flat surface. For example, the transmittance at an incident angle of 20° for APS3 is 92.5%, which is 4.8% less than that of flat surface. It is worth mentioning that the transmittance results agree well with the far-field intensity distribution results shown in Fig. 5(e). Flat surface has higher transmittance at small incident angles, so the normal LED also has higher light intensity at small incident angles. APSs have higher transmittance at large angles, so the LEDs with APSs have higher light intensity at large angles than the flat one.
The transmittance results can be explained by Benedek’s electromagnetic theory that was early proposed to explain why corneas are transparent [25]. According to Benedek’s theory, the scattering of light is produced only by those fluctuations of refractive index whose Fourier components have a wavelength equal to or larger than one half of the wavelength in the medium. The 2-D Fourier power spectra of SEM images of cross-sections of APSs are shown in Fig. 7. The ring-shaped patterns indicate that there is no preferential orientation in the arrangement of the pillar array, which is a distinct feature of the amorphous structure. In long range, the pillars distribute in orientation randomly. The peak spatial frequencies of the first rings of different APSs are all between 2 $\mathrm{\mu }{\textrm{m}^{ - 1}}$ and 2.8 $\mathrm{\mu }{\textrm{m}^{\textrm{ - 1}}}$, i.e. the wavelengths of peak Fourier components lie in the range of 0.36 $\mathrm{\mu }\textrm{m}$ and 0.50 $\mathrm{\mu }\textrm{m}$. This range of spatial frequencies corresponds to center-to-center distances between adjacent pillars. Given that the wavelength of light is 450 nm, the light will be scattered. Therefore, the light which incident angle larger than the critical angle can be scattered into light extraction cone. Meanwhile, the light which incident angle smaller than the critical angle may also be scattered outside light extraction cone. This explains the difference of the transmittance between flat surface and APSs. Besides, the second rings of Fourier power spectra of APS2 and APS3, which correspond to a wavelength range of 0.20 $\mathrm{\mu }\textrm{m}$ and 0.25 $\mathrm{\mu }\textrm{m}$, also contribute to light scattering. By contrast, the second ring of that of APS1, which correspond to a wavelength range of 0.12 $\mathrm{\mu }\textrm{m}$ and 0.17 $\mathrm{\mu }\textrm{m}$, makes no contribution to light scattering. The difference of light scattering ability leads to the difference of transmittance curves shown in Fig. 6(b), which ultimately leads to the difference of LEE enhancements shown in Table 1. The difference between these three 2-D FFT power spectra in Fig. 7 is mainly caused by different diameters or filling factors, which will be discussed in the following FDTD simulation section.
Fig. 7. Two-dimensional Fourier power spectra from SEM images of (a) APS1, (b) APS2, and (c) APS3. The power spectra have been log-scaled for better display and to bring out more spectral details.
To confirm the influence of APSs on the LEE of LED packages, we established a simplified FDTD simulation model for an LED package shown in Fig. 8(a). A custom source with a Lambertian distribution is used as the light source for the model to simulate an LED [38]. The refractive indexes of IPS, silicone and the air are set as 1.41, 1.41 and 1, respectively. Considering the huge difference in the dimensions between the FDTD model and an actual LED package, the absorption coefficient of silicone is set as 240 $\textrm{c}{\textrm{m}^{ - 1}}$, which is far greater than the actual value. The lateral dimensions of the computational domain are 7 μm×7 μm. The boundary conditions for top, bottom and the four lateral boundaries are PML, PML and metal boundary conditions, respectively. Metal boundary conditions behave as perfect electric conductor and are perfectly reflecting. In order to avoid the obvious oscillation of light in the FDTD model acting as a micro cavity, which would not occur in the actual LED package, we simulated the light extraction process by using a relay form of multistage simulations. In the first stage, light propagating upward from the light source is incident on an APS, some of it goes out into the air and recorded by the top monitor, while some of it is reflected back to the bottom. The light reflected to the bottom is recorded by the bottom monitor and then absorbed by bottom PML. In the next stage, the light recorded by the bottom monitor in the previous stage is reversed to propagate upward and is set as the light source for this stage to start this stage of simulation. Each stage has a LEE value, defined as the light power recorded by the top monitor at that stage divided by the light source power at the first stage. The total LEE is the sum of the LEEs of each stage. Based on the actual simulation experience, the contribution of the LEEs after six stages to total LEE is negligible.
Fig. 8. (a) The schematic diagram of FDTD model for LED packages; (b) the calculated transmittance curves for APS4, APS5 and APS3. APS4 and APS5 were created by scaling the diameter normal distribution of APS3 to that of APS1 and APS2 while keep the pillar arrangement of APS3 unchanged. (c) The calculated transmittance curves for APS6, APS7 and APS3. APS6, APS7 were created by scaling their diameter normal distribution to that of APS3 while keep their pillar arrangements unchanged. The values in the legends are the corresponding LEEs calculated by the model in (a). (d) The calculated LEEs for different mean center-to-center distances when other pattern parameters of APS3 except the fill factor remained unchanged; (e) the calculated LEEs for different mean center-to-center distances when the diameters of APS3 also change to keep the fill factor constant. The red words and markers indicate the LEEs of APS3.
The situations of flat surface, IPS1, IPS2 and IPS3 were simulated firstly. The simulated results of LEEs are 91.3%, 93.1%, 94.3% and 94.7%, which are in good agreement with the experimental results shown in Table 1, indicating the FDTD model is a reasonably simplified model for LEE calculation of the LED package. Secondly, to investigate the influence of the diameter of APS on LEE, the diameter normal distribution of APS3 was scaled to that of APS1 and APS2 while keeping the pillar arrangement of APS3 unchanged. The pillar array obtained were denoted as APS4 and APS5, respectively. The corresponding transmission curves and LEE are shown in Fig. 8(b). The transmission curves show similar trends with the transmission curves in Fig. 6(b). Under the premise of the same pillar arrangement, when the diameter increases, the transmittance above the critical angle increases and the LEE of the LED package also increases. The 2-D Fourier power spectra (not shown here) of APS4, APS5 and APS3 look almost exactly like those in Figs. 7(a-c) and show the similar trend. When the diameter increases, the number of recognizable rings increases, the sharpness of the rings increases, and a second ring that corresponds to one half wavelength of light also appears. It indicates that stronger scattering may be brought by the APS. Thirdly, the diameter normal distribution of APS1 and APS2 were scaled to that of APS3 while keep their pillar arrangement unchanged. The pillar array obtained were denoted as APS6 and APS7, respectively. As can be seen from the transmission curves in Fig. 8(c), different APSs with the same diameter distribution and different pillar arrangement have almost equal transmittance above the critical angle. The 2-D Fourier power spectra (not shown here) of these APSs look almost exactly like Fig. 7(c) and also show the same number of recognizable rings and almost the same sharpness of rings. As mentioned above, the RDF curve shows that APS7 (or APS2) has the highest degree of order in pillar arrangement, but its LEE is the lowest. APS3 has an intermediate degree of order in pillar arrangement and obtains the highest LEE. The difference of the transmittance in Fig. 8(c) is smaller than that of the transmittance in Fig. 8(b), which means that the change in diameter of an APS may have a greater effect on the results of LEE than the pillar arrangement. It can be concluded from the above results that large diameter is conducive to the light extraction above the critical angle, which is conducive to improving LEE. The pillar arrangement of an APS also affects LEE.
In order to find the optimized APSs with the highest LEE, we created some APSs based on APS3 in FDTD simulations and the corresponding LEEs are shown in Fig. 8(d-e). When other pattern parameters of APS3 except the fill factor remain unchanged, the influence of mean center-to-center distance or the fill factor on LEE is shown in Fig. 8(d). In this case, an increase in mean center-to-center distance means a decrease in the fill factor. The LEEs don’t vary monotonously with mean center-to-center distance. When the mean center-to-center distance of APS3 increases to 480 nm, the best LEE obtained is 95.2%. When the filling factor of APS3 remains unchanged, we increased or decreased the mean center-to-center distance and the diameters simultaneously. The curve of LEE changing with mean center-to-center distance is shown in Fig. 8(e). When the mean center-to-center distance reaches 650 nm, we obtained the highest LEE of 95.4%. According to the above simulation results, LEE can be further improved on the basis of APS3. Although it’s experimentally difficult to obtain larger mean center-to-center distance of APSs by AAO and serious problems such as burning or breakdown will be encountered [28], to obtain higher LEE, the mean center-to-center distance needs to be further greatly increased while keeping the fill factor constant by increasing diameters simultaneously.
In this work, the reproducibility can be assured by nanoimprint, Si-based AAO template and surface-submount techniques. As to long-term stability, during our measurement in a few weeks, there were no spalling, delamination and other problems affecting the stability of the samples. Further long-term work is needed to investigate the problems of long-term stability, such as long-term aging and pattern contamination. Moreover, the irregular nano-hole pattern in Fig. 2 may limit the LEE performance. It is due to large fluctuation of anode voltage, short period pore-widening process, and curing, demolding of the imprinting process. These processes can be improved by adjusting the AAO and nanoimprint conditions.
4. Conclusion
In summary, we have demonstrated the LED package with surface-mounted APS using nanoimprint and intermediate polymer stamp techniques. The LEE of the LED package with the APS was achieved as high as 94.6%, which was enhanced by 3.0% compared with the normal one. The RDF and diameter distribution histogram results of APSs showed that the larger diameter and smaller disorder of APS benefited for higher LEE of the APS-mounted LED. The experimental far-field intensity distribution curves and the transmittance curves obtained by 3D-FDTD simulations confirm that the APS can improve the light extraction above the critical angle. Two-dimensional Fourier power spectra from SEM images showed that the LEE positively related to the rings area within a certain spatial frequency. A novel multistage simulations in a simplified FDTD model for the LED package were carried out where the LEE values can be simulated more accurately. Further improvement of the LEE can be made by greatly increasing mean center-to-center distance of the APS while keep the fill factor constant by increasing diameters simultaneously. The method of improving LEE has the potential to be used in micro-LEDs that is sensitive to etching damage or in the ultra-thin LED devices that are not suitable for packaging or fabricating lens.
Funding
National Key Research and Development Program of China (2017YFB0403100); National Natural Science Foundation of China (61674005, 61927806); Science and Technology Major Project of Guangdong Province (2016B010111001); Guangdong Basic and Applied Basic Research Foundation (2020B1515120020); Science and Technology Planning Project of Henan Province (161100210200).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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