1. Introduction

Environmentally friendly, compact AlGaN-based deep ultraviolet light-emitting diodes (DUV LEDs) with an emission wavelength (λ) below 240 nm have attracted increasing interest due to new potential applications, especially in gas sensing, sterilization, and medical diagnostics [1–4]. For example, gases such as NO (λ = 226 nm) or NH₃ (λ = 217 nm) can be detected by UV irradiation from their specific absorption lines [4]. Recently, it has been found that DUV light at 207–222 nm can sterilize bacterial cells effectively without damaging the exposed human tissues [2,3]. This suggests that the DUV emission at this wavelength range can be safe for treating bacterial infections in mammals. Despite the substantial advancements in such short wavelength AlGaN-based DUV LEDs, their external quantum efficiency (EQE) and output power are still extremely low, which are far from satisfactory to support their potential market. The typical EQE of such DUV LEDs is below 0.5% [2–7], which further drops rapidly as the emission wavelength decreases (even down to 10⁻⁶% for 210 nm AlN LEDs [8]). This is mainly attributed to the intrinsic material properties of AlGaN causing poor internal quantum efficiency (IQE) and light extraction efficiency (LEE) [9–11].

In particular, the LEE of AlGaN-based DUV LEDs is severely limited due to the strong absorption of DUV photons by the top narrower bandgap p-type GaN contact layer used in most DUV LEDs designs and the serious light trapping by total internal reflection (TIR) caused by the large contrast in the refractive indices of AlGaN and air. Furthermore, the phenomenon of intrinsic optical polarization switching is another major factor that limits the LEE [12–15]. Specifically, for c-plane AlGaN-based DUV LEDs, the emission from the multi-quantum wells (MQWs) active region gradually switches from transverse-electric (TE) polarization to transverse-magnetic (TM) polarization as the Al component increases owing to the rearrangement of the topmost valence sub-bands of AlGaN [16,17]. The TE-polarized light mainly propagates in the vertical direction, and thus it is relatively easier for it to escape from the top surface. On the other hand, the TM-polarized light mainly propagates laterally toward the sidewall, and thus it is difficult to extract it from the top surface, which results in extremely low top-surface LEE.

Since optical polarization has a profound impact on light extraction behavior, intensive experimental [14,15,18–22] and theoretical [4,12,13,23–27] studies have been carried out to investigate the influence of optical polarization on the LEE. Most of the theoretical studies employ the finite-difference time-domain (FDTD) method [23–26] or the Monte Carlo ray-tracing method [4,12,13,27]. The FDTD method is based on wave optics. It solves Maxwell’s equations directly and provides rigorous solutions for electromagnetic wave propagation. It is especially suitable for the LEE simulation of nanostructure LEDs (nanorod or nanowire LEDs). However, the FDTD simulation requires a large amount of memory and an extremely long computation time. Thus, it is difficult to analyze the large structures, such as the planar LEDs. Therefore, in the FDTD simulation of planar LEDs, a simplified simulation model is inevitably employed. The lateral dimension of the computational domain is usually several µm, which is much smaller than the actual size of real planar LEDs (hundreds of µm). In order to truncate the lateral dimension of the actual LED structures, perfect mirrors are placed at the four lateral boundaries to represent the limited lateral dimension as infinite [23–26]. Thus, it is not possible to simulate the real device geometry and the size effect, which have a significant influence on the LEE. Furthermore, the emission from the sidewalls cannot be detected. Since AlGaN-based DUV LEDs exhibit strong side emission, this might provide incorrect information on their overall LEE and emission pattern.

On the other hand, the Monte Carlo ray-tracing method, which is based on geometrical optics, is able to effectively simulate a range of geometrical optical phenomena in LED chips, such as ray reflection, transmission, Fresnel losses, material absorption, and even the behavior of randomly-emitted photons from the active region. This technique is quick and highly accurate for structures that are much larger than the wavelength of light, where the diffraction and interference effects can be neglected. Consequently, the Monte Carlo ray-tracing method has been widely applied to study the LEE and light structure design of GaN-based LEDs [28–31]. However, the relevant studies on the polarization-dependent LEE of AlGaN-based LEDs are still relatively lacking at the current stage [4,12,13,27].

Additionally, although tremendous progress has been made to date, the extraction mechanisms of polarized light in AlGaN-based DUV LEDs are far from clear. Therefore, a systematic and comprehensive investigation has been carried out in this study using simple Monte Carlo ray-tracing simulations with Snell's law to perform an in-depth exploration of the polarization-dependent light extraction mechanisms of AlGaN-based DUV LEDs.

While performing the study, the light sources corresponding to all degrees of polarization were created first in order to describe the behavior of the polarization-dependent light emitted from the AlGaN MQWs. Except for the conventional study on the total LEE, the LEE of the individual escape route was further resolved to clearly elucidate the light extraction behavior of each escape route. The impact of the key factors, such as the p-GaN thickness, material absorption coefficient, and chip size, on the total LEE and the LEE of each escape route were comprehensively investigated to reveal the fundamental limitations of the LEE. Unlike the usual expectation, our results from this work indicate that the total LEE of TM-polarized emission is not always lower than that of TE-polarized emission. Although the top-surface LEE of TM-polarized emission is only one-tenth of that of TE-polarized emission, the light extracted from the sidewalls can be substantial if treated appropriately to allow it to escape. It is especially worth noting that the structures of the p-type electron blocking layer (p-EBL), as well as the MQWs have a significant impact on photon propagation, which is especially critical for extracting TM-polarized light but is ignored in the conventional device design. Interestingly, by adjusting the structures of the p-EBL, MQWs, and sidewalls, the adverse TIR that causes serious light trapping, can be used in a positive manner to fully utilize the inherently strong TM-polarized emission that would otherwise be absorbed inside the device. In light of this, an artificial vertical escape channel of light, named guided laterally redirected vertically (GLRV) structure, was constructed to efficiently extract the TM-polarized light through the top surface, and thus a high top-surface LEE and favorable emission pattern for the AlGaN-based DUV LED dominated by TM-polarized emission have been achieved.

2. Device structures and parameters

Sapphire is the most popular epitaxial substrate for AlGaN-based DUV LEDs because of its low cost and DUV transparency. Despite fully absorbing the UV light generated in the MQWs, p-GaN is still generally used as an ohmic contact and a hole injection layer due to the extremely poor doping efficiency of the Al-rich p-AlGaN [9–11]. Thus, the typical AlGaN-based DUV LEDs employ the flip-chip architecture with a highly-reflective p-side down, i.e., extracting the light through the substrate side of the wafer to suppress light absorption [1,2], as schematically shown in Fig. 1(a). Since the electrode structure might vary from one LED to another, the etched mesa structure and contact electrodes in a real chip were neglected in the simulation model. This not only simplified the calculation but also enabled a clear understanding of the fundamental limitations of the LEE in AlGaN-based DUV LEDs. A schematic of the simulated LED chip model is presented in Fig. 1(b), where the layer structures are similar to that of the typical DUV LEDs [32]. It should be noted here that the active region, i.e., the Al_xGa_1-xN/Al_yGa_1-yN MQWs (x < y) structure, is reasonably represented by a single 10 nm layer with the optical characteristics of the MQWs, as the total thickness of the highly absorptive Al_xGa_1-xN well layers is usually small [5,32].

 

Fig. 1. Device schematic (not to scale). (a) A typical AlGaN-based flip chip DUV LED. (b) The simulated chip model.

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To ensure the reliability of the simulation results, it is very important to properly choose the refractive index and absorption coefficient for each material layer [28,29]. The details of the structural and optical parameters in the simulations are listed in Table 1, where all the parameters were set by either referring to the relevant studies or based on real devices.

Table 1. Structural and Optical Parameters Used in the Simulations^a

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The refractive indices of sapphire, AlN, and GaN were taken from the relevant studies [33–35]. Vegard’s law was employed to determine the refractive index of the ternary AlGaN material, where the Al content for each layer was selected based on the reported values [32]. The dopant was assumed to have a slight impact on the refractive index [29]. Thus, the refractive indices of n-AlGaN and p-AlGaN were set to be the same as that of AlGaN. The MQWs were modeled as a uniform medium with an effective refractive index [28,29]. This is a reasonable approximation when the MQWs structure is properly designed, as discussed in detail later. Since the refractive indices of the p-EBL and the MQWs can strongly affect the LEE of the sidewalls, as shown below, and can be adjusted by suitably modifying their structures, their values were taken as variable parameters. In addition, although the refractive index of AlGaN can be different for each polarization, the difference is not significant [36], and thus the dispersion was not considered in the simulations.

It is well-known that LEE strongly depends on the optical absorption of different materials. The light absorption for sub-bandgap energy is mainly affected by the epilayer quality and doping [28,29], which highly depends on growth conditions. Thus, the sub-bandgap absorption coefficient of the epilayers was taken as variable parameters.

On the other hand, in the absorptive p-GaN layer with a narrower bandgap, the absorption coefficient is extremely high due to the band-edge absorption. This value is also dependent on the wavelength of light and is approximately 2.3 × 10⁴mm⁻¹ at 230 nm, according to experimental results [36,37].

The re-absorption of light by the active region has a large Stokes shift from its emission edge, and only the tail of the absorption curve overlaps with the emission spectrum [38]. Thus, the absorption is estimated to be two orders of magnitude weaker than that at the band edge. Here, its absorption coefficient was set to 100 mm⁻¹, which is similar to the recent experimental value of 66.7 mm⁻¹ [21].

Photon recycling, i.e., the re-absorption of a photon and its subsequent partial re-emission in the active region, is known to play an important role in the light extraction in GaAs material. However, the photon recycling effect is negligible in AlGaN MQWs due to the large Stokes shift [38], in addition to the low IQE, and thus was ignored in the simulations.

An Al-based reflector with high reflectivity in the DUV region is usually deposited on the bottom of p-GaN as a reflective p-type contact to redirect the downward-propagating light upward. The reflectivity was set to 80% [39] in the simulations.

The LED chip model was exposed to air to simulate the on-wafer performance of DUV LEDs [4,7], since the DUV transparency and durable encapsulation resin is not available.

In the simulations, 200,000 light rays were randomly generated within the MQWs in all directions with a wavelength of 230 nm. A representative emission wavelength of 230 nm was chosen to refer to such DUV LEDs as the light emission wavelengths approach 210 nm. Although the emission from the AlGaN MQWs in this range is predominantly TM-polarized [1,2], the dependence of LEE on the variation of polarization was investigated to gain insight into the polarization-dependence of LEE. Furthermore, the optical polarization is highly dependent on the composition of the MQWs, QW thickness, and strain [16,17], which means that the degree of polarization of the same wavelength emission can be different for different growth conditions. Since the radiation pattern of the MQWs is determined by the degree of polarization, it varies for each polarization. For each light ray, the trajectory and energy were determined by Snell’s law, Fresnel loss, and material absorption in its propagation path. The criterion for the termination of a light ray was that its energy dissipates to be less than 5% of its original energy emitted from the MQW or is absorbed by the external detector.

By using dipole radiation, the angle-dependent intensity, I(θ_E), of the TE- and TM-polarized emission, can be described by [27,40,41]

By mixing the TE- and TM-polarized emission, the radiation pattern of the MQWs for different degrees of polarization can be obtained. Here, the emission sources with the degree of polarization of 1, 0.5, 0, –0.5, –1 were created, which are referred to as fully TE-polarized, dominantly TE-polarized, unpolarized, dominantly TM-polarized, fully TM-polarized emission of the MQWs, respectively. Thus, the impact of the different degrees of polarization on the LEE can be investigated in contrast to the restricted investigations involving only the TE-polarized emission and TM-polarized emission considered in the previous studies [23–26].

For the typical AlGaN-based flip-chip DUV LEDs, schematically shown in Fig. 1, the emitted light can be extracted through the sapphire top surface, sapphire sidewalls, and epilayer sidewalls. To obtain an in-depth understanding of the light extraction mechanisms, except for the total LEE, the individual LEE for each escape route was also calculated. Furthermore, since most of the light extracted downward will be absorbed by package materials, it does not contribute to usable light output. We further identified the light extracted in the upward or downward directions for each LEE.

3. Results and discussion

First, a set of reasonable geometrical and optical parameters was chosen to perform the simulations to obtain an overview of the impacts of optical polarization on the LEEs. It should be noted here that this set of parameters was used as the default values, as given in Table 1. In the other simulations described below, we started from these default values and varied one parameter at a time to further study its impacts on the LEEs, i.e., unless stated otherwise, except for the varied parameter, the other parameters were their corresponding default values.

It is surprising to see that the total LEE decreases only slightly from 17.1% to 15.6% as the degree of polarization changes from 1 to –1, as shown in Fig. 2(a). To understand this rather unexpected result more clearly, the individual LEE through each escape route was further analyzed. As the degree of polarization decreases from 1 to –1, the top-surface LEE drops drastically from 7.3% to 0.7%. In other words, the top-surface LEE of TM-polarized emission is only one-tenth of that of TE-polarized emission, which agrees with the results reported in the previous studies [24]. While the LEE of the sapphire sidewalls decreases slightly. Thus, it has only a minor contribution to the total LEE difference among the different degrees of polarization. It should be especially noted here that the LEE of the epilayer sidewalls increases significantly, leading to a drastic increase in the total LEE, thereby making the total LEE of TM-polarized emission comparable to that of TE-polarized emission.

 

Fig. 2. Impacts of the optical polarization on the LEEs. (a) Total LEE and individual LEE of each route for different degrees of polarization. (b)–(f) Far-field emission patterns of DUV LEDs with different degrees of polarization. (g) Epilayer-sidewalls LEE for TM-polarized emission as a function of epilayer depth (from p-GaN to AlN).

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In order to elucidate the light extraction behavior of each escape route, the corresponding emission polar patterns were further analyzed, and the corresponding results are shown in Figs. 2(b) to 2(f). As expected, the emission intensity pattern of the top surface exhibits a Lambertian shape for TE-polarized emission, which is desirable for LED applications, whereas the TM-polarized emission exhibits a rabbit-ear pattern. For the sapphire sidewalls, the features of the polar pattern for each polarization are similar. It is especially worthwhile to focus on the polar pattern selected from the epilayer sidewalls. As the degree of polarization decreases, the polar pattern becomes increasingly larger, thus, coinciding with the increase in the proportion of the light extracted from the epilayer sidewalls. In particular, in the case of TM-polarized emission, the polar pattern of the epilayer sidewalls is almost the same as that of the total, which indicates that the majority of the light is extracted through the epilayer sidewalls, wherein the LEE of the epilayer sidewalls amounts to 79.2% of the total LEE, as observed from the results shown in Fig. 2(a). Further, it is observed that the light escaping from the epilayer sidewalls propagates mostly in the near horizontal direction, and nearly half of it is extracted downward, which would be absorbed by package materials. Furthermore, a considerable proportion of the light escaping upward would be absorbed by the n-type contact and bond pads, as schematically illustrated in Fig. 1(a). In other words, most of the light extracted from the epilayer sidewalls does not contribute to usable light output, which can partially explain the significant decrease in EQE as a function of decreasing wavelength. Since the light generated in the MQWs of AlGaN-based DUV LEDs is predominantly TM polarized, it is critically important to efficiently make use of such epilayer-sidewalls emission to achieve high performance.

To understand this substantial emission from the epilayer sidewalls for TM-polarized emission, the LEE of the epilayer sidewalls as a function of epilayer depth was further analyzed, and the result is shown in Fig. 2(g). There is almost no light extracted through the sidewalls of the epilayer above the p-EBL layer. The majority of the light is extracted through the sidewalls of the n-AlGaN layer, and a small part comes from the sidewalls of the AlN layer. Thus, the LEE of the epilayer sidewalls was divided into that of the n-AlGaN sidewalls and AlN sidewalls in the following simulations. The above results suggest that considerable TM-polarized light can be extracted from the n-AlGaN sidewalls by modifying the device structure appropriately, the underlying mechanism of this will be discussed in detail later.

In order to gain a comprehensive understanding of the light extraction mechanisms, some of the important parameters were varied to further study their impacts on the LEEs. Since the absorption in the p-GaN layer has been believed to be one of the main factors restricting the LEE of DUV LEDs and p-GaN layers of different thicknesses are usually used by different researchers [5,32], the impacts of the p-GaN thickness on the LEEs were investigated, and the corresponding results are shown in Fig. 3. The p-GaN thickness was varied from 0 to 70 nm, whereas the other parameters were set to their corresponding default values given in Table 1.

 

Fig. 3. Impacts of the p-GaN thickness on the LEEs. (a)–(e) Total LEE and individual LEE of each route for different degrees of polarization as a function of p-GaN thickness. (f) Normalized LEE of each route for different degrees of polarization as a function of p-GaN thickness.

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The total LEE is observed to decrease significantly as the thickness of the p-GaN increases for all degrees of polarization. When the p-GaN layer is thicker than 60 nm, the total LEE maintains a nearly constant value due to the almost complete absorption of the light incident on the p-GaN layer. The drop decreases gradually with the decrease in the degree of polarization, from 37.7% for TE-polarized emission to 19.6% for TM-polarized emission. However, the LEE of each route exhibits considerably different dependent behaviors, as shown in Figs. 3(b) to 3(e), indicating the different extraction behaviors for each route. The different dependent behaviors can be seen more clearly by normalizing each curve to its corresponding maximum value, as shown in Fig. 3(f). There is almost identical dependent behavior for all degrees of polarization in the same escape route, which indicates that the light extraction behavior for each escape route is independent of the degree of polarization. It is clear that the light escapes through the top surface in two different ways, illustrated schematically in Fig. 6(a): one is directly escaping through the top surface (denoted as ray 1), as the light is emitted upward from the MQWs and falls into the escape cone of the top surface, whereas the other is that the originally downward-emitted light is redirected upward through the top surface by the reflective p-contact (ray 2). The amount of light extracted in each way is comparable, as evidenced by the fact that the top-surface LEE decreases down to approximately half the value corresponding to the case without the p-GaN layer. It should be noted that the optical cavity effect that is introduced by the interference of the upward-emitted light and the downward-reflected light can make the top-surface LEE vary periodically as the distance between the MQWs and the p-electrode reflector changes [24], which cannot be simulated by the Monte Carlo ray-tracing method. According to the interference theory, the period can be calculated using Δd = λ/2n, where n is the average refractive index of the epilayers between the MQWs and the p-electrode reflector. Therefore, in practice, we can intentionally optimize the MQWs position relative to the p-electrode reflector to achieve constructive interference, namely optimizing the total thickness of the EBL, p-AlGaN, p-GaN, thus maximizing the top-surface LEE.

The LEE of the sapphire sidewalls has an exponentially decreasing behavior similar to that of the top surface, indicating that most of the light escapes through the sapphire sidewalls in ways similar to the top surface, as schematically illustrated by rays 3 and 4. Light can also escape from the sapphire sidewalls by multiple reflections, i.e., the light travels in the air/p-GaN–sapphire/air waveguide structure by multiple reflections to arrive at the sidewalls and subsequently escapes out. However, the amount of light extracted in this manner is small, as evidenced by the minor difference in the dependent behaviors between the top surface and the sapphire sidewalls. It can be easily explained by the fact that most of the allowed light reaching the sapphire sidewalls directly rather than by multiple reflections since the thickness of the sapphire is comparable to the lateral dimension of the chip.

In the case of the escape route of the AlN sidewalls, nearly half of the light escapes from the AlN sidewalls by multiple reflections through the air/p-GaN–AlN/sapphire waveguide structure when the p-GaN layer is absent, as verified by the observation of the LEE of the AlN sidewalls decreasing rapidly by half as the thickness of the p-GaN layer increases from 0 to 10 nm. As the AlN layer is thin, far less than the lateral size of the chip, the light propagating in this waveguide structure should undergo multiple reflections to reach the sidewalls. However, the multiple reflections are suppressed due to the strongly absorptive p-GaN layer. Therefore, for a p-GaN layer larger than 10 nm, only the light generated at the periphery of the MQWs can directly escape without multiple reflections, as schematically illustrated by rays 5 and 6.

It is especially worth noting that the LEE of the n-AlGaN sidewalls is nearly independent of the p-GaN thickness. This is because the light is mostly escaping outward by multiple reflections through the p-EBL/MQWs–n-AlGaN/AlN waveguide structure without passing the p-GaN layer, as schematically illustrated by rays 7 and 8.

As the contribution of the light extracted from the n-AlGaN sidewalls to the total LEE increases with the decreasing degree of polarization, the dependence of the total LEE on the p-GaN thickness decreases, as seen in Fig. 3(a). The above results certainly imply that except for the light confined in the p-EBL/MQWs–n-AlGaN/AlN waveguide structure, more than half of the remaining light generated from the MQWs can be absorbed by the p-GaN layer, including the originally downward-propagating light to the p-GaN layer, and some of the light reflected from the AlN/sapphire and sapphire/air interfaces. Therefore, light extraction is seriously limited by the strong absorption in the p-GaN layer. It has been reported that the approaches such as the laterally over-etched p-GaN [42], meshed p-type contact electrode [43], and surface plasmon coupling [44] can somewhat reduce the absorption of the p-GaN layer.

It is especially interesting to note that the light confined in the p-EBL/MQWs–n-AlGaN/AlN waveguide structure can be free from the absorption by the p-GaN layer. Thus, properly designing this waveguide structure to confine as much light as possible can weaken the adverse effect of the p-GaN layer, thus increasing the light extraction.

Except for the optical absorption in the MQWs and p-GaN layer, the optical absorption in other passive regions, such as the AlN and n-AlGaN layers, also have an important impact on the LEE. Since this sub-bandgap absorption coefficient is highly dependent on epilayer quality [28,29], its value usually varies from one structure to another for different growth conditions. Thus, the impacts of the sub-bandgap absorption coefficient of the epilayers on the LEEs were also simulated, and the results thus obtained are shown in Fig. 4. The sub-bandgap absorption coefficient was varied from 0 to 30 mm^–1, whereas the other parameters were set to their corresponding default values, as given in Table 1.

 

Fig. 4. Impacts of the absorption coefficient of the epilayers on the LEEs. (a)–(e) Total LEE and individual LEE of each route for different degrees of polarization as a function of absorption coefficient. (f) Normalized LEE of each route for different degrees of polarization as a function of absorption coefficient.

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As is clearly seen from Fig. 4(a), the total LEE decreases drastically as the absorption coefficient increases for all degrees of polarization. The drop increases gradually as the degree of polarization decreases, from approximately 48.3% for TE-polarized emission to 75.8% for TM-polarized emission. As can be seen from Figs. 4(b) to 4(e), the LEE exhibits considerably different dependent behaviors for each escape route, which can be seen more clearly by normalizing each curve to its corresponding maximum value as shown in Fig. 4(f). The LEEs of the n-AlGaN sidewalls and the AlN sidewalls exhibit an exponentially decreasing trend, which is typical of the influence of the sub-bandgap optical absorption on the LEE [29]. In the case of the top surface and the sapphire sidewalls, the corresponding LEEs exhibit a relatively weaker linear dependence. These differences can be explained by the different light extraction behaviors for each route stated previously in Fig. 3. The results imply that the optical absorption of the p-GaN layer has a primary effect on the LEE in the routes of the top surface and sapphire sidewalls, where the light is partly passing through the strongly absorptive p-GaN layer before escaping out. In addition, the light path from the sapphire sidewalls is longer than that from the top surface, and thus has a somewhat stronger decreasing trend. Since most of the light extracted from the AlN sidewalls comes from the periphery of the MQWs, the average light path is much smaller than that from the n-AlGaN-sidewalls route, where the light mostly travels in the waveguide structure with multiple reflections before escaping out, and thus exhibits a weaker exponential decrease.

As the contribution of the emission from the n-AlGaN sidewalls to the total LEE increases with the decreasing degree of polarization, the dependence of the total LEE on the absorption coefficient increases, as shown in Fig. 4(a). The simulation results indicate that the TM-polarized light is more sensitive to the sub-bandgap optical absorption due to the longer propagating distance before being extracted. In fact, a high-quality epilayer with low dislocations and defects can not only reduce optical absorption but also increase IQE significantly [45]. Thus, it is very important to find ways to improve the epilayer quality. Several growth techniques, such as the nanoscale epitaxial lateral overgrowth (ELO) [46], high temperature annealed sputtered ELO [47], and graphene-driving strain engineering [48] have been recently proposed to improve the epilayer quality.

Since different chip sizes are usually designed for different applications, the impacts of the chip size on the LEEs were also simulated, and the results are shown in Fig. 5. The chip size was varied from 20 × 20 µm² to 1000 × 1000 µm² (from micro-size to large-size), whereas the other parameters were set to their corresponding default values given in Table 1.

 

Fig. 5. Impacts of the chip size on the LEEs. (a)–(e) Total LEE and individual LEE of each route for different degrees of polarization as a function of chip size. (f) Normalized LEE of each route for different degrees of polarization as a function of chip size.

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As the chip size increases, the total LEE decreases rapidly for all degrees of polarization. The drop gradually increases with the decreasing degree of polarization, from 49.4% for TE-polarized emission to 71.1% for TM-polarized emission. The LEE of each route also shows considerably different dependent behaviors, as shown in Figs. 5(b) to 5(e), which are shown more clearly by normalizing each curve to its corresponding maximum value in Fig. 5(f). The different dependent behaviors are consistent with their corresponding light extraction behaviors, as stated previously in Fig. 3. For the top-surface route, the LEE is nearly independent of the chip size. This is because the light escapes vertically from the top surface, which is independent of the lateral dimension of the chip. In the sapphire-sidewalls route, the LEE is almost insensitive to the chip size when the chip size is smaller than 200 × 200 µm² since light can directly reach the sidewalls without multiple reflections. On the other hand, in the case of a large-size chip, part of the light travels to the sidewalls by multiple reflections through the air/p-GaN–sapphire/air waveguide structure, where the optical absorption is dominantly by the p-GaN layer, as mentioned above, and thus the LEE shows a linear dependence similar to the result seen in Fig. 4(f). In the case of the AlN-sidewalls route, the proportion of the periphery of the MQWs decreases as the chip size increases, resulting in a decrease in the LEE. For the route of the n-AlGaN sidewalls, the light path traveling in the p-EBL/MQWs–n-AlGaN/AlN waveguide structure is proportional to the chip size. Which causes the increased optical absorption by the n-AlGaN and MQWs and the increased Fresnel loss by reflections, resulting in a exponential decrease in the LEE.

As the contribution of the emission from the n-AlGaN sidewalls to the total LEE increases with the decreasing degree of polarization, the dependence of the total LEE on the chip size increases, as shown in Fig. 5(a). These results imply that the TM-polarized light is more sensitive to the chip size as it mostly propagates laterally and escapes from the sidewalls. If the sub-bandgap optical absorption is higher, the LEE drop becomes even more severe, which might be a problem when designing large-area DUV LEDs for high-power applications.

As discussed thus far, by studying the impacts of the key factors on the total LEE as well as the LEE of each escape route, the light extraction mechanisms of the typical AlGaN-based DUV LEDs have been clearly elucidated. Based on the above results, the light extraction behavior for each escape route can be concluded, as schematically illustrated in Fig. 6(a), which has already been discussed in Fig. 3.

 

Fig. 6. Schematic illustrations of the light extraction mechanisms of AlGaN-based DUV LEDs and the concept of creating an artificial vertical escape channel for the TM-polarized light. (a) Typical light extraction behavior for each escape route. (b) Different ranges of the emission angle (θ_E) of the light generated in the MQWs for different light extraction behaviors. Impacts of the refractive indices of the p-EBL (c) and the MQWs (d) on the LEE of the n-AlGaN sidewalls for TM-polarized emission. (e) Schematic illustration of the mechanism by which the light is redirected vertically by the inclined sidewall and then escapes through the top surface and the design method for the inclined sidewall. (f) LEEs of the top surface and the n-AlGaN sidewalls for TM-polarized emission as a function of inclination angle. The inset in (c) illustrates the behavior of the light guided laterally in the waveguide structure by multiple reflections. The inset in (d) illustrates the radiation patterns of the MQWs for full TE-polarized emission and TM-polarized emission. The inset in (f) illustrates the optimized design rule for the inclined sidewall.

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Next, the light trajectories and light extraction behaviors on the different interfaces were further analyzed in detail using Snell’s law. It is well-known that light propagating from an optically denser medium to an optically rarer medium might induce considerable TIR depending on the contrast between their refractive indices. For the typical AlGaN-based flip-chip DUV LEDs, along the light propagation direction from the MQWs to the sapphire substrate, the refractive index of each layer decreases successively as illustrated in Fig. 6(a), thus the TIR is induced at each interface in sequence. According to Snell's law, the respective critical angle, θ_C, of each TIR can be given by [28]

Table 2. Detailed Spatial Angular Range of the Different Regions Inside the LED

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In region A, when light is emitted within the angle range of (0°, 24.6°) and (335.4°, 360°), which is well-known as the light escape cone of the top surface, it can directly escape from the top surface just as ray 1 illustrated in Fig. 6(a). On the other hand, the light emitted between (155.4°, 204.6°) can be reflected by the reflective p-contact and then escape through the top surface as ray 2. However, ray 2 will be completely absorbed when the p-GaN layer is thick. In region B, light is trapped within the air/p-GaN–sapphire/air waveguide structure due to the TIR at the interfaces. Thus, it is guided laterally in the waveguide structure and is gradually reabsorbed by materials and eventually converted into heat. In the case of region C, most of the light falling into this region can directly propagate to the sapphire sidewalls without requiring multiple reflections (rays 3 and 4), as the thickness of the sapphire is comparable to the lateral dimension of the chip, as evidenced by the results shown in Figs. 3, 4, and 5. However, when the thickness of the sapphire is decreased to be much smaller than the chip size, this light extraction will be severely compromised as the multiple reflections are suppressed by the strongly absorptive p-GaN layer. In region D, light is trapped as a guided mode in the air/p-GaN–AlN/sapphire waveguide structure and finally dissipates through absorption. In region E, though the light falling into this region can be extracted through the AlN sidewalls, most of the light guided in the air/p-GaN–AlN/sapphire waveguide structure cannot reach the sidewalls as the multiple reflections are suppressed by the strongly absorptive p-GaN layer. Thus, only the light generated at the periphery of the MQWs can directly escape out, represented by rays 5 and 6, resulting in the low LEE of the AlN sidewalls. The behavior of light in region F is similar to that in region E. The guided light hardly reaches the sidewalls, and only the light generated at the periphery of the MQWs can escape out through the AlN sidewalls or n-AlGaN sidewalls. In region G, light is guided laterally in the p-EBL/MQWs–n-AlGaN/AlN waveguide structure, where the absorption is relatively low. Therefore, considerable light can reach the sidewalls and then escape (rays 7 and 8), which explains the substantial observed emission from the epilayer sidewalls shown in Fig. 2.

It has been clearly shown that the strong TIR, in addition to the highly absorptive p-type GaN layer, fundamentally restrict the LEE of AlGaN-based DUV LEDs. For example, in regions B and D, the light is completely trapped by TIR, whereas in regions A, C, E, and F, light extraction is severely compromised by the p-GaN layer. Furthermore, as shown in the inset of Fig. 6(d), in the case of TE-polarized emission, since the light is mainly emitted in the vertical direction, a sizable portion of it falls into the top-surface escape cone and directly escapes out, thus leading to a relatively high top-surface LEE. On the other hand, in the case of TM-polarized emission, most of the light is emitted in the lateral direction, and the light propagated in the vertical direction is almost negligible. This indicates that most of the light cannot escape from the top surface, thus resulting in extremely low top-surface LEE.

Since the vertical propagation channel for the TM-polarized light is inherently blocked due to the strong TIR, it is critically important to create another escape channel for it in the AlGaN-based DUV LEDs, where the light emitted from the MQWs would be dominated by TM polarization. As the TM-polarized light mainly propagates laterally, it seems that a lateral propagation channel could be more effective. Furthermore, it is sensible to utilize TIR in a positive manner as much as possible since its occurrence is inevitable. As expected, the above simulation results have already demonstrated that the TM-polarized light can effectively escape outward through the p-EBL/MQWs–n-AlGaN/AlN waveguide structure by TIR, as illustrated in the inset of Fig. 6(c). This waveguide structure can be constructed by sandwiching the MQWs and the n-AlGaN layer between the two cladding layers with a lower refractive index, similar to the AlN template and the p-EBL layer.

In order to guarantee a highly favorable effect of the waveguide structure, a proper adjustment of the epitaxial structure is needed. Because a thick AlN layer is usually grown first as the template for the following epitaxial structure growth, the AlN template is fixed in the device structure [1,2]. In contrast, the p-EBL layer can function as a TIR barrier for the generated photons to enter the absorptive p-GaN layer. It should be designed to block the photons as much as possible, which would otherwise be absorbed by the p-GaN layer. In this sense, the refractive index of the p-EBL should be designed as low as possible. To understand this more clearly, the dependence of the LEE of the n-AlGaN sidewalls on the refractive index of the p-EBL was further simulated. In the simulation, the refractive indices of the other layers were fixed, except for the p-EBL. The LEE of the n-AlGaN sidewalls for TM-polarized emission dramatically improves from 3.3% to 11.5% as the refractive index of the p-EBL decreases from 2.4 to 2.3, as shown in Fig. 6(c). When the refractive index of the p-EBL is equal to that of the MQWs, the photons can freely enter the p-GaN layer. In this situation, only the light generated at the periphery of the MQWs can escape from the n-AlGaN sidewalls as mentioned above, and thus the low observed LEE. On the other hand, as their refractive index contrast increases, an increasing number of photons can be blocked within the waveguide structure and escape from the sidewalls.

Interestingly, the result indicates that the p-EBL that is initially designed to block electron leakage to increase IQE can also block photons to avoid them being absorbed by the p-GaN layer. Therefore, except considering the impact on electron and hole transport as the conventional point for the p-EBL structure design, the impact on photon propagation must also be taken into account, which is especially critical for the predominantly TM-polarized AlGaN-based DUV LEDs. One of the practical approaches to introduce the effective TIR barrier can be to grow a thin AlGaN epitaxial layer with a higher Al composition or even an AlN layer between the MQWs and the conventional p-EBL. In this way, holes can be injected into the MQWs through such a thin layer by tunneling [7,49]. Consequently, the electrical property will not deteriorate. However, the TIR barrier based on AlN ceases to be effective when the fraction of Al in the AlGaN MQWs is close to 1. On the other hand, it has been reported that incorporating boron into AlN can reduce its refractive index [50]. Therefore, BAlN might be a suitable substituent that can serve as the TIR barrier for high-Al content AlGaN MQWs.

In addition, an appropriate design for the structure of the MQWs is also required to achieve the desired effect of the waveguide structure. In conventional AlGaN-based DUV LEDs, the MQWs generally has a relatively higher refractive index than the adjacent layers. This will cause severe light loss inside the MQWs, especially for TM-polarized emission. To understand this more clearly, the impact of the refractive index of the MQWs on the LEE of the n-AlGaN sidewalls for TM-polarized emission was also simulated. Figure 6(d) shows that the LEE of the n-AlGaN sidewalls decreases dramatically from 11.5% to 2.1% with the increasing refractive index of the MQWs from 2.4 to 2.5. Due to the higher refractive index of the MQWs compared to the adjacent layers, a significant portion of the generated photons will be trapped in such a thin and highly absorptive MQWs layer and re-absorbed thereafter. Thus, it is very important to weaken this TIR to reduce the light loss inside the MQWs. In terms of the practical device structure, the following appropriate measures can be taken: using a thin well layer (specifically with a thickness of 1–2 nm or less), minimizing the Al composition difference between the well and the barrier, keeping the Al composition of the n-AlGaN layer lower than that of the barrier layer. These measures are feasible in practice. The thin well layer has been used in DUV LEDs to mitigate the quantum-confined Stark effect, thus enhances IQE [4,5,7,32]. Furthermore, the thin well design can also minimize the refractive index contrast between the well and the barrier, as the refractive index is often graded between the layers of different compositions [51]. Moreover, although the decrease in the Al composition difference between the well and the barrier might reduce the electron-hole confinement to some extent, this can be solved by either adding the number of QWs or increasing the bandgap of p-EBL. In addition, if the relatively high refractive index for the MQWs is inevitable, the difference should be minimized as much as possible since even a small modulation in the refractive index contrast leads to a significant reduction in the light loss in the MQWs.

It is clearly shown that the structures of the p-EBL, as well as the MQWs, have a significant impact on photon propagation, and thus absorption loss and LEE. In the conventional strategies of either the p-EBL or the MQWs, only the impact on electron and hole transport is considered for the structure design. Therefore, a new strategy for designing the p-EBL and MQWs should be developed, i.e., the impact on carrier transport and photon propagation should be taken into account together, which is especially critical for demonstrating the high performance of the AlGaN-based DUV LEDs dominated by TM-polarized emission.

The vertical light extracted from the top surface is more practically desirable for LED applications compared to the side emission. Furthermore, most of the light extracted from the epilayer sidewalls, which is either emanated in less useful directions or absorbed, does not contribute to usable light output, as shown in Figs. 2(b) to 2(f). Thus, it is urgently required to think of a method that can make use of such a large amount of side emission more effectively. The most direct method involves redirecting the side emission to the upward direction. Since TIR can reflect light, it can also be used to redirect the side emission. It has been reported that the inclined sidewalls covered by SiO₂/Al [18] or MgF₂/Al [20] layers can serve as an omnidirectional reflector to efficiently redirect the TM-polarized light. Recently, it has also been reported that the Al coating layer on the inclined sidewalls can cause light absorption, and the air-cavity-shaped inclined sidewall exhibits even a better reflectivity [14]. This result suggests that the inclined sidewalls formed by inductively coupled plasma etching could be quite smooth (the measure of roughness is the ratio of the corrugation depth to the light wavelength), leading to the light being reflected at the sidewalls rather than being scattered or diffracted. Thus, the inclined sidewall can serve as a good reflector to redirect the side emission via TIR, when the inclination angle is designed properly.

Since most of the side emission comes from the n-AlGaN sidewalls, according to the simulation results, it is reasonable to incline the sidewalls from the p-GaN to the n-AlGaN layer. This can not only redirect the side emission efficiently but can also reduce the sacrifice of the active region area.

The light incident on the sidewalls can be divided into two parts, namely, one below the horizontal line and the other above the horizontal line, as denoted by rays 1 and 2 in Fig. 6(e), respectively. To redirect these rays at the sidewall by TIR, the relationship among the inclination angle of the sidewall (α), θ_E, and θ_C can be determined by Snell's law. As the guided light is emitted between the angular range of (73.4°, 90°), it can be calculated that the light suffers TIR at the sidewall for α > 8°, and all the guided light will be redirected by TIR for α > 41.2°. However, only the redirected light falling into the top-surface escape cone can be extracted from the top surface. In this case, these three angle values should meet the relationship,

To check the feasibility of the design method for the inclined sidewall, the impacts of the inclination angle on the LEEs for TM-polarized emission were further simulated, and the results thus obtained are shown in Fig. 6(f). It can be seen that the LEE of the n-AlGaN sidewalls obviously reduces once α increases to 8° and then gradually decreases to nearly zero as α increases to 41°, which clearly indicates once again that the emission from the n-AlGaN sidewalls is mostly coming from the waveguided light. On the other hand, the LEE of the top surface does not increase until α increases to 25° and then increases gradually to a nearly saturated value as α keeps on increasing to 49°. However, the LEE begins to decrease when α increases beyond 49°, as a result of the redirected light beginning to suffer from a new TIR at the top surface. Thus, the optimal α for the best LEE of the top surface is between (41°, 49°), in which almost all of the side emission is redirected to the top-surface emission. These results demonstrate the effectiveness of the developed design method for an inclined sidewall.

Based on the above results, a new strategy to fully utilize the inherently strong TM-polarized emission in AlGaN-based DUV LEDs, which would otherwise be absorbed inside the device, was further proposed. To this end, an artificial vertical escape channel (named GLRV structure) for TM-polarized light was constructed by adjusting the structures of the p-EBL, MQWs, sidewalls, and using TIR in a positive manner. Where the light is guided laterally in the p-EBL/MQWs–n-AlGaN/AlN waveguide structure to reach the inclined sidewall and is thereafter redirected vertically via TIR, thus eventually escapes through the top surface. Specifically, as the p-EBL layer can function as a TIR barrier for the generated light to enter the absorptive p-GaN layer, its refractive index should be designed as low as possible to increase the refractive index contrast between the p-EBL and the MQWs, thus blocking as much light as possible to weaken the adverse effect of the p-GaN layer. On the other hand, the MQWs will cause severe light trapping and light loss when its refractive index is higher than that of the adjacent layers. Thus, their refractive index contrast should be minimized as much as possible to reduce the light loss inside the MQWs. By this two means, the designed p-EBL/MQWs–n-AlGaN/AlN waveguide structure can effectively guide the TM-polarized light laterally to reach the inclined sidewall by multiple reflections. Further, the inclined sidewall can be optimized to maximize the redirected top-surface emission base on the developed design method.

To check the effectiveness of the artificial vertical escape channel, a single GLRV structure was constructed in the 300 × 300 µm² chip, and then its impacts on the LEEs were simulated. The refractive indices of the p-EBL and the MQWs were set to 2.3, 2.4, respectively. The inclined angle was set to 45°.

Shown in Fig. 7(a) is a representative simulated far-field emission pattern for TM-polarized emission from the AlGaN-based DUV LED with the GLRV structure. (The emission patterns of other degrees of polarization are similar and thus not shown here). Compared to the conventional chip (Fig. 2(f)), the GLRV structure exhibits significantly enhanced emission from the top surface and reduced emission from the epilayer sidewalls, thereby providing a more convergent emission pattern and stronger emission intensity along the axial direction, which is practically desirable for LED applications. In addition, the GLRV structure also exhibits a top-surface dominant emission, where the top-surface emission amounts to 66.9% of the total emission, whereas this value is only 4.3% in the conventional chip. These results demonstrate that the artificial vertical escape channel can not only improve the top-surface LEE but also achieve a more useful emission pattern.

 

Fig. 7. Impacts of the GLRV structure on the LEEs. Far-field emission pattern for TM-polarized emission in a 300 × 300 µm² chip with a single GLRV structure (a) and a 4 × 4 micro-GLRV array structure (d). Enhancement times (b) and normalized enhancement (c) of the top-surface LEE for different degrees of polarization as a function of chip size. Top-surface LEE (e) and normalized enhancement in the top-surface LEE (f) for the chip with different structures as a function of polarization degree.

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Since the chip size strongly affects the emission from the n-AlGaN sidewalls, it would also affect the enhancement of the top-surface LEE yielded by the artificial vertical escape channel. Therefore, the enhancement of the top-surface LEE as a function of chip size was further simulated. As can be seen from Fig. 7(b), the enhancement times decreases rapidly for all degrees of polarization as the chip size increases, corresponding to the decrease in the emission from the n-AlGaN sidewalls, as shown in Fig. 5(e). The more the TM-polarized emission, the more sensitive the enhancement to the chip size, which can be seen more clearly by normalizing each curve to its corresponding maximum value, as shown in Fig. 7(c). Moreover, the enhancement times increases significantly with the decreasing degree of polarization for the same chip size. Both these results can be satisfactorily explained by the fact that as the degree of polarization decreases, the contribution of the top-surface emission to the total LEE decreases, whereas the emission from the n-AlGaN sidewalls increases. In particular, for TM-polarized emission, the enhancement times suffers a serious exponential decrease and thus a substantial decrease in the top-surface LEE, which could pose a severe problem for the large-area DUV-LEDs required to sustain high-injection current for high-power applications. Therefore, special design solutions should be elaborated to avoid huge light loss in large-area devices.

Since the emission from the n-AlGaN sidewalls is sensitive to the chip size, decreasing the light path traveling in the waveguide structure should be an efficient approach to enhance the side emission, and consequently, more top-surface emission is attained by redirecting. It has been reported that the micro-cell array design is a powerful approach that alleviates current crowding and efficiency droop for large-area AlGaN LEDs due to the intrinsic high resistivity of Al-rich AlGaN [21,52]. More importantly, the micro-cell array design should play an important role in the extraction of TM-polarized light as it can reduce the traveling path of light reaching the sidewall [18–21]. Therefore, a 4 × 4 micro-GLRV array structure was further constructed within the 300 × 300 µm² chip area, and then the impacts on the LEEs were simulated. In these simulations, 40,000 light rays were generated for each micro-GLRV MQWs, thus the total number of rays is 640,000.

As can be seen from Fig. 7(d), the micro-GLRV array structure also shows a favorable emission pattern, as expected. From Fig. 7(e), it can be seen that the top-surface LEE drops drastically as the portion of TM-polarized emission increases in the conventional chip due to the intrinsic propagation manner of the TM-polarized light. However, the GLRV structure can overcome such an inherent defect, removing the polarization-dependent effect on the light extraction and thus maintaining a high top-surface LEE for TM-polarized emission. Further, by combining the GLRV structure with the micro-cell array design, the enhancement effect can be maximized further. These phenomena can be explained by the fact that the artificial vertical escape channel can considerably enhance the top-surface LEE for all degrees of polarization, but it is particularly efficient for TM-polarized emission. As is observed more clearly by normalizing the enhancement for each degree of polarization in Fig. 7(f), the enhancement times increases with the decreasing degree of polarization, especially the enhancement times for TM-polarized emission is up to 18 by a single GLRV structure, and further increases to 25 by dividing this single GLRV structure into a 4 × 4 micro-GLRV array structure. These results indicates that the micro-GLRV array structure should be an ideal design solution for the large-area DUV LEDs for high-power applications, which not only alleviates current crowding and efficiency droop, but also significantly increases top-surface LEE. In theory, the smaller the micro-GLRV size, the more enhancement in top-surface LEE that should be expected since the lateral traveling path for light is considerably reduced. Nevertheless, the Shockley-Read-Hall non-radiative recombination caused by surface recombination and sidewall damage becomes increasingly deleterious to IQE as the micro-cell size decreases and the surface-area-to-volume ratio increases [53,54]. The experimental results indicate that the non-radiative recombination coefficient increases rapidly as the chip is smaller than 40 × 40 µm² [53]. Since the EQE is the product of the IQE and the LEE, therefore a trade-off exists between the EQE and the micro-GLRV dimension.

4. Conclusion

In summary, a systematic and comprehensive study on the polarization-dependent light extraction mechanisms of AlGaN-based DUV LEDs has been carried out using simple but effective Monte Carlo ray-tracing simulations with Snell's law. The in-depth device physics corresponding to the polarization-dependent light extraction mechanisms has been explored, the light extraction behavior of each escape route has been clearly elucidated, and the fundamental limitations of LEE for AlGaN-based DUV LEDs have also been revealed. Based on the simulated results, a new strategy for designing the p-EBL and MQWs has been developed, i.e., not only considers their impact on carrier transport, but also photon propagation, which is especially critical for the light extraction of TM-polarized light. Further, an artificial vertical escape channel has been constructed to efficiently extract the TM-polarized light through the top surface, by adjusting the structures of the p-EBL, MQWs, sidewalls, and using TIR in a positive manner. Consequently, a high top-surface LEE and favorable emission pattern for the DUV LED dominated by TM-polarized emission have been achieved. The enhancement times of the top-surface LEE increases drastically as the degree of polarization decreases. In particular, for TM-polarized emission, the enhancement times is up to 18 in the 300 × 300 µm² chip comprising a single GLRV structure and increases further to 25 by dividing this single GLRV structure into a 4 × 4 micro-GLRV array structure. By optimizing design of the structures of the p-EBL/MQWs and the micro-GLRV size, such as inserting a thin BAlN interlayer with a lower refractive index than AlN between the p-EBL and the MQWs, or further decreasing the micro-GLRV size, a higher top-surface emission can be expected. This work is significant for understanding and modulating the extraction mechanisms of polarized light to realize high-efficiency and high-power AlGaN-based DUV LEDs.