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  • Editor: Bernard Kippelen
  • Vol. 19, Iss. S4 — Jul. 4, 2011
  • pp: A1008–A1021
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Optical polarization properties of m-plane Al x Ga1- x N epitaxial films grown on m-plane freestanding GaN substrates toward nonpolar ultraviolet LEDs

Kouji Hazu and Shigefusa F. Chichibu  »View Author Affiliations


Optics Express, Vol. 19, Issue S4, pp. A1008-A1021 (2011)
http://dx.doi.org/10.1364/OE.19.0A1008


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Abstract

Light polarization characteristics of the near-band-edge optical transitions in m-plane Al x Ga1- x N epilayers suffering from anisotropic stresses are quantitatively explained. The epilayers were grown on an m-plane freestanding GaN substrate by both ammonia-source molecular beam epitaxy and metalorganic vapor phase epitaxy methods. The light polarization direction altered from Ec to E//c at the AlN mole fraction, x, between 0.25 and 0.32, where E is the electric field component of the light and ⊥ and // represent perpendicular and parallel, respectively. To give a quantitative explanation for the result, energies and oscillator strengths of the exciton transitions involving three separate valence bands are calculated as functions of strains using the Bir-Pikus Hamiltonian. The calculation predicts that the lowest energy transition (E1) is polarized to the m-axis normal to the surface (X3) for 0<x≤1, meaning that E1 emission is principally undetectable from the surface normal for any in-plane tensile strained Al x Ga1- x N. The polarization direction of observable surface emission is predicted to alter from c-axis normal (X1) to c-axis parallel (X2) for the middle energy transition (E2) and X2 to X1 for the highest energy transition (E3) between x = 0.25 and 0.32. The experimental results are consistently reproduced by the calculation.

© 2011 OSA

1. Introduction

Wurtzite AlxGa1- xN alloys are an attractive candidate for realizing ultraviolet (UV) light emitters and high-power high-frequency electronic devices, because they have large bandgap energies ranging from 3.43 eV (x = 0) to 6.01 eV (x = 1) and they principally are a hard material. Recently, a 210-nm electroluminescence (EL) has been demonstrated for c-plane AlN p-i-n homojunction light-emitting-diodes (LEDs) [1

1. Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006). [CrossRef] [PubMed]

]. However, the external quantum efficiency (EQE) was as low as 10-6% at 300 K, which was extremely lower than that of conventional blue or violet InGaN LEDs being ~84.3% for a 444 nm InGaN LED [2

2. Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010). [CrossRef]

]. To improve overall performance of AlGaN-based deep UV (DUV) LEDs, many researchers have been trying to improve AlGaN quality and to optimize the multiple-quantum-well (MQW) design. As a consequence, the EQE values of 6.7% for a 345 nm LED [3

3. H. Tsuzuki, F. Mori, K. Takeda, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, H. Yoshida, M. Kuwabara, Y. Yamashita, and H. Kan, “Novel UV devices on high-quality AlGaN using grooved underlying layer,” J. Cryst. Growth 311(10), 2860–2863 (2009). [CrossRef]

], over 3% for 244-280 nm LEDs [4

4. X. Hu, J. Deng, J. P. Zhang, A. Lunev, Y. Bilenko, T. Katona, M. S. Shur, R. Gaska, M. Shatalov, and A. Khan, “Deep ultraviolet light-emitting diodes,” Phys. Stat. Solidi A 203(7), 1815–1818 (2006). [CrossRef]

], and 0.003% for a 222 nm LED [5

5. H. Hirayama, N. Noguchi, and N. Kamata, “222 nm Deep-Ultraviolet AlGaN Quantum Well Light-Emitting Diode with Vertical Emission Properties,” Appl. Phys. Express 3(3), 032102 (2010). [CrossRef]

] have been achieved. Obviously, the values are still insufficient for practical use.

Currently, above mentioned UV LEDs are grown along the c-axis. In these structures, spontaneous and piezoelectric polarization discontinuity at the heterointerfaces induces the electric fields in the structure, which are parallel to the growth direction. These electric fields separate the electron (e) and hole (h) wavefunctions to the opposite interfaces of quantum wells (QWs), resulting in low optical efficiency and the forward-current-induced blueshift of the c-plane LEDs. These effects are called as quantum-confined Stark effects (QCSEs) [6

6. D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984). [CrossRef]

]. To avoid QCSEs in (Al, In, Ga)N heterostructures, epitaxial growths on off-polar orientations such as (110) a-plane, and (100) m-plane (nonpolar planes) and (112), (201), and (10) planes (semipolar planes) have been attracting attentions [7

7. P. Waltereit, O. Brandt, A. Trampert, H. T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, and K. H. Ploog, “Nitride semiconductors free of electrostatic fields for efficient white light-emitting diodes,” Nature 406(6798), 865–868 (2000). [CrossRef] [PubMed]

13

13. R. Sharma, P. M. Pattison, H. Masui, R. M. Farrell, T. J. Baker, B. A. Haskell, F. Wu, S. P. DenBaars, J. S. Speck, and S. Nakamura, “Demonstration of a semipolar (10) InGaN/GaN green light emitting diode,” Appl. Phys. Lett. 87(23), 231110 (2005). [CrossRef]

]. In 2006, m-plane InGaN LEDs, whose EQEs were 3.1% at 435 nm [14

14. K. Okamoto, H. Ohta, D. Nakagawa, M. Sonobe, J. Ichihara, and H. Takasu, “Dislocation-Free m-Plane InGaN/GaN Light-Emitting Diodes on m-Plane GaN Single Crystals,” Jpn. J. Appl. Phys. 45(45), L1197–L1199 (2006). [CrossRef]

] and 38.9% at 405 nm [15

15. M. C. Schmidt, K.-C. Kim, H. Sato, N. Fellows, H. Masui, S. Nakamura, S. P. DenBaars, and J. S. Speck, “High Power and High External Efficiency m-Plane InGaN Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(7), L126–L128 (2007). [CrossRef]

], have been demonstrated using the low threading-dislocation (TD) density, free-standing (FS) GaN substrates [16

16. K. Fujito, K. Kiyomi, T. Mochizuki, H. Oota, H. Namita, S. Nagao, and I. Fujimura, “High-quality nonpolar m-plane GaN substrates grown by HVPE,” Phys. Stat. Solidi A 205(5), 1056–1059 (2008). [CrossRef]

], which were sliced from a sub-cm-thick c-plane FS-GaN grown by halide vapor phase epitaxy (HVPE). Schematic drawing of a c-plane FS-GaN boule grown on a c-plane Al2O3 substrate and a sliced m-plane FS-GaN is shown in Fig. 1(a)
Fig. 1 (a) Schematic drawing of a c-plane FS-GaN boule grown on a c-plane Al2O3 substrate by HVPE and a sliced m-plane FS-GaN. (b) X-ray rocking curves for the (100) diffraction of the m-plane FS-GaN. The x-rays were irradiated along the c-axis or a-axis, as shown in panel (c). (d) Schematic diagram of the notations of three axes.
. Subsequently, longer wavelength, 468 nm m-plane InGaN LEDs with EQEs higher than 15% have been reported [17

17. K. Iso, H. Yamada, H. Hirasawa, N. Fellows, M. Saito, K. Fujito, S. P. DenBaars, J. S. Speck, and S. Nakamura, “High Brightness InGaN/GaN Light Emitting Diode on Nonpolar m-plane Bulk GaN Substrate,” Jpn. J. Appl. Phys. 46(40), L960–L962 (2007). [CrossRef]

]. However, drastic decrease in the output power cannot be suppressed for the m-plane InGaN LEDs whose peak wavelength is longer than 470 nm. The reason for this is often attributed to the degradation of crystal quality, which is caused by the low growth temperatures required for achieving high InN mole fraction InGaN. To the best of our knowledge, nonpolar DUV LEDs have not been reported yet.

Possible reason for the low EQEs of DUV LEDs is the increase of TD and point defect densities [18

18. S. F. Chichibu, A. Uedono, T. Onuma, S. P. DenBaars, U. K. Mishra, J. S. Speck, and S. Nakamura, “Impact of Point Defects on the Luminescence Properties of (Al,Ga)N,” Mater. Sci. Forum 590, 233–248 (2008). [CrossRef]

] with increasing AlN mole fraction x. Indeed, high quality GaN and AlGaN alloys of reduced nonaradiative recombination center (NRC) concentration are indispensable to realize high efficiency UV LEDs. In addition to the extended defects such as TDs and stacking faults (SFs), there exist microscopic ones such as point defects, complexes, and impurities (O, C, and Si) in (Al, In, Ga)N crystals. From the results of the time-resolved photoluminescence (TRPL) and positron annihilation measurements, the origin of NRCs have been proposed to be certain point-defect complexes containing cation vacancies (VIII-X) [18

18. S. F. Chichibu, A. Uedono, T. Onuma, S. P. DenBaars, U. K. Mishra, J. S. Speck, and S. Nakamura, “Impact of Point Defects on the Luminescence Properties of (Al,Ga)N,” Mater. Sci. Forum 590, 233–248 (2008). [CrossRef]

]. Quite recently, radiative lifetime (τR) of AlN has been shown to increase with increasing point defect and impurity concentrations [19

19. T. Onuma, K. Hazu, A. Uedono, T. Sota, and S. F. Chichibu, “Identification of extremely radiative nature of AlN by time-resolved photoluminescence,” Appl. Phys. Lett. 96(6), 061906 (2010). [CrossRef]

,20

20. S. F. Chichibu, T. Onuma, K. Hazu, and A. Uedono, “Major impacts of point defects and impurities on the carrier recombination dynamics in AlN,” Appl. Phys. Lett. 97(20), 201904 (2010). [CrossRef]

], meaning that point defects play an important role in determining the recombination dynamics.

In order to optimize nonpolar AlxGa1- xN LED structures, the oscillator strengths (f) of three interband optical transitions in ideal, defect-free ones must be quantified as functions of light polarization direction and strains. With respect to the effect of anisotropic strain, optical polarization properties of (Al, In, Ga)N films and QWs of various orientations have been investigated [21

21. K. Domen, K. Kondo, A. Kuramata, and T. Tanahasi, “Gain analysis for surface emission by optical pumping of wurtzite GaN,” Appl. Phys. Lett. 69(1), 94–96 (1996). [CrossRef]

31

31. J. Bhattacharyya, S. Ghosh, and H. T. Grahn, “Optical polarization properties of interband transitions in strained group-III-nitride alloy films on GaN substrates with nonpolar orientation,” Appl. Phys. Lett. 93(5), 051913 (2008). [CrossRef]

]. Among them, Bhattacharyya et al. [31

31. J. Bhattacharyya, S. Ghosh, and H. T. Grahn, “Optical polarization properties of interband transitions in strained group-III-nitride alloy films on GaN substrates with nonpolar orientation,” Appl. Phys. Lett. 93(5), 051913 (2008). [CrossRef]

] have calculated the light polarization characteristics of the transitions involving three separate valence bands for m-plane AlxGa1- xN films on GaN, which suffer from anisotropic tensile stresses. They have estimated the anticrossing AlN mole fraction x = 0.10, and predicted that the lowest energy transition of AlxGa1- xN is predominantly polarization parallel to the substrate normal.

In this paper, the results of polarized CL measurement on m-plane AlxGa1- xN epilayers grown on the m-plane FS-GaN substrate are shown. All of the epilayers grown by ammonia-source molecular beam epitaxy (NH3-MBE) and metalorganic vapor phase epitaxy (MOVPE) suffer from in-plane anisotropic tensile stresses. The results are quantitatively explained by calculating the transition energies and oscillator strengths of excitonic transitions involving three separate valence bands, as functions of in-plane strains. For the calculation, Bir-Pikus Hamiltonian [32

32. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effect in Semiconductors, (Wiley, New York, 1974).

] was used without fitting parameters.

2.Experimental details and results

Samples investigated are approximately 100 to 400-nm-thick m-plane AlxGa1- xN epilayers grown on an 1-μm-thick GaN homoepitaxial layer, which was grown on the m-plane FS-GaN substrates [16

16. K. Fujito, K. Kiyomi, T. Mochizuki, H. Oota, H. Namita, S. Nagao, and I. Fujimura, “High-quality nonpolar m-plane GaN substrates grown by HVPE,” Phys. Stat. Solidi A 205(5), 1056–1059 (2008). [CrossRef]

]. The surface of as-received substrates was inspected by atomic-force microscopy (AFM) and found to have smooth morphology with monolayer atomic steps [16

16. K. Fujito, K. Kiyomi, T. Mochizuki, H. Oota, H. Namita, S. Nagao, and I. Fujimura, “High-quality nonpolar m-plane GaN substrates grown by HVPE,” Phys. Stat. Solidi A 205(5), 1056–1059 (2008). [CrossRef]

,33

33. T. Hoshi, K. Hazu, K. Ohshita, M. Kagaya, T. Onuma, K. Fujito, H. Namita, and S. F. Chichibu, “Impacts of anisotropic lattice relaxation on crystal mosaicity and luminescence spectra of m-plane AlxGa1-xN films grown on m-plane freestanding GaN substrates by NH3 source molecular beam epitaxy,” Appl. Phys. Lett. 94(7), 071910 (2009). [CrossRef]

,34

34. S. F. Chichibu, H. Yamaguchi, L. Zhao, M. Kubota, K. Okamoto, and H. Ohta, “Optical properties of nearly stacking-fault-free m-plane GaN homoepitaxial films grown by metal organic vapor phase epitaxy on low defect density freestanding GaN substrates,” Appl. Phys. Lett. 93(12), 129901 (2008) (erratum). [CrossRef]

]. However, the x-ray rocking curves (XRCs) exhibited multiple-peak or asymmetric line shapes [33

33. T. Hoshi, K. Hazu, K. Ohshita, M. Kagaya, T. Onuma, K. Fujito, H. Namita, and S. F. Chichibu, “Impacts of anisotropic lattice relaxation on crystal mosaicity and luminescence spectra of m-plane AlxGa1-xN films grown on m-plane freestanding GaN substrates by NH3 source molecular beam epitaxy,” Appl. Phys. Lett. 94(7), 071910 (2009). [CrossRef]

], as shown in Fig. 1(b). This multiple grain structure principally originates from the bowing of the original c-plane FS-GaN. Because the state-of-the-art m-plane FS-GaN [16

16. K. Fujito, K. Kiyomi, T. Mochizuki, H. Oota, H. Namita, S. Nagao, and I. Fujimura, “High-quality nonpolar m-plane GaN substrates grown by HVPE,” Phys. Stat. Solidi A 205(5), 1056–1059 (2008). [CrossRef]

] is prepared by slicing nearly 1-cm-thick c-plane FS-GaN grown in Ga-polar [0001] direction, the c-plane tilt (including the wafer bowing) and twist mosaics of the initial crystal are transferred to blurring of the c-axis and the greater m-plane tilt mosaic along the a-axis, respectively, as shown schematically in Fig. 1(a). For instance, the values of full width at half-maximum (FWHM) of XRCs for the present substrate were Δωmc = 76 and Δωma = 110 arcsec for the (100) diffraction along <0001> and <110> azimuths, respectively, [Fig. 1(b)] and Δωr = 100 arcsec for the (102) diffraction. The TD and stacking fault (SF) densities were lower than 5 × 106 cm−2 and 1 × 103 cm−1, respectively [33

33. T. Hoshi, K. Hazu, K. Ohshita, M. Kagaya, T. Onuma, K. Fujito, H. Namita, and S. F. Chichibu, “Impacts of anisotropic lattice relaxation on crystal mosaicity and luminescence spectra of m-plane AlxGa1-xN films grown on m-plane freestanding GaN substrates by NH3 source molecular beam epitaxy,” Appl. Phys. Lett. 94(7), 071910 (2009). [CrossRef]

,34

34. S. F. Chichibu, H. Yamaguchi, L. Zhao, M. Kubota, K. Okamoto, and H. Ohta, “Optical properties of nearly stacking-fault-free m-plane GaN homoepitaxial films grown by metal organic vapor phase epitaxy on low defect density freestanding GaN substrates,” Appl. Phys. Lett. 93(12), 129901 (2008) (erratum). [CrossRef]

]. The NH3-MBE of m-plane AlxGa1- xN epilayers (0≤x≤0.70) were carried out at 870-970 °C using metallic Ga (7N) and Al (6N) sources. The beam-equivalent-pressures of metallic Ga and NH3 were (2.1-4.0) × 10−5 and (1.3-4.1) × 10−2 Pa, respectively. The growth details are found in Ref. 35

35. R. People and J. C. Bean, “Calculation of critical layer thickness versus lattice mismatch for GexSi1-x/Si strained-layer heterostructures,” Appl. Phys. Lett. 47(3), 322–324 (1985). [CrossRef]

. A 150-nm-thick Al0.73Ga0.27N and approximately 2.1-μm-thick AlN epilayers were grown at 1120 °C on the same m-plane FS-GaN substrates by MOVPE. The reactor pressure was 2.02 × 104 Pa. Trimethylaluminum, triethylgallium, and NH3 were used as the precursors.

High-resolution x-ray diffraction (XRD) measurements were carried out using a four-crystal monochromator and an analyzer crystal (Bruker D8). A system with a one-dimensional detector array was used to obtain the x-ray reciprocal space mapping (X-RSM) images. The m-plane AlxGa1- xN epilayers of low x (0<x≤0.32) were confirmed by X-RSM to grow coherently on the GaN base layers. Other high AlN mole fraction epilayers (x≥0.35) were partially or nearly fully relaxed. Due to the tensile strain, the epilayers of x≥0.35 had macroscopic surface cracks. Representative X-RSM images for the pseudomorphic Al0.25Ga0.75N and mostly relaxed Al0.70Ga0.30N epilayers grown by NH3-MBE are displayed in Fig. 2
Fig. 2 Representative X-RSM images for the pseudomorhic m-plane Al0.25Ga0.75N epilayer grown on the m-plane FS-GaN taken in the vicinity of (a) (130) and (b) (201) diffraction spots. The X-RSM images for partially lattice-relaxed Al0.70Ga0.30N epilayers taken for (c) (120) and (d) (201) diffractions. Both the epilayers were grown by NH3-MBE. The closed circle in each panel shows the location of strain-free AlN, for comparison.
. In each panel, the ideal location for strain-free AlN is shown by a closed (red) circle. We note that critical layer thicknesses calculated by the model given by People and Bean [35

35. R. People and J. C. Bean, “Calculation of critical layer thickness versus lattice mismatch for GexSi1-x/Si strained-layer heterostructures,” Appl. Phys. Lett. 47(3), 322–324 (1985). [CrossRef]

] are 202 nm for x = 0.25 and 31 nm for x = 0.52, taking in-plane anisotropic lattice and thermal-expansion mismatches into account. Because both the pseudomorphic and relaxed films suffered from anisotropic strains, x values were calculated from the out-of-plane (m-axis) and in-plane (c- and a-axes) lattice parameters, which were obtained from a 2θ-ω scan for the (100) XRD and X-RSM results for (201) and (120) diffractions, respectively (see Fig. 2, for example). The relation εX3X3=(C12εXX1C13εX2X2)/C11 was used, where εX3X3, εX1X1and εX2X2 are the strains along m-, a-, and c-axes and Cijare the elastic stiffness constants of AlxGa1- xN alloys were assumed to obey [36

36. T. Onuma, T. Koyama, A. Chakraborty, M. McLaurin, B. A. Haskell, P. T. Fini, S. Keller, S. P. DenBaars, J. S. Speck, S. Nakamura, U. K. Mishra, T. Sota, and S. F. Chichibu, “Radiative and nonradiative lifetimes in nonpolar m-plane InxGa1-xN/GaN multiple quantum wells grown on GaN templates prepared by lateral epitaxial overgrowth,” J. Vac. Sci. Technol. B 25(4), 1524–1528 (2007). [CrossRef]

] Vegard’s law. In-plane tensile strains increased with x for the pseudomorphic (coherently grown) films, as shown in Fig. 3(a)
Fig. 3 (a) FWHM values for the XRCs (Δωmc, Δωma, and Δωr) of m-plane AlxGa1- xN epilayers grown by NH3-MBE and MOVPE. (b) Strain components εX1X1, εX2X2, and εX3X3 of the m-plane AlxGa1- xN films as a function of AlN mole fraction x.
. Conversely, the strains were gradually relaxed by the partial relaxation for x>0.32. For the quantitative discussion of polarization properties, we define the notations for the three axes: X 1 (perpendicular to the c-axis in the growth plane); X 2 (parallel to the c-axis in the growth plane); and X 3 (normal to the growth plane), as shown in Fig. 1(d).

The surface of the MOVPE epilayers exhibits well-aligned 0.26-nm-high monolayer atomic step lines. In contrast, the MBE epilayers exhibit surface striations parallel to the c-axis. We note that the striations have already been formed during the underlayer GaN growth [33

33. T. Hoshi, K. Hazu, K. Ohshita, M. Kagaya, T. Onuma, K. Fujito, H. Namita, and S. F. Chichibu, “Impacts of anisotropic lattice relaxation on crystal mosaicity and luminescence spectra of m-plane AlxGa1-xN films grown on m-plane freestanding GaN substrates by NH3 source molecular beam epitaxy,” Appl. Phys. Lett. 94(7), 071910 (2009). [CrossRef]

]. Therefore, different from the MOVPE case, it seems difficult for NH3-MBE [33

33. T. Hoshi, K. Hazu, K. Ohshita, M. Kagaya, T. Onuma, K. Fujito, H. Namita, and S. F. Chichibu, “Impacts of anisotropic lattice relaxation on crystal mosaicity and luminescence spectra of m-plane AlxGa1-xN films grown on m-plane freestanding GaN substrates by NH3 source molecular beam epitaxy,” Appl. Phys. Lett. 94(7), 071910 (2009). [CrossRef]

,37

37. E. C. Young, C. S. Gallinat, F. Wu, and J. S. Speck, “Ammonia molecular beam epitaxy of m-plane GaN and InGaN for long wavelength optoelectronics,” presented at International Workshop on Nitride Semiconductors (IWN), Montreux, Switzerland, 6–10, Oct. 2008.

] to eliminate such striations, even for the binary GaN growth. The reason for this may be an inappropriate surface preparation or insufficient migration of Ga adatoms due to lower growth temperature (Tg) in comparison with MOVPE, because NH3-MBE is a surface-sensitive growth method. Indeed, the depth of the striations in the AlxGa1- xN films was deeper than the GaN case, where Al-containing materials need higher Tg to ensure sufficient surface migration. Here, we note that the in-plane polar direction of the epilayers was confirmed by convergent-beam electron diffraction (CBED) measurement to be the same as the substrate.

Despite the presence of such surface striations, all the m-plane AlxGa1- xN films grown by NH3-MBE exhibit a single (100) XRD peak, similar to the case for the MOVPE films. The results mean that both the MOVPE and MBE epilayers did not show noticeable phase separation or compositional ordering along the m-axis. However, similar to FS-GaN, XRCs for the pseudomorphic AlxGa1- xN films exhibit a multiple-peak or asymmetric line shape. Because this is also the case for both underlying GaN homoepitaxial films [34

34. S. F. Chichibu, H. Yamaguchi, L. Zhao, M. Kubota, K. Okamoto, and H. Ohta, “Optical properties of nearly stacking-fault-free m-plane GaN homoepitaxial films grown by metal organic vapor phase epitaxy on low defect density freestanding GaN substrates,” Appl. Phys. Lett. 93(12), 129901 (2008) (erratum). [CrossRef]

,38

38. S. F. Chichibu, H. Yamaguchi, L. Zhao, M. Kubota, T. Onuma, and H. Ohta, “Improved characteristics and issues of m-plane freestanding GaN substrates by metalorganic vapor phase epitaxy,” Appl. Phys. Lett. 93(15), 151908 (2008). [CrossRef]

] and the substrate [16

16. K. Fujito, K. Kiyomi, T. Mochizuki, H. Oota, H. Namita, S. Nagao, and I. Fujimura, “High-quality nonpolar m-plane GaN substrates grown by HVPE,” Phys. Stat. Solidi A 205(5), 1056–1059 (2008). [CrossRef]

], the multidomain structure (bowing) of the original c-plane FS-GaN must be the major reason [see Fig. 1(a)]. In contrast, relaxed AlxGa1- xN films exhibit broad but single-peaked XRCs. In those films, the multiple domain fine structure seems to be hidden due to the broadness of the line shape.

As long as coherent growth was maintained, Δωmc of the AlxGa1- xN epilayers are the same as the substrate, regardless of the presence of striations, as shown in Fig. 3(b). The result is similar to the case with pseudomorphic m-pane InxGa1- xN (x≤0.14) epilayers [38

38. S. F. Chichibu, H. Yamaguchi, L. Zhao, M. Kubota, T. Onuma, and H. Ohta, “Improved characteristics and issues of m-plane freestanding GaN substrates by metalorganic vapor phase epitaxy,” Appl. Phys. Lett. 93(15), 151908 (2008). [CrossRef]

] grown on the m-plane FS-GaN prepared by the same provider (Mitsubishi Chemical Holdings Group). However, Δωma and Δωr immediately increased for 0<x≤0.25, presumably because the twist mosaic along the c-axis of the initial c-plane FS-GaN was exaggerated by the lattice and thermal-expansion mismatches between AlGaN and GaN during surface-sensitive NH3-MBE. This must be another origin for the deeper striations in the AlxGa1- xN films, in comparison with GaN films. The broader horizontal width of the (120) X-RSM spot the Al0.25Ga0.75N epilayer [Fig. 2(a)] also reflects the result. For the Al0.32Ga0.68N film, Δω values were larger than those for x≤0.25, reflecting the increase in misfit dislocation densities.

Steady-state CL was excited with an electron beam operated at 3.0 kV. The probe current density was 1.0 × 10−2 A/cm2 at sample. The emission was dispersed by a 30-cm-focal-length grating monochromator, and detected using a multi-channel charge-coupled device. A Glan-Thompson prism polarizer was used for the polarized CL measurement. Polarized near-band-edge (NBE) CL spectra at 12 K of the m-plane AlxGa1- xN films are shown as a function of x in Fig. 4(a)
Fig. 4 (a) Polarized CL spectra at 12 K of m-plane AlxGa1- xN epilayers grown on the m-plane FS-GaN substrates. (b) Polarization ratios, which are defined as (IX1IX2)/(IX1+IX2), of the AlxGa1- xN films as a function of AlN mole fraction x. Corresponding values calculated using the relative oscillator strengths are also shown. The films of x≤0.70 were grown by NH3-MBE and x≥0.73 were grown by MOVPE.
. The intensities are normalized to that of stronger polarization direction (X 1 or X 2) for each x. The entire spectra shifted to the higher energy with increasing x, although some of them exhibited double emission peaks. As shown, the light polarization direction altered from X 1 to X 2 between x = 0.25 and 0.32. The value of polarization ratio ρ was defined as(IX1IX2)/(IX1+IX2), where IX2 and IX1 are the spectrally-integrated CL intensities of the NBE emission. The values are plotted by closed circles in Fig. 4(b).

3. Theoretical analysis

To quantitatively explain the experimental findings, the energies and oscillator strengths of the interband transitions involving three separate valence bands (VBs) are calculated using the Bir-Pikus Hamiltonian [32

32. G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effect in Semiconductors, (Wiley, New York, 1974).

], taking the anisotropic strains into account. At the Γ point, the states at the conduction band minimum (CBM) have an atomic s orbital with wavefunctions of |S〉 symmetry. The three valence band maximum (VBM) states have atomic p orbitals with wavefunctions of a combination of |X〉, |Y〉, and |Z〉 symmetries. For simplicity, excitonic effects are neglected in the calculation. The Hamiltonian for the strain dependence of VB is given by the following 6 × 6 matrixH=[F0H0K00GΔH0KHΔλ0I00H0λΔIK0IΔG00K0I0F], whereF=Δ1+Δ2+λ+θ, G=Δ1Δ2+λ+θ, H=i(A6kzk++A7k++D6εz+), I=i(A6kzk+A7k++D6εz+), K=A5k+2+D5ε+, λ=A1kz2+A2k2+D1εzz+D2(εxx+εyy), θ=A3kz2+A4k2+D3εzz+D4(εxx+εyy), Δ=2Δ3, k2=kx2+ky2, k+=kx+iky, εz+=εxz+iεyz, and

ε+=εxxεyy+2iεxy.
(1)

The parameters Dj (j = 1 to 6) denote the deformation potential constants for the valence band and Aj (j = 1 to 7) are Luttinger parameters, and εlm and kl (l, m = X 1, X 2, X 3) are the strain and wavevector components, respectively. Here we assume that non-diagonal elements of the strain tensor are zero. Δ1 = Δcr is the crystal field splitting, while 3Δ2 = 3Δ3 = Δso are the spin-orbit splitting under quasi-cubic approximation. The basis functions of Bir-Pikus Hamiltonian are (1/2)|X+iY,α, (1/2)|X+iY,β, (1+2)|XiY,α, (1/2)|XiY,β,, |Z,α and |Z,β. Here |α〉 and |β〉 denote the spin-wave functions corresponding to up spin and down spin, respectively. The method described here is universal, and Bhattacharyya et al. [31

31. J. Bhattacharyya, S. Ghosh, and H. T. Grahn, “Optical polarization properties of interband transitions in strained group-III-nitride alloy films on GaN substrates with nonpolar orientation,” Appl. Phys. Lett. 93(5), 051913 (2008). [CrossRef]

] have also used the same approach for calculating the electronic states of m-plane (Al, In, Ga)N alloys.

The exciton transition energies are obtained from the band energies and exciton binding energy:Ej=E+EcEjvEexb, where E* = Eg + Δ1 + Δ2. The parameters Eg, Ec, Evj, and Ebex are the band gap energy, the CBM energy, the VBM energies, and the exciton binding energy, respectively. The Ebex values for the A-, B-, and C-transition were set identical to 26 meV [39

39. A. Shikanai, T. Azuhata, T. Sota, S. Chichibu, A. Kuramata, K. Horino, and S. Nakamura, “Biaxial strain dependence of exciton resonance energies in wurtzite GaN,” J. Appl. Phys. 81(1), 417–424 (1997). [CrossRef]

] for GaN and 51.3 meV for AlN [40

40. T. Onuma, T. Shibata, K. Kosaka, K. Asai, S. Sumiya, M. Tanaka, T. Sota, A. Uedono, and S. F. Chichibu, “Free and bound exciton fine structures in AlN epilayers grown by low-pressure metalorganic vapor phase epitaxy,” J. Appl. Phys. 105(2), 023529 (2009). [CrossRef]

].

The oscillator strength components for the transitions are obtained from momentum matrix elements |ΨCB|pl|ΨVB|2 with l = x, y, and z. Here, ΨCB|=S| and |ΨVB|=a1|X+a2|Y+a3|Z represent the orbital parts of the CB and VB basis functions, respectively. The coefficients aj are obtained by determining the eigenvectors of Hamiltonian. The relative values of |S|px|X|2, |S|py|Y|2, and |S|pZ|X|2 are set unity under the quasi-cubic approximation, i=13fi,β=1. The calculations stated herein are carried out exclusively at k = 0, meaning that the 6 × 6 matrix was effectively treated as 3 × 3.

For the practical calculation on AlxGa1- xN alloy films, the material parameters of end-point compounds, namely GaN and AlN, are taken from the literature, as shown in Table 1

Table 1. Optical Constants of Thin Films of Materialsa

table-icon
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. The parameters for the alloys are assumed to obey the Vegard's law, and the bowing parameter for the bandgap energy of strain-free AlxGa1- xN is chosen as 0.82 eV [41

41. T. Onuma, S. F. Chichibu, A. Uedono, T. Sota, P. Cantu, T. M. Katona, J. F. Keading, S. Keller, U. K. Mishra, S. Nakamura, and S. P. DenBaars, “Radiative and nonradiative processes in strain-free AlxGa1-xN films studied by time-resolved photoluminescence and positron annihilation techniques,” J. Appl. Phys. 95(5), 2495–2504 (2004). [CrossRef]

]. We use energy notations E 1, E 2, and E 3 hereafter, because the crystal symmetry of the AlxGa1- xN films suffering from anisotropic stresses is no longer C6v4.

The three exciton transition energies calculated for m-plane GaN, Al0.03Ga0.97N, Al0.70Ga0.30N, and AlN films under isotropic in-plane strain (εX1X1=εX2X2) are shown in Figs. 9(a)
Fig. 9 Calculated E 1, E 2, and E 3 exciton transition energies for the m-plane (a) GaN, (b) Al0.03Ga0.97N, (c) Al0.70Ga0.30N, and (d) AlN films. The energy difference between E 2 and E 1, (E 2-E 1), as functions of in-plane strains (εX1X1,εX2X2) for the m-plane (e) GaN, (f) Al0.03Ga0.97N, (g) Al0.70Ga0.30N, and (h) AlN films. Closed circles indicate respective in-plane strains.
, 9(b), 9(c), and 9(d), respectively. In the case of GaN and Al0.03Ga0.97N, the VB anticrossing immediately takes place when in-plane biaxial tensile strain is introduced. On the contrary, the VB anticrossing gradually takes place with increasing the tensile strain for Al0.70Ga0.30N and AlN. The latter result means that corresponding VBs are strongly hybridized, which gives rise to much lower oscillator strength contrast for Al0.70Ga0.30N and AlN, as shown in Figs. 7 and 8. The energy differences between E 1 and E 2 bands for the GaN, Al0.03Ga0.97N, Al0.70Ga0.30N, and AlN films are shown as functions of εX1X1 and εX2X2 in Figs. 9(e), 9(f), 9(g), and 9(h), respectively, using contour lines. Similar to Figs. 5, 6, 7, and 8, the measured strain coordinates are plotted by closed black circles. The E 2-E 1 values, in the same order, are predicted to be 7.7 meV, 6.2 meV, 106 meV, and 142 meV.

Table 2

Table 2. Calculated polarization directions for E1, E2, and E3 transitions and energy differences between E1 and E2 band (E2-E1).

table-icon
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summarizes the polarization directions for the transitions and E 2-E 1 values calculated for m-plane AlxGa1- xN suffering from the experimentally obtained strain values. As shown, E 1 transition is X 3-polarized regardless of x. The result means that E 1 (exciton) emission is essentially undetectable from the surface normal. Apart from E 1, the polarization directions alter from X 1 to X 2 for E 2 emission (X 3 to X 2 for E 3 emission) between x = 0.25 and 0.32. Assuming that the experimentally observed CL peaks principally originate from E 2 and E 3 transitions, the calculated prediction is consistent with the experimental results, as shown in Fig. 4(b). In Fig. 4(b), ρ values of m-plane AlxGa1- xN films calculated using the oscillator strengths for the measured(εX1X1,εX2X2) coordinates are plotted as a function of x by open circles. As shown, the experimental data nearly agree with the calculated ones, except rather low ρ values for x≤0.25. The low ρ values may be due to the light depolarization caused by high density surface striations along the c-axis, which had been disclosed using atomic force microscopy observation [33

33. T. Hoshi, K. Hazu, K. Ohshita, M. Kagaya, T. Onuma, K. Fujito, H. Namita, and S. F. Chichibu, “Impacts of anisotropic lattice relaxation on crystal mosaicity and luminescence spectra of m-plane AlxGa1-xN films grown on m-plane freestanding GaN substrates by NH3 source molecular beam epitaxy,” Appl. Phys. Lett. 94(7), 071910 (2009). [CrossRef]

]. We must note in Fig. 4(a) that overall CL intensity for the samples of x≥0.58 is much weaker than that for x≤0.32. From Table 2, it is obvious that E 2-E 1 increases with x. Therefore, Boltzmann distribution gives rise to very low hole populations in E 2 and E 3 bands in comparison with E 1 band for high x samples. This may be one of the reasons for the low CL intensities at low temperature, where nonradiative recombination channels are in principle frozen.

Finally, calculated E 2 transition energies (closed squares), CL peak energies (open circles), and their energy differences (ΔE) for the m-plane AlxGa1- xN films are plotted as a function of x in Fig. 10
Fig. 10 Calculated E 2 transition energies (closed squares), measured CL peak energies (open circles), and their energy differences (closed diamonds) for the m-plane AlxGa1- xN films as a function of x.
. The ΔE value, which is similar to the Stokes-type shift, ranges between 3 and 577 meV for the alloys. These values are slightly larger than those reported for c-plane AlGaN films grown by MOVPE (100 ~250 meV) [40

40. T. Onuma, T. Shibata, K. Kosaka, K. Asai, S. Sumiya, M. Tanaka, T. Sota, A. Uedono, and S. F. Chichibu, “Free and bound exciton fine structures in AlN epilayers grown by low-pressure metalorganic vapor phase epitaxy,” J. Appl. Phys. 105(2), 023529 (2009). [CrossRef]

], indicating the difficulties in growing homogeneous, excellent quality m-plane AlGaN epilayers. Leastwise, current m-plane AlxGa1- xN films exhibit UV emission peaks between 360 nm (x = 0) and 210 nm (x = 1).

4. Conclusion

Interband optical polarization characteristics of UV-light-emitting m-plane AlxGa1- xN alloy films grown on the m-plane FS-GaN substrates were interpreted by means of polarized CL measurements and theoretical calculations. The predominant light-polarization direction of the emission peak for the films suffering from in-plane anisotropic tensile stresses was shown to alter from Ec (X 1) to E//c (X 2) between x = 0.25 and 0.32. Theoretical analysis of the oscillator strengths of interband transitions and exciton transition energies was carried out using Bir-Pikus Hamiltonian, taking the anisotropic strain into account. The calculation predicted that the lowest energy transition (E 1) is X 3-polarized regardless of x, meaning that edge-emitting LED configuration is preferred for E 1 exciton emission. For surface-emitting configuration, the calculated polarization direction altered from X 1 (Ec) to X 2 (E//c) for E 2 transition and X 3 to X 2 for E 3 transition between x = 0.25 and 0.32. The variations of polarization ratio and overall CL intensity as a function of x were quantitatively reproduced through the calculation. These achievements may open the way of designing UV LEDs using nonpolar AlGaN alloys.

Acknowledgments

The authors would like to thank K. Fujito, H. Namita, T. Nagao, and H. Itoh of Mitsubishi Chemical Holdings Group for providing the m-plane FS-GaN substrates. They also would like to thank T. Hoshi, M. Kagaya, and Dr. T. Onuma for their help in the experiments. This work was supported in part by Grant-in-Aids of CANTech, IMRAM, Tohoku University, Scientific Research in Priority Area No. 18069001 under MEXT, NEDO program under METI, Japan, and AFOSR/AOARD Grant (FA2386-09-1-4013 and FA2386-10-1-4100) monitored by Dr. G. Jessen.

References and links

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4.

X. Hu, J. Deng, J. P. Zhang, A. Lunev, Y. Bilenko, T. Katona, M. S. Shur, R. Gaska, M. Shatalov, and A. Khan, “Deep ultraviolet light-emitting diodes,” Phys. Stat. Solidi A 203(7), 1815–1818 (2006). [CrossRef]

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H. Hirayama, N. Noguchi, and N. Kamata, “222 nm Deep-Ultraviolet AlGaN Quantum Well Light-Emitting Diode with Vertical Emission Properties,” Appl. Phys. Express 3(3), 032102 (2010). [CrossRef]

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D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984). [CrossRef]

7.

P. Waltereit, O. Brandt, A. Trampert, H. T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, and K. H. Ploog, “Nitride semiconductors free of electrostatic fields for efficient white light-emitting diodes,” Nature 406(6798), 865–868 (2000). [CrossRef] [PubMed]

8.

M. D. Craven, P. Waltereit, J. S. Speck, and S. P. DenBaars, “Well-width dependence of photoluminescence emission from a-plane GaN/AlGaN multiple quantum wells,” Appl. Phys. Lett. 84(4), 496–498 (2004). [CrossRef]

9.

T. Koida, S. F. Chichibu, T. Sota, M. D. Craven, D. A. Haskell, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Improved quantum efficiency in nonpolar (110) AlGaN/GaN quantum wells grown on GaN prepared by lateral epitaxial overgrowth,” Appl. Phys. Lett. 84(19), 3768–3770 (2004). [CrossRef]

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J. S. Speck and S. F. Chichibu, “Nonpolar and Semipolar Group III Nitride-Based Materials,” MRS Bull. 34(05), 304–312 (2009). [CrossRef]

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M. Masui, T. J. Baker, R. Sharma, P. M. Pattison, M. Iza, H. Zhong, S. Nakamura, and S. P. DenBaars, “First-Moment Analysis of Polarized Light Emission from InGaN/GaN Light-Emitting Diodes Prepared on Semipolar Planes,” Jpn. J. Appl. Phys. 45(34), L904–L906 (2006). [CrossRef]

13.

R. Sharma, P. M. Pattison, H. Masui, R. M. Farrell, T. J. Baker, B. A. Haskell, F. Wu, S. P. DenBaars, J. S. Speck, and S. Nakamura, “Demonstration of a semipolar (10) InGaN/GaN green light emitting diode,” Appl. Phys. Lett. 87(23), 231110 (2005). [CrossRef]

14.

K. Okamoto, H. Ohta, D. Nakagawa, M. Sonobe, J. Ichihara, and H. Takasu, “Dislocation-Free m-Plane InGaN/GaN Light-Emitting Diodes on m-Plane GaN Single Crystals,” Jpn. J. Appl. Phys. 45(45), L1197–L1199 (2006). [CrossRef]

15.

M. C. Schmidt, K.-C. Kim, H. Sato, N. Fellows, H. Masui, S. Nakamura, S. P. DenBaars, and J. S. Speck, “High Power and High External Efficiency m-Plane InGaN Light Emitting Diodes,” Jpn. J. Appl. Phys. 46(7), L126–L128 (2007). [CrossRef]

16.

K. Fujito, K. Kiyomi, T. Mochizuki, H. Oota, H. Namita, S. Nagao, and I. Fujimura, “High-quality nonpolar m-plane GaN substrates grown by HVPE,” Phys. Stat. Solidi A 205(5), 1056–1059 (2008). [CrossRef]

17.

K. Iso, H. Yamada, H. Hirasawa, N. Fellows, M. Saito, K. Fujito, S. P. DenBaars, J. S. Speck, and S. Nakamura, “High Brightness InGaN/GaN Light Emitting Diode on Nonpolar m-plane Bulk GaN Substrate,” Jpn. J. Appl. Phys. 46(40), L960–L962 (2007). [CrossRef]

18.

S. F. Chichibu, A. Uedono, T. Onuma, S. P. DenBaars, U. K. Mishra, J. S. Speck, and S. Nakamura, “Impact of Point Defects on the Luminescence Properties of (Al,Ga)N,” Mater. Sci. Forum 590, 233–248 (2008). [CrossRef]

19.

T. Onuma, K. Hazu, A. Uedono, T. Sota, and S. F. Chichibu, “Identification of extremely radiative nature of AlN by time-resolved photoluminescence,” Appl. Phys. Lett. 96(6), 061906 (2010). [CrossRef]

20.

S. F. Chichibu, T. Onuma, K. Hazu, and A. Uedono, “Major impacts of point defects and impurities on the carrier recombination dynamics in AlN,” Appl. Phys. Lett. 97(20), 201904 (2010). [CrossRef]

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K. Domen, K. Kondo, A. Kuramata, and T. Tanahasi, “Gain analysis for surface emission by optical pumping of wurtzite GaN,” Appl. Phys. Lett. 69(1), 94–96 (1996). [CrossRef]

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T. Ohtoshi, A. Niwa, and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” J. Appl. Phys. 82(4), 1518–1520 (1997). [CrossRef]

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38.

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39.

A. Shikanai, T. Azuhata, T. Sota, S. Chichibu, A. Kuramata, K. Horino, and S. Nakamura, “Biaxial strain dependence of exciton resonance energies in wurtzite GaN,” J. Appl. Phys. 81(1), 417–424 (1997). [CrossRef]

40.

T. Onuma, T. Shibata, K. Kosaka, K. Asai, S. Sumiya, M. Tanaka, T. Sota, A. Uedono, and S. F. Chichibu, “Free and bound exciton fine structures in AlN epilayers grown by low-pressure metalorganic vapor phase epitaxy,” J. Appl. Phys. 105(2), 023529 (2009). [CrossRef]

41.

T. Onuma, S. F. Chichibu, A. Uedono, T. Sota, P. Cantu, T. M. Katona, J. F. Keading, S. Keller, U. K. Mishra, S. Nakamura, and S. P. DenBaars, “Radiative and nonradiative processes in strain-free AlxGa1-xN films studied by time-resolved photoluminescence and positron annihilation techniques,” J. Appl. Phys. 95(5), 2495–2504 (2004). [CrossRef]

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OCIS Codes
(160.6000) Materials : Semiconductor materials
(300.6250) Spectroscopy : Spectroscopy, condensed matter

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: June 24, 2011
Revised Manuscript: June 29, 2011
Manuscript Accepted: June 30, 2011
Published: July 1, 2011

Virtual Issues
Optics in LEDS for Lighting (2011) Optics Express

Citation
Kouji Hazu and Shigefusa F. Chichibu, "Optical polarization properties of m-plane AlxGa1-xN epitaxial films grown on m-plane freestanding GaN substrates toward nonpolar ultraviolet LEDs," Opt. Express 19, A1008-A1021 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S4-A1008


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References

  1. Y. Taniyasu, M. Kasu, and T. Makimoto, “An aluminium nitride light-emitting diode with a wavelength of 210 nanometres,” Nature 441(7091), 325–328 (2006). [CrossRef] [PubMed]
  2. Y. Narukawa, M. Ichikawa, D. Sanga, M. Sano, and T. Mukai, “White light emitting diodes with super-high luminous efficacy,” J. Phys. D Appl. Phys. 43(35), 354002 (2010). [CrossRef]
  3. H. Tsuzuki, F. Mori, K. Takeda, M. Iwaya, S. Kamiyama, H. Amano, I. Akasaki, H. Yoshida, M. Kuwabara, Y. Yamashita, and H. Kan, “Novel UV devices on high-quality AlGaN using grooved underlying layer,” J. Cryst. Growth 311(10), 2860–2863 (2009). [CrossRef]
  4. X. Hu, J. Deng, J. P. Zhang, A. Lunev, Y. Bilenko, T. Katona, M. S. Shur, R. Gaska, M. Shatalov, and A. Khan, “Deep ultraviolet light-emitting diodes,” Phys. Stat. Solidi A 203(7), 1815–1818 (2006). [CrossRef]
  5. H. Hirayama, N. Noguchi, and N. Kamata, “222 nm Deep-Ultraviolet AlGaN Quantum Well Light-Emitting Diode with Vertical Emission Properties,” Appl. Phys. Express 3(3), 032102 (2010). [CrossRef]
  6. D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect,” Phys. Rev. Lett. 53(22), 2173–2176 (1984). [CrossRef]
  7. P. Waltereit, O. Brandt, A. Trampert, H. T. Grahn, J. Menniger, M. Ramsteiner, M. Reiche, and K. H. Ploog, “Nitride semiconductors free of electrostatic fields for efficient white light-emitting diodes,” Nature 406(6798), 865–868 (2000). [CrossRef] [PubMed]
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