Influence of strain on the indium incorporation in (0001) GaN

T. Schulz, L. Lymperakis, M. Anikeeva, M. Siekacz, P. Wolny, T. Markurt, and M. Albrecht

Phys. Rev. Materials 4, 073404 – Published 24 July 2020

Abstract

The incorporation of indium in GaN (0001) surfaces in dependence of strain is investigated by combining molecular-beam epitaxy (MBE) growth, quantitative transmission electron microscopy, and density-functional theory (DFT) calculations. Growth experiments were conducted on GaN, as well as on $30 % \pm 2 %$ partially relaxed $I n_{0.19} G a_{0.81} N$ buffer layers, serving as substrates. Despite the only $0.6 %$ larger in-plane lattice constant of GaN provided by the buffer layer, our experiments reveal that the In incorporation increases by more than a factor of two for growth on the $I n_{0.19} G a_{0.81} N$ buffer, as compared to growth on GaN. DFT calculations reveal that the decreasing chemical potential due to the reduced lattice mismatch stabilizes the In–N bond at the surface. Depending on the growth conditions (metal rich or N rich), this promotes the incorporation of higher In contents into a coherently strained layer. Nevertheless, the effect of strain is highly nonlinear. As a consequence of the different surface reconstructions, growth on relaxed $I n_{x} G a_{1 - x} N$ buffers appears more suitable for metal-rich MBE growth conditions with regard to achieving higher In compositions.

Received 4 March 2020
Accepted 6 July 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.073404

Physics Subject Headings (PhySH)

Chemical bonding Composition Crystal growth Crystal structure First-principles calculations Structural properties

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Schulz ^1,*, L. Lymperakis^2,†, M. Anikeeva¹, M. Siekacz³, P. Wolny³, T. Markurt¹, and M. Albrecht¹

¹Leibniz-Institut für Kristallzüchtung, Max-Born-Str. 2, 12489 Berlin, Germany
²Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Düsseldorf, Germany
³Institute of High Pressure Physics, Polish Academy of Sciences, Sokolowska 29/37, 01–142 Warsaw, Poland

^*tobias.schulz@ikz-berlin.de
^†l.lymperakis@mpie.de

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Issue

Vol. 4, Iss. 7 — July 2020

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Images

Figure 1
(a), (b) Sketches of the two samples investigated in this study. (c) The In, Ga, and N fluxes during the epitaxy process.
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Figure 2
AFM of the as-grown surfaces of the samples grown on the (a) GaN substrate and (b) $I n_{0.19} G a_{0.81} N$ buffer.
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Figure 3
STEM-HAADF images recorded in the $〈 11 \bar{2} 0 〉$ projection showing the nominal $I n_{x} G a_{1 - x} N$ QW region of the sample grown on (a) the GaN substrate and (b) the $I n_{0.19} G a_{0.81} N$ buffer. (c), (d) Horizontally averaged intensities of STEM-HAADF images (a) and (b), respectively. The vertical dashed lines enclose the QW region.
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Figure 4
Laterally averaged lattice parameter maps obtained from TEM images in the region of the $I n_{x} G a_{1 - x} N$ QWs grown on the (a) GaN and (b) $I n_{0.19} G a_{0.81} N$ buffer. Additionally, (a) and (b) show laterally averaged lattice maps obtained from image simulations of supercells consisting of a single ML thick $I n_{0.25} G a_{0.75} N$ QW (dashed line).
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Figure 5
PL measurements of $I n_{x} G a_{1 - x} N$ MLs grown on a GaN substrate (solid line) and on an $I n_{0.19} G a_{0.81} N$ buffer (dashed line) at 4 K.
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Figure 6
(a), (b) Composition $x$ in $I n_{x} G a_{1 - x} N$ as function of the chemical potential $Δ μ = μ_{In} - μ_{Ga}$ and the equivalent change in In fluxes [see Eq. (1)] at $T = 1229 K$ as function of $x$ for different basal plane tensile strains for metal-rich (a) and N-rich (b) growth conditions. The chemical potential to incorporate 1/12 In content at the GaN substrate (0.0% biaxial strain) is used as reference. $F_{0}$ is the reference flux at $Δ μ = - 0.2163 eV$ , i.e., the chemical potential required to incorporate 1/12 In content at 2% tensile strain under metal rich conditions. The horizontal red line indicates the experimentally relevant metal-rich conditions. The solid black lines in (a) are linear fits in the composition region $x = 1 / 12$ to $x = 4 / 12$ . The dashed lines in (a) and (b) are guides to the eye. Insets: Ball and stick models in side view of the strain-free (0001) ${In}_{1 / 12} {Ga}_{11 / 12} N$ covered with an In bilayer (left) and the $2 \times 2$ N-adatom reconstruction (right). Large red and green balls indicate In and Ga atoms, respectively. Small gray balls are N atoms. (c) Calculated ratio $x / x 0$ of the In content as a function of the substrate's biaxial strain state for metal-rich conditions [derived from (a)]. The values are referenced to the $I n_{x} G a_{1 - x} N$ composition of $x_{0} = 0.1$ as realized on a GaN substrate (filled circles). Open rectangles correspond to experimental data.
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