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Abstract
The AlGaN-based deep ultraviolet light-emitting diode (DUV LED) has advantages of environmentally friendly materials, tunable emission wavelength, and easy miniaturization. However, an increase in Al composition leads to a decline in the lattice quality, thereby reducing the internal quantum efficiency (IQE). In addition, the light extraction efficiency (LEE) is limited due to the strong transverse magnetization polarization emission from the multiple quantum wells. Here, we designed the topological corner structure in AlGaN-MQWs, and the high electric field intensity in a tiny space at the corner results in an extremely high local density of optical states (LDOS), which could shorten the luminescence decay time of the emitter and increase the radiative rate by 26 times. Meanwhile, because the excited topological corner state resonance mode is a transverse-electric mode, enhancing only the transverse-electric luminescence without any gain for transverse-magnetic luminescence, thereby significantly improving the light extraction efficiency. Finally, according to theoretical calculations, the IQE could reach 68.75% at room temperature.
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1. Introduction
Advanced deep ultraviolet (DUV) light sources, ranging from 200-280 nm, such as AlGaN-based multiple quantum wells (MQWs) light-emitting diodes (LEDs), have a wide range of applications in biological, environmental, and medical fields [1–3]. However, compared with visible and ultraviolet LEDs, the lower external quantum efficiency (EQE) of DUV LEDs limits the development prospects. Only a few studies have realized EQE exceeding 10% [4,5]. Furthermore, as the emission wavelength becomes shorter, the EQE decreases dramatically, even only 0.1% at 230 nm [6].
The EQE of DUV LEDs is constrained by three factors: the internal quantum efficiency (IQE), the light extraction efficiency (LEE), and the carrier injection efficiency [7]. Although efforts of crystal quality improvement, efficient p-doping strategy, energy band structure design, light extraction structure design, and electrode optimization have been widely made to enhance device performance [8–21], inevitable dislocation induced non-radiative recombination competition with radiative recombination [22–24], which leads to low IQE, as well as poor LEE caused by a large fraction of transverse-magnetic (TM) polarized light [2526,21] are still two primary bottlenecks for DUV LEDs.
It has been reported that the introduction of localized surface plasmon resonance (LSPR) can improve both IQE and LEE. LSPR, by coupling with radiation dipoles, can reduce the recombination lifetime, thereby increasing the proportion of radiative recombination relative to non-radiative recombination and consequently improving the IQE. At the same time, TM light can recombine through resonance with metal NPs and emit light efficiently, thereby enhancing LEE. By fabricating high-density aluminum nanoparticle arrays near the active region of QW, Lee et al. improved the IQE by 57.7% at 285 nm [24]. Jiang et al. designed a graphene/aluminum nanoparticle/graphene (Gra/Al NPs/Gra) hybrid plasmonic structure on QWs. The strong resonance coupling of localized surface plasmons enables the photoluminescence (PL) of DUV LEDs to be increased by 2.9 times [27].
However, LSPR does not directly interact with the radiative dipoles, but couples to the dipoles located near the interface between the metal NPs and the dielectric material through the form of evanescent waves, and thus the radiative enhancement is limited. In recent years, topological photonics has attracted great attention, providing new ideas and methods for manipulating light fields, and enabling nanophotonic devices to achieve distinctive new functions [28,29]. Using photonic crystal structures to strongly localize light has always been a key research direction in enhancing light-matter interactions. The introduction of topological photonics allows the photonic crystal structure to restrict light in three dimensions: edge, corner, and bulk. It is worth noting that the 0-dimensional topological corner state, induced by the 1-dimensional topological edge state, confines light in a tiny space, demonstrating advantages in applications such as high-density photonic integration [30–32].
In this article, we designed AlGaN-MQWs with the topological corner structure. The high local density of optical states (LDOS) is induced at the corner, achieving the Purcell factor of 26 at 280 nm. At the same time, only the luminescence of transverse-electric (TE) light is enhanced since the excited corner state is a TE mode (E-inplane), which benefits the LEE. Finally, our estimates suggest that the luminescence IQE could be increased from approximately 8% to nearly 70% at room temperature.
2. Structure and materials
Figure 1(a) presents the schematic diagram of the structure we designed. The quantum well active area is situated on the hollowed substrate and etched into two different regions with the topological structure and the trivial structure. At the corner where these two regions intersect, a potent local light field is excited at a specific wavelength, which we call the topological corner state. According to the Purcell effect, the lifetime of an excited state is not an intrinsic property of a quantum, it strongly depends on the electromagnetic environment through the LDOS [33]. Therefore, the higher LDOS at the corner can enhance the spontaneous emission rate, thereby improving the luminous efficiency of the quantum well active region. Fig 1(b) reveals the mechanism by which the luminous efficiency of the quantum well active region is enhanced by the topological corner state. We have used the vibration of electric dipoles to characterize luminescence. In the original quantum well active region, the dipole luminescence does not bring about field enhancement basically, thus making only a minimal contribution to the enhancement of luminescence. However, in the topological corner structure, at the luminous wavelength, the TE mode electric dipole can excite the topological corner state to form resonance. This results in a strong electric field at the corner position, indicating high LDOS, and further enhancing the luminous efficiency. At the same time, because the excited topological corner state is the TE mode (E-inplane), there is generally no electric field in the z direction, so there is no enhancement for TM light.
Fig. 1. (a) Schematic diagram of the topological corner structure of AlGaN-MQWs. The MQWs layer is etched into a topological region and a trivial region, which are connected by two edges and form an included angle of 90°. The entire MQWs layer is placed on a hollowed substrate. (b) The internal mechanism of the topological corner state enhancing the excitation efficiency of TE light. In the topological corner structure, deep ultraviolet luminescence forms a TE mode (E-inplane) local electric field, which brings high LDOS and further enhances the spontaneous emission rate. There is no electric field in the z direction, so the TM light is not enhanced. (c) The refractive index of materials used in FDTD simulation calculations.
The MQWs consist of 5 cycles of Al0.6Ga0.4N (5 nm)/Al0.85Ga0.15N (10 nm). Figure 1(c) displays the refractive index of materials used in the FDTD simulation. The refractive index of AlGaN material is given as follows: AlxGa1−xN = xnAlN + (1 − x)nGaN, where n is the refractive index [27]. The specific refractive indices of AlN and GaN are given by J. Pastrňák [34] and Sadao Adachi [35].
3. Topological corner state mechanism
The topological region is arranged by individual square topological lattices, as is the trivial region. These two regions form a 90° corner through two edges as shown in Fig. 2(a). The period of a single lattice is a, and the side length of the etched square is s = a/3. The distance d between the center of the etched square and the middle line of the lattice is a key parameter that we need to pay attention to. Topological properties could be controlled by adjusting d. In the topological lattices, d = 0.33a, while d = 0.17a in the trivial lattices. We calculated the photonic energy bands of lattices with different topological properties, and it can be observed that as d changes, the bands experience an obvious process from opening to gapless and then opening again, as shown in Fig. 2(b). Although still at the same frequency position, the inverted photonic energy bands have opposite parity, supporting different bulk polarizations.
Fig. 2. (a) Schematic plan view of the structure. A single lattice is defined by the period a, the square side length s, and the distance d. (b) Calculation of photonic energy bands for three types of lattices with different d. (c) From the topological edge state to the corner state. The electric field distributions in the plane of these two modes were calculated.
In one-dimensional systems, the topological properties of photonic energy bands are usually described by a Zak phase ${\mathrm{\theta }_{{Zak}}}$, which is defined as the integration of Berry connection within the band over the first Brillouin zone, and the calculation equation is given by [36],
4. Results and discussion
In order to align the resonance peak of the topological corner state with the luminous wavelength of MQWs, we set a = 112.6 nm for our simulations. Based on the simulation results, we observed the electric field distribution in the xz plane of the topological corner state excited by TE light in this structure, and the results were consistent with the in-plane electric field, with strong localized electric fields at the corner position. Additionally, we analyzed the Ez component of the electric field. This component exhibited minimal presence in the z direction, thereby substantiating that the excited mode is indeed the TE mode. Furthermore, we also observed the electric field excited by TM light at the same luminescence wavelength. No resonance modes were formed within the structure, except for the oscillating field of the TM dipole itself. The results of all electric field distributions are shown in Fig. 3(a). Synthesizing these observations, the topological corner state primarily exhibits in-plane electric fields and negligible electric fields in the z direction. And combined with the fact that TM light fails to excite any resonance modes, it is reasonable to deduce that within the luminescence wavelength, only TE light radiation is enhanced, while TM light is not.
Fig. 3. (a) The electric field distributions in the xz plane excited by TE light and TM light respectively. TE light excites the topological corner state, consistent with the in-plane electric field distribution, with strong localized fields at the corner, and there is basically no z component of the electric field in the active region. TM light does not excite any resonance modes. (b) Purcell factor calculated by simulation. For different emission wavelengths, the structural parameters are adjusted to achieve corresponding matching. (c) Purcell factors were calculated separately for TE dipole and TM dipole. (d) The IQE of luminescence at different temperatures was estimated. At room temperature, only considering the impact of high LDOS enhanced radiation rate, IQE can be increased from about 8% to nearly 70%.
For decades, Purcell factors have been used to explain cavity-assisted interactions. It essentially represents the ratio of the spontaneous emission rate of a quantum system in a resonator to that in a vacuum environment [41,42]. We calculated the Purcell factor in the topological corner structure AlGaN-MQWs, which can reach 26 at deep ultraviolet 280 nm. The high LDOS caused by the formation of the corner state can very effectively enhance the spontaneous emission rate. In addition, when the Al composition, potential well and barrier layer thicknesses in the multi-quantum well materials change, the wavelength of the light emitted will change as well. This structure can completely adjust the corresponding structural parameters to match different deep ultraviolet luminescence wavelengths. The results of adjusting the excitation of the topological corner state from 260 nm to 280 nm are shown in Fig. 3(b). It is also worth noting that the Purcell factor is directly proportional to the mode Q of the resonator and inversely proportional to the square of the mode volume [43]. Therefore, a higher Purcell factor usually also means a higher Q value, which could also be seen from the extremely narrow resonance peaks in the spectral curves. According to spectral line calculations, the Q of the topological corner state in this structure is approximately 300. For the light source, this means that purer light could be achieved.
Next, we calculated the Purcell factors obtained at 280 nm by using the TE dipole and the TM dipole respectively. It can be seen in Fig. 3(c) that compared with the TE dipole, the TM dipole radiation rate is not enhanced, which also corresponds to our previous analysis of the field distribution of the topological corner state. The significant improvement in the emission efficiency of TE light means that more light could be extracted from the vertical direction, which can also further improve the LEE of the system. We also estimated the IQE of luminescence based on the Purcell factor. The luminescence IQE is defined as the ratio of generated photons per charge carrier pair in the active region. It is mainly governed by the ratio between nonradiative and radiative recombination processes [7]. The ${\mathrm{\eta }_{{IQE}}}$ is given by [44],
where krad and knon are the radiative and nonradiative recombination rates of carriers, respectively. The enhancement multiple of krad could be obtained from the calculation of the Purcell factor. For AlGaN-MQWs, it is generally accepted that the IQE is 100% at a temperature of 10 K, and it drops to approximately 8% at the room temperature of 300 K [24]. In our structure, if we only consider the enhancement of the spontaneous emission rate due to the enhancement of LDOS, the IQE could theoretically reach 68.75% at room temperature, as shown in Fig. 3(d).The Purcell factors at various positions on the topological corner were calculated, as shown in Fig. 4(a). It could be seen that the closer to the topological lattice on the corner, the stronger the enhancement effect. As the distance increases, the Purcell effect shows a gradually weakening trend. Among the positions we analyzed, the highest Purcell factor can reach 26 and the lowest is 4 at 280 nm. Additionally, the Purcell factors located in the same in-plane position but located in different potential well layers were calculated, and the results are shown in Fig. 4(b). It is evident that at the same in-plane position, the Purcell factor at the top potential well position is only about 0.3 times that at the center position. Another factor that has a great influence on the topological corner state is the refractive index of the substrate. To ensure the best light confinement effect of the MQWs layer, the refractive index of the upper and lower contact layers should be as small as possible. Since the refractive index of AlGaN-MQWs itself is not high, when the refractive index of the substrate increases, the LDOS decreases rapidly, causing the Purcell factor to also decrease rapidly, and the calculation results are shown in Fig. 4(c). When the refractive index of the substrate is 1.2, the Purcell factor rapidly decreases to about 6, and the radiation enhancement effect from the topological corner state almost disappears when the refractive index of the substrate is above 1.6. Therefore, to achieve the most ideal spontaneous emission rate enhancement effect, it is best to prepare a hollow substrate. The influence of the number of lattice periods on the luminescence enhancement effect is also within our consideration, and the calculation results are shown in Fig. 4(d). The excitation of the topological corner state still requires a certain number of lattice periods to support. When the number of lattice periods reaches 9 or more, the Purcell factor tends to stabilize around 90. However, since the luminescence enhancement only occurs at the corner, an excessively large structural area will reduce the space utilization of the entire device. In alignment with the current trend towards device miniaturization, all simulations in this paper were calculated using 5 lattice periods. At this scale, good enhancement effects could be achieved, and an increased number of topological corner structure arrays can be arranged within the same device area to yield more luminescence enhancement zones. Of course, the selection of the number of lattice periods can be flexibly adjusted to meet different needs.
Fig. 4. (a) Purcell factor at different positions on the corner. The further away from the topological lattice, the weaker the radiation rate enhancement effect. (b) Purcell factor at different potential well positions for the same in-plane position. (c) Purcell factor changes when the refractive index of the substrate is different. It can be seen that the excitation of the topological corner state requires a very low refractive index substrate to ensure the confinement of light, so it is best to form a hollow substrate. (d) The effect of the number of lattice periods on the Purcell factor. (e) Schematic diagram of topological corner structure AlGaN-MQWs light emitting arrays.
There are several fabrication challenges that need to be overcome before topological corner structure AlGaN-MQWs could be effectively utilized. First of all, the requirement for the low refractive index of the contact layer under MQWs leads to the need for a hollow substrate. One possible solution could be to initially grow the MQWs on a sapphire substrate, and then transfer the MQWs to the hollow substrate using laser lift-off technology [45]. However, another issue arises at this point: the lattice quality of AlGaN material grown directly on sapphire is quite poor, and it is necessary to grow an AlN layer first [46]. If the AlN layer is transferred along with MQWs, it will also seriously affect the light limiting effect in the active region. How to obtain thin-layer MQWs separately while ensuring material quality and put them into use with the hollow structure is still a problem we need to solve. Despite these challenges, we believe that the topological corner structure AlGaN-MQWs, which demonstrates a remarkable enhancement effect on the emission efficiency of TE light, will bring significant advancements to the industry once it could be applied to DUV LEDs.
Looking ahead, we envision the potential application of topological corner structure AlGaN-MQWs in conjunction with Micro-LED display technology, which has recently become a hot topic in the display field. Micro-LED transfers semiconductor light-emitting units to a rigid or flexible driver circuit substrate by means of Mass transfer technology, thereby integrating LEDs on a chip in a high-density, matrixed arrangement. Following this strategy, the topological corner structure AlGaN-MQWs could also form an array as shown in Fig. 4(e), serving as a pure color, high luminous efficiency DUV light source.
5. Conclusion
In conclusion, we design the AlGaN-MQWs with topological corner structure in this study. At the corner of the topological/trivial region interface, the transformation of the topological properties of the photonic band leads to a very strong local electric field at the corner position. According to the Purcell effect, high LDOS can enhance the spontaneous emission rate of the emitter. The calculation results show that under TE light excitation, the Purcell factor of this corner state can reach 26, and since this mode is also a TE mode (E-inplane), there is no enhancement to TM light. In addition, when the Al composition of MQWs and the thickness of the potential well and barrier layers change, the luminescence wavelength will vary, and we can adjust the structure size accordingly to achieve a match. Furthermore, the luminescence IQE has been estimated and could be increased from about 8% to nearly 70% at room temperature. However, this structure requires a very low refractive index substrate to support the great light confinement effect, so it is best for the substrate to have a hollow structure. We also discussed the problems that may be encountered in fabricating the topological corner structure AlGaN-MQWs and looked forward to the future application prospects of this structure.
Funding
National Key Research and Development Program of China (2022YFB3605102); National Natural Science Foundation of China (12174036).
Acknowledgments
The authors would like to thank the Advanced Semiconductor Laboratory of Beijing University of Posts and Telecommunications for their support.
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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