Independence of solitary-cation properties on the atomic neighborhood in ${\mathrm{In}}_{1\ensuremath{-}x}{\mathrm{Ga}}_{x}\mathrm{N}$ alloys: A novel perspective for material engineering

Independence of solitary-cation properties on the atomic neighborhood in ${In}_{1 - x} {Ga}_{x} N$ alloys: A novel perspective for material engineering

Francesco Filippone, Giuseppe Mattioli, and Aldo Amore Bonapasta

Phys. Rev. Materials 1, 064606 – Published 29 November 2017

Abstract

In InN, a genuine band gap opening observed after hydrogenation has been explained by means of the “solitary cation” model, a multi-H complex in which the central cation, In*, is fully separated from the structure [Pettinari et al., Adv. Funct. Mater. 25, 5353 (2015)]. Similar effects of H on the host band gap have been observed in In-rich ${In}_{1 - x} {Ga}_{x} N$ alloys. Paying attention to these materials, we have theoretically investigated the In* properties against three kinds of disorder, structural, compositional, and configurational, all of them possibly occurring in ${In}_{1 - x} {Ga}_{x} N$ alloys. As a first major result we have found that a same, general solitary-cation model and mechanism explain the effects of hydrogenation on the electronic properties of both InN and In-rich ${In}_{1 - x} {Ga}_{x} N$ alloys. Even more interestingly, in these alloys, both the energetics of the In* solitary cations and their effects on the band gap result to be thoroughly independent of their atomic neighborhood, in particular, of the number and spatial distribution of their cation neighbors. Significantly, this implies that band-gap opening effects can be safely predicted in whatever hydrogenated In-rich nitride alloy containing different In companions (e.g., B, Al, or Ga) as well as in InN-containing, unconventional compounds (e.g., ZnO-InN), thus offering novel opportunities for material engineering.

Received 21 June 2017
Revised 13 September 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.064606

Physics Subject Headings (PhySH)

Band gap Chemical bonding Defects Electronic structure Local density of states Point defects

3-dimensional systems Alloys Crystalline systems Doped semiconductors Semiconductors

Density functional theory Density functional theory development

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Francesco Filippone^*, Giuseppe Mattioli, and Aldo Amore Bonapasta

Istituto di Struttura della Materia (ISM) del Consiglio Nazionale delle Ricerche, Via Salaria Km 29.5, CP 10, 00016 Monterotondo Stazione, Italy

^*francesco.filippone@ism.cnr.it

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Vol. 1, Iss. 6 — November 2017

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Figure 1
A schematic view of the In* solitary cation $(3 H_{ab}$ + $H_{BC}$ complex) is given. Light gray and light blue circles indicate In and N atoms. Darker gray and blue circles indicate In and N atoms involved in the multi-H complex, white circles indicate H atoms. The arrows indicate the direction of displacements of the complex atoms with respect to the lattice positions. The morphology of the cluster is the same for all the ${In}_{1 - x} {Ga}_{x} N$ alloy compositions illustrated in the text, pure GaN included. Note that some atoms have been dropped from the sketch to facilitate the view.
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Figure 2
(a) Band gap shifts induced by the main $n$ H-complexes in InN and GaN, reported as a function of $E_{ass} [n H]$ , Eq. (6); $n$ ranges from 1 to 4 [also in panel (b)]. (b) pDOS of $n$ H complexes. Red lines; projection on the $s$ states of the central cation. Green lines; summed projections on the remaining In (Ga) cations $s$ states. The zero in the energy is located on TVB $(E_{b}$ in the figure). Shading indicates the energy spans of the VB, light blue, and of the CB, light magenta. Dotted lines represent the Fermi level; for $2 H_{ab}$ + $H_{BC}$ in GaN, $E_{F}$ is slightly out of the energy range. (c) Geometries of representative H complexes in InN and GaN. Gray, red-brown, light-blue, and small white circles represent In, Ga, N, and H atoms, respectively. Relevant distances are shown in Å.
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Figure 3
Trends with respect to Ga content of the alloys. Panel (a): band energy gap. Red squares indicate values from all configurations considered for every concentration of pristine alloys. Blue triangles indicate values for all the systems with $H_{BC}$ complex, while green circles represent data for all the systems with solitary cations, either In* or Ga*. A gray dashed line shows the linear behavior of Vegard's law. Light blue lines represent quadratic fits, both for hydrogenated and unhydrogenated alloys. Panel (b): bulk moduli with respect to Ga content. Symbols like in left panel. Shading highlights the region of Ga content where we simulated hydrogenation.
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Figure 4
Dispersion graphs of electronic states for solitary cations at various concentration of Ga. Aside each dispersion graph, the corresponding plot of the density of states projected on some atomic states; red the $s$ state of the solitary cations, green the sum of all the other cations' $s$ states of the same element. Zero of energy is on TVB $(E_{b})$ . Dashed gray lines indicate the Fermi level pertaining to each system.
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Figure 5
Left: filled (empty) triangles are relative to $H_{BC}$ -In $(H_{BC}$ -Ga) complexes. Right: filled (empty) squares are relative to In* (Ga*) complexes. Empty circles are relative to 4- $H_{BC}$ configurations lowest in energy. Formation energies for $H_{BC}$ complexes and clustering energies for In*/Ga* complexes are reported in (a) and (d) panels, respectively. BTS ratios are reported in panel (b) for $H_{BC}$ complexes, in panel (e) for In*/Ga* and 4- $H_{BC}$ complexes. Variation of stress $(Δ σ)$ per H atom is shown in panels (c) and (f).
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Figure 6
The band gap of different ${In}_{1 - x} {Ga}_{x} N$ alloys containing In* (squares) and Ga* (circles) complexes is reported with respect to the $E_{cl}$ clustering energies of the same complexes. Ga concentration grows from the bottom panel to upper panel. Dashed horizontal lines indicate the band gap relative to the pristine alloys compositions. Zero of energy is highlighted by a vertical dotted line.
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Physical Review Materials

Independence of solitary-cation properties on the atomic neighborhood in In1−xGaxN alloys: A novel perspective for material engineering

Francesco Filippone, Giuseppe Mattioli, and Aldo Amore Bonapasta

Phys. Rev. Materials 1, 064606 – Published 29 November 2017

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Independence of solitary-cation properties on the atomic neighborhood in ${In}_{1 - x} {Ga}_{x} N$ alloys: A novel perspective for material engineering