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Investigation and direct observation of sidewall leakage current of InGaN-Based green micro-light-emitting diodes

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Abstract

Electrical and optical characteristics of InGaN-based green micro-light-emitting diodes (µLEDs) with different active areas are investigated; results are as follows. Reverse and forward leakage currents of µLED increase as emission area is reduced owing to the non-radiative recombination process at the sidewall defects; this is more prominent in smaller µLED because of larger surface-to-volume ratio. Leakage currents of µLEDs deteriorate the carrier injection to light-emitting quantum wells, thereby degrading their external quantum efficiency. Reverse leakage current originate primarily from sidewall edges of the smallest device. Therefore, aggressive suppression of sidewall defects of µLEDs is essential for low-power and downscaled µLEDs.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The growing interest in mobile devices and their numerous potential applications have highlighted the need for high-performance displays with microscale pixels. Recently, Gallium nitride (GaN)-based micro-light-emitting diodes (µLEDs) have gained significant interest for next-generation display applications [1,2]. The µLEDs offer several clear advantages, such as long operation stability, high brightness, high luminous efficiency, fast response time and chemical robustness [35]. These advantages make them potential candidates for next-generation display devices, effectively surpassing liquid crystal displays (LCD) and organic LED displays. Additionally, it has been reported that current crowding remarkably decreases due to poor current spreading and is alleviated as the LED size is reduced [6]. Near-eye head-mounted displays, small- and large-area self-emitting displays without pixel burn-in, outdoor signage, and power-efficient displays for wearable devices have strict requirements. These strict requirements can be fulfilled only by inorganic materials-based µLEDs. Therefore, they are the only viable choice of display technology among their incumbent counterparts for these applications. Furthermore, µLEDs have been developed for wide-bandwidth transmitters in visible-light communication applications [79]. Therefore, tremendous efforts have been devoted to studying the relevant optoelectronic properties of µLEDs, as well as manufacturing various displays that use them.

Although µLEDs exhibit outstanding performance from the perspective of next-generation displays, several problems remain. For example, significant reduction in the external quantum efficiency (EQE) of smaller µLEDs has been reported [1,6,1012]. The EQE reduction of µLEDs both occurs at low and high current density regime. Under a low current density regime, the Shockley-Read-Hall (SRH)-like non-radiative recombination process via the surface defects at the sidewall of the LEDs appears to be dominant. This is because of the relatively higher band offset of the conduction band. Thus, it leads to EQE degradation. In addition, under a high current regime, the EQE of µLEDs gradually decreases. This is because of several possible reasons, such as electron overflow, Auger recombination, and current crowding [1316]. Furthermore, the SRH-like non-radiative recombinations of µLEDs at lower driving current densities have been reportedly ascribed to the exposed surface of non-passivated active layer. More specifically, they have been ascribed to the dangling bonds and Ga adatoms at the surface of InGaN/GaN multiple quantum wells after dry etching [1719]. These surface-related non-radiative recombinations are a major source of leakage current in µLEDs. Although, the surface passivation and chemical treatment have been employed to alleviate the leakage current of µLEDs [6,20], the work related to the passivation effects on the performance of green µLEDs has been rarely reported. Because of the high indium concentration in quantum wells (QWs), green LEDs show different quantum confined Stark’s effects (QCSEs) and accompany relevant efficiency loss compared to blue LEDs. Hence, it is important that the leakage current behavior of green µLEDs and precise locations of leakage paths should be further identified.

In this study, we investigated the electrical and emission characteristics of surface-passivated green µLEDs with different active areas. The results revealed that smaller active areas of µLEDs tend to exhibit higher leakage tunneling currents, presumably arising from the surface of the active layer. Images obtained from the high-resolution emission microscope indicated that the leakage current of the smallest µLED, 37 × 37 µm2, occurred at its sidewall. Furthermore, spatial emission analysis revealed that the surface leakage tunneling current gives rise to a larger population of injected carriers into the quantum wells and an associated shorter wavelength shift by the QCSEs.

2. Experimental details

Green-emitting epitaxial layers were grown on a (0001) c-plane sapphire wafers using metal-organic chemical vapor deposition (MOCVD). The epitaxial structure comprised a 3.2 µm undoped GaN layer, 4.2 µm Si-doped GaN layer, 9 period of 3 nm/10 nm InGaN/GaN multiple quantum well (MQW), and 100 nm Mg-doped GaN layer. After the growth of the epitaxial layers, Cl2-based inductively coupled plasma reactive ion etching (ICP-RIE) was performed to electrically isolate each µLED. Next, the mesa structure of the active LED device was defined using Cl2-based ICP-RIE to expose n-GaN. In this etching step, the µLEDs were shaped in squares of sizes 90, 70, 50, and 37 µm on an identical epitaxial wafer. A 60 nm indium tin oxide (ITO) transparent electrode as current spreading layer was deposited on the p-GaN surface using electron beam evaporation. Rapid thermal annealing was performed in air at 650 °C for 1 min to recover the sidewall damage from ion etching and reduce the sheet resistance [20]. The 50/250 nm thick Cr/Au layer was deposited as p-/n-metal contact by electron beam evaporation. A 700 nm layer of silicon dioxide was deposited by plasma-enhanced chemical vapor deposition (PECVD) to suppress leakage current through the exposed surface of the active layer. After that, contact via formation through SiO2 was carried out using wet chemical etching with a diluted buffered oxide etchant (HF:H2O = 1:6). Finally, the contact metals for n-GaN and p-GaN were bridged to the probing pad on the sapphire substrate for the characterization of the µLED using electron-beam-evaporated Ti/Ni/Cu/Au (100/100/700/100 nm) metal layers.

The structure of the µLEDs was observed using a field-emission scanning electron microscope (FESEM) (Hitachi SU-5000) at an accelerating voltage of 20 kV and emission current of 11.7 µA. The current–voltage characteristics and EQE of the µLED were measured and characterized using a source meter (Keithley 2636 B) with pulsed current driving (pulse period = 10 Hz and duty cycle = 0.99%). Note that DC current driving often results in noticeable degradation of LEDs [16,21]. A photo emission microscope (Hamamatsu PHEMOS-200) was employed to further characterize the spatial distribution of defect-induced emission. Next, the spectrum of the reverse bias luminescence from the µLED was measured by confocal scanning electroluminescence spectrometer (Nanobase Xperam S500) to identify the microscopic location of the defect-related luminescence.

3. Results and discussion

Figure 1(a) shows the schematic of the µLEDs used in this study. Herein, the active areas of the devices were varied for comparison of their size-dependent electrical and emission characteristics while maintaining all process conditions identical. Owing to the different sizes of the µLEDs, the via contact with ITO was proportionally varied in the shape of the square pattern and bridged to the contact pad for electrical biasing. The FESEM images of the µLEDs show that the clear mesa structure with almost vertical etching profile, the well-defined electrical contacts to the n-and p-GaN, and the bridging electrodes, as shown in Fig. 1(b).

 figure: Fig. 1.

Fig. 1. (a) Schematic of green-emitting µLED devices used in this study, and (b) FESEM images of the device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. Final image is a tilted view of the 37 × 37 µm2 size.

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The electrical characteristics of the µLEDs were measured and compared to observe their leakage current behavior depending on the different active areas, as shown in Fig. 2(a). The current of conventional LED devices follows an ideal p-n junction current–voltage behavior. Therefore, it can be expected that the currents of µLEDs are suppressed at a lower bias voltage (2.1–2.4 V) and follow the exponential increase in the forward bias regime. A gradual increase in the current density was observed for µLEDs of size 90 × 90 µm2, 70 × 70 µm2, and 50 × 50 µm2, whereas a significantly higher current density was observed for the 37 × 37 µm2 µLED. Despite SiO2 passivation, this increase in forward current density is ascribed to the proportionally increased specific sidewall of the µLEDs and their relevant leakage current behavior. However, the excessively high leakage current of the smallest µLED could be due to overestimation of the sidewall effect, the epitaxy quality, and the device structure such as the small contact via area and narrow width of bridging electrode.

 figure: Fig. 2.

Fig. 2. (a) Current density vs. voltage characteristic curves of µLEDs with device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. (b) Electroluminescence images of the green-emitting µLED under the forward bias from 2.4 to 2.7 V.

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To investigate the emission pattern of µLEDs with different active areas, different driving voltages were applied to µLEDs and their emission characteristics were obtained. As shown in Fig. 2(b), under the forward bias within the range of 2.4–2.7 V, the emission images of all the µLEDs show the active green emission area and p-contact metal pattern in black. It should be noted that all the emission patterns of the µLEDs were fairly uniform within the emission area. This suggests that the electrical and emission behaviors of the µLED appear to be dominated by carrier transport through the junction area. Additionally, this demonstrates the fidelity of our fabrication process for µLEDs with an active area as small as 37 × 37 µm2. Moreover, this uniform green emission can be partially linked to less severe current crowding due to the small active area of the µLED-based display application.

The current density vs. voltage (J–V) characteristics of µLEDs with different active areas were measured and compared, as shown in Fig. 3(a), to determine the size dependence of the leakage current characteristics. It appears that the J–V curve of the smallest µLED (37 × 37µm2) shows a noticeably higher leakage current level in both the forward and reverse voltage regions compared to the relatively larger ones. Such extraordinary leakage behavior may be due to the non-uniformity of the fabrication process. However, tens of arrays of µLEDs with different active areas were fabricated on the same wafer. Therefore, it is less probable that the sidewall damage occurred more severely in 37 µm µLEDs. Therefore, we assume that the PECVD passivation layer is not efficient to suppress the leakage current of 37 µm µLEDs. The leakage current was higher than that of previous reported by Horng et al. [11]. This may due to the high RF power which causes additional damage to the sidewall of QW. Furthermore, it is observed that the reverse current level of µLEDs gradually increases as their active area decreases. In particular, the shape of the J–V curve of the smallest µLED has a symmetrical current behavior centered around zero voltage, which is somewhat different from the typical J–V curve of the p-n junction-based diode. The symmetrical J–V curve of the µLED with a 37 µm is reminiscent of the defect-related tunneling current of conventional LEDs with excessive threading dislocations and unpassivated active regions [22].

 figure: Fig. 3.

Fig. 3. (a) Forward and reverse current density vs. voltage characteristics curves of µLEDs with device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. (b) Plot of current density at 2.4 V vs. the ratio of sidewall to active area (SA) relation of µLEDs. (c) Ideality factor vs. current density relation; its inset shows the recombination regime $\left( {n \cong 2} \right)$ of µLEDs at low current density.

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It is apparent that a µLED with a smaller device layout has a relatively small sidewall surface. To fairly evaluate the leakage current level of µLED with different active areas, it is necessary to compare the sidewall to active area (SA) ratio of the µLEDs. The current densities at 2.4 V vs SA ratios are plotted in Fig. 3(b). The current densities of the µLED at 2.4 V with device sizes of 90, 70, 50, and 37 µm reached 0.13, 0.15, 0.29, and 7.05A/cm2, respectively. The forward current characteristics of an ideal diode can be expressed as follows:

$$I = {I_0}\textrm{exp} \left( {\frac{{qV}}{{nkT}}} \right)$$
where I0 is the pre-exponential factor, q is the elementary charge, V is the bias applied to the LED device, k is the Boltzmann constant, T is the absolute temperature, and n refers to the ideality factor describing the dominant conduction process at the p-n junctions. If n is close to 2, recombination dominates; if n is close to 1, the diffusion current dominates the I–V behavior. Therefore, plotting the ideality factor n over various ranges of applied voltage V enables us to determine the dominant conduction mechanism of LEDs.

Figure 3(c) shows the relationship between the ideality factors extracted from the µLED with different dimensions and the forward current density; the figure clearly indicates a much greater integer than 2. The fairly high ideality factors of all µLED seem apparent, regardless of their dimensions, in the low-bias regime, which can be associated with the defect-assisted tunneling process. These high ideality factors (n > 2) often arise from the high dislocation density of conventional InGaN-based LEDs. In addition to the behavior of leakage current with respect to the size of µLED, the sidewall of µLEDs could be a primary tunneling path, thereby yielding high ideality factors. Sugimoto et al. [23] reported that when GaN epitaxial film is processed by Cl2-based ICP-RIE for device fabrication, the sidewall surface of the GaN is damaged by ion bombardment and relevant nonstoichiometric defects of the Ga-N system. Because the lack of N generates electrons, the Ga+-rich regions at the sidewall function as leakage current paths in GaN-based diodes [19,23]. In µLEDs, the non-radiative recombination center on the surface of the LED sidewall has been reported as the main reason for the large leakage current. This is consistent with our analysis [6,24]. In this regard, our results confirm the origin of the leakage current in µLEDs and their dependence on the dimensions of the µLEDs.

To investigate the relationship between electroluminescence and the dimensions of µLEDs, relative EQE measurements of µLEDs were performed depending on their dimensions, as shown in Figs. 4(a) and (b). The EQE of the LED can be expressed by Eq. (2)

$${\eta _{EQE}} = \frac{{\hbox{$P$} \!\mathord{\left/ {\vphantom {P {\left( {hv} \right)}}}\right.}\!\lower0.7ex\hbox{${\left( {hv} \right)}$}}}{{{I / q}}} = {\eta _{IQE}} \times {\eta _{ext}}$$
where P is the optical power, q is the elementary charge, h is Planck’s constant, I is the current through the LED, ηIQE is the internal quantum efficiency, and ηext is the light-extraction efficiency. The ηEQE is a product of ηIQE and ηext. Assuming that all samples have identical ηext by neglecting the device configuration and structure, variation in the EQE shape is expected to be dominated primarily by the ηIQE of µLEDs with different dimensions. It can be observed that the EQE curves of all µLEDs increase quickly from the low current density, reach the maximum value of EQE, and subsequently, decrease quickly. This results in an almost symmetrical parabolic curve in this fitting condition.

 figure: Fig. 4.

Fig. 4. (a) Plot of relative EQE vs. current density curves of µLEDs with different device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. (b) Plot of the current density for EQE peak value vs. the size of µLEDs.

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It is apparent that Fig. 4(a) exhibits relatively higher EQE values for larger µLEDs. This trend appears because of the larger emission area with relatively less sidewalls for larger µLEDs. However, the EQE was significantly deteriorated by a higher leakage current for the smallest µLED. In addition, it was found that the current density corresponding to the maximum point of EQE shifted to a higher value as the dimensions of the µLEDs decreased. To highlight this tendency, we plotted the corresponding behavior of the measured current density for the maximum EQE and dimensions of the µLEDs, as shown in Fig. 4(b). It can be observed that the EQE peak position of smaller µLEDs appears to gradually shift toward a higher current density regime. Such size-dependent EQE characteristics of µLEDs have been reported in the literature [10]. At low current densities, such a low EQE originates from defect-related nonradiative recombination. The SA ratio of the 37 µm LED is higher than those of the larger LEDs. This indicates that the EQE of the smaller µLED at a low current density is strongly affected by the relatively high number of sidewall defects. Therefore, it is expected that a smaller µLED will have a lower EQE at low current densities and an EQE peak at a higher current density.

The electroluminescence spectra of µLEDs at different injection current densities were measured and compared to further investigate the effects of the size of µLEDs on their electroluminescence characteristics. Their spectra are shown in Fig. 5. Consistent with other conventional LEDs, the electroluminescence spectra of all µLEDs tended to shift toward shorter wavelengths because of band filling and flattening by injected carriers into the quantum well. This phenomenon is known as the QCSEs. It was observed for µLEDs, regardless of their dimensions. In addition, the µLED with smallest device size of 37 × 37 µm2 exhibited the lowest blue shift (Δλ = -2.89 nm; the negative sign denotes blue shift) of the emission wavelength up to the injection current density of 6.47 A/cm2. This lowest blue shift appears to be related to the lowest population of injected carriers within the quantum wells due to the significant leakage current along the side wall of the active layer. This blue shift of the emission wavelength gradually increases with the size of µLEDs, as shown in Figs. 5(a)–(d), which is qualitatively consistent with their leakage current behavior, shown in Fig. 3. Therefore, the magnitude of the blue shift is linked to the relative population of injected carriers into the quantum wells, which becomes less prominent owing to the non-radiative leakage current along the sidewall of µLEDs.

 figure: Fig. 5.

Fig. 5. Electroluminescence spectra of µLEDs at different injection current densities with different device areas of (a) 37 × 37, (b) 50 × 50, (c) 70 × 70, and (d) 90 × 90 µm2.

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To confirm and further visualize the origin of the leakage current of µLEDs, a high-resolution emission microscope with a high-sensitivity cooled charge-coupled detector (CCD) was employed to record and identify the leakage current points of all µLEDs. The corresponding images are shown in Figs. 6(a)–(d) [25,26]. It was expected that carriers would be transported to the QWs by relatively large reverse bias through trap-state-assisted tunneling at the sidewall. Because the intensity of the light escaping from the LEDs was extremely low, the light was collected by the CCD inside dark box. For these experiments, a reverse bias was applied by Keithley 2450 and the LEDs were electrically contacted by a microprobe on the wafer. When -10 V was applied to the 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2-sized LEDs, the current densities were 58.3 A/cm2, 0.2 mA/cm2, 48.9 µA/cm2, and 13.2 µA/cm2, respectively. The emission patterns overlapped on the optical microscope images of the µLEDs and revealed the leakage spots of the µLEDs under reverse bias. As shown in Fig. 6, it is found that the emission spots are not uniform around the mesa structure of µLED devices. This is because the process of µLED fabrication often appears to have non-uniformities such as random distribution of threading dislocation-related defects in the epitaxy and locally different etching profiles of sidewall. So, non-uniform emission spots can be associated with this combination of epitaxy-related defects and slightly different etching profile. These emission spots can be directly linked to the leakage current path of those µLEDs in which the emission area and its intensity are proportional to the magnitude and density of the corresponding defects. In contrast, as shown in Figs. 6(b)–(d), the defect-related emission appears almost unobservable for the larger µLEDs.

 figure: Fig. 6.

Fig. 6. High-resolution leakage current emission microscope images of µLEDs biased at −10 V with different device areas of (a) 37 × 37, (b) 50 × 50, (c) 70 × 70, and (d) 90 × 90 µm2.

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The results of this emission pattern analysis further justify those of our previous analysis and the relevant inference of our electrical measurement of µLEDs with different dimensions, as shown in Fig. 3. From the previous J–V curves of µLEDs, it was observed that the smallest µLEDs showed significantly larger leakage currents in both the forward and reverse bias regimes. Thus, the significantly higher leakage current behavior of the smallest µLED coincides with the optical emission pattern to some extent. In addition, significant attention should be paid to the location of the reverse-bias emission spots of the smallest µLED. More specifically, the emission spots due to the leakage current were distributed primarily around the sidewall edges of the LED active layer. Furthermore, it was found that the light emission at a lower reverse bias evolved from fewer and smaller spots and developed into much larger and more intense spots, as shown in the inset of Fig. 6(a). As reported in other studies, this local distribution of the light emission further confirms that small-sized LEDs tend to suffer from leakage current along the dry-etched sidewall of LED structures [27].

We further attempted to investigate the emission phenomenon and spectrum of µLEDs, in which the emission patterns originated from the leakage current along the sidewall of the patterned LED structure. Therefore, the local emission spectrum was collected from point A under the reverse bias condition and its spectrum was compared to the typical emission pattern of µLEDs under a forward bias, as shown in Figs. 7(a) and (b). It was observed that the emission wavelength of µLEDs under the reverse bias noticeably shifts to a shorter wavelength (as low as 493.8 nm) compared to the original emission wavelength (528.6 nm) under the forward bias (2.64 V). This blue shift of the emission wavelength of the smallest µLED can be associated with the alleviation of the piezoelectric field within the InGaN/GaN multiple quantum well structure. It is commonly known that the growth of an InGaN/GaN active layer on a foreign substrate yields a significant piezoelectric field. This is because of the lattice mismatch between the InGaN quantum well and GaN quantum barriers. Therefore, the reverse bias applied to µLEDs compensates for the piezoelectric field of green-emitting InGaN/GaN MQWs, thereby rendering the bandgap of the InGaN quantum well wider, as depicted in Fig. 7(c). Therefore, the defect-assisted tunneling process and non-biased wavefunctions (of electrons and holes) under reverse bias seem to make a synergistic contribution to the emission pattern with shorter wavelengths [25]. It is also worth noting that most of the reverse-bias luminescence points were located near the sidewall edges in the smallest LED.

 figure: Fig. 7.

Fig. 7. (a) Luminescence image under reverse bias, (b) spectrum under reverse bias VRB (−10 V) and forward bias VFB (2.64 V) at point A, and (c) relevant energy band diagram describing reverse bias luminescence with large emission energy.

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4. Conclusion

This work investigated the size-dependent electrical and optical characteristics of green-emitting µLEDs with dimensions varying from 37 × 37 to 90 × 90 µm2. This systematic electrical and optical analysis of µLEDs with different device sizes revealed that the leakage current of µLEDs is significantly deteriorated by sidewall defects along the active layer. High-resolution emission microscopy enabled us to directly observe this defect-related emission along the edges of the smallest µLED sidewall. Additionally, it confirmed the less severe QCSE phenomenon due to less carrier injection into the quantum wells. Thus, our work suggests that the effective suppression or elimination of sidewall defects of µLED is a prerequisite for the commercialization of high-efficiency µLED-based displays.

Funding

Ministry of Education (2021R1A6C101A405); Ministry of Trade Industry and Energy, (MOTIE) and Korea Institute for Advancement of Technology (KIAT) (p0006305); Ministry of Trade Industry and Energy (p0002397).

Acknowledgments

This research was funded and conducted under the Competency Development Program for Industry Specialists” of the Korean Ministry of Trade, Industry and Energy (MOTIE), operated by Korea Institute for Advancement of Technology (KIAT). (No. P0002397, HRD program for Industrial Convergence of Wearable Smart Devices). Furthermore, this research was financially supported by the Ministry of Trade, Industry and Energy (MOTIE) and Korea Institute for Advancement of Technology (KIAT) through the International Cooperative R&D program. (No. P0006305). In addition, this research was partially supported by Korea Basic Science Institute (National Research Facilities and Equipment Center) grant funded by the Ministry of Education.

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) Schematic of green-emitting µLED devices used in this study, and (b) FESEM images of the device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. Final image is a tilted view of the 37 × 37 µm2 size.
Fig. 2.
Fig. 2. (a) Current density vs. voltage characteristic curves of µLEDs with device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. (b) Electroluminescence images of the green-emitting µLED under the forward bias from 2.4 to 2.7 V.
Fig. 3.
Fig. 3. (a) Forward and reverse current density vs. voltage characteristics curves of µLEDs with device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. (b) Plot of current density at 2.4 V vs. the ratio of sidewall to active area (SA) relation of µLEDs. (c) Ideality factor vs. current density relation; its inset shows the recombination regime $\left( {n \cong 2} \right)$ of µLEDs at low current density.
Fig. 4.
Fig. 4. (a) Plot of relative EQE vs. current density curves of µLEDs with different device areas of 37 × 37, 50 × 50, 70 × 70, and 90 × 90 µm2. (b) Plot of the current density for EQE peak value vs. the size of µLEDs.
Fig. 5.
Fig. 5. Electroluminescence spectra of µLEDs at different injection current densities with different device areas of (a) 37 × 37, (b) 50 × 50, (c) 70 × 70, and (d) 90 × 90 µm2.
Fig. 6.
Fig. 6. High-resolution leakage current emission microscope images of µLEDs biased at −10 V with different device areas of (a) 37 × 37, (b) 50 × 50, (c) 70 × 70, and (d) 90 × 90 µm2.
Fig. 7.
Fig. 7. (a) Luminescence image under reverse bias, (b) spectrum under reverse bias VRB (−10 V) and forward bias VFB (2.64 V) at point A, and (c) relevant energy band diagram describing reverse bias luminescence with large emission energy.

Equations (2)

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I = I 0 exp ( q V n k T )
η E Q E = P / P ( h v ) ( h v ) I / q = η I Q E × η e x t
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