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Abstract
In this study, we propose a micro-sized photonic structure that extracts 89% of the intrinsic trapped photons from the spectrum conversion film into free space using the Monte-Carlo ray-tracing method. Furthermore, the spectrum of the spectral-shifting film can be accurately simulated based on a mean free path concept, providing the estimation of its overall performance including the external quantum efficiency and the self-absorption efficiency. The simulations show that the spectrum conversion film with micro-structures shows a two-fold increase in the total external quantum efficiency and a four-fold increase in the external quantum efficiency in the forward viewing direction compared to the planar spectrum conversion films without micro-structures.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past decades, various strategies have been developed to increase the light extraction efficiency of light-emitted diodes (LEDs), including plasmonics [1], photonic crystals [2,3], surface roughness [4,5], surface plasmon resonance [6], graded refractive index material [7], and corrugated structures [8]. In addition, micro-domes [9], micropillars [10], micro-lenses [11], oblique mesa sidewalls [12,13], nanowires [14,15], nano- and micro-pyramids [16,17], and shape design [18] were also adopted to enhance the light extraction efficiency. For instance, the use of the GaN micro-domes formed by reactive ion etching of the GaN layer led to an increase in light extraction efficiency of thin-film flip-chip (TFFC) InGaN quantum wells (QWs) light-emitting diodes (LEDs) by 2.7-2.8 times at specific wavelength, compared to that of the conventional TFFC InGaN QWs LEDs with flat surface [19]. However, all these efficient light extraction methods reported to date rely critically on a back reflector (Fig. 1(a)), typically made of a distributed Bragg mirror [20], high-reflectance metals [21], a photonic crystal with stop band [22,23], or omnidirectional reflectors [24]. The back reflector increases the light extraction efficiency by recycling the otherwise trapped photons and directing them into the forward viewing direction. However, the backside reflector inevitably stops the transmittance of incident sunlight (Fig. 1(a)), which prohibits its application to see-through emissive systems. A representative example is the spectral conversion film. In this light, it is necessary to explore light extracting photonics particularly suitable for the spectral conversion film where the back reflector is not allowed in order to maintain its high transmission of sunlight, as shown in Fig. 1(b).
Fig. 1. Schematic illustration of (a) the LEDs and (b) the spectral conversion film with surface light-extracting structures.
Spectral conversion materials are attractive for a wide range of applications ranging from natural/artificial photosynthesis [25,26] and photocatalysis [27] to photochemistry [28] and photovoltaics [29]. For a representative spectral conversion material, it consists of a high optical quality plastic or glass doped or coated by organic or inorganic converters that selectively absorb direct and diffused sunlight and re-emit at different wavelengths. For example, Detweiler et al. [30] fabricated a spectral conversion panel by coating suitable amounts of Lumogen F red 305 (LF305), an organic perylene-based fluorescent dye manufactured by BASF, on a clear acrylic sheet. These panels transmit blue and red wavelengths in the sunlight for algae photosynthesis with high efficiency, while absorbing the green wavelengths and re-emitting them as red wavelengths to boost algal productivity, compared to algal growth under the full solar spectrum. The augmentation is mainly due to the good correlation between the maximum transmission of the LF305 panels and the maximum absorbance of photosynthetic pigments in algae. The external quantum efficiency $({{\eta_{\textrm{EQE}}}} )$ of the spectral conversion materials can be expressed as the product of the light extraction efficiency $({{\eta_{\textrm{extraction}}}} )$, the internal quantum efficiency (${\eta _{\textrm{QE}}})$ and the self-absorption efficiency $({{\eta_{\textrm{self}\_\textrm{absorption}}}} )$ of the converters, assuming an optically transparent host material where there is no light attenuation when the internally generated photon propagates inside the matrix,
In this study, we propose a method for asymmetrical interface design on a reflector-free spectrum conversion film to achieve enhancement of light extraction and directional emission control. For this purpose, different geometries were discussed in microscale sizes with respect to light extraction when considering their scalable manufacturability. The optimized structural parameters of the selected geometries were obtained by numerical simulations with the Monte Carlo ray-tracing method. These optical structures lead to a substantial enhancement in the light extraction efficiency and thereby the external quantum efficiency of the film. More importantly, the film with surface structures shows a substantial increase of the light extraction efficiency in the forward viewing direction from less than 13% for the planar film to 65%. Moreover, the physical mechanisms for unidirectional light extraction and the spectral-shifting and self-absorption behaviors of the fluorophores in the host materials are also discussed in detail based on the simulations, which provide theoretical guidance for the application of asymmetrical interfaces to see-through spectrum conversion films for enhancing directional emission.
2. Monte Carlo simulations
We examined a series of ease-to-manufacturing micro-structures as asymmetrical material-air interfaces for unidirectional light extraction from the spectrum conversion film using the Monte-Carlo ray-tracing methods. The method simulates the photon transport in optical systems based on a mathematical model using both a probability theory and mathematical statistics [11,37,38]. During the numerical simulations, light rays are generated in a random way and propagate isotropically. Reflection and refraction occur once the light rays reach an interface between two different media with varied refractive indexes. The Monte Carlo ray-tracing method can accurately assess transmittance, reflectance, and absorbance of the optical systems and, more importantly, provides an effective way to simulate multiple photophysical processes of spectral-shifting and self-absorption behaviors of fluorophores in the host materials. From this viewpoint, the ray-tracing method is regarded as one of the most suitable ways to simulate light propagation in spectral-shifting films. However, this ray optics-based technique fails to address the sub-wavelength geometric features including coherent effects like diffraction and interference [39]. Instead, rigorous electromagnetic wave optics-based techniques, such as a rigorous coupled-wave analysis (RCWA) or finite-difference time-domain (FDTD) method can be used for modeling the wavelength- and subwavelength-scale structures and enable a comprehensive analysis of polarization of light and directionality. While successful in many applications, these wave-based methods also exhibit difficulty, especially in analyzing the larger structures due to computational limitations [40,41]. In considering both the large simulation domain and the large light-extracting structures in this specific study, the ray-based Monte-Carlo ray-tracing method was preferred over the RCWA or FDTD method.
Constraining our photonic designs with scalable manufacturability, we thereby examined some structures only in microscale for unidirectional light extraction including micro-domes, -prisms, -pyramids, and -cones. These micro-sized structures can be fabricated in large area with low cost [42,43], making them particularly suitable for practical applications. For instance, large-area plastic optical films with a micro-lens array pattern were fabricated using a continuous roll-to-roll film extrusion in combination with a roller embossing process [44]. Moreover, these structures do not cause significant wavelength dependence or spectral distortion due to their much larger size than the operating wavelength [8].
For illustration purposes, micro-domes were first selected as model structures. Figure 2(a) illustrates a schematic of the film with micro-domes on the top surface. These micro-dome structures are closely packed in a square lattice. The detailed model can be seen in Fig. 2(b), a side view of the fluorophore-doped film with micro-domes. The fluorophores (red dots) with a mean free path, l, are homogeneously distributed in the host materials. Here, the mean free path represents an average distance that a photon travels through the host matrix without being absorbed by adjacent fluorophores. Its value is inversely proportional to the number (<n>) of the fluorophores per unit volume of the host materials,
Here ${\sigma _{eff}}$ is the effective absorption cross-section area of the fluorophore which is integrated over all spectra. The host material has a refractive index n for the wavelength of interest. For a fair comparison, we defined an effective thickness (${\textrm{d}_{\textrm{eff}}}$) of the micro-structured film at which its total volume is equal to that of the planar film. In a typical fluorophore-doped film irrespective of micro-structures, the fluorophores first absorb the incident sunlight and re-emit photons at different wavelengths. From this viewpoint, the internally re-emitted photons (${\mathrm{\Phi }_{\textrm{emitted}}}$) partly escape from the forward (${\mathrm{\Phi }_{\textrm{backward}}}$) and backward (${\mathrm{\Phi }_{\textrm{forward}}}$) directions and the rest is still trapped inside the film due to total internal reflection. To ensure complete integration of the escaped photons in the forward and backward directions, two receivers are respectively placed next to the top and bottom surfaces of the film with a fixed gap distance of 1 µm.Fig. 2. (a) 3-D illustration of the films with micro-dome structures on top surface. (b) Cross-sectional schematic of the fluorophore-doped films with micro-dome structures on top surface. Fluorophores are shown as red dots and the host matrix materials has a refractive index of n. The schematic is not scaled.
The light extraction in total (${\eta _{\textrm{extraction}}}$), in the backward ($\eta _{\textrm{extraction}}^{\textrm{backward}}$) and forward direction ($\eta _{\textrm{extraction}}^{\textrm{forward}}$) are straightforwardly defined as follows,
3. Design of unidirectional light-extracting micro-structures
For the films with micro-dome structures, the light extraction efficiency in Fig. 3(a) is predominantly determined by the size parameters of the micro-domes. The total light extraction efficiency (${\eta _{\textrm{extraction}}}$) presents a peak with a maximum at a specific combination of dome heights and widths. And this trend is more apparent for the micro-domes with less width. Similar observations were found in the forward light extraction efficiency ($\eta _{\textrm{extraction}}^{\textrm{forward}}$), as shown in Fig. 3(b). The micro-domes on the top surface of film function as a reflector, recycling the otherwise trapped light with large incidence angles, changing the light propagation direction, making them escape from the plat side of the film in the forward viewing direction. From this viewpoint, the micro-domes show the best performance only at optimal parameters. Differently, the backward light extraction efficiency keeps increasing as the dome height increases (Fig. 3(c)) since increasing dome height increases the surface area and therefore the escape probability of the internally emitted light in the backward direction. According to simulations, the maximum $\eta _{\textrm{extraction}}^{\textrm{forward}}$ was obtained for the films with micro-domes at a dome width of 400 µm and a dome height of 65 µm, where the micro-structured films show the minimum light extraction efficiency ($\eta _{\textrm{extraction}}^{\textrm{backward}}$) in the backward direction (Fig. 3(c)).
Fig. 3. (a) Total light extraction efficiency (${\eta _{\textrm{extraction}}}$) and (b,c) light extraction efficiency in the forward ($\eta _{\textrm{extraction}}^{\textrm{forward}}$) (b) and backward ($\eta _{\textrm{extraction}}^{\textrm{backward}}$) (c) directions for the fluorescent films with micro-domes as a function of dome height (h) and width (w). The micro-dome has a radius of $R = ({w^2} + 4{h^2})/8h$.
As shown in Fig. 4, we further compared the light extraction performance of the films without and with the micro-domes at the optimal parameters, i.e. 400 µm in width and 65 µm in height.
Fig. 4. (a, b) Visualization of ray trajectories in the fluorophore-doped film without (a) and with (b) micro-domes (width: 400 µm; height: 65 µm). The backward direction is along the z-axis. For visual clarity, only 500 rays were traced. The film and micro-domes are highlighted in red. The schematic is not to scale. (c-e) Total (c), forward (d), and backward (e) emission from the fluorescent planar film and the fluorescent film with micro-domes.
Figure 4(a) shows the ray trajectories of the planar fluorescent film without micro-structures. Only a small portion of the internally emitted photons could equally exist from the forward and backward directions to air. In contrast, Fig. 4(b) shows the ray trajectories of the fluorescent film with 625 micro-domes patterned in an area of 10 mm×10 mm. It is evident that the micro-domes substantially enhance light extraction. The internally emitted photons are much more effectively extracted in the forward direction. The normalized emission spectrum of the fluorescent films without and with micro-domes in the forward and backward directions are shown in Fig. 4(c)-(e). For a planar fluorescent film, only 26% of the internally generated photons in total (Fig. 4(c)) can escape to free space, emitting approximately 13% of the internally generated photons equally in the forward (Fig. 4(d)) and backward (Fig. 4(e)) directions, which is consistent with the theoretically calculated value of 12.7%. Impressively, the micro-dome structures realize a total light extraction efficiency of up to 89% and the forward light extraction efficiency of 65%. To achieve high unidirectional light extraction efficiency, the key is to increase the escape probability of the internally emitted photons in the forward viewing direction and to give the photons multiple opportunities to find the escape cone in right direction. In this case, the asymmetrically corrugated interfaces provide an efficient mechanism that redirects photons which are emitted out of the escape cone, back into the escape cone especially in the forward viewing direction. More specifically, the micro-dome array on the top surface increases the surface area but narrows the angular distribution of internally reflected light. By this way, the micro-domes recycle the otherwise trapped light with large incidence angles by redirecting them into the forward light cone and guiding them to escape from the forward viewing direction. Unlike the light being extracted from the micro-structured side of the LEDs in Fig. 1(a), the originally trapped light mostly escapes to free space from the plat side of the spectral conversion films (Fig. 1(b)). For the LEDs, they are generally equipped with a back reflector. The reflector recycles the trapped light and guides them to escape from the micro-structures due to the reduced total internal reflection. The light extraction in LEDs is therefore enhanced due to a synergetic effect of the back reflector and the micro-structures. In contrast, the micro-domes in the reflector-free spectral conversion film also function as a reflector, changing the light propagation direction inside the films and making them escape from the plat side of the film. Differently, Ouyang et al. reported a scintillator covered with a hemispherical microlens array in which the internally emitted light is mainly extracted from the microlenses rather than the plain surface while its light extraction efficiency is much lower [8]. More importantly, the micro-domes do not stop the transmittance of incident sunlight.
According to Eq. (1), the external quantum efficiency $({{\eta_{\textrm{EQE}}}} )$ of the fluorescent films, regardless of the micro-structures, is not only limited by the light extraction efficiency $({{\eta_{\textrm{extraction}}}} )$, but also the internal quantum efficiency (${\eta _{\textrm{QE}}})$. and the self-absorption efficiency $({{\eta_{\textrm{self}\_\textrm{absorption}}}} )$ of the fluorophores. The latter two factors are essentially determined by the intrinsic properties of the fluorophores. In the same manner, we could also define the external quantum efficiency of the spectrum conversion film in the forward direction as,
Fig. 5. The forward spectral irradiance based on the Monte Carlo simulations. The fluorophores in the host material of the film have the mean free path of 0.1 mm and the internal quantum efficiency of 90%. The micro-domes on film surface have a dome width of 400 µm and a dome height of 65 µm. The spectral irradiance was normalized to AM1.5.
Quantitative analysis in Fig. 6 indicates that the fluorescent film with micro-domes at the mean free path of 0.1 mm has the ${\eta _{\textrm{EQE}}}$ of ∼47% and the $\eta _{\textrm{EQE}}^{\textrm{forward}}$ of ∼31%, respectively. In sharp contrast, the fluorescent planar film without micro-domes at the same mean free path shows respectively the ${\eta _{\textrm{EQE}}}$ of ∼18% and the $\eta _{\textrm{EQE}}^{\textrm{forward}}$ of ∼9%. Furthermore, as the mean free path (l) of the LF305 increases, which implies a decrease in the fluorophore concentration, both the ${\eta _{\textrm{EQE}}}$ and the $\eta _{\textrm{EQE}}^{\textrm{forward}}$ increase especially for the fluorescent films with micro-domes. Clearly, self-absorption of the fluorophores remains a key limitation in the performance of the fluorescent film, and the self-absorption efficiency $({{\eta_{\textrm{self}\_\textrm{absorption}}}} )$ can be straightforwardly derived according to Eq. (6) in which the forward light extraction efficiency ($\eta _{\textrm{extraction}}^{\textrm{forward}}$) is 65% for the micro-domes at width of 400 µm and height of 65 µm and the internal quantum efficiency (${\eta _{\textrm{QE}}})$ of fluorophores is assumed to be 90%. Figure 6(c) shows that the ${\eta _{\textrm{self}\_\textrm{absorption}}}$ decreases significantly at large mean free path (i.e., low fluorophore concentration). In all cases, the fluorescent film with micro-domes shows higher ${\eta _{\textrm{self}\_\textrm{absorption}}}$ because of the structure-induced photon recycling and therefore elongated light paths. These results suggest that there is still considerable opportunity for improvements in both the ${\eta _{\textrm{EQE}}}$ and the $\eta _{\textrm{EQE}}^{\textrm{forward}}$ by decreasing the ${\eta _{\textrm{self}\_\textrm{absorption}}}$.
Fig. 6. (a-c) ${\eta _{\textrm{EQE}}}$, $\eta _{\textrm{EQE}}^{\textrm{forward}}$ and ${\eta _{\textrm{self}\_\textrm{absorption}}}$ of the fluorescent films without (green symbols) and with (red symbols) micro-domes at width of 400 µm and height of 65 µm at various mean free path. The solid lines are used for eye guidance only.
As we know, the material characteristics e.g., refractive index (n) of the host materials determine the critical angle ${\theta _c} = {\sin ^{ - 1}}(\frac{1}{n})$ and therefore the light paths when the light propagates inside the films. We further investigate the impacts of refractive index of the host materials on efficiency of the films. Figure 7 shows a correlation between them in a refractive index range of 1.3-1.8. Total external quantum efficiency $({{\eta_{\textrm{EQE}}}} )$ keeps dropping as increasing refractive index. As shown in Fig. S2(a), total light extraction efficiency hardly changes upon refractive index. Therefore, the decreased ${\eta _{\textrm{EQE}}}$ at high refractive index is mainly attributed to the increased self-absorption efficiency (Fig. S2(b)). On the other hand, forward external quantum efficiency ($\eta _{\textrm{EQE}}^{\textrm{forward}}$) shows a maximum when the host materials have a refractive index around 1.5. In this case, both forward light extraction efficiency and self-absorption efficiency increase as an increasing refractive index. Despite high forward light extraction efficiency at high refractive index, the $\eta _{\textrm{EQE}}^{\textrm{forward}}$ is still limited due to high self-absorption efficiency.
Fig. 7. ${\eta _{\textrm{EQE}}}$ and $\eta _{\textrm{EQE}}^{\textrm{forward}}$ of the fluorescent films with micro-domes (width: 400 µm; height: 65 µm) at various refractive indexes of the host materials.
Besides micro-domes, we also examine other micro-structures for light extraction using the Monte Carlo ray-tracing methods mentioned above, and these micro-structures include micro-prisms, -pyramids, and -cones. In all cases, these micro-structures substantially improve the light extraction from the fluorophore-doped films, while their efficiency varies dramatically with the geometries and their size parameters of the selected micro-structures on top, as shown in Fig. 8. Among these micro-structures, micro-pyramids (Fig. 8(b) and (e)) lead to high ${\eta _{\textrm{extraction}}}$, however, relatively low $\eta _{\textrm{extraction}}^{\textrm{forward}}$ of less than 50% compared with the micro-dome structures. Nevertheless, micro-pyramids show comparatively high $\eta _{\textrm{EQE}}^{\textrm{forward}}$ and ${\eta _{\textrm{EQE}}}$ due to the less ${\eta _{\textrm{self}\_\textrm{absorption}}}$ (Table 1). In comparison, micro-prisms (Fig. 8(a) and (d)) perform worst among the selected micro-structures, and the performance of micro-cones for light-extraction are in between. In addition, Table 1 shows that the selected micro-structures do not change the overall transmittance of the fluorophore-free films.
Fig. 8. Light extraction in total (${\eta _{\textrm{extraction}}}$) and in the forward viewing direction ($\eta _{\textrm{extraction}}^{\textrm{forward}}$) of the fluorophore-doped films with micro-prisms (a, d), -pyramids (b, e) and -cones (c, f).
Table 1. Spectral performance of the fluorophore-doped films with various micro-structures after optimization. The transmittance of the fluorophore-free films without and with micro-structures.
4. Conclusion
In summary, we have examined a series of ease-to-manufacturing micro-structures for enhanced light extraction in the spectral conversion films without using any back reflectors. Our model, based on the Monte Carlo ray-tracing method, provides a simple design tool for accurately predicting the forward spectral irradiance of the films by taking multiple photophysical processes including self-absorption and light extraction into accounts. Among these micro-sized photonics structures, the micro-domes show the best performance in terms of light extraction. The films with micro-domes show a substantially enhanced light extraction efficiency of 89% and this in comparison with that of the conventional planar fluorescent films of 25%. More importantly, the micro-dome structures extract 65% of the intrinsic trapped light into the forward viewing direction, approximately 4-fold higher than that of the planar fluorescent films. As a result, the forward external quantum efficiency is increased by a factor of 3.44, and the simulated result is consistent with our experimental observation [49]. On the other hand, the micro-structured films can be fabricated via a blade coating method or a hot embossing approach. These methods can be readily scaled up for larger size arrays, making them compatible with the low-cost fabrication of large-area spectrum conversion films for applications particularly in protected agricultures for augmenting photosynthesis and crop production [51,52].
Funding
National Institute of Food and Agriculture (2017- 07652); Gordon and Betty Moore Foundation (6884).
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.
Supplemental document
See Supplement 1 for supporting content.
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