Abnormal Radiative Interband Transitions in High-Al-Content AlGaN

Article pubs.acs.org/journal/apchd5

Abnormal Radiative Interband Transitions in High-Al-Content AlGaN Quantum Wells Induced by Polarized Orbitals Li Chen,† Jinjian Zheng,† Wei Lin,*,† Jinchai Li,† Kongyi Li,† Pai Sun,† Guang-yu Guo,‡ and Junyong Kang*,† †

Department of Physics, OSED, Fujian Provincial Key Laboratory of Semiconductor Materials and Applications, Xiamen University, Xiamen 361005, China ‡ Department of Physics, National Taiwan University, Taipei 10617, Taiwan ABSTRACT: AlGaN has attracted considerable interest as a wide (direct)-band-gap semiconductor with high thermal and mechanical stability. Thus, it can be used to develop optoelectronic devices operating within the ultraviolet region at high power and under harsh environmental conditions. Despite their recognized prospective applications, Al-rich AlGaN optical devices suffer from low external quantum efficiency. To trace the origin of the said problem, a cathodoluminescence system combined with two scanning probes was set up to investigate the cross-section luminescence of the sample related to application bias. The luminescence from the quantum wells in a deep ultraviolet light-emitting device was identified by layerresolved spectroscopy. Results show that the primary radiative emission at the band edge exhibits an abnormal behavior, which is different from the other emission that is dependent on external electric fields. First-principles simulations demonstrate that the dispersive crystal field split-off hole (CH) band caused by hole deconfinement is responsible for the abnormal radiative emissions. Analysis of the constituent orbitals of the hole bands reveals a strong head-overhead lobe structure in the barrier along the [0001] direction in the pz orbitals, contributing mainly to the CH band. Meanwhile, a weak side-by-side (0001) in-plane lobe structure is present in the px and py orbitals, contributing to the heavy and light hole bands. This study may serve as a basis for further investigations on quantum efficiency improvement in high-Al-content AlGaN optoelectronic devices. KEYWORDS: AlGaN, UV, quantum structure, III−V semiconductors based LEDs. The internal electric field in AlGaN quantum wells (QWs) brings in a large spatial separation between electron and hole wave functions, thereby generating a low radiative recombination rate and IQE. In addition, a high hole concentration in p-AlGaN is hardly accessible due to the high activation energy of Mg. The resulting large electron leakage leads to the low EIE. Another serious problem is the polarization switch from transverse-electron emissions to transverse-magnetic emissions and the lack of available transparent electrodes, which cause the low LEE in AlGaNbased DUV LEDs. Many works have attempted to improve these efficiencies. A high-quality AlN template with a low threading dislocation density was obtained by using multilayer buffer or patterned sapphire substrates.2−6 To improve IQE, different types of electric blocking layer have been introduced to reduce electron leakage.7−9 The strong internal electric field in AlGaN QWs was studied to control the polarization of emitting light.10−12 In a recent study, different doping methods, such as Mg modulation doping in the barrier of the AlxGa1−xN/GaN superlattices, Mg and Si-δ co-doping of AlGaN superlattices,

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ltraviolet (UV) light has many practical applications, such as in high-density optical storage, extreme ultraviolet lithography, label tracking, barcoding, currency detection, optical sensing, disinfection, surface water decontamination, polymer and printer ink curing, bug zappers, and medical processes. UV light-emitting diodes (LEDs) and laser diodes are common environmentally friendly, energy-conserving, safe, and portable solid-state sources of UV light. III-Nitrides as direct-band-gap semiconductors are promising materials for the fabrication of short-wavelength optical and high-power electronic devices. Meanwhile, AlGaN as a direct-band-gap material with a tunable band-gap energy ranging from 3.4 eV for GaN to 6.2 eV for AlN shows promise in UV LED fabrication. An LED with a short-wavelength emission of 210 nm was fabricated by p−i−n homojunction AlN in 2006.1 However, the quantum efficiency of AlGaN-based deep UV (DUV) LEDs decreases rapidly with increasing Al composition in the intrinsic material properties of AlGaN. External quantum efficiency (EQE) is the product of internal quantum efficiency (IQE), electron injecting efficiency (EIE), and light extraction efficiency (LEE). All of these efficiencies are responsible for the low EQE in AlGaN-based DUV LEDs. Given the lack of native substrates, high threading dislocation density and large stress are found in epitaxial layers, resulting in the low IQE of AlGaN© XXXX American Chemical Society

Received: March 30, 2017

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Figure 1. (a) Schematic of the AlGaN DUV LED. (b) SEM image of the cross-section sample. Four typical points are marked as A, B, C, and D.

orbitals on the polarization field was recognized via the confinement characteristic.

and multidimensional Mg-doped superlattices have been employed to obtain p-AlGaN with high hole concentrations.13−15 In addition, AlGaN has been replaced with p-GaN to form a good contact layer. However, the emitting light is absorbed by GaN. In light of the absorption, Flip-chip was fabricated to enhance LEE through the removal of the sapphire substrate.16 The EQE of DUV LEDs is still limited to 2−3%, with an output power of 176 mW. Light emission in AlGaN is predominated by transverse-magnetic-polarized light propagating perpendicular to the c-axis, with the light’s electric field parallel to the c-axis (E||c). The strongly anisotropic emission is attributed to the unique valence band structure of high-Alcontent AlGaN. The topmost VB of high-Al-content AlGaN is the CH band. Compared to the small spin split off between heavy hole (HH) and light hole (LH), the CH bands are more split off from HH and LH bands. Accordingly, the primary emission light exhibits E||c polarization, which limits the LEE and finally the EQE. Intensive efforts have been exerted to understand light polarization degree. Although previous studies have attempted to switch the light polarization via surface plasmon polariton and localized surface plasmon, the fundamental mechanism behind the quantum states in CH band coupling and the characteristics of the related interband transition remain unclear to date. In general, the electronic properties of semiconductors depend sensitively on their orbital structure, including the relative energies, filling, and intermixing of the orbitals. A wellknown example is the optical transition between s-like conduction and p-like valence bands in AlGaN, yielding the strongly anisotropic light emission. The transition between the s and p states in AlGaN plays a key role in light emission. In the present work, we investigated the influence of the internal electric field in AlGaN quantum wells (QWs) and the interaction between IQE and LEE in DUV LEDs. We constructed a cathodoluminescence (CL) system combined with two scanning probes while applying variable biases. The CL spectra of different epitaxial layers were obtained, and each emission was identified. The variation in CL emissions was characterized by applying different biases to form an additional electric field between AlGaN QWs. On the basis of firstprinciples calculations, the relationship between the emission peak and the interband transition was established. The band structure and the partial charge distribution of relevant quantum states in the QW were considered to shed light on the constituent orbitals of the CH, heavy hole, and light hole in the radiative transition. The different dependence of the

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EXPERIMENTAL SECTION The CL mode of a scanning electron microscope (SEM) in an ultra-high-vacuum chamber was used. The use of a thermal field emitter as the source of SEM (Orsay ECLIPSE) conferred high brightness, high angular intensity, small virtual source size, relatively low energy spread, low noise, and stable operation. Additionally, it can obtain SEM images with a lateral resolution of 10 nm. Electrons from the source can be used to excite the sample. A moveable optical fiber was set to collect the light emitted from the sample. The collected light was dispersed by a 320 mm focal-length monochromator (Horiba Jobin Yvon iHR320) with a wavelength range of 200−1500 nm. The monochromator, equipped with 1200 grooves/mm gratings, has a spectral resolution of 0.06 nm. A cooled photomultiplier tube was mounted to the monochromator. Two scanning probes in the system were used to apply bias to the sample by contacting it. The whole system was placed inside a cooling cryostat, allowing it to be excited at various temperatures. We prepared AlGaN-based MQW LEDs on a c-plane (0001) sapphire substrate via metalloorganic chemical vapor deposition, with the complete structures shown in Figure 1a. AlN and AlGaN buffer layers were first grown on sapphire, followed by a 2.5μm-thick n-Al0.55Ga0.45N layer, an active layer, a 25-nm-thick AlGaN electron blocking layer, a 25-nm-thick p-AlGaN layer, and a 150-nm-thick p-GaN layer. The active layer comprised five pairs of 10 nm Al0.60Ga0.40N/10 nm Al0.65Ga0.36N QWs with the Al content and thickness determined by the secondary ion mass spectroscopy. The cross-section of the sample was cleaved and set on a sample stage in the ultra-high-vacuum chamber (1 × 10−10 Torr). Under the SEM image (Figure 1b), the electron beam was moved to selected points of the cross-section with an interval of 50 nm along the c-axis. The fiber probe was driven close to the electron beam injection point for light emission collection. Two tips interacted with the p-type and n-type. The CL spectra of the selected points were obtained under different biases. To examine the conductivity of each layer, the electronbeam-induced current (EBIC) was measured through the ptype. APSYS simulation with complete LED structure was conducted to check the variations in the voltage-dependent band. The structural and electronic properties of AlGaN/AlN QWs were studied through first-principles simulations using a B

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increased (Figure 2b). The emission intensities of P2 and P3 were high while electron beam injection was performed at the active layers (Figure 2c). Both P2 and P3 emissions decreased after injecting at the p-type layers (Figure 2d). The emission intensity of P1 decreased as the electron beam separated from the n-type layer. Hence, the P1 emission was considered to relate to the Si-doping AlGaN layer. This assignment was further confirmed by the agreement between the P1 emission energy of 4.729 eV and the estimation value of the band-gap energy for the Al0.55Ga0.45N layer. As the primary electrons underwent a series of both elastic and inelastic stochastic scattering events, the distribution of electron trajectories can be estimated by classical Monte Carlo simulation, and, in our case, the generation volume would be about 500 nm in diameter. As shown in Figure 2b, peak P3 was observed clearly as QWs were excited by the electrons scattering into it. With electron beam injection from point A to point B in the n-type layer, the intensity of P1 gradually decreased, whereas those of P2 and P3 gradually increased. This result may be attributed to the increased excited volume in QWs due to distance. Both P2 and P3 emission intensities were relatively high in the active layer because of the large number of electron−hole pairs. For these reasons, P2 and P3 emissions originated from the recombination of electrons and holes in QWs. Except for P1, P2, and P3 emissions, no other emission was associated with the p-AlGaN layer. This observation is reasonable because only a 25-nm-thick p-AlGaN layer was contained in the p-type layers of our DUV LED sample. Even for the main part of the 150 nm p-GaN layer, GaN:Mg emission remained weak at around 390 nm from the band gap of AlGaN. The above analysis indicates that the P2 and P3 emissions are closely linked to the QWs. The transitions between quantum levels depend on the band structures in the QWs. Band bending can be modified by the internal electric field, leading to a shift in quantum level energy. Thus, the emission energy from quantum levels varies depending on the strength of the internal electric field. To further assign P2 and P3 emissions, we applied different external electric fields to modify the polarization field in the AlGaN QWs. By using tips to contact p-type and n-type, similar CL spectra were measured at the selected points of the crosssection DUV LED. At +10 V and −10 V, typical CL spectra were observed (Figure 3a) by electron beam injection in point C; only P2 emission was found with a shift of 17.5 meV. APSYS simulations showed that the energy difference in quantum levels between the positive voltage and zero voltage applications was up to 12 meV. Hence, the shift of P2 emission is influenced dominantly by the external electric field, which confirms that the radiative recombination of electron−hole pairs between quantum levels is responsible for the P2 emission. However, no distinct shift was observed for the P3 emission between the two biases, as shown in Figure 3a. As we discussed above, the P3 emission is closely related to QWs, but it disobeys the rules of quantum level shift under addition of electric fields. This abnormal behavior in the P3 emission could be the weak external electric field in the QW region if large voltage drops were present in the p-type and n-type layers because of poor conductivity. To check the conductivity of our sample, the EBIC was determined, as shown in Figure 3b. The induced currents in the p-type layer remained unchanged, and the same occurs in the n-type layer. It is visible that a steep slope was formed between the p-type and n-type layers, which

projector-augmented-wave approach for Perdew−Wang 91 generalized-gradient approximations as implemented in the Vienna Ab Initio Simulation Package. A plane-wave basis set with a 500 eV cut off was used to expand the electronic wave functions. A Monkhorst−Pack k-point mesh of 8 × 8 × 8 was used throughout the calculations to obtain well-converged results. Ga 3d electrons were included in the valence band. A theoretical model of AlGaN QWs was constructed with supercells containing 2 × 2 × 4 unit cells. For simplicity, the well was constructed by 2 × 2 × 2 unit cells of AlGaN with Al substitutional composition x = 0.75, and the barrier was composed of 2 × 2 × 2 unit cells of AlN. Geometric optimization was performed by relaxing all degrees of freedom using the conjugate gradient algorithm in which the total energy was converged within 1 meV.

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RESULTS AND DISCUSSION With electron beam injection at selected points in the crosssection of the LED sample, CL spectra were obtained in the wavelength range of 200−800 nm. An intense CL emission band composed of three peaks at 262, 266, and 273 nm, which were marked as P1, P2, and P3, respectively, was observed near the band edge. Since the emission around 390 nm was much weaker and it was difficult to deduce reliable values, only the band edge emissions were considered below. The band edge emissions varied from different layers or structures, as shown by the typical line shapes of points A, B, C, and D in Figure 2. On account of the electron beam injection at the n-type AlGaN layer, P1 emission was dominant with a shoulder appearing at a lower energy (Figure 2a). When the electron beam moved closer to an active layer, the emission intensity of P1 gradually decreased, whereas those of P2 and P3

Figure 2. CL spectrum of point A (a), point B (b), point C (c), and point D (d). C

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Figure 3. (a) CL spectra under +10 V and −10 V bias. (b) EBIC testing for different layers of the cross-section DUV LED sample.

Figure 4. QW band structure together with the projected density of states (DOS) of the pz (a), py (b), and px (c) orbitals. The magnitude of the projected DOS is represented by the solid dot size. (d−f) Corresponding partial charge density. The isosurfaces of the charge density are represented in yellow with an isovalue of 0.02.

band contributes to P3 emission, whereas HH and LH have larger contributions to P2 emission. The ratios of optical transition elements of the 1e-CH transition to that of the 1eHH and 1e-LH transitions were estimated to be 2.1 and 1.1, respectively. This result suggests that the strong light emission from the QWs was caused by the recombination of the 1e-CH transition. The higher CH band emission conforming to the experimental observation of the P3 emission further demonstrated the assignment of P3 emission to the 1e-CH transition. Compared with the HH/LH-bands, which are discrete quantum states, the CH-band consists of atomic p orbitals parallel to the c-axis. Thus, the CH transitions did not contribute to the optical emission along the c-axis. The dispersion of the CH-band accounted for the abnormal radiative emission. In general, the CBM is dominated by the s orbitals that are highly isotropic, and the overlap integral with s orbitals is insensitive to the orientation.17−19 However, close inspection of

implied that the conductivity in the vertical direction of the ptype and n-type layers is good and that substantial electrons are depleted in the QW region. After applying an external electric field on the QW region, a distinct shift in P3 emission was barely observed, which is attributed to other underlying causes in large part. The quantum levels in AlGaN QWs were further characterized by first-principles calculations. In general, the band edge emission for AlGaN is closely related to the transition from the conduction band minimum (CBM) to the valence band maximum (VBM). The quantum levels that are involved in the transition are composed of 1e at the CBM, HH, LH, and CH at the VBM. On the basis of the calculated band structure in Figure 4a−c, the valence band exhibited some unconventional features when the topmost valence band was the CH band. The resulting negative crystal-field splitting was estimated to be −0.12 eV. Inspection of Δcr consistent with the energy difference between P2 and P3 validated that the CH D

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strated by the hole deconfinement in the dispersive CH-band. Close inspection of the constituent orbitals of the hole bands revealed a strong head-over-head lobe structure in the barrier along the [0001] direction in the pz orbitals, contributing mainly to the CH-band. Meanwhile, a weaker side-by-side (0001) in-plane lobe structure appears in the px and py orbitals, contributing to the heavy and light hole bands. The results could serve as a basis for exploring orbital-dependent properties to improve quantum efficiency in high-Al-content AlGaN optoelectronic devices.

the constituent orbitals in the valence band revealed that the CH-bands are composed of pz orbitals overlapping in a strong head-over-head fashion along the [0001] direction. By contrast, the HH and LH bands are dominated by the N px and py orbitals exhibiting (0001) in-plane lobe structures and only overlapping with one another in a weak side-by-side fashion. The constituent orbitals are evident in the charge density map shown in Figure 4d−f. Compared with the in-plane px and py orbitals, the short tunneling distance between the out-of-plane lobes for the pz orbital is more accessible along the [0001] direction. The magnitude of the tunneling effect of the hole bands in the barrier was measured in terms of electric conductivity given by σ = nV qμ (1)

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Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected].

where nV is the charge densities of related states at the VBM and μ is the hole mobility. The charge densities of related states nV at the VBM can be evaluated by integrating the partial densities of states DV(E) projected on a given orbital. nV =

ORCID

Wei Lin: 0000-0003-2504-9452 Notes

EV

∫−∞ D V (E) dE

AUTHOR INFORMATION

The authors declare no competing financial interest.

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(2)

On the basis of the simulation results, the ratios of electric conductivity σCH, σHH, and σLH to σCH were estimated to be 1.0, 0.90, and 0.87, respectively. This result indicates that σCH is higher than σHH and σLH. The σCH, with higher conductivity, was caused by the capability of the carriers to transport through the barrier. Deconfinement of the CH band in the QW is responsible for the unusual optical phenomenon. To provide better confinement, we theoretically consider AlGaN/AlN QWs with a 7 times thicker barrier. Figure 5 illustrates the band

ACKNOWLEDGMENTS This work was supported by National Key R&D Program of China (2016YFB0400101), the Fundamental Research Funds for the Central Universities (20720170012, 20720160121, and 20720150027), and the Natural Science Foundations of Fujian Province (2015J01028).

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REFERENCES

(1) Taniyasu, Y.; Kasu, M.; Makimoto, T. An aluminium nitride lightemitting diode with a wavelength of 210 nanometres. Nature 2006, 441, 325−328. (2) Hirayama, H.; Yatabe, T.; Noguchi, N.; Ohashi, T.; Kamata, N. 231−261 nm AlGaN deep-ultraviolet light-emitting diodes fabricated on AlN multilayer buffers grown by ammonia pulse-flow method on sapphire. Appl. Phys. Lett. 2007, 91, 2007−2009. (3) Hirayama, H.; Noguchi, N.; Yatabe, T.; Kamata, N. 227 nm AlGaN Light-Emitting Diode with 0.15 mW Output Power Realized using a Thin Quantum Well and AlN Buffer with Reduced Threading Dislocation Density. Appl. Phys. Express 2008, 1, 51101. (4) Hirayama, H.; Fujikawa, S.; Noguchi, N.; Norimatsu, J.; Takano, T.; Tsubaki, K.; Kamata, N. 222−282 nm AlGaN and InAlGaN-based deep-UV LEDs fabricated on high-quality AlN on sapphire. Phys. Status Solidi A 2009, 206, 1176−1182. (5) Imura, M.; Nakano, K.; Narita, G.; Fujimoto, N.; Okada, N.; Balakrishnan, K.; Iwayaa, M.; Kamiyamaa, S.; Amanoa, H.; Akasakia, I.; Norob, T.; Takagib, T.; Bandoh, A. Epitaxial lateral overgrowth of AlN on trench-patterned AlN layers. J. Cryst. Growth 2007, 298, 257−260. (6) Kim, M.; Fujita, T.; Fukahori, S.; Inazu, T.; Pernot, C.; Nagasawa, Y.; Hirano, A.; Ippommatsu, M.; Iwaya, M.; Takeuchi, T.; Kamiyama, S.; Yamaguchi, M.; Honda, Y.; Amano, H.; Akasaki, I. AlGaN-based deep ultraviolet light-emitting diodes fabricated on patterned sapphire substrates. Appl. Phys. Express 2011, 4.09210210.1143/APEX.4.092102 (7) Hirayama, H.; Tsukada, Y.; Maeda, T.; Kamata, N. Marked enhancement in the efficiency of deep-ultraviolet AlGaN light-emitting diodes by using a multiquantum-barrier electron blocking layer. Appl. Phys. Express 2010, 3.03100210.1143/APEX.3.031002 (8) Kim, M.; Schubert, M.; Dai, Q.; Kim, J.; Schubert, E.; Piprek, J.; Park, Y. Origin of efficiency droop in GaN-based light-emitting diodes. Appl. Phys. Lett. 2007, 91, 8−10. (9) Chen, F.; Liou, B.; Chang, Y.; Chang, J.; Kuo, Y.; Kuo, Y. Numerical analysis of using superlattice-AlGaN/InGaN as electron blocking layer in green InGaN light-emitting diodes. Proc. SPIE 2013, 8625, 862526.

Figure 5. QW band structure with the thicker barrier.

structure of AlGaN/AlN QWs with a thicker barrier. The CH band was less dispersive along the high-symmetry lines from Γ to A in the Brillouin zone corresponding to the [0001] direction, suggesting that the CH band was localized in the QW. Drawn from the above discussion, the deconfinement of the CH band is disadvantageous for efficient light emission.

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CONCLUSION In this work, we described an advanced SEM-CL system with two scanning probes, where biases were applied to the sample. We investigated the spectra of a cross-section DUV LED point by point, recognizing the emission light from different layers or structures. After applying different biases, we observed the different characteristics of HH/LH-band and CH-band emissions. The CH-band emission at the band edge exhibited abnormal behavior in contrast to the other emission, dependent on the external electric fields. First-principles calculations showed abnormal radiative interband transitions, as demonE

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(10) Park, S.; Chuang, S. Spontaneous polarization effects in wurtzite GaN/AlGaN quantum wells and comparison with experiment. Appl. Phys. Lett. 2000, 76, 1981. (11) Leroux, M.; Grandjean, N.; Laügt, M.; Massies, J.; Gil, B.; Lefebvre, P.; Bigenwald, P. Quantum confined Stark effect due to built-in internal polarization fields in (Al, Ga) N/GaN quantum wells. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, R13371−R13374. (12) Zhou, L.; Dimakis, E.; Hathwar, R.; Aoki, T.; Smith, D.; Moustakas, T.; Goodnick, S.; McCartney, M. R. Measurement and effects of polarization fields on one-monolayer-thick InN/GaN multiple quantum wells. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 1−5. (13) Liu, Z.; Yi, X.; Yu, Z.; Yuan, G.; Liu, Y.; Wang, J.; Li, J.; Lu, N.; Ferguson, I.; Zhang, Y. Impurity Resonant States P-Type Doping in Wide-Band-Gap Nitrides. Sci. Rep. 2016, 6, 19537. (14) Li, J.; Yang, W.; Li, S.; Chen, H.; Liu, D.; Kang, J. Enhancement of p-type conductivity by modifying the internal electric field in Mgand Si-δ-codoped AlxGa1−xN/AlyGa1−yN superlattices. Appl. Phys. Lett. 2009, 95, 151113. (15) Zheng, T. C.; Lin, W.; Liu, R.; Cai, D. J.; Li, J. C.; Li, S. P.; Kang, J. Y. Improved P-Type Conductivity in Al-Rich AlGaN Using Multidimensional Mg-Doped Superlattices. Sci. Rep. 2016, 6, 21897. (16) Tanikawa, T.; Sano, T.; Kushimoto, M.; Honda, Y.; Yamaguchi, M.; Amano, H. Fabrication of InGaN/GaN multiple quantum wells on (1−101) GaN. Jpn. J. Appl. Phys. 2013, 52, 08JC05. (17) Lin, W.; Jiang, W.; Gao, N.; Cai, D.; Li, S.; Kang, J. Optical isotropization of anisotropic wurtzite Al-rich AlGaN via asymmetric modulation with ultrathin (GaN)m/(AlN)n superlattices. Laser Photon. Rev. 2013, 7, 572−579. (18) Uenoyama, T.; Suzuki, M. Valence subband structures of wurtzite GaN/AlGaN quantum wells. Appl. Phys. Lett. 1995, 67, 2527. (19) Miao, M.; Janotti, A.; Van De Walle, C. Reconstructions and origin of surface states on AlN polar and nonpolar surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 1−9.

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