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Abstract
We investigated the excitation-dependent spatially resolved luminescence properties of InGaN/GaN light-emitting diodes (LEDs) with air-cavity arrays using scanning near-field optical microscopy (SNOM), and quantified the effect of the air-cavity structure on the spatial distributions of light-extraction efficiency, internal quantum efficiency, and external quantum efficiency through experiments and numerical simulations. We found that higher light-extraction efficiency and less stress were always observed in the air-cavity areas. Compared to flat areas, the average light-extraction efficiency of the air-cavity areas was improved by 65%, and the residual stress of the air-cavity center was reduced by 89 MPa, which resulted in increased PL intensity, reduced wavelength shift, and narrowed full width at half maximum. The highest external quantum efficiency and aggravated efficiency droop were found in the air-cavity center. At 3.1 W/cm2, the external quantum efficiency and internal quantum efficiency of the air-cavity center were enhanced by 255% and 223%, respectively.
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1. Introduction
Due to breakthroughs in epitaxial growth of III-nitride materials, GaN-based light-emitting diodes (LEDs) have shown great potential in a wide range of applications such as solid-state lighting (SSL), full-color displays, visible light communications (VLC), and wearable devices [1–5]. LEDs grown on c-plane sapphire substrate suffer from a high density of defects due to a large mismatch in lattice constant and thermal expansion coefficient. Patterned sapphire substrate (PSS) technology acting as an effective method can reduce the defect density [6,7] and residual stress [8,9] in epitaxy. However, these improvements occur mainly in the patterned regions, resulting in nonuniform luminescence intensity. To design a patterned substrate structure that can maximize LED efficiency, it is important to study the luminescence characteristics among the patterned and nonpatterned regions. In addition to luminous efficiency, full width at half maximum (FWHM), wavelength stability and efficiency droop are important metrics for evaluating LED performances. Crystal quality and stress may affect these properties in different ways. Therefore, distinguishing their specific contributions to different properties is significant to draw conclusions about which type of PSS or structure parameters are most suitable for LED applications.
There have been various demonstrations of GaN-based LEDs grown on the PSS [10–18]. Most reports were mainly focused on the evaluation of overall performance by standard far-field electroluminescence or photoluminescence (PL) tests. Direct observation of spatial luminescence characteristics among patterned and nonpatterned regions is not easy due to limited resolution. In our work, we prepared blue LEDs with an air-cavity array and explored light-extraction efficiency (LEE) and stress distributions through experiments and numerical simulations. Near-field PL properties as a function of excitation power density were measured using scanning near-field optical microscopy (SNOM). Position-dependent PL intensity, peak wavelength, FWHM, and efficiency droop between the air-cavity area and flat area were analyzed.
2. Experimental methods
The concave hemispherical PSS was fabricated on c-plane (0001) sapphire by laser drilling with a nanosecond pulsed laser, and the details can be found elsewhere [19]. The hemispherical array was with 5 µm diameter, 2.5 µm depth, and 10 µm spacing. The LED sample was grown on the concave hemispherical PSS by metal organic chemical vapor deposition (MOCVD). As shown in Fig. 1, the epitaxial structure consists of a 30 nm low-temperature (LT) GaN buffer layer, a 3 µm undoped GaN layer, a 2 µm Si-doped n-type GaN layer, an active region with 9 pairs of InGaN (3 nm)/GaN (12 nm) MQWs and a 150 nm Mg-doped p-type GaN layer. The air-cavity arrays in the GaN/sapphire interface are formed due to the epitaxial lateral overgrowth (ELOG) process and are underneath the buffer GaN film. The detailed formation mechanism of the air-cavity array has been reported elsewhere [20].
Near-field PL measurements were performed at room temperature with a SNOM apparatus in collection mode. PL was excited directly into QWs from the polished backside of the substrate by a 405-nm continuous wave (CW) laser diode through a 100x objective lens. The excitation power density was changed from 2.3 to 9.1 W/cm2. PL signal was collected by an aluminum-coated fiber probe with a 100 nm diameter and was directed to a photomultiplier tube (PMT) for PL mapping after passing a 413 nm long-pass filter. PL spectra were recorded by a diffraction grating spectrometer with an optical resolution of 0.02 nm. Room temperature micro-Raman spectroscopy measurements were performed using the LabRAM HR Evolution system with a 532 nm solid-state laser diode as the excitation source. The Raman spectra were measured from the GaN top surface using a 50x objective to focus and collect the scattered laser light. Laser power at the sample was about 50 mW. To obtain the Raman mapping, the sample was scanned underneath the laser beam using a motorized XY stage with a resolution of 500 nm. A Transmission Electron Microscope (TEM) specimen was prepared by focused ion beam using an in-situ liftoff method. Then the crystalline quality of the PSS-LED was evaluated by TEM operating at 200 kV.
3. Results and discussion
Figure 2(a) shows the near-filed PL intensity mapping of the PSS-LED with air-cavity arrays at 3.1 W/cm2. The periodic distribution of bright and dark regions was observed, where the bright area shown by a dashed circle corresponded to the air cavity. Figure 2(b) displays the near-field PL spectra acquired at positions A, B, C, and D (marked in the inset of Fig. 2(b)). The PL intensity gradually increases from positions A to D. Compared to position A, the peak PL intensities from B to D increase by about 0.78, 1.87, and 2.55 times, respectively. The FWHM at positions A to D is 25.7, 19.4, 19.4, and 19.0 nm, respectively. The PL peak wavelength for positions A, B, C, and D is located at 458.79 nm, 458.74 nm, 458.03 nm, and 457.93 nm, respectively. Compared to position A, PL peaks of B to D show increased blue-shift. A properly designed PSS can mitigate the compressive stress in the patterned areas, and thereby reducing the quantum confined stark effect (QCSE) [8,9,21]. Therefore, the blueshift of PL peaks of B to D compared with position A may result from the reduced QCSE in the air-cavity area. A cross-sectional TEM image for GaN on the PSS-LED with an air-cavity array was measured (Fig. 2(c)). The threading dislocations (TDs) were marked by red arrows. TDs were formed in the flat sapphire area, as commonly observed in the GaN grown on a planar sapphire substrate due to the lattice mismatch between the GaN and sapphire. When the growth mode changing from three-dimension (3D) nucleation to 2D lateral growth, TDs were bent and merged towards the air-cavity center, and eventually stopped from extending upward [22–26]. It results in lower defect density in the air-cavity area than that in the flat area. It is believed that the competitive recombination occurs at the deep energy levels induced by TDs [27,28], resulting in the reduction of PL intensity. In addition, TDs can also contribute to the PL peak broadening by enhancing the transition from higher energy extended states [29–31]. Thus, one reason for stronger PL intensity and narrowed FWHM in the air-cavity areas is the reduction of dislocation density through lateral growth behavior.
Fig. 2. (a) Near-field PL image mapped from the surface of the PSS-LED with an air-cavity array. The region surrounded by a dashed circle indicates the air-cavity patterned region. (b) Near-field PL spectra recorded from positions A to D. (c) a cross-sectional TEM image of GaN on PSS-LED with an air-cavity array.
The Monte-Carlo ray-tracing method was used to calculate the LEE distribution of PSS-LED. To simplify the simulation, only four layers were considered, including the p-GaN layer, active layer (InGaN), n-GaN layer, and sapphire substrate. The PSS-LED model contained a 3 × 3 air-cavity array embedded in a sapphire substrate. The depth, diameter, and period of the air-cavity array were set as 2.5, 5, and 10 µm. The LED model with the flat sapphire substrate (FSS-LED) was designed as a reference. The simulation results of the LEE from the p-GaN surface are shown in Fig. 3. Figure 3(a) is the LEE map for the PSS-LED model, and Fig. 3(b) depicts the cross-sectional distribution along the dark dashed line in Fig. 3(a). These results of FSS-LED under the same condition are shown in Fig. 3(c) and (d). In the PSS-LED, the LEE distribution replicated the air-cavity array and a higher LEE was always found in air-cavity areas (dashed circles). The average LEE in air-cavity areas is improved by 65% compared to flat areas. On the other hand, the LEE in FSS-LED is uniform and almost equal to the flat regions of PSS-LED. According to the refractive index of GaN, sapphire, and air, the critical angle of total internal reflection at GaN/sapphire interfaces is 45.4° while the critical angle at GaN/air interfaces is 23.3°. Compared to GaN/sapphire interfaces, more light rays will be reflected from GaN/air interfaces, thus increasing the light ray number extracted from the p-GaN surface. LEE in air-cavity areas is higher than in flat regions, which also contributes to the stronger PL intensity in air-cavity areas.
Fig. 3. (a) Simulated LEE map from the p-GaN side and (b) cross-sectional LEE distribution along the dark dashed line in (a) of PSS-LED model; (c) simulated LEE map from the p-GaN side and (d) cross-sectional LEE distribution along the dark dashed line in (c) of FSS-LED model.
Figure 4(a) depicts the peak PL intensity versus excitation power density at positions A, B, C, and D. As can be seen, the peak PL intensity gradually increases from A to D due to improved crystal quality and LEE in the air cavity areas. Figure 4(b) shows the corresponding peak wavelength variation. The peak wavelength exhibits blueshift for 8.7 nm, 7.6 nm, 6.2 nm, and 6.1 nm at positions A to D, respectively. Additionally, at low excitation, the peak wavelength from A to D becomes shorter, while at high excitation, it gradually becomes longer. When carriers are injected into the QWs, the QCSE is compensated by the electron screening effect and the wavelength is blueshift [32]. The more the QCSE is compensated, the larger the blueshift. Therefore, the strength of QCSE can be estimated from the magnitude of the blueshift [33,34]. The reduced blueshift from A to D indicates the weakened QCSE and thus leads to a shorter peak wavelength at low excitation. Difference in the degree of energy band tilt caused by QCSE may result in different screening speed of carrier to QCSE. The greater the energy band tilt, the more sensitive it is to the screening of the carrier, thereby leading to faster blueshift of peak wavelength with the excitation increased. Hence, we presume that at high excitation the longer wavelength from A to D is due to slower blueshift speed induced by weakened QCSE.
Fig. 4. Excitation-dependent (a) peak PL intensity and (b) peak wavelength at positions A, B, C, and D, respectively.
Figure 5(a) shows the Raman intensity mapping of the GaN ${\textrm{EH}}_{2}^{\rm H} $ peak, which also replicates the air-cavity array. The air cavity is marked by a dotted circle. Figure 5(b) shows the GaN ${\textrm{EH}}_{2}^{\rm H} $ peak position variation from the flat area to the air-cavity center. The inset of Fig. 5(b) displays a typical Raman spectrum collected from the Raman mapping. When approaching the air-cavity center, the GaN ${\textrm{EH}}_{2}^{\rm H} $ phonon peak shows a blueshift from 570.13 to 569.91 cm−1, indicating a gradually decreased compressive stress [26,35]. The stress (σxx = σyy) can be calculated using the equation [36–38]:
where $\Delta \omega $ is the ${\textrm{EH}}_{2}^{\rm H} $ phonon peak shift, and k is the absolute calibration constant of 2.56 cm-1/GPa [39]. Compared to flat areas, compressive stress is reduced by 86 MPa in the air-cavity center.Fig. 5. (a) The mapping of GaN ${\textrm{EH}}_{2}^{\rm H} $ phonon peak intensity; (b) the ${\textrm{EH}}_{2}^{\rm H} $ phonon peak position variation from the flat area to the air-cavity center; (c) residual stress distribution within GaN film grown on FSS (top) and air-cavity PSS (bottom) when cooling from 1040 to 26.8 ℃; (d) the GaN cross-sectional residual stress recorded at one micrometer from the sapphire/GaN interface in FSS-LED and PSS-LED models.
During the epitaxial growth of GaN/sapphire template, compressive stress was generated due to different thermal expansion coefficients. Using the finite element analysis software COMSOL Multiphysics 5.5, we calculated the residual stress distribution in the GaN film within FSS-LED and PSS-LED models. The fabrication of GaN-based LEDs typically starts with the deposition of a GaN film on a sapphire wafer at a temperature of 1040℃, after which it is cooled to room temperature. The detailed models and parameters are provided in Supplement 1. Figure 5(c) presents the residual stress in FSS-LED and PSS-LED after the cooling process. The negative values indicate that the residual stress in GaN is compressive stress due to the relatively small thermal expansion coefficient. The GaN cross-sectional stress at one micrometer from the sapphire/GaN interface in FSS-LED and PSS-LED models is shown in Fig. 5(d). The residual compressive stress of about 790 MPa was distributed homogeneously in the FSS-LED model after the cooling process. However, periodic stress gradients were generated in the PSS-LED. The stress in the air cavity and flat areas is smaller than that in the FSS-LED model, which significantly reduces the overall residual stress in PSS-LED. The smallest stress appears in the air-cavity center and is reduced by 96 MPa compared to the flat areas. Since the GaN shrinkage in this area is not hindered by sapphire during cooling, less compressive stress is generated. Such reduced residual stress weakens the QCSE. Therefore, the increased PL intensity and the reduced blueshift from positions A to D were observed in Fig. 2 and 4.
Figure 6(a) presents the PL external quantum efficiency (EQE) at different positions [40–42], which was normalized to the maximum of all curves. From A to D, the normalized EQEs gradually increase within the excitation power density range. Compared to position A, the EQE at 3.1 W/cm2 was improved by 78%, 187%, and 255% for positions B, C, and D, respectively. The efficiency droop, which is calculated as the percentage of efficiency reduction at 9.1 W/cm2 with respect to its peak efficiency, was aggravated by 2.09%, 6.02%, 8.55%, and 16.97% from A to D, respectively. The Pmax, defined as the excitation power density corresponding to the peak EQE, is about 8.1, 6.1, 6.1, and 5.5 W/cm2 at positions A, B, C, and D, respectively. Although the EQE increases gradually when approaching the air cavity center due to smaller QCSE and fewer defects, smaller Pmax and severer efficiency droop were exhibited. These results suggest that smaller QCSE and fewer defects have little impact or even a negative influence on the reduction of efficiency droop [43]. Figure 6(b) shows the variation of FWHM at different positions. Compared to position A, the FWHM of positions B to D was significantly narrowed. On the one hand, fewer TDs can reduce the transition from higher energy extended states [29–31,44]. On the other hand, QSCE can also lead to a PL peak linewidth broadening, which has been observed earlier in the GaAs materials [45,46]. Consequently, the smaller FWHM at positions B to D can be attributed to its reduced defect density and QCSE. In addition, at high excitation, the FWHM for positions A to D broadens faster as the excitation power increases. The PL spectral broadening with excitation power results from the band-filling effect of the accumulated carriers in the MQWs. A faster broadening in FWHM demonstrates a stronger band-filling effect in the air cavity area, which implies that the effective carrier concentration is increased due to improved crystal quality. Consequently, the high-carrier density-related non-radiative recombination process may be responsible for severer droop behavior in the air-cavity areas [43,47,48].
To quantify the contribution of crystal quality and QCSE of air-cavity areas, the PL internal quantum efficiency (IQE) at different positions can be calculated using the power law relation linking the integrated PL intensity of the spectrum and the excitation pumping power [49–51]. The relation between the integrated PL intensity (LPL) and the excitation pumping power (PPL) is given by
Figure 7(a) illustrates the excitation power versus integrated PL intensity to extract APL, BPL, and CPL coefficients. The experimental results are presented by different dot symbols, while the fits of Eq. (2) are presented by solid lines. Figure 7(b) shows the IQE calculated using Eq. (3). The photon recycling factor is assumed to be zero in this calculation. The calculated IQE increased gradually from positions A to D. Compared to position A, the IQEs at 3.1 W/cm2 increased by 61.8%, 137%, and 223% for positions B, C, and D, respectively. As the excitation power increases, the IQE keeps increasing for positions A and B since the effective carrier concentration is too low to reach a density where the high-carrier density-related non-radiative recombination dominates. While for positions C and D, the IQE exhibit a droop phenomenon at high excitation. These results also demonstrate that the effective carrier concentration is increased gradually from A to D, which also coincides with the EQE and FWHM results.
Fig. 7. (a) Power-dependent integrated PL intensity of positions A to D; (b) IQE versus the excitation power density at positions A to D.
4. Conclusion
In summary, we distinguished the difference in the local luminous properties and calculated the spatial-resolved LEE, IQE, and EQE between the air-cavity and flat areas of the PSS-LED. It was revealed that the enhancement of LEE by air-cavity array structure only occurs in the air-cavity area, while the improvement of stress occurs in both air-cavity and flat areas. Compared to flat areas, the average LEE of air-cavity areas is improved by 65%, and the residual stress is reduced by 89 MPa. At 3.1 W/cm2, such increased LEE and reduced stress combined with reduced defect density, result in a 255% increase in EQE and a 223% increase in IQE in the air-cavity center. Additionally, the narrowed FWHM and reduced blueshift were observed in the air-cavity areas due to improved crystal quality and reduced stress. More pronounced band filling occurs in the air cavity area due to increased effective carriers, thus resulting in aggravated efficiency droop due to the high-carrier density-related nonradiative recombination. We believe that the fundamental understanding of the effect of the air-cavity array on the LEE, stress, and local PL properties gained through this quantitative study will provide a valuable baseline for the design of advanced devices.
Funding
National Key Research and Development Program of China (2021YFB3602000); Natural Science Foundation of Shaanxi Province (2020JQ-074); National Natural Science Foundation of China (6210030651); National Natural Science Foundation of China (61905191); China Postdoctoral Science Foundation (2019M653640).
Acknowledgments
The micro-Raman work was done at the Instrumental Analysis Center of Xi'an Jiaotong University. The authors also thank Y. Wang for her help.
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.
Supplemental document
See Supplement 1 for supporting content.
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