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Abstract
In this report, the impact of different mesa designs on the optical and electrical characteristics for GaN-based micro-light emitting diodes (µLEDs) has been systematically and numerically investigated by using TCAD simulation tools. Our results show that an enhanced light extraction efficiency can be obtained by using beveled mesas. The inclined mesa angles can more effectively reflect the photons to the substrate, and this helps to extract the photons to free air for flip-chip µLEDs. However, it is found that the current injection is influenced by inclination angles for the investigated µLEDs, such that the beveled mesas make stronger charge-coupling effect and increase the electric field magnitude in the multiple quantum wells at the mesa edge, so that the carriers cannot be effective consumed by radiative recombination. As a result, this gives rise to stronger defect-induced nonradiative recombination at mesa surfaces. Therefore, there are tradeoffs between the LEEs and IQEs when changing the beveled angle, to maximize external quantum efficiency for GaN-based µLEDs, the beveled mesa angle shall be carefully designed and optimized.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
When compared to the conventional liquid crystal display (LCD) and organic light-emitting diode (OLED) display [1,2], the III-nitride based micro-light emitting diode (µLED) display has attracted extensive research attention owing to the advantages of high resolution and brightness, low consumption, and long lifetime. Over the last few decades, GaN-based µLEDs have shown potential applications in such as ultra-high-resolution display, flexible wearable devices, and virtual/augmented reality [3,4]. Meanwhile, µLEDs are also suitable candidates for visible light communication (VLC) and underwater communication due to the excellent property of high modulation bandwidth and data safety [5,6]. Despite the promising prospective for µLED-based systems, there are still several technological challenges required to be solved, such as mass transfer, full-color conversion and damage-repairing technology [7–9]. Furthermore, a low external quantum efficiency (EQE) for µLED is also a key obstacle for making high-quality optoelectronic systems [10]. Firstly, although the enhanced current spreading and reduced thermal heating effect can be obtained with the decrease of µLED size [11,12], such a µLED with decreased size also has an increased surface-volume ratio. It is well known that surface defects can be generated at the sidewall surface during the mesa etching process, which serve as nonradiative recombination centers and decrease the internal quantum efficiency (IQE) especially for the µLED with even smaller chip size [13,14]. Hence, countermeasures have been proposed to suppress the sidewall defects and increase the IQE. On one hand, during the µLED fabrication process, a convenient method to eliminate the surface defects is to deposit the dielectric passivation layer on the mesa surface, which is mainly doable by using the plasma-enhanced chemical vapor deposition (PECVD) method or atomic layer deposition (ALD) [15,16]. Chemical-etching treatment is also conducted together with sidewall passivation to further reduce the surface defect density [17,18]. Besides optimizing the chip fabrication process, managing the carrier transport paths is an alternative approach to minimize the defect-induced nonradiative recombination, i.e., one can keep free carriers apart from the defective mesa surface [19,20].
In addition to the surface-damage-caused low IQE, the EQE is also affected by the light extraction efficiency (LEE). Previous studies have demonstrated that decreasing the LED size helps to enhance the LEE, which is attributed to the fact that more light escapes from mesa sidewalls [10,11]. However, for conventional flip-chip µLEDs, such light propagations shall be tuned in the way of being extracted from the substrate rather than the sidewalls. For achieving that goal, a highly reflective Ag metal contact that is fabricated by using electron beam irradiation is proposed [21]. The light beams can be even better guided by using an omnidirectional-reflector (ODR) based passivation layer, which can effectively reflect the light from the sidewall region to the substrate [22]. The similar purpose can be achieved by adopting the superlattice (SL)/GaN DBR structure to replace the entire p-type region, which can also effectively enhance the LEE [23]. It is worth noting that a natural dry etching process even without specific treatment will produce mesa with an inclination angle of ∼ 35° [24]. Hence, an inclined mesa favors the optical reflection towards the substrate and can be an easier approach to increase the LEE [25,26]. However, in this work, we find that in spite of the enhanced LEE, inclined mesas generate coupled electric field at the mesa edge of the quantum wells, which suppresses the radiative recombination and thus gives rise to the surface nonradiative recombination. Thus, the optimized mesa angle shall be achieved, and the impact of the mesa angles on the surface nonradiative recombination shall also be discussed for GaN-based µLEDs.
2. Device structure and numerical parameters
To investigate in-depth the effect of beveled mesa angles on the optoelectronic performance for GaN-based µLED, different µLED structures are designed. All µLEDs consist of a 4-µm-thick n-type GaN layer with the Si doping concentration of 5 × 1018 cm-3, on which four periods of 3-nm In0.15Ga0.85N/8-nm GaN multiple quantum wells (MQWs) follow. A 20-nm-thick p-type Al0.12Ga0.88N electron blocking layer (p-EBL) covers the top of MQWs, and the hole concentration for the p-EBL is set to 3 × 1017 cm-3. Subsequently, a 100-nm-thick p-GaN layer with the hole concentration of 3 × 1017 cm-3 is employed as the hole injection layer. Then, a 20-nm-thick heavily doped p+-GaN layer is adopted for achieving the p-type ohmic contact. In this work, we design five µLEDs with the beveled mesa angles of 45°, 53°, 63°, 79°, and 90°, respectively. The dimension and mesa height for all the devices are set to 20 × 20 µm2 and 702 nm, respectively. Detailed information can be found in Table 1.
Table 1. Beveled angles setting for different devices. Note, the sidewall defects are considered only for Devices I, II, III, IV and V
We firstly utilize the two-dimensional finite-difference time-domain (2D FDTD) simulation to analyze the light extraction efficiency for different devices. A single dipole source with the peak wavelength of 450 nm is placed at the center of the MQW region as the light source, and a reflector is set on the top of the device. The absorption coefficient for the InGaN layer is set to 2000 cm-1 [27]. The refractive indices for the GaN, InGaN, and the sapphire are assumed to be 2.45, 2.6 and 1.78 [28], respectively. The boundary conditions are both set to be perfectly matched layer (PML). The optical monitor is placed at 500 nm below the sapphire layer to collect the light emitted from the bottom. The LEE is defined as the ratio between the total extracted power collected from the power monitor and the total light power emitted from dipole source. Furthermore, detailed investigations into physics on semiconductor device are conducted by using APSYS software, which can self-consistently solve the drift-diffusion equation, Poisson’s equation and Schrödinger equation with proper boundary conditions. The energy band offset ratio of the conduction/valence band is set as 70/30 for InGaN/GaN MQWs [29]. A 40% polarization level is considered for calculating the polarization charges at the lattice-mismatched interfaces [29]. The Auger recombination coefficient and the Shockley-Read-Hall (SRH) recombination lifetime are set as 1 × 10−30 cm6/s and 100 ns [30], respectively. In addition, the SRH nonradiative recombination induced by sidewall defects is also considered for p-type, MQWs and n-type region. The trap level for electrons and holes are located at 0.24 eV below the conduction band (i.e., Ec - 0.24 eV) and 0.46 eV above the valence band (i.e., Ev + 0.46 eV) [31,32], respectively. Furthermore, it is assumed that the capture cross-section and trap density for electron traps are 3.4 × 10−17 cm2 and 1 × 1013 cm−3, respectively, the capture cross-section of 2.1 × 10−15 cm2 and the trap density of 1.6 × 1013 cm−3 are set for holes [31–33]. The width of the defected region at the sidewall is set to 4 µm according to previous reports [14,20]. Other parameters can be found elsewhere [34].
3. Results and discussion
For the purpose of demonstration, we firstly define the Devices 1-5 with the beveled mesa angles of 45°, 53°, 63°, 79° and 90°, respectively. By using 2D FDTD simulation, we calculate the electric field profiles for Devices 1 and 5 with the beveled mesa angles of 45° and 90° in Figs. 1(a) and (b), respectively. It can be found that more light can escape from the sidewall in Device 5 when compared with Device 1. Meanwhile, Fig. 1(c) also shows that the one-dimensional electric field intensity collected by Device 1 is larger than that by Device 5 at the positions around x= -10 and 10 μm. This is attributed to the fact that more light can be reflected at the sidewall interface and is finally extracted from the substrate in Device 1. Furthermore, Fig. 1(d) presents the LEE in terms of the mesa inclination angle for different devices. It is indicated that the LEE increases with the decrease of the inclination mesa angle for µLEDs.
Fig. 1. Electric field distributions in the cross-section and schematic diagrams for the propagation paths of the light for (a) Device 1 and (b) Device 5, respectively. (c) One-dimensional electric field intensity profiles collected at the position of y = -2.5 µm for Devices 1 and 5. (d) Calculated light extraction efficiency for µLEDs with different mesa angles. The arrows in figures (a) and (b) indicate the light propagation paths, such that the black, blue and red arrows represent the light emitted by the source dipole, the light reflected by the mesa sidewall and the light escaping into the air from sidewall, respectively.
Besides investigating the impact of inclined sidewall on the LEE, we also study the effect of inclined sidewall on the electrical properties. We firstly present the hole distribution profiles in p-GaN layer for Devices 1 to 5 without considering any sidewall defects in Fig. 2. It can be found that the hole concentration decreases at the mesa edge for Devices 1 to 4 when compared with Device 5. Such trend becomes most obvious for Device 1 with the smallest mesa inclination angle. We then selectively show the schematic diagrams of the current injection for µLEDs with vertical mesa and beveled mesa in insets (a) and (b) in Figs. 2. It indicates that current is injected straight down into the µLED with vertical sidewall, such that a uniform hole distribution can be obtained in Device 5. However, the ohmic contact area at the top of the device decreases as the mesa angle decreases, which means only the current at the middle of device can inject vertically into the device, then diffuse laterally to the edge of mesa. Accordingly, the hole density at the sidewall region is lower than that in the center of device for Devices 1 to 4 with beveled mesas.
Fig. 2. Lateral hole distribution in the p-GaN layer for different µLEDs at the current density of 100 A/cm2. Insets (a) and (b) refer to the schematic diagram of current injection paths for devices with vertical mesa and beveled mesa, respectively.
Further studies are also carried out to reveal the effect of beveled mesa angle on the electric field in the sidewall region. The electric field profiles along the y-direction in the last quantum well for Devices 1 to 5 are numerically demonstrated in Fig. 3 (a). We define the positive direction of electric field to be along the [0001] orientation. The electric field magnitude increases with the decreasing inclined angle because the beveled mesa can cause charge-coupling effect [35]. It is worth noting that such increased electric field magnitude in sidewall region shall enhance the quantum confined Stark effect (QCSE) therein. To prove that, we selectively show the energy bands in MQWs for Devices 1 and 5 in Figs. 3(b) and (c), respectively. The tilted energy levels for the quantum well are 0.372 eV and 0.207 eV for Devices 1 and 5, respectively. The increased tilted energy level is a manifestation of increased QCSE in the mesa edge for µLEDs with beveled mesas.
Fig. 3. (a) Electric field profiles along the y-direction in the last quantum well closed to the p-EBL for Devices 1 to 5. Energy band profiles along the marked position in the MQW for (b) Device 1 and (c) Device 5. Data are both selected at the current density of 100 A/cm2. Ec, Ev, Efe, and Efh denote the conduction band, the valence band, and quasi-Fermi levels for electrons and holes, respectively.
As has been mentioned previously, the beveled mesa generates charge-coupling effect and increases the electric field magnitude in the mesa edge for µLEDs, which shall affect the bending profile for the lateral energy band. For the purpose of demonstration, the lateral energy band profiles in the last quantum well closest to the p-EBL layer for different µLEDs are presented in Figs. 4(a), (b), (c), (d) and (e), respectively. It is shown that the energy level of the edge region is slightly higher than that in the central area for Devices 1 to 4 when compared with Device 5. We define △φ as the curved level for the lateral energy band between the position of the center and the edge for µLED, and such △φ for different µLEDs are calculated in Fig. 4 (f). It indicates that with the decrease of mesa angle, the bending level of energy band becomes more significant. The results agree well with the trend of electric field profiles in Fig. 3 (a). It is worth noting that, after the holes enter the MQW region from the p-GaN layer, such bending profile for the energy band facilitates the hole spreading to the edge of mesa especially for µLEDs with smaller mesa angles.
Fig. 4. (a)-(e) Lateral energy band profiles in the last quantum well closest to the p-EBL for Devices 1, 2, 3, 4 and 5, respectively. (f) Calculated curved level of the lateral energy band (△φ) for different µLEDs.
For further demonstration, we show the lateral carrier distribution in the last quantum well closest to the p-EBL in Fig. 5(a). Note the carrier concentration in the last quantum well is the highest among the quantum wells. The results illustrate that the hole concentration at the mesa edge increases for Devices 1 to 4 when compared with Device 5. This is consistent with the lateral energy band profiles in Fig. 4. Meanwhile, the electrons are crowded in the center for the device with beveled mesa. We then show the lateral radiative recombination rate in MQWs for different devices in Fig. 5(b). The radiative recombination at the sidewall region decreases as the mesa angle decreases, which is ascribed to the increased QCSE therein. If we study the integrated radiative recombination rate according to the inset for Fig. 5(b), we find that the µLED with beveled mesa possesses the reduced radiative recombination rate. This is caused by the stronger QCSE at the mesa edge that leads to the reduced radiative recombination rate, and the carrier crowding effect in the central mesa may generate larger Auger recombination so that fewer carriers can participate the radiative recombination.
Fig. 5. (a) Lateral hole and electron concentration profiles in the last quantum well closest to the p-EBL, (b) radiative recombination rate in the last quantum well for Devices 1, 2, 3, 4, and 5. Inset in figure (b) shows the integrated radiative recombination rate along with the marked position. Data are both selected at the current density of 100 A/cm2.
Next, the IQEs and EQEs in terms of the injection current density are shown in Fig. 6. It can be seen that the µLED with a small inclination mesa angle possesses a lower IQE. e.g., Device 1. This is mainly due to the current crowding effect in the central mesa and the stronger QCSE at the sidewall region when the mesa angle decreases. The efficiency droop levels at the current density of 100 A/cm2 are 47.7%, 52.9%, 51.2%, 49.4% and 50.5% for Devices 1 to 5, respectively. Therefore, according to the IQEs and EQEs in terms of injection current density in logarithmic scale shown in the insets of Fig. 6, the current densities corresponding to the peak IQEs and EQEs for Devices 1-5 are not significantly different, which is attributed to that the SRH recombination induced by the sidewall defects is not considered for Devices 1-5. However, as we have aforementioned, the LEE can be increased when the beveled mesa is adopted. Hence, by considering the LEEs in Fig. 1(d), we can obtain the EQEs as a function of the injection current density for Devices 1-5 in Fig. 6(b). It is worth noting that Device 1 with the smallest inclination mesa angle has the largest EQE when compared with the other counterparts. It means that if the sidewall defects are not considered in µLEDs, adopting a beveled mesa with proper small inclination angle can enhance the EQEs for GaN-based µLEDs.
Fig. 6. Calculated (a) IQEs and (b) EQEs as the function of injection current density in linear scale for different devices. Insets in figures (a) and (b) show the IQEs and EQEs in terms of current density in logarithmic scale, respectively.
Nevertheless, it is well known that the defect-induced SRH nonradiative recombination is even more remarkable for µLEDs. As we have mentioned previously, beveled mesa seems to transport the holes to the mesa sidewall in the MQW region. These holes are likely to be captured by the defects and increase the SRH nonradiative recombination. In this work, the size of the mesa bottom is set to 20 × 20 µm2 for all µLEDs, and then the calculated surface areas in the mesa sidewall for µLEDs with mesa angles of 45°, 53°, 63°, 79° and 90° are 97.48, 87.24, 79.12, 72.88 and 72.16 µm2, respectively, representing an increased surface-volume-ratio for µLEDs with beveled mesas. Hence, considering the dry-etching-cause surface damages, nonradiative surface recombination for µLEDs with beveled mesas is well worth investigating. We then also define the Devices I to V with the inclined mesa angles of 45°, 53°, 63°, 79° and 90°, respectively as presented in Table 1.
Figure 7 shows the SRH nonradiative recombination current density in terms of the injection current density for Devices I to V. It is found that the SRH nonradiative recombination current increases with the decrease of inclination mesa angle. The inset (a) in Fig. 7 shows the lateral SRH nonradiative recombination rate in the p-GaN layer. We can infer that the SRH recombination current is likely to be dominated by the surface nonradiative recombination. Moreover, the strongest surface nonradiative recombination rate for Device I indicates that the holes are captured by the surface defect for beveled mesa with small inclination angle, and this leads to the reduced hole injection efficiency into the MQW in the mesa surface region according to the inset (b) for Fig. 7. This conclusion is consistent with our previous report [14], such that the surface defects can substantially reduce the hole injection for GaN-based µLEDs.
Fig. 7. SRH nonradiative recombination current density in terms of injection current density. Inset (a) is the lateral SRH recombination rate in p-GaN layer, and inset (b) is the lateral hole concentration in the last quantum well closest to the p-EBL layer for Devices I to V. All the data are selected at the injection current density of 100 A/cm2.
Next, we demonstrate the IQEs as the function of injection current density in linear scale in Fig. 8(a) for Devices I to V, respectively. We demonstrate that the efficiency droop levels at the current density of 100 A/cm2 are all smaller than 5%. Clearly, we can see that the efficiency droop levels for Devices I to V are significantly suppressed when compared with Devices 1 to 5. The reduced efficiency droop also illustrates the enhanced SRH nonradiative recombination [36], and then the Auger recombination cannot be triggered without a high carrier concentration in the MQWs. However, Fig. 8(a) also shows the smallest IQE for Device I, the efficiency droop has not been observed even at the current density level of 100 A/cm2. For better illustration, we show the IQE in the semi-logarithmic scale in Fig. 8(b). The inset of Fig. 8(b) demonstrates the current density at which the peak IQE occurs for different devices. The current density for peak IQE increases with the decrease of inclined mesa angle and it means that the device with much stronger SRH recombination rate shall be pushed to an even higher current density level before a large number of holes are injected into the MQWs. Moreover, the peak IQE is also the smallest for Device I because of the strongest surface nonradiative recombination.
Fig. 8. Calculated IQE in terms of the injection current density in (a) linear scale and (b) semi-logarithmic scale for Devices I to V, respectively. Inset in (b) is the peak IQE and current density at which the peak IQE is generated for each device.
After considering the LEEs in Fig. 1(c) and the IQEs in Fig. 8(a), the EQEs for Devices I to V can be obtained and shown in Fig. 9. It is indicated that the EQE for Device IV with 79° inclination mesa angle is the strongest. These results here are different from that in Fig. 6(b) in which Device 1 with the inclination mesa angle of 45° shows the strongest EQE. The difference here is well attributed to the fact that, during designing actual GaN-based µLEDs, a decreased inclination mesa angle shall lead to an increased surface defect-induced nonradiative recombination rate in spite of the enhanced LEE. As a result, there is a trade-off between the enhancement of LEE and the increase of SRH nonradiative recombination when designing beveled mesas for GaN-based µLEDs.
4. Conclusion
In summary, we have numerically investigated and demonstrated the impact of different inclination mesa angles on the optical and electrical properties for GaN-based µLEDs. We demonstrate that an enhanced LEE can be obtained by properly decreasing the mesa angle for µLEDs. However, a charge-coupling effect can take place for beveled mesas, which on one hand will increase the QCSE in the sidewall region, and on the other hand, the charge-coupling effect will realign the energy band so that the holes tend to transport to the sidewall region in the MQWs. As a result, the enhanced SRH recombination current can be obtained when the inclination angle further decreases for beveled mesa. Consequently, properly designing the inclination mesa angle is critical to improve the EQE for GaN-based µLEDs with naturally formed beveled mesas. We believe that the findings in this work provide a unique understanding to GaN-based µLEDs especially those with beveled mesas for optoelectronic and display communities.
Funding
National Natural Science Foundation of China (61975051, 62074050); State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology (EERI_PI2020008, EERIPD2021012); Joint Research Project for Tunghsu Group and Hebei University of Technology (HI1909).
Disclosures
The authors declare no conflicts of interest related to this paper.
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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