Electronic and mechanical properties of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers and their heterostructures

Inspired by the successful synthesis of bulk ScSI in a recent work [Ferrenti et al., Chem. Mater. 34, 5443 (2022)], we have systematically investigated the mechanical and electronic properties of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers and their heterostructures by using first-principles calculations. Our calculations verify the experimental speculation that the bulk ScSI is readily exfoliatable and the monolayers of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ are stable. The Young's moduli with strong anisotropy $\left(50.2\text{–}91.5\mathrm{N}{\mathrm{m}}^{-1}\right)$ of $\text{Sc}X\mathrm{I}$ monolayers are comparable to those of phosphorene $\left(26\text{–}105\mathrm{N}{\mathrm{m}}^{-1}\right)$, but smaller than those of isotropic graphene $\left(349\mathrm{N}{\mathrm{m}}^{-1}\right)$, $\mathrm{Mo}{\mathrm{S}}_2$ $\left(122.3\mathrm{N}{\mathrm{m}}^{-1}\right)$, and $h\text{−}\mathrm{BN}$ $\left(276\mathrm{N}{\mathrm{m}}^{-1}\right)$, indicating their lower stiffness. In addition, ScSI/ScSeI monolayers show good flexibility with critical strain of 29%/33%. Application of strain can effectively regulate the band gap $\left(E_g\right)$ and band edge of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers. For instance, the $E_g$ of the ScSeI monolayer is reduced from 1.83 to 1.59 eV and the band gap type is changed from indirect to direct band gap when a compressive strain of 6% is applied along the $x$ direction, which is attributed to the orbital hybridization between the $d$ orbital of Sc and $p$ orbital of the elements at the $X$ and I sites. More importantly, $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers can form type II vertical heterostructure with typical two-dimensional semiconductors due to the deeper energy levels of their valence band maximum and conduction band minimum. In addition, $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers can also be used to form type I lateral heterostructure with the ScSeBr monolayer. The excellent ductility, strain-tuned electronic properties, and heterostructure design make $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers promising candidates for the application of flexible electronic devices.

Figure 1

The atomic structures of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers. (a) Top and (b,c) side views of the $\text{Sc}X\mathrm{I}$ monolayers. The red rectangle with Bravais lattice vectors (a,b) is the corresponding primitive unit cell.

Figure 2

Phonon dispersion curves and projected phonon density of states (DOS) of (a) ScSI and (b) ScSeI monolayers.

Figure 3

Chemical bonding nature of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers. The upper plane is ScSI monolayer and the bottom plane is ScSeI monolayer. (a), (e) 2D ELF along (010) and (100) planes. (b), (f) The ELF profiles along the Sc–I and $\mathrm{Sc}\text{−}X$ bonds. The ELF profiles along the Na-Cl bond of ionic crystal NaCl and the C-C bond of covalent crystal diamond as a reference for ionic and covalent bonds, respectively. (c), (g) Crystal orbital Hamilton Population (COHP) of Sc-I and $\mathrm{Sc}\text{−}X$ bonds. (d), (h) Crystal orbital bond indices (COBIs) of Sc-I and $\mathrm{Sc}\text{−}X$ bonds. COHPs and COBIs of NaCl and diamond are given for a purely covalent element and a strongly ionic material with negligible covalency, respectively. Absolute values in brackets are corresponding and integrated crystal orbital Hamilton population (ICOHP) and integrated crystal orbital bond indices (ICOBIs).

Figure 4

Calculated orientation-dependent (a) Young's modulus $E$(θ) and (b) Poisson's ratio ν(θ) of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ monolayers.

Figure 5

(a–d) and (e–f) are stress-strain curves, bond length evolution, in-plane transverse strain evolution, and normal strain evolution along the $x$ and $y$ directions for ScSI and ScSeI monolayers, respectively.

Figure 6

(a–c) and (d–f) are band structure, projected density of states (PDOS), and band gap as a function of biaxial compressive strain using the HSE06 method for ScSI and ScSeI monolayers, respectively. The dotted line represents the Fermi energy level.

Figure 7

(a–c) and (d–f) are the energy of the VBM and CBM relative to vacuum potential at HSE06 level of $\text{Sc}X\mathrm{I}$ $(X=\mathrm{S},\text{Se})$ under uniaxial strain along $x$, uniaxial strain along $y$, and biaxial strain for ScSI and ScSeI monolayers, respectively. CBM and VBM are marked as blue and brown, respectively.

Figure 8

Conduction and valence band edges relative to vacuum potential at HSE06 and PBE level for the 2D crystals. CBM and VBM for HSE06 level are marked as blue and brown, respectively. CBM and VBM for PBE level are marked as green and red, respectively.

Figure 9

(a) Energy surface of $E_{\mathrm{b}}$ of ScSeI/GeS heterostructure with a series of configurations. (b) Side view and (c) top view of GeS/ScSeI heterostructure with minimum of $E_{\mathrm{b}}$. (d) Band structure of corresponding ScSeI/GeS heterostructure at HSE06 level. (e) Plane-averaged charge density difference $\mathrm{\Delta }\rho \left(z\right)$ of corresponding ScSeI/GeS heterostructure. Sc, Se, I, S, and Ge atoms are displayed in green, yellow, purple, blue, and pink, respectively.

Figure 10

(a) Top view of atomic configurations of ${\left(\mathrm{ScSeI}\right)}_3/{\left(\mathrm{ScSeBr}\right)}_3$ LHs along the $x$ and $y$ directions, respectively. (b,c) are HSE06 band structures of ${\left(\mathrm{ScSeI}\right)}_3/{\left(\mathrm{ScSeBr}\right)}_3$ LHs along the $x$ and $y$ directions, respectively. Sc, Se, I, and Br atoms are displayed in green, yellow, purple, blue, and bluish purple, respectively.