Aluminium incorporation in polar, semi- and non-polar AlGaN layers: a comparative study of x-ray diffraction and optical properties

Growth of AlxGa1−xN layers (0 ≤ x ≤ 1) simultaneously on polar (0001), semipolar (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\bar{{\rm{1}}}$$\end{document}101¯3) and (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$11\bar{{\rm{2}}}2$$\end{document}112¯2), as well as nonpolar (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\bar{{\rm{1}}}0$$\end{document}101¯0) and (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$11\bar{{\rm{2}}}0$$\end{document}112¯0) AlN templates, which were grown on planar sapphire substrates, has been investigated by metal-organic vapour phase epitaxy. By taking into account anisotropic in-plane strain of semi- and non-polar layers, their aluminium incorporation has been determined by x-ray diffraction analysis. Optical emission energy of the layers was obtained from room-temperature photoluminescence spectra, and their effective bandgap energy was estimated from room-temperature pseudo-dielectric functions. Both x-ray diffraction and optical data consistently show that aluminium incorporation is comparable on the polar, semi- and non-polar planes.

www.nature.com/scientificreports www.nature.com/scientificreports/ we have successfully produced untwinned semipolar (1013) AlN templates on m-plane sapphire using directional sputtering 33 . Therefore, to extend compositional study of AlGaN with different surface orientations, in this paper, we report on MOVPE-growth of Al x Ga 1−x N layers simultaneously on polar (0001), semipolar (1013) and (1122), as well as nonpolar (1010) and (1120) AlN/sapphire templates over the entire range of composition. Compositional study of these layers has been investigated by x-ray diffraction (XRD), room-temperature photoluminescence (RT-PL) and pseudo-dielectric functions (DFs) measurements.
To investigate crystal twinning and the epitaxial in-plane relationship of the grown (1013) Al x Ga 1−x N layers and m-plane sapphire, XRD off-axis φ-scans were measured. The skew-symmetric {2024} sapphire diffraction peak of m-plane sapphire substrate was measured with a tilt angle of: 32 Figure 1(b) shows 2θ scans of the (1013) AlGaN layers grown with different R AlGaN . Various diffraction peak positions indicate different x AlN of these layers. A similar result has been found for the other layers with different surface orientations.
Semi-and non-polar AlGaN layers hetero-epitaxially grown on sapphire substrates generally have triclinic and orthorhombic distortions of their wurtzite unit cells, respectively. Anisotropy in the lattice and thermal expansion mismatches along two in-plane directions results in anisotropic in-plane strain causing these distortions. This makes lattice parameter measurements, and thus x AlN determination, difficult. By taking into account these distortions, XRD methods have been developed to determine x AlN of nonpolar 34 and semipolar AlGaN layers 35 .
For the differently oriented AlGaN layers studied here, their a and c lattice constants have been calculated by measuring different symmetric, skew-symmetric and asymmetric 2θ diffraction peaks, as shown in Table 1. An example of lattice measurements for m-plane AlGaN can be seen in ref. 30. Figure 2(a) shows the measured lattice constants of the layers as a function of R AlGaN . The lattice constants of all the layers show a linear behaviour with R AlGaN . Additionally, all layers in this study have an expected ratio of a to c lattice constant with a corresponding composition, indicating that they are fully relaxed.
Based on these measured lattice constants, x AlN of all the layers with different surface orientations has been estimated, as shown in Fig. 2(b). At each growth condition (R AlGaN ), x AlN values of these layers are slightly different. For example, maximum differences (Δx) of 0.02/0.08/0.03 are estimated for the layers grown with R AlGaN = 0.1/0.4/0.8, respectively. Given these scattered data points, x AlN values of all the layers can be considered to be comparable. In contrast to a linear behaviour of R AlGaN -x AlN observed for c-and m-plane layers grown at 1050°C reported in ref. 30, for the samples studied here grown at 1150°C, a non-linear behaviour has been observed. This is attributed to TMAl:NH 3 pre-reactions and gallium desorption 36,37 .    www.nature.com/scientificreports www.nature.com/scientificreports/ tudes because of their rougher interfaces 30 . From these <ε 1 > parts, the fundamental bandgap energy (E g AlGaN ) of the grown layers is approximately estimated from a sharp excitonic E 0 peak [39][40][41] .
E g AlGaN of all the AlGaN layers is plotted as a function of x AlN in Fig. 3(b). Their E g AlGaN values are comparable over the entire range of composition. This indicates comparable x AlN values, consistent with the values estimated by XRD (Fig. 2(b)). The dependence of E g AlGaN on x AlN can be described as: where b denotes the bandgap bowing parameter. To fit the experimental data, a measured E g AlN of 6.11 eV and a measured Photoluminescence. A correlation between the bandgap energy with optical emission properties has also been investigated. Due to the excitation energy of laser (E ex = 5 eV), only samples grown with R AlGaN < 0.8 (i.e., x AlN < 0.7) can be measured. Figure 4(a) exemplifies RT-PL spectra measured on the differently oriented AlGaN layers grown with R AlGaN = 0.4. The near band-edge (NBE) emission energy of these samples, which was estimated from a Gaussian fit of the corresponding band, is following (1120) 3.92 eV < (1122) 3.98 eV = (1013) < (0001) = (1010) 4.04 eV . This order is slightly different from the order shown in XRD data ( Fig. 2(b)). However, the maximum NBE difference is of about 120 meV, which is equal to about a difference of 0.06 in x AlN . This composition difference is comparable with the maximum Δx of 0.08 estimated from the XRD data.
The PL emission energy vs x AlN is also well reproduced with a bowing parameter of about 0.9 eV, as shown in Fig. 4(b). For the bowing fitting, an NBE of 3.42 eV obtained from the grown GaN layers and an NBE of 6.035 eV of c-, a-and m-plane AlN homo-epilayers taken from ref. 42 were used. The PL data correlates very well with the optical bandgap data indicating a random alloy and almost negligible Ga clustering. This is different from the case of InGaN QWs, where a strong In clustering has often been reported, which results in a large Stokes shift between NBE and effective bandgap [43][44][45][46] .
To study In incorporation in different InGaN surface orientations, a few theoretical calculations have also been performed by taking into account surface kinetics 47,48 or strain energy dependent surface orientations 49,50 . However, they also show contrary results, e.g., In incorporation in m-plane InGaN was found to be smaller 47 or higher than c-plane InGaN 49,50 . Additionally, it has been theoretically 49,50 and experimentally 19,23 reported that different growth conditions (e.g., pressure, temperature, and V/III) might result in different In incorporations on different surface orientations.
Of the relaxed AlGaN layers with five different surface orientations studied here, their x AlN is comparable over the entire range of composition, as consistently confirmed by XRD and optical data. The comparable x AlN of the www.nature.com/scientificreports www.nature.com/scientificreports/ m-plane and c-plane layers is in good agreement with a previous report 30 , even though the growth temperature used here is 100°C higher. Given the slightly scattered data points of the a-plane and c-plane layers, their comparable x AlN also can be considered as a consistent result with a previous report 29 , where only a slightly higher x AlN of c-plane layers was found (Δx AlN ≤ 0.05).
For the c-plane and (1122) AlGaN layers studied here, their comparable x AlN is contrary to previous results reported for (1122) vs c-plane layers, where x AlN of (1122) layers was found to be lower (Δx ≤ 0.1) 32 or higher (Δx ≤ 0.2) 31 than that of c-plane layers. This might be due to different growth conditions and/or calculation methods used. So far no theoretical study about composition dependent surface orientations has been done for AlGaN. In case of InGaN, most experimental data seems to indicate a higher In incorporation for orientations with almost upright metal dangling bonds. This can indicate that the bonding and incorporation of In versus In desorption are the most important step. Since the AlGaN layers studied here have a similar Al incorporation for all orientations, one may argue that the strong polarity of Al(Ga)N together with the lower total strain facilitates Ga incorporation and makes Ga desorption the less likely process. Further investigations and calculations need to be performed to clarify this.

conclusions
Compositional study of relaxed co-loaded AlGaN layers with polar (0001), semipolar (1013) and (1122), as well as nonpolar (1010) and (1120) surface orientations has been investigated. By taking into account the compositional effects of anisotropic in-plane strain, aluminium incorporation in semi-and non-polar layers was determined by x-ray diffraction analysis. The AlN mole fraction of all the co-loaded layers estimated by x-ray diffraction is comparable. This is consistent with their comparable optical bandgap energy and near band-edge emission energy, which were determined from room-temperature pseudo-dielectric functions and photoluminescence measurements, respectively. The dependence of the bandgap and emission energy on composition indicates a bowing parameter of 0.9 eV.
All the 2-inch AlN/sapphire wafers were diced into 1 × 1 cm 2 pieces. These pieces were then co-loaded into the reactor chamber for AlGaN epitaxy. Initially, about 100-nm-thick AlN layer was grown on these templates at 1290°C at a reactor pressure of 27 hPa. Afterwards, AlGaN layers with a nominal thickness of 1.5 μm were grown on these templates at 1150°C at a reactor pressure of 100 hPa. To vary x AlN , different R AlGaN ratios were employed (0 ≤ R AlGaN ≤ 1), while keeping NH 3 flow rate constantly. Growth parameters of these layers are reported in ref. 30; however, the AlGaN growth temperature at 1050°C was used in that study.
The crystal orientation of the AlGaN/AlN samples was characterized using a PANalytical X'pert triple-axis high-resolution X-ray diffraction (HR-XRD) system equipped with an asymmetric four-crystal monochromator (4 × Ge220) for CuK α1 source. On-axis ω-2θ scans have been measured using an open detector without any receiving slit to distinguish between all possible orientations of the epilayers. For lattice calculations, different 2θ diffraction peaks of the samples were measured using an HR analyzer detector, as shown in Table 1.
For room-temperature photoluminescence (RT-PL) measurements, the samples were excited by a Krypton Fluoride (KrF) excimer laser (ExciStar XS-200) with excitation wavelength of 248 nm (E ex = 5 eV) and a spot size of 50 × 500 μm 2 . During PL measurements, a pulse energy of 7 mJ and a repetition rate of 200 Hz were employed, giving a power density of 5.6 kW/cm 2 . PL signals were recorded by a high-sensitivity Ocean Optics spectrometer (QE65 Pro).
The fundamental bandgap energy of the layers was estimated from real and imaginary parts of the pseudo-dielectric functions (DFs). DFs were recorded at RT using a Horiba UVISEL 2 spectroscopic ellipsometer at an incident angle of 70° and a spot size of 705 × 2030 μm 2 . The photon energy was varied from 1.45 to 6.45 eV with the spectral resolution of 0.02 eV.