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Enhancing the light extraction efficiency for AlGaN-based DUV LEDs with a laterally over-etched p-GaN layer at the top of truncated cones

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Abstract

It is known that light extraction efficiency (LEE) for AlGaN-based deep ultraviolet light-emitting didoes (DUV LEDs) can be enhanced by using truncated cone arrays with inclined sidewalls. In this work, the air-cavity-shaped inclined sidewall is applied and the p-GaN layer at the top of the truncated cone is laterally over-etched so that more light escape paths are generated for AlGaN-based DUV LEDs. The experimental results manifest that when compared with DUV LEDs only having the air-cavity-shaped inclined sidewall, the optical power for the DUV LEDs with laterally over-etched p-GaN at the top of the truncated cone is enhanced by 30% without sacrificing the forward bias. It is because the over-etched p-GaN makes little effect on the carrier injection and does not affect the ohmic contact resistance. Moreover, the simulation results show that the truncated cone with laterally over-etched p-GaN layer can enhance the LEE because the reduced p-GaN area can suppress the optical absorption and supplies additional light paths for DUV photos. Then, more light will be reflected into escape cones at the sapphire side.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

AlGaN-based deep ultraviolet light-emitting diodes (DUV LEDs) have a wide range of potential applications in the fields of communication, photo-ionization, water purification, printing, medical diagnostics and plant lighting because of their narrow spectra, smart design, energy conservation and environmental friendliness [15]. However, DUV LEDs now still confront the low optical power and low external quantum efficiency (EQE). At present, the reported EQE for AlGaN-based DUV LEDs grown on sapphire substrate is typically lower than 10% [6]. The low EQE in AlGaN-based DUV LEDs are mainly caused by the low light extraction efficiency (LEE), which results from the large refractive index contrast between AlGaN material and air. The p-GaN layer can also strongly absorb the DUV photons [7], which is another reason for the extremely low LEE for AlGaN-based DUV LEDs. Moreover, the increasing portion of the transverse magnetic (TM) polarized light that features the in-plane propagation will further decrease the escape probability for the photons, such that most of the TM-polarized light emits from the sidewalls for DUV LEDs [8]. For the purpose of enhancing the LEE, various methods have been proposed such as roughening the DUV LEDs surface [9,10], growing DUV LEDs on nanopatterned sapphire substrate [1113], utilizing advanced metal reflectors [1416] and fabricating inclined sidewalls [1719]. Among those technologies, the design of inclined sidewall shows tremendous potential in enhancing the LEE for both TM- and TE- polarized light. It is because the inclined sidewall structures can scatter the laterally propagating light that includes TM- and TE- polarized light into the escape cones for the c-plane [20]. Investigations indicate that inclined sidewall structures can more effectively improve the EQE when the mesa size decreases. However, consideration has to be taken, because small mesas can sacrifice the emissive area, which may lead to the decreased optical power [18]. Therefore, the mesas with inclined sidewalls have to be optimized so that the optical reflection by the inclined sidewalls can be fully increased. In addition, to further enhance the LEE of DUV LED with inclined sidewall, the omni directional reflector (ODR) structure also is proposed to increase the reflectivity of inclined sidewall [21]. As a matter of fact, it is less possible for the metal reflector on the inclined sidewalls to obtain the reflectivity of 100%. However, a hybrid structure made of the air cavity and the inclined sidewalls with optimum inclination angle can enable the total internal reflection so that a 100% optical reflectivity can be possible [22,23]. Although great progress has been made in fabricating DUV LEDs with inclined sidewalls, the strong optical absorption by the p-GaN layer still greatly limits the further enhancement for the LEE. The micro-ring structured p-GaN region has been fabricated to further enhance the LEE for inclined-sidewall-shaped DUV LEDs. In this device, the center region for the p-GaN layer is etched and the p-GaN ring can be obtained [24]. However, the series resistance becomes increased due to the decreased ohmic contact area. Therefore, it is important to find another effective way to improve the LEE without sacrificing electrical property for inclined-sidewall-shaped DUV LEDs.

Our previous work finds that the air-cavity-shaped inclined sidewall is more beneficial for the performance of DUV LEDs. And for the inclined-sidewall-shaped DUV LEDs with truncated cone arrays, the radiative recombination mainly occurs at the center for each truncated cone [25]. Thus, we conclude that the periphery for each truncated cone mesa makes less contribution to the optical power when compared to the center region. Furthermore, the optical absorption effect by the periphery p-GaN layer on the truncated cone mesa further decreases the photons coming out from the periphery of the truncated cone mesa. Therefore, in this work, we propose a truncated cone structure with laterally over-etched p-GaN layer to further improve the LEE for DUV LEDs, i.e., the periphery p-GaN layer on the truncated cone mesa is partially etched. Experimental results show that the enhanced LEE dramatically improve the light output power (LOP) for the DUV LED with the proposed laterally over-etched p-GaN at the top of the truncated cone structure. More importantly, such design with reduced p-GaN does not increase the forward bias for DUV LEDs due to the constant p-type ohmic contact area.

2. Experiment

AlGaN-based DUV LED wafer is grown on sapphire substrate by using metal organic chemical vapor deposition (MOCVD) system. First, we grow a 2 μm-thick AlN buffer layer on the sapphire substrate. Then, a 1.0 µm-thick Si-doped n-Al0.60Ga0.40N is grown as the electron injection layer. Next, five periods of 3-nm-thick Al0.45Ga0.55N/12-nm-thick Al0.56Ga0.44N multiple quantum wells (MQWs) are designed. After that, a 20 nm-thick Mg-doped p-Al0.60Ga0.40N electron blocking layer (p-EBL) is grown before it is capped by a 50 nm-thick p-Al0.40Ga0.60N layer and a 50 nm-thick p-GaN layer.

After growing the DUV LED epitaxial wafers, the wafers are fabricated into the truncated cone-shaped array with the matrix of 14×14 by using photolithography and dry etching. Figure 1(a) shows the detailed flow charts for making different DUV LEDs with conventional inclined sidewall (Device 1) and the proposed inclined sidewall with laterally over-etched p-GaN layer (Device 2) by using processes A and B, respectively. For Devices 1 and 2, the diameter for each truncated cone is 20 µm and the distance between two adjacent truncated cones is 25 µm. The Ti/Al/Ti/Au multi-layers are used as the n-contact, which is annealed in the N2 ambient for 1 min at the temperature of 650 ℃ and the Ni/Au as p-electrode is fabricated by using photolithography and electron-beam deposition processes for both Devices 1 and 2, which is annealed in the O2 ambient for 3 min at the temperature of 450 ℃. For Device 1, a layer of 100 nm thick SiO2 is deposited at the growth temperature of 80 ℃. The deposited SiO2 layer is patterned and etched so that the Ni/Au p-electrode can be exposed. Then, a 5 µm-width Al/Ti/Au metal belts are evaporated on the wafers to connect all Ni/Au p-ohmic contact electrodes on truncated cone array [see Fig. 1(a)]. Device 2 is fabricated by following process B as shown in Fig. 1(a). The deposition and the thermal annealing processes for the n- and p-type electrodes are the same as that for Device 1. However, the additional fabrication steps are conducted: the low temperature SiO2 layer is used as the hard mask to etch the periphery p-GaN layer on the truncated cones, and the radius for the remaining p-GaN layer is 6 µm now. After that, the residual SiO2 layer is removed by using buffer oxide etchant (BOE). The next process of depositing SiO2 passivation layer and evaporating Al/Ti/Au are the same as Device 1. By using the conventional fabrication process [26], a conventional plane device as Reference is also fabricated that has the continuous p-GaN layer at the mesa region. The size for all the devices is 350 × 350 µm2 and they are not encapsulated. Figures 1(b)-(d) show top view for Reference, Devices 1 and 2 under the optical microscope. It can be seen from Figs. 1(c) and (d) that the truncated cone arrays for Devices 1 and 2 have been connected by Al/Ti/Au belts to form air-cavity-shaped inclined sidewall. The air cavity structure can improve effectively the reflectivity of inclined sidewall by total internal reflection leading to the enhanced LEE for DUV LEDs [25].

 figure: Fig. 1.

Fig. 1. (a) Process flow charts for DUV LEDs with inclined sidewall (Process A) and the proposed inclined sidewall with laterally over etched p-GaN layer (Process B). (b)-(d) Top views for Reference, Device 1 and Device 2 under the optical microscope.

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3. Results and discussion

After depositing the p-electrode and etching the periphery p-GaN layer on the truncated cones, the atomic force microscopy (AFM) is used to probe the surface morphology for Devices 1 and 2, which are shown in Figs. 2(a) and (b), respectively. It can be seen that the truncated coned arrays have been fabricated for Devices 1 and 2. The comparison between Figs. 2(a) and (b) indicates that the p-GaN layer on the truncated cone for Device 2 has been laterally over etched. To attain the inclined angle for the truncated cones and the thickness of the laterally over etched p-GaN, AFM profiles of line along truncated cones for Devices 1 and 2 are shown in Fig. 2(c). It can be found that the height of a truncated cone is about 800 nm and the inclined angle can be calculated to be about 40°. We can also get that the top diameter of truncated cone is about 20 µm, which is consistent with our design. The bottom diameter is tested to be 22 µm and is larger than 20 µm, which may be caused by the reflow of photoresist during ICP etching. To attain the thickness of laterally over etched p-GaN for Device 2, the height of the periphery p-GaN layer for Devices 1 and 2 is zoomed in as shown in the inset of Fig. 2(c). It can be seen that there is a small step for the blue line profile for Device 1 caused by Ni/Au p-ohmic contact electrodes on truncated cone array. Then we can get from the inset of Fig. 2(c) that the height of mesa for Device 1 is about 780 nm and the thickness of the p-electrode is 20 nm. In addition, the step for the red line profile for Device 2 is caused by both Ni/Au p-ohmic contact electrodes and laterally over etched p-GaN. The height is about 70 nm. Hence, the thickness of laterally over etched p-GaN for Device 2 can be calculated to be about 50 nm, which indicates that the periphery p-GaN on the truncated cone arrays for Devices 2 has been removed completely because the thickness of p-GaN layer for the DUV LED wafer is 50 nm.

 figure: Fig. 2.

Fig. 2. AFM 3D image of the (a) Device 1 and (b) Device 2. (c) Height as a function of position of truncated cones for Devices 1 and 2. Inset in Fig. 2(c): large version of periphery p-GaN layer.

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Figure 3(a) shows the current-voltage (I-V) curves for all studied devices. The forward bias at the current of 30 mA for Reference device, Devices 1 and 2 are 13.64 V, 14.92 V, 14.99 V, respectively. The forward biases for Devices 1 and 2 (DUV LEDs with inclined sidewalls) are higher than that for Reference device. Obviously, the effective mesa areas for Devices 1 and 2 are smaller than that for Reference device. Hence, compared with Reference, the series resistance for Devices 1 and 2 will increase leading to the higher voltage. In addition, according to the AFM test results in Fig. 2, the ratio of p-GaN area for Device 2 to Device 1 is only about 36%. Etching periphery p-GaN for Device 2 will increase the resistance for p-GaN. However, it is surprising that the I-V curves for Devices 1 and 2 are almost same, which means that etching periphery p-GaN makes little effect on the electrical properties for the inclined-sidewall-shaped DUV LEDs. Normally, the work voltage for LED is determined by the combination of the voltage drop at the p-n junction, resistances for both n- and p-type semiconductors and ohmic contact resistances. But it is very difficult for DUV LEDs to get low ohmic contact resistances for both p-GaN and n-AlGaN. Hence, the ohmic contact resistance on n-AlGaN and p-GaN are dominant for AlGaN-based DUV LEDs [24]. For Device 2, the part of p-GaN uncovered by the electrode is proposed to be etched and the laterally over-etched p-GaN layer structure does not sacrifice the electrode contact area. As a result, although etching periphery p-GaN for Device 2 will increased the resistance for p-GaN, the forward biases for Devices 1 and 2 are almost same because the ohmic contact areas for the two devices are same. The inset in Fig. 3(a) shows the current-voltage characteristics for all devices under reverse voltage. It can be seen that the leakage current for Device 1 and Device 2 are larger than Reference due to the sidewall defect from the truncated cones. However, the leakage currents for Device 1 and Device 2 are similar. It is because the etched p-GaN depth is far smaller than the height of mesa structure. And the etched p-GaN is far away from the active region of DUV LED. Therefore, compared with Device 1, the leakage current of Device2 is not deteriorated by the laterally over-etched p-GaN. In addition, the breakdown voltage for Device 1 and Device 2 are also similar because both the ohmic contact area and the area of active region are same for Device 1 and Device 2. The inset in Fig. 3(b) shows the electroluminescence (EL) spectra at the injection current of 30 mA. The EL spectra for the three devices are measured from the sapphire side through a calibrated integrating sphere at room temperature. The peak wavelengths for all devices are ∼280 nm, which means that the fabricating process of truncated cone does not shift the wavelength. It also shows that the EL intensities for all the DUV LEDs with inclined sidewalls are higher than that for Reference. And the EL intensity for Device 2 is higher than that for Device 1. The detailed comparison about the optical power for the three devices can be found from the optical power-current curves in Fig. 3(b). The optical powers for Devices 1 and 2 are enhanced by 104% and 155% at the injection current of 30 mA when compared with Reference device. The enhanced optical power for inclined-sidewall-shaped DUV LEDs can be attributed to the higher LEE caused by the reflection escape cone from the inclined sidewall [25]. In addition, Device 2 shows the highest optical power. Compared with Device 1, the optical power for Device 2 is enhanced by 30% at the injection current of 30 mA. It is because etching periphery p-GaN layer for Device 2 can decrease effectively the optical absorption from p-GaN. Note, since the chip is not packaged and is tested on wafer, the heat dissipation performance for the devices are very poor. Hence, as the current increases, the optical power fast reach saturation point and then drop due to the serious thermal effect as we can see in Fig. 3(b). The optical power curves for Devices 1 and 2 reach faster the rollover points than that for Reference, which is due to the lower current density for Reference device under same inject current.

 figure: Fig. 3.

Fig. 3. (a) Current-voltage characteristics for Reference, Devices 1 and 2. Inset: current-voltage characteristics for Reference, Devices 1 and 2 under reverse voltage. (b) Optical power as a function of the injection current for Reference, Devices 1 and 2. Inset: EL spectra for Reference, Devices 1 and 2 at the injection current of 30 mA.

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Furthermore, the effect of etching the periphery p-GaN layer on the electrical characteristics for DUV LEDs with inclined sidewalls is explored by using APSYS, which manages to solve Poisson’s equation, Schrodinger equation, the current continuity equation and the drift-diffusion equation consistently. The detailed setting parameters can be found in Refs. [27] and [28]. We compute the internal quantum efficiency (IQE) and the radiative recombination distribution in multiple quantum wells (MQWs) for Devices 1 and 2. Figure 4(a) shows IQE in terms of the current for Devices 1 and 2. It can be seen that the IQE for Device 2 become slightly lower than that for Device 1 due to the etched periphery p-GaN. It can be concluded from Fig. 4(a) that the IQE for Device 2 is reduced by 0.54% at the current density of 50 A/cm2. In order to explain the reason for decreased IQE, the radiative recombination rate profiles in the first quantum well for the two devices are shown in Fig. 4(b). It can be found that the radiative recombination rate for Device 2 is higher than that for Device 1 in the middle region of the quantum well while it becomes lower in the peripheral region. Note, periphery p-GaN is etched that can decrease the current spreading effect leading to a high local hole concentration under the p-electrode for Device 2. As a result, the IQE for Device 2 becomes decreased. If we compare Figs. 3(b) and 4(a), we also conclude that the enhanced optical power for Device 2 is more likely attributed to the improved LEE.

 figure: Fig. 4.

Fig. 4. (a) IQE in terms of the injection current density. (b) Radiative recombination rate profiles in the first quantum well for Devices 1 and 2.

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We then analyze the LEEs for Devices 1 and 2 by using Lumerical FDTD solution. Figure 5 illustrates the simulation models for Reference device, Devices 1 and 2. All the simulation parameters are set according to the experimental structures. However, due to the limitation of computer memory, the thickness of sapphire substrate is reduced to 500 nm, and the lateral size for simulation structure is set to 120 µm. The boundary conditions for the two lateral boundaries are set as metal with 100% reflectivity so that the limited lateral dimensions can be deemed as infinity [29]. In addition, to make the filling factor for the 2D simulation model consistent with the realistic device, the top diameter and the period for truncated cones are set to 20 µm and 40 µm, respectively. As Fig. 4(b) has demonstrated, the light is mainly emitted from the middle position of the quantum well for both Devices 1 and 2. Hence, a single dipole source is placed at the center of the MQW region as the light source for LED. The dipole source is polarized in the direction either parallel to the Y-axis for TM-mode light or parallel to the X-axis for TE-mode light. The peak emission wavelength of the dipole source is set to 280 nm in our model. The top and bottom boundary conditions are set as perfectly matched layers (PMLs) to completely absorb the electromagnetic energy [30]. Furthermore, a non-uniform mesh with the smallest mesh size of 5 nm is applied for accurately calculating the LEE, which is defined as the ratio between the total extracted power collected from the power monitor and the total light power emitted from dipole source.

 figure: Fig. 5.

Fig. 5. Schematic diagram of 2D-FDTD simulation models for Reference device, Devices 1 and 2.

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Figures 6(a) and 6(b) show the LEEs for TM- and TE-polarized light for Reference device, Devices 1 and 2. It shows that the LEEs of the TM- and TE- polarized light for Reference device are 1.47% and 8.9%, respectively. The LEE for the TM- polarized light is far lower than that for the TE- polarized light as a result of lateral propagation of the TM-polarized light. Furthermore, it can be found that a significant enhancement of the LEEs for TM- and TE-polarized light occurs in Device 1 and Device 2 when the inclined sidewalls are applied. When compared with the Reference device, the LEEs of the TM- and TE-polarized light for Device 1 (Device 2) are enhanced by 700% and 68% (880% and 92%), respectively. It is because the inclined sidewalls provide more reflection escape cones and then the LEE is enhanced [20]. All the light propagating into the reflection escape cones can be reflected into external space by the inclined sidewalls. In addition, Device 2 with laterally over-etched p-GaN shows the largest LEE. When compared with Device 1, the LEEs of the TM- and TE-polarized light for Device 2 are enhanced by 23% and 14%, respectively, and this is attributed to the fact that the absorption is reduced after the periphery p-GaN is removed. Here, by comparing Figs. 4(a), 6(a) and 6(b), we can confirm that the increased optical power for Device 2 in Fig. 3(b) is uniquely ascribed to the enhanced LEE.

 figure: Fig. 6.

Fig. 6. LEEs for (a) TM- and (b) TE-polarized light for Reference device, Devices 1 and 2.

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To better understand the observations in Figs. 6(a) and (b), the electric field distributions in the XY cross section for the TM-polarized light in Devices 1 and 2 are shown in Figs. 7(a) and (b). It can be found that the internal electric field intensity for Device 2 in Fig. 7(b) is stronger than that for Device 1 in Fig. 7(a). Moreover, it can also be observed that Device 2 has the more uniform electric field distribution for than Device 1. It means that before the photons are absorbed, they can be scattered more times in Device 2 than in Device 1. The reduced number of reflection times arises from the more significant optical absorption by the periphery p-GaN layer on the truncated cone mesa for Device 1. The light propagation paths in Devices 1 and 2 are also indicated in Figs. 7(a) and (b). The removal of the periphery p-GaN layer can provide the addition propagation path ④ for Device 2. The intensity of extracted light at the position of the monitor in terms of the position for Devices 1 and 2 are shown in Fig. 7(c). Note, Fig. 7(c) only shows the light intensity in the right half for the simulated structures due to the symmetric optical profiles in Figs. 7(a) and (b). There are three main peaks indicated in Fig. 7(c). Peak ① is from the light that is emitted from the light source and propagates directly into the escape cone as indicated by light path ① shown in Figs. 7(a) and (b). According to Snell’s Law, the angles are calculated to be -22.62° ∼ 22.62° as the fundamental escape cone. Peak ③ originates from path ③ shown in Figs. 7(a) and (b), which is reflected into escape cone by inclined sidewalls after being scattered many times. Figure 7(c) shows that the intensity for peaks ① and ③ for Devices 1 and 2 are similar. Hence, the difference of the LEE for Devices 1 and 2 is mainly from the peak ②. We zoom-in peak ② in the inset of Fig. 7(c). We can clearly see that the intensity of peak ② for Device 2 is larger than that for Device 1. Therefore, the higher LEEs for Device 2 mainly result from the larger intensity of peak ② for Device 2. For Device 1, peak ② is from the light directly reaching the inclined sidewall and then reflected into the escape cone by following light path ② [see Fig. 7(a)]. To make more light reflected into the escape cones by inclined sidewall with 40° inclination angle, the incident angle α for the light reaching the inclined sidewall shall satisfy the condition of 17.38° < α < 62.62°. Then, the angle scope is transformed into the θ coordinate system as shown in Fig. 7(d). The corresponding angle scope is 77.38° < θ < 122.62°, which is defined as the reflection escape cone in Fig. 7(d). For Device 2, peak ② in Fig. 7(c) comes from both the light paths ② and ④ as shown in Fig. 7(b). The emitted light that reaches the range of the laterally over-etched p-GaN will be totally internally reflected towards the inclined sidewall. According to the structural parameters for Device 2, the angle range of light path ④ is calculated to be 91.2° ∼ 92.41°after being reflected by the top interface, which is fully within the angle scope of the reflection escape cone, such that, these beams will be reflected into escape cone again by the inclined sidewall. Therefore, etching periphery p-GaN supplies additional light escape path i.e. light path ④ and makes more light reflected into escape cone by the inclined sidewall. This leads to the increased intensity of peak ② for Device 2.

 figure: Fig. 7.

Fig. 7. Electric field distributions in the XY cross section and schematic diagrams for the propagation paths of the TM-polarized light for (a) Device 1, (b) Device 2. Optical beam paths of ①, ② and ③ denote different propagations paths in all Devices. (c) Optical intensity of extracted light versus the position. (d) Angle scope of various escape cones in the θ coordinate system. Inset in Fig. 7(c) shows the zoom-in peak ②

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4. Conclusions

In summary, we have experimentally removed the periphery p-GaN to engineer the photon propagation for AlGaN-based inclined-sidewall-shaped flip-chip DUV LEDs. Both experimentally and numerically, the inclined-sidewall-shaped DUV LEDs with laterally over-etched p-GaN is superior to the conventional inclined-sidewall-shaped cones. Etching periphery p-GaN effectively suppresses the optical absorption by the p-GaN layer and supplies additional light escape paths. Therefore, the laterally over-etched p-GaN can enhance the LEE without deteriorating the electrical property due to the unaffected ohmic contact area for inclined-sidewall-shaped DUV LEDs. We strongly believe that the findings in this work can help the community further understand the photon propagation process and increase the LEE for AlGaN-based DUV LEDs.

Funding

National Natural Science Foundation of China (61975051, 62074050); Natural Science Foundation of Hebei Province (F2018202080, F2020202030); State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology (EERI_PI2020008).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. (a) Process flow charts for DUV LEDs with inclined sidewall (Process A) and the proposed inclined sidewall with laterally over etched p-GaN layer (Process B). (b)-(d) Top views for Reference, Device 1 and Device 2 under the optical microscope.
Fig. 2.
Fig. 2. AFM 3D image of the (a) Device 1 and (b) Device 2. (c) Height as a function of position of truncated cones for Devices 1 and 2. Inset in Fig. 2(c): large version of periphery p-GaN layer.
Fig. 3.
Fig. 3. (a) Current-voltage characteristics for Reference, Devices 1 and 2. Inset: current-voltage characteristics for Reference, Devices 1 and 2 under reverse voltage. (b) Optical power as a function of the injection current for Reference, Devices 1 and 2. Inset: EL spectra for Reference, Devices 1 and 2 at the injection current of 30 mA.
Fig. 4.
Fig. 4. (a) IQE in terms of the injection current density. (b) Radiative recombination rate profiles in the first quantum well for Devices 1 and 2.
Fig. 5.
Fig. 5. Schematic diagram of 2D-FDTD simulation models for Reference device, Devices 1 and 2.
Fig. 6.
Fig. 6. LEEs for (a) TM- and (b) TE-polarized light for Reference device, Devices 1 and 2.
Fig. 7.
Fig. 7. Electric field distributions in the XY cross section and schematic diagrams for the propagation paths of the TM-polarized light for (a) Device 1, (b) Device 2. Optical beam paths of ①, ② and ③ denote different propagations paths in all Devices. (c) Optical intensity of extracted light versus the position. (d) Angle scope of various escape cones in the θ coordinate system. Inset in Fig. 7(c) shows the zoom-in peak ②
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