Refractive Index Engineering as a New Degree of Freedom for Designing High‐Performance AlGaN‐Based Ultraviolet C Light‐Emitting Diodes

This study delves into a profound exploration, using simple yet effective Monte Carlo ray‐tracing simulations, of the influence of the refractive indices of multiple quantum wells (MQWs) and p‐type electron blocking layer (p‐EBL) on the photon propagation and subsequent light extraction behavior in AlGaN‐based ultraviolet‐C (UVC) light‐emitting diodes (LEDs), covering both transverse‐electric (TE) and transverse‐magnetic (TM) polarized light. Remarkably, the refractive index contrasts at the heterointerfaces of p‐EBL/MQWs/n‐AlGaN have a relatively minor impact on the extraction efficiency of TE‐polarized light but exert a significant influence on TM‐polarized light. This discrepancy arises from the substantial effect of total internal reflection at these heterointerfaces on the propagation of photons emitted at large angles. Thus, this observation elucidates the oversight of photon propagation in the conventional design of MQWs and p‐EBL in AlGaN‐based UVA and UVB LEDs, where TE‐polarized emission predominates. Building upon simulation results, a highly effective strategy for extracting TM‐polarized light in AlGaN‐based UVC LEDs is further demonstrated by combining refractive index engineering with inclined sidewalls. The findings suggest refractive index engineering can serve as a novel design parameter for AlGaN‐based UVC LEDs dominated by TM‐polarized emission, expanding the range of techniques available for enhancing device performance.


Introduction
[3] Research has shown that UVC LEDs emitting at 226 and 217 nm can detect harmful gases such as NO and NH 3 , [2] respectively.Furthermore, recent studies have demonstrated that UVC light in the range of 207-222 nm can effectively sterilize bacterial cells without harming human tissues. [1,3]Despite significant advancements in AlGaN-based UVC LEDs with these short wavelengths, their widespread commercialization remains challenging due to their extremely low external quantum efficiency (EQE).The EQEs of such UVC LEDs are typically below 1% [1][2][3][4][5] and decrease dramatically as the emission wavelength decreases, reaching as low as 10 À6 % in 210 nm AlN-based LEDs. [6]he low EQEs are directly linked to the inherent material properties of high-Al-composition AlGaN, which result in poor internal quantum efficiency (IQE) and poor light extraction efficiency (LEE). [1,7]The former issue is mainly attributed to high dislocation density, [8][9][10] inadequate hole injection, [11][12][13] high electron overflow, [14] and the strong quantum-confined Stark effect (QCSE) in multiple quantum wells (MQWs). [15,16]The latter issue primarily arises from significant UV light absorption by the p-type GaN contact layer, severe This study delves into a profound exploration, using simple yet effective Monte Carlo ray-tracing simulations, of the influence of the refractive indices of multiple quantum wells (MQWs) and p-type electron blocking layer (p-EBL) on the photon propagation and subsequent light extraction behavior in AlGaN-based ultraviolet-C (UVC) light-emitting diodes (LEDs), covering both transverse-electric (TE) and transverse-magnetic (TM) polarized light.Remarkably, the refractive index contrasts at the heterointerfaces of p-EBL/MQWs/n-AlGaN have a relatively minor impact on the extraction efficiency of TE-polarized light but exert a significant influence on TM-polarized light.This discrepancy arises from the substantial effect of total internal reflection at these heterointerfaces on the propagation of photons emitted at large angles.Thus, this observation elucidates the oversight of photon propagation in the conventional design of MQWs and p-EBL in AlGaN-based UVA and UVB LEDs, where TE-polarized emission predominates.Building upon simulation results, a highly effective strategy for extracting TM-polarized light in AlGaN-based UVC LEDs is further demonstrated by combining refractive index engineering with inclined sidewalls.The findings suggest refractive index engineering can serve as a novel design parameter for AlGaN-based UVC LEDs dominated by TM-polarized emission, expanding the range of techniques available for enhancing device performance.light trapping due to strong total internal reflection (TIR), and the unique optical polarization of strong transverse-magnetic (TM) polarized emission. [1,17,18]To achieve high-EQE UVC LEDs, extensive research has been conducted to address these challenges through the proper design of LED epitaxial structures, particularly the MQWs and p-type electron-blocking layer (p-EBL).
It is well know that the [0001]-oriented AlGaN-based MQWs suffer from strong QCSE due to the substantial inherent polarization field.This leads to a significant spatial separation of electron and hole wavefunctions, resulting in poor IQE.To overcome this issue, various innovative MQW designs have been proposed, including quasi-2D GaN quantum wells (QWs), [15] ultrathin GaN/AlN MQWs, [19,20] thin AlGaN QWs, [4,21,22] staggered AlGaN QWs, [23] wavy AlGaN MQWs, [16] inclined AlGaN MQWs with different polar planes, [24] lateral-polarity AlGaN MQWs, [25] and lattice-matched BAlGaN MQWs. [26]ue to the poor hole concentration and low hole mobility in AlGaN-based UVC LEDs, there is an imbalance between electrons and holes, resulting in high electron overflow.This issue is typically addressed by implementing an EBL with a higher Al composition than the MQWs.However, the EBL can impede hole injection into the MQWs due to its wider bandgap and polarization effect.To overcome this challenge, several innovative EBL strategies have been developed, including composition-graded AlGaN EBL, [14] AlGaN multiquantumbarrier EBL, [27] Al x Ga 1Àx N/Al y Ga 1Ày N/Al x Ga 1Àx N (x > y) EBL, [28] and AlGaN EBL with a thin AlN preinsertion layer. [29]In addition to extensive research on p-EBL, some studies have explored modifications to the MQWs to enhance electron confinement, such as gradually increased barrier thicknesses, [30] composition-graded quantum barriers (QBs), [31] delta-accelerating QBs, [32] and Mg delta-doped last quantum barrier (LQB). [33]Conversely, to mitigate the detrimental effect of the EBL on hole injection, EBL-free LED designs have been proposed by engineering the MQWs to self-suppress electron overflow, including graded staircase QBs, [34] linear graded QBs, [35] multiple-symmetrical-stair QBs, [36] and graded Al-content AlGaN insertion layer. [37]revious studies on the design of MQWs and EBL have primarily focused on improving carrier injection or confinement to enhance IQE.However, it is important to note that there is an inevitable refractive index contrast among the MQWs, EBL, and their adjacent epilayers with different Al compositions.Although the refractive index contrasts are typically small, they significantly impact the propagation of photons with large-emitting angles due to TIR and, consequently, light extraction behavior.Therefore, it is expected that the refractive indices of the MQWs and EBL have a substantial influence on the LEE of AlGaN-based UVC LEDs, particularly when the emitting photons are predominantly TM polarized.Since the EQE is the product of IQE and LEE, achieving high EQE requires consideration and optimization of both IQE and LEE.
In this study, we conduct a systematic and comprehensive investigation into the effects of MQWs and EBL structures on photon propagation and LEE for both transverse-electric (TE) and TM-polarized light in AlGaN-based UVC LEDs using Monte Carlo ray-tracing simulations.Building upon simulation results, we further demonstrate the construction of a highly efficient channel for extracting TM-polarized light in AlGaN-based UVC LEDs through refractive index engineering, involving adjustments to the refractive index contrasts at the heterointerfaces of p-EBL/MQWs/n-AlGaN, combined with inclined sidewalls.The feasibility and implications of refractive index engineering are thoroughly examined and discussed.

Results and Discussion
TE-polarized light is mainly emitted at small angles, while TM-polarized light is mainly emitted at larger angles, resulting in distinct propagation and light extraction behaviors within the device.][40][41][42][43] For a typical AlGaN-based flip-chip UVC LED, as illustrated in Figure 1a, the emitted light is predominantly extracted through the sapphire substrate side, including the top surface, sapphire sidewalls, AlN sidewalls, and n-AlGaN sidewalls.Here, the LEE was evaluated for each extraction route to better elucidate the light extraction mechanisms.
As depicted in Figure 1b, the LEEs of TM-polarized light are significantly lower than those of TE-polarized light for the top surface and sapphire sidewall routes but higher for the AlN sidewall and n-AlGaN sidewall routes.Notably, the LEE of TM-polarized light at the top surface (0.67%) is only one-tenth of that of TE-polarized light (7.29%),consistent with previous findings obtained via the finite-difference time-domain method. [42]Conversely, the LEE of TM-polarized light at the n-AlGaN sidewalls reaches 11.49%, approximately twice the value of 5.99% for TE-polarized light.These results indicate substantial disparities in light extraction behaviors based on polarization.Specifically, TE-polarized light is predominantly extracted through the top surface, while TM-polarized light is mainly extracted from the n-AlGaN sidewalls.Importantly, the LEE of the n-AlGaN sidewalls is highly dependent on the refractive indices of the MQWs and p-EBL.Appropriately modifying these refractive indices can achieve unexpectedly high total LEE for TM-polarized light, comparable to or even surpassing that of TE-polarized light.The detailed mechanisms underlying these findings will be further elucidated in this study.In the typical AlGaN-based flip-chip UVC LEDs illustrated in Figure 1a, each layer in the structure has different Al compositions, resulting in an inevitable refractive index contrast between the heterointerfaces.The trajectory of light at these interfaces is known to be highly influenced by the refractive index contrast.Particularly, when light travels from a more optically dense medium to a less dense one, TIR occurs.Since the n-AlGaN layer needs to be optically transparent to the emitted light from the MQWs, its Al composition is typically higher than that of the MQWs, resulting in a lower refractive index.The Al composition of the n-AlGaN layer is determined based on the target emission wavelength of the MQWs, leading to a somewhat fixed refractive index contrast at the heterointerface of n-AlGaN/AlN.In contrast, the MQWs offer more flexibility in achieving the desired emission wavelength by adjusting various structural parameters such as QW and QB thickness, QW and QB composition, absolute compositional offset between QW and QB, strain in QWs and QBs, and polarization field in MQWs.This implies that different MQW structures with corresponding refractive indices can achieve the same target emission wavelength.Since TIR is highly dependent on the refractive index contrast, the MQWs structure significantly impacts the TIR at the heterointerface between the MQWs and n-AlGaN, thereby affecting the LEE.To investigate this relationship, the impact of the MQWs refractive index on the LEE was simulated for both TE-and TM-polarized light.The simulations varied the refractive index of the MQWs from 2.4 to 2.5, while keeping other parameters at their default values (Table 1).
As shown in Figure 2a, the total LEE decreases as the refractive index of the MQWs increases for both polarizations.However, the decline is more significant for TM polarization, dropping from 15.56% to 5.31%, compared to the drop from 17.07% to 11.41% for TE polarization.To better understand this difference, the normalized LEE for each escape route was further analyzed.Figure 2b reveals distinct dependency patterns of LEE for each route.Additionally, the drop in LEE is slightly greater for TM polarization compared to TE polarization for the same route.These results can be explained by variations in the escape cones caused by the increase in the refractive index of the MQWs, coupled with differences in the angle-dependent emission intensity distribution between TE and TM polarization.
Applying Snell's law allows us to calculate the critical angle (θ C ) for TIR at each interface between different media.This information enables us to determine the emitting angle (θ E , relative to the c-axis) of light generated in the MQWs for each zone, as shown in Table 2.The data reveals that as the refractive index of the MQWs increases from 2.4 to 2.5, the zone for each escape route decreases, while the trapped zone within the MQWs significantly expands.
The angle-dependent intensity, I(θ E ), of the TE-and TM-polarized emission can be expressed utilizing dipole radiation. [44,45] where I x0 and I z0 are determined by the thermal occupation following the Fermi-Dirac distribution.Utilizing this information, we can derive the radiation patterns of the MQWs for complete TE-and TM-polarized emission.Subsequently, we can obtain the emission intensity distribution for each route for both polarizations, as depicted in Figure 2c,d.It is evident from the figures that the emission intensity for each escape cone decreases as the refractive index of the MQWs increases from 2.4 to 2.5, regardless of polarization.The reductions in the escape cones of the top surface and sapphire sidewall are relatively small, while the drop in the escape cone of the n-AlGaN sidewall is notably significant.Additionally, the decrease in emission intensity is more pronounced for TM polarization compared to TE polarization in the same escape route.This can be attributed to the fact that the emission intensity of TM polarization increases as the emitting angle rises, contrary to the behavior of TE polarization.The distinct drop behaviors in the emission intensity for each escape cone provide a clear explanation for the varying-dependent behaviors of the LEEs shown in Figure 2b.
When the refractive index of the MQWs is higher than that of its adjacent epilayers, a significant portion of the generated light becomes trapped within the MQWs' waveguide structure due to TIRs at the heterointerfaces of p-EBL/MQWs/n-AlGaN, as illustrated in Figure 1a.Despite the reabsorption in the MQWs being estimated to be two orders of magnitude weaker than band-edge absorption due to the large Stokes shift, [43] it is still relatively high.In the simulations, the absorption coefficient was set to 100 mm À1 , which aligns with previous simulation studies [2,42] and corresponds to the recent experimental value of 66.7 mm À1 . [41]On the one hand, the MQW is thin, requiring the trapped light to undergo multiple reflections before reaching the sidewalls.On the other hand, the MQW has a high absorption rate, suppressing multiple reflections.As a result, most of the trapped light gradually reabsorbs and converts into heat during waveguide propagation, with only the light generated at the periphery of the MQWs able to escape outward.As clearly observed in Figure 2c,d, light with large-emitting angles experiences significant trapping in the MQWs as the refractive index increases, leading to substantial reduction in the LEE of the n-AlGaN sidewalls.Notably, a considerable amount of TE-polarized light can directly escape through the top surface, as it is primarily emitted at small angles.Hence, the influence of MQWs' trapping on the total LEE is relatively minor, possibly explaining why MQWs trapping is often disregarded in TE-polarized-dominant AlGaN-based UVA or UVB LEDs.However, the TM-polarized light is mainly extracted from the n-AlGaN sidewalls, as it is predominantly emitted at large angles.Therefore, the total LEE of TM-polarized light is severely compromised by MQW trapping.Consequently, the drop in the total LEE of TM-polarized light is greater than that of TE-polarized light.The above results reveal that MQWs trapping significantly reduces light extraction in AlGaN UVC LEDs.This issue becomes more critical as the wavelength decreases, since the proportion of TM polarization emission increases.
Due to the random directionality of light generated in the MQWs, approximately half of the light is emitted downward toward the p-GaN side.Since p-GaN has a narrower bandgap than the AlGaN MQWs, it exhibits high absorption coefficients due to band-edge absorption, reaching up to 2.3 Â 10 4 mm À1 at a wavelength of 230 nm, according to experimental results. [39]herefore, light extraction is severely hindered by the significant absorption in the p-GaN layer.The p-EBL, with a higher bandgap than MQWs, is typically utilized to prevent electron overflow but can also impede hole injection.Alternatively, some EBL-free LED  designs have been proposed to overcome EBL-related issues.Interestingly, it should be noted that p-EBL has a higher Al composition than the MQWs, resulting in a lower refractive index.This can induce TIR at the heterointerface of p-EBL/MQWs, causing total reflection of some light.In other words, the p-EBL can function as a TIR barrier, preventing the generated light from entering the highly absorptive p-GaN layer and thus influencing the LEE.To investigate this further, the dependence of the LEE on the refractive index of the p-EBL was simulated.These simulations varied the refractive index of the p-EBL from 2.4 (corresponding to the EBL-free case) to 2.3 (representing the smallest refractive index in the AlGaN material system), while keeping other parameters at their respective default values listed in Table 1.
The findings presented in Figure 3a reveal an overall increase in the total LEE for both TE and TM polarizations.Notably, the increase for TM polarization is significantly larger, rising from 7.42% to 15.56%, compared to the increase from 12.80% to 17.07% for TE polarization.To better understand this discrepancy, the normalized LEE for each route was further examined.As depicted in Figure 3b, the LEE of the n-AlGaN sidewalls experiences a substantial increase for both polarizations, while the LEE of the other routes remains relatively unchanged.This can be attributed to the small refractive index contrast between the MQWs and p-EBL, causing only light with large-emitting angles to participate in TIR.The light escaping through routes other than the n-AlGaN sidewall has smaller emitting angles than the TIR critical angle (θ C of 73.4°-90°), as shown in Table 2. Since TE polarization light primarily escapes through the top-surface route, its total LEE is less sensitive to the refractive index of the p-EBL.
These results clearly demonstrate that the refractive indices of the MQWs and p-EBL have a significant impact on photon propagation and LEE, particularly the LEE of the n-AlGaN sidewalls, as depicted more explicitly in Figure 3c,d.This can be explained by the light extraction behavior of the n-AlGaN sidewall route, wherein light is laterally guided by multiple reflections within the p-EBL/MQWs-n-AlGaN/AlN waveguide structure until it reaches the sidewalls and escapes outward, as schematically illustrated in Figure 1a.As the refractive index contrast at the MQWs/n-AlGaN heterointerface increases with a higher refractive index of the MQWs, more generated light becomes trapped and guided within the thin and highly absorptive MQWs, resulting in a significant reduction in the amount of light entering into this waveguide structure.Conversely, as the refractive index contrast at the p-EBL/MQWs heterointerface increases with a lower refractive index of the p-EBL, more generated light is confined within this waveguide structure.By appropriately modifying the refractive indices of the MQWs and p-EBL, a considerable amount of TM-polarized light can be extracted through the n-AlGaN sidewalls, which would otherwise be absorbed within the device.
Additionally, it should be noted that the LEE of the AlN sidewall route is low for both polarizations, despite a significant amount of generated light entering this escape cone, as shown in Figure 2c,d.This is due to the fact that the AlN layer is much thinner than the lateral size of the device, resulting in most of the guided light within the air/p-GaN-AlN/sapphire waveguide structure unable to reach the sidewalls and escape outward, as the absorptive p-GaN layer suppresses multiple reflections.
The aforementioned findings once again emphasize the significance of the n-AlGaN sidewall route as the primary  To maximize the utilization of the extracted light, it is essential to take into account the emission intensity pattern of the chip for practical LED designs.Therefore, the far-field emission intensity patterns of the chip with an optimized structure were further analyzed, setting the refractive indices of the MQWs and the EBL as 2.4 and 2.3, respectively.
Figure 4a,b shows that, apart from the top-surface route, light is extracted in both upward and downward directions through the other routes.Since the downward-extracted light is mostly absorbed by the package materials, the light extracted from the top surface is more effective.Notably, the light escaping through the n-AlGaN and AlN sidewalls predominantly propagates in a near-horizontal direction, with nearly half of this light being extracted downward.Furthermore, for the n-AlGaN sidewall route, a significant portion of the upward-extracted light is absorbed by the n-type contact and bond pads surrounding the mesa.This implies that a substantial amount of light extracted from the n-AlGaN sidewalls is absorbed and does not contribute to the usable light output.This partially explains the notable decrease in the EQE of UVC LEDs as the wavelength decreases.Therefore, it is crucial to effectively utilize such extracted light, particularly for AlGaN-based UVC LEDs with dominant TM-polarized emission, as the overall LEE is primarily determined by this extracted light.Redirecting such side light in the upward direction is a more direct approach.Previous studies have reported that inclined sidewalls covered by MgF 2 /Al layers can act as reflectors to redirect TM-polarized light. [46]dditionally, it has recently been found that an Al coating layer can absorb light, and an air cavity-shaped inclined sidewall exhibits better reflectivity. [47]These results suggest that smooth inclined sidewalls can serve as reflectors to redirect light through TIR.
Given that light extracted from the top surface is more effective, it is more reasonable to redirect the side light toward the escape cone of the top surface for direct extraction, as illustrated in Figure 4c.This can be achieved by designing the proper inclined angle (α) of the sidewall.The dependence of the LEE for each route on α is shown in Figure 4d, providing a clearer understanding of the concept.In the simulations, the sidewalls were inclined from the p-GaN to the n-AlGaN layer to fully redirect the side light without significantly compromising the active region area.As α increases from 8°to 41°, the LEE of the n-AlGaN sidewalls gradually decreases to nearly zero.This can be explained by the fact that the guided light (with emitting angles, θ E , between 73.4°and 90°) begins to experience TIR at the inclined sidewall when α > 8°and is entirely redirected by TIR when α > 41.2°, as determined by Snell's law.Conversely, the LEE of the top surface starts to increase until α reaches 25°, progressively increases and saturates as α continues to increase to 49°, and finally begins to gradually decrease for α larger than 49°.According to Snell's law, to redirect the guided light to fall within the escape cone of the top surface, the values of α, θ E , and θ C should satisfy the following equations. [17] Based on the equations mentioned above, the minimum and maximum values of α for redirecting the guided light into the top-surface escape cone are 24.4°and41°, respectively.Additionally, the minimum value of α is required for the redirected light to experience a new TIR at the top surface is 49°.These results align well with the trend observed in the LEE of the top surface as a function of α.It is also evident that the guided light can be redirected to escape through other routes, such as the sapphire sidewalls, or be trapped within the chip, depending on the value of α.Clearly, redirecting the guided light to escape through the top surface not only yields the highest effectiveness but also demonstrates the highest efficiency.Notably, nearly all of the LEE associated with the n-AlGaN sidewalls is transformed into LEE through the top surface when α falls within the range of 41°-49°.Hence, in practical applications, optimizing α based on the derived equations allows for the maximum utilization of such side light.
To further illustrate the impact of the inclined sidewall, the far-field emission intensity patterns of the chip with an inclined angle of 45°were analyzed.As depicted in Figure 4e,f, the chip with an inclined sidewall exhibits a more convergent emission pattern and a stronger emission intensity along the axial direction for both TE and TM polarizations, making it more desirable for LED applications.Moreover, the inclined sidewall significantly enhances the emission from the top surface while dramatically reducing the emission from the n-AlGaN sidewalls.These findings indicate that a proper designed inclined sidewall not only enhances the LEE through the top surface but also achieves a more favorable emission pattern.
It is reasonable to increase the refractive index contrast between the MQWs and p-EBL to block as much light as possible, thereby reducing adverse absorption in the p-GaN layer and increasing LEE.Among the materials in the Al x Ga 1Àx N system, Al x Ga 1Àx N/AlN heterostructures offer the largest refractive index contrast, as AlN possesses the lowest refractive index.The refractive index contrast gradually decreases as the Al composition in Al x Ga 1Àx N increases.Therefore, it is advisable to use another material with a lower refractive index than AlN to introduce a substantial refractive index contrast for high-Al composition Al x Ga 1Àx N MQWs.
Experimental observations have revealed that incorporating boron into AlN significantly reduces the refractive index. [48]dditionally, wurtzite BAlN is compatible with AlGaN.High-quality BAlN/AlN and BAlN/AlGaN heterostructures have been successfully fabricated using metal-organic vapor phase epitaxy. [48,49]Therefore, BAlN is particularly suitable as a TIR barrier for high-Al composition AlGaN MQWs.In practical applications, a thin BAlN layer can be inserted between the p-EBL and MQWs or directly utilized as the EBL.Furthermore, if a thin BAlN layer is also inserted between the AlN layer and n-AlGaN layer, the increased blocked light can be guided in the p-EBL(-BAlN)/MQWs-n-AlGaN/BAlN-AlN waveguide structure, which can subsequently escape through the top surface after being redirected by inclined sidewalls, as illustrated in Figure 4c.The effects of the B x Al 1Àx N inserted layer, with a decreasing refractive index (from 2.3 to 2.2), on the LEEs were further simulated, with the inclined angle set at 45°.
As shown in Figure 5a, the total LEE increases as the refractive index of the B x Al 1Àx N inserted layer decreases for both polarizations.Specifically, it increases from 18.62% to 20.57% for TE polarization and from 18.18% to 21.65% for TM polarization.Furthermore, the top-surface LEE for each polarization exhibits a similar dependence trend to their corresponding total LEE, indicating that the increased light is primarily extracted through the top surface, as expected.Of particular interest, it is surprising to observe that both the total LEE and the top-surface LEE of TM-polarized light can even surpass those of TE-polarized light as the refractive index of the B x Al 1Àx N inserted layer decreases to a certain extent.
The aforementioned findings demonstrate that an efficient and effective channel for extracting TM-polarized light in AlGaN-based UVC LEDs can be created by simply adjusting the refractive index contrasts between the heterolayers of the p-EBL/MQWs-n-AlGaN/AlN waveguide structure, along with the incorporation of inclined sidewalls.Figure 5b presents the detailed LEEs for different structures, providing a clearer illustration of the effects of the refractive index engineering and inclined sidewalls.By increasing the refractive index contrast at the heterointerface of p-EBL/MQWs using the AlN EBL, the LEE of the n-AlGaN sidewall route is amplified by 3.4 times compared to the EBL-free structure, resulting in a 2.1 times increase in total LEE.Moreover, by implementing inclined sidewalls with an angle of 45°, nearly all of the sidewall LEE is transformed into the highly effective top-surface LEE, leading to an 18.2 times increase in top-surface LEE.It is worth noting that the inclined sidewalls also enhance the LEE of the sapphire sidewalls (as can be also observed in Figure 4d) by redirecting the trapped light (θ E of 37.7°-42.3°)to fall into the escape cone of the sapphire sidewall.Since the extracted light through the sapphire sidewalls predominantly travels upward (as shown in Figure 4f ), this increased light also contributes to the usable light output.Furthermore, sandwiching the MQWs and n-AlGaN layer between two thin BAlN inserted layers with a refractive index of 2.2 results in a remarkable increase of 23.8 times in top-surface LEE and 2.9 times in total LEE.By optimizing design of the p-EBL/MQWs-n-AlGaN/AlN waveguide structure, such as reducing the chip size or increasing the thickness of n-AlGaN layer, which can effectively mitigate sub-bandgap optical absorption, a higher effect of the refractive index engineering can be expected.
To achieve high-performance AlGaN-based UVC LEDs, it is crucial to fully harness the inherent strength of TM-polarized emission, which would otherwise be absorbed within the device.The findings of this study emphasize the significance of considering the influence of the refractive indices of the MQWs and p-EBL on photon propagation, when designing the MQWs and p-EBL structures in AlGaN-based UVC LEDs.
More specifically, the refractive index of the p-EBL should be to be appropriately low to enhance the refractive index contrast at the heterointerface of p-EBL/MQWs, thereby preventing more generated light from passing through the p-GaN layer and weakening the detrimental optical absorption.In practice, an additional thin layer with a high TIR barrier effect (such as higher Al composition of AlGaN or wurtzite BAlN) can be inserted between the MQWs and the conventional p-EBL.This thin layer allows for hole injection into the MQWs through tunneling without deteriorating the electrical properties. [4,29]tudies have shown that inserting a thin AlN layer between the LQB and the p-EBL can significantly enhance hole injection due to hole accumulation, hot hole effect, and intraband tunneling. [29]Alternatively, a new p-EBL with a high TIR barrier effect can be designed to replace the conventional p-EBL.Recent research has demonstrated that alloying boron into AlN can form a type-II BAlN/AlGaN heterojunction with a large conduction band offset, making BAlN a promising material candidate for the EBL in AlGaN-based UVC LEDs. [49]Hence, the BAlN EBL is expected to reduce electron overflow and enhance photon blocking simultaneously.
On the other hand, if the refractive index of the MQWs is much higher than that of the n-AlGaN layer, it can lead to significant light trapping and light loss.Therefore, it is necessary to minimize the refractive index contrast at the heterointerface of MQWs/n-AlGaN to reduce light loss within the MQWs.Since the MQWs has more flexibility in setting the emission wavelength, several practical measures can be implemented.These include increasing the Al composition in the barrier layer to match that of the n-AlGaN layer, minimizing the Al composition difference between the barrier and well layers, and utilizing thin well layers.Although reducing the Al composition difference between the barrier and well layers may slightly decrease electron-hole confinement, this can be mitigated by either increasing the bandgap of the p-EBL or increasing the number of QWs. [50]The use of thin well layers has already been implemented in UVC LEDs to reduce QCSE and improve IQE. [4,21,22]urthermore, the utilization of thin well layers can also minimize the refractive index contrast between the barrier and well layers, as the refractive index is graded between layers with different Al compositions. [51]In recent proposals for high-efficiency UVC LEDs, the BAlGaN alloy has been suggested as a promising material for the active region. [52]The incorporation of boron in BAlGaN can mitigate the QCSE by reducing the built-in internal polarization field. [26]The BAlGaN MQWs may also be a favorable candidate for minimizing the refractive index contrast at the heterointerface of MQWs/n-AlGaN due to the reduced refractive index resulting from boron incorporation.

Conclusion
In summary, the adjustment of refractive indices in MQWs and p-EBL has the potential to greatly enhance the EQE of AlGaN-based UVC LEDs, even if the IQE is slightly compromised.This improvement arises from the significant influence of refractive index contrasts at the heterointerfaces of p-EBL/MQWs/n-AlGaN on the LEE of TM-polarized light.Therefore, refractive index engineering can serve as a novel degree of freedom in the structural design of AlGaN UVC LEDs especially when the TM-polarized emission is dominant, offering additional techniques to enhance device performance.

Simulational Section
The Monte Carlo ray-tracing method was employed to conduct the simulations due to its speed and high accuracy, making it suitable for structures much larger than the wavelength of light.This method is commonly used to investigate light extraction in planar LEDs. [2,4,17,44,46,53]The simulated models were developed using typical structures of AlGaN-based UVC LEDs, [22] as illustrated in Figure 1a.In order to emphasize the focus of this study, the electrode structures were omitted to simplify the simulation.To ensure the reliability of the simulation results, all structural and optical parameters were appropriately determined by referring to relevant studies or real devices, [17,22,[38][39][40][41][42][43] as outlined in Table 1.
During the simulations, 200 000 light rays were randomly generated in the MQWs in all directions.To represent the UVC LEDs with wavelengths close to 210 nm, an emission wavelength of 230 nm was selected.For each light ray, its trajectory and energy were determined based on Snell's law, Fresnel's law, and material absorption along its propagation path.The criterion for terminating a light ray was either its energy dissipating to less than 5% of its original energy emitted from the MQW or its absorption by an external detector.

Figure 1 .
Figure 1.a) Schematic of a typical AlGaN-based flip-chip UVC LED.b) Total LEE and individual LEE of each route for TE-and TM-polarized light.

Figure 2 .
Figure 2. The a) total LEE and b) normalized LEE of each route for TE-and TM-polarized light as a function of the refractive index of the MQWs.Angle-dependent emission intensity distribution of the different regions inside the LED for c) TE polarization and d) TM polarization.

Figure 3 .
Figure 3. a) The total LEE and b) normalized LEE of each route for TE-and TM-polarized light as a function of the refractive index of the p-EBL.Detailed LEE distributions of the LEDs with different refractive indices of the MQWs and p-EBL for c) TE polarization and d) TM polarization.
channel for the escape of TM-polarized light.This observation also elucidates the high sensitivity of the total LEE of TM-polarized light to the refractive indices of the MQWs and p-EBL.Therefore, when designing AlGaN-based UVC LEDs that are predominantly dominated by TM-polarized emission, the refractive indices of the MQWs and p-EBL should be carefully considered.

Figure 4 .
Figure 4. Detailed far-field emission patterns of the LED without the inclined sidewalls for a) TE polarization and b) TM polarization.c) The mechanism of the strategy of refractive index engineering together with the inclined sidewalls, through which light is laterally guided by multiple reflections in the waveguide structure and redirected vertically by the inclined sidewall to escape through the top surface.d) The LEE of each route for TM-polarized light as a function of the inclined angle of the sidewall.Detailed far-field emission patterns of the LED with the inclined sidewalls for e) TE polarization, and f ) TM polarization.(Note: the emission pattern of each route has been calibrated by its corresponding LEE ratio.)

Figure 5 .
Figure 5. a) The LEEs for TE-and TM-polarized light as a function of the refractive index of the BAlN inserted layer.b) Detailed LEE distributions of the LEDs with different structures for TM-polarized light.

Table 1 .
Structural and optical parameters used in the simulations.

Table 2 .
Detailed spatial angular range of the different regions inside the LED.
Zone Range of θ E [°]n MWQs of 2.4 n MWQs of 2.5