Defects and oxidation resilience in InSe

We use density functional theory to study intrinsic defects and oxygen related defects in indium selenide. We find that InSe is prone to oxidation, but however not reacting with oxygen as strongly as phosphorene. The dominant intrinsic defects in In-rich material are the In interstitial, a shallow donor, and the Se vacancy, which introduces deep traps. The latter can be passivated by oxygen, which is isoelectronic with Se. The dominant intrinsic defects in Se-rich material have comparatively higher formation energies.

Figure 1

Top (0001) and side ($11\overline{2}0$) views of various intrinsic point defects and substitutional oxygen in monolayer InSe, grouped by similarity. (a) PS: pristine supercell. (b) ${\mathrm{V}}_{\mathrm{In}}$: indium vacancy. (c) ${\mathrm{Se}}_{\mathrm{In}}$: selenium-in-indium antisite. (d) Swap: swapping adjacent selenium and indium. (e) ${\mathrm{In}}_{\mathrm{Se}}$: indium-in-selenium antisite. (f) ${\mathrm{V}}_{\mathrm{Se}}$: selenium vacancy. (g) ${\mathrm{In}}_{ac}$: indium hovering above the center of the hexagonal interstitial cage. (h) ${\mathrm{In}}_{ic}$: interstitial indium at center of hexagonal cage. (i) ${\mathrm{O}}_{\mathrm{Se}}$: oxygen atom substituting a selenium. (j) ${{\mathrm{O}}_2}_{\mathrm{Se}}$: oxygen molecule substituting a selenium.

Figure 2

DFT band structure plots of various intrinsic point defects and substitutional oxygen defects in monolayer InSe: (a) ${\mathrm{V}}_{\mathrm{In}}$: indium vacancy. (b) ${\mathrm{Se}}_{\mathrm{In}}$: selenium-in-indium antisite. (c) Swap: swapping adjacent selenium and indium. (d) ${\mathrm{In}}_{\mathrm{Se}}$: indium-in-selenium antisite. (e) ${\mathrm{V}}_{\mathrm{Se}}$: selenium vacancy. (f) ${\mathrm{In}}_{ac}$: indium hovering above the center of the hexagonal interstitial cage. (g) ${\mathrm{In}}_{ic}$: interstitial indium at center of hexagonal cage. (h) ${\mathrm{O}}_{\mathrm{Se}}$: oxygen atom substituting a selenium. (i) ${{\mathrm{O}}_2}_{\mathrm{Se}}$: oxygen molecule substituting a selenium. Refer to Fig. 1 for the respective defects. Majority and minority spin bands are represented by continuous and dashed lines, respectively. Fermi levels are represented by blue dash-dotted horizontal lines.

Figure 3

Formation energies $E_f$ as a function of chemical potential ${\mu }_{\mathrm{Se}}$ (arbitrary units) for intrinsic defects. $\mathrm{\Delta }{\mu }_{\mathrm{Se}}=1.05$ eV. Refer to text for constraints and definitions.

Figure 4

Top (0001) and side ($11\overline{2}0$) views of the stable single oxygen molecule addition defects in monolayer InSe (physisorption), in increasing order of relative energy cost of formation. (a) ${\mathrm{O}}_2$–A: above indium, perpendicular to bridge bond. (b) ${\mathrm{O}}_2$–B: above center of hexagonal cage, perpendicular to bridge bonds. (c) ${\mathrm{O}}_2$–C: above center of hexagonal cage, along bridge bonds. (d) ${\mathrm{O}}_2$–D: above selenium, along bridge bond. (e) ${\mathrm{O}}_2$–E: above selenium, perpendicular to bridge bond. (f) ${\mathrm{O}}_2$–F: above indium, along bridge bond. (g) ${\mathrm{O}}_2$–G: interstitial molecule at center of hexagonal cage, perpendicular to monolayer.

Figure 5

DFT band structure plots of various stable single oxygen molecule defects in monolayer InSe (physisorption) in increasing order of relative energy cost of formation. (a) Pristine $3\times 3$ supercell; (b)–(h) different configurations of oxygen defects. Refer to Fig. 4 for the respective defects. Minority spin is shown in dashed line. Color makes deeply embedded impurity states easier to see.

Figure 6

Top (0001) and side ($11\overline{2}0$) views of the stable single oxygen atom addition defects in monolayer InSe (chemisorption), in increasing order of relative energy cost of formation. (a) O–A: interstitial oxygen defect between two indium atoms, with angled bonds like in water molecule, venturing out into the hexagonal interstitial cage. (b) O–B: interstitial oxygen in angled bond between two indium atoms, underneath (bridge) bond of indium-selenium. (c) O–C: oxygen in angled bond between indium and selenium. (d) O–D: interstitial oxygen at center of hexagonal cage. (e) O–E: oxygen above selenium. (f) O–F: three-coordinated oxygen between two selenium atoms, also bonded with indium atom. (g) O–G: oxygen above indium. The case of oxygen atom hovering above the center of the hexagonal interstitial cage is not stable.

Figure 7

DFT band structure plots of various stable single oxygen atom defects in monolayer InSe (chemisorption) in increasing order of relative energy cost of formation. (a) Pristine $3\times 3$ supercell; (b)–(h) different configurations of oxygen defects. Refer to Fig. 6 for the respective defects. (e) A magnetic spin calculation without spin-orbit coupling. Minority spin in dashes.

Figure 8

Formation energies $E_f$ as a function of chemical potential ${\mu }_{\mathrm{Se}}$ (arbitrary units) for oxygen substitution defects. $\mathrm{\Delta }{\mu }_{\mathrm{Se}}=1.05$ eV. Refer to text for constraints and definitions.