Janus single layers of ${\mathrm{In}}_2\text{SSe}$: A first-principles study

By performing first-principles calculations, we propose a stable direct band gap semiconductor Janus single-layer structure, ${\mathrm{In}}_2\mathrm{SSe}$. The binary analogs of the Janus structure, InS and InSe single layers are reviewed to evince the structural and electronic relation with ${\mathrm{In}}_2\mathrm{SSe}$. The structural optimization calculations reveal that a Janus ${\mathrm{In}}_2\mathrm{SSe}$ single layer has hexagonal geometry like the InS and InSe single layers, which are also its structural analogs. The Janus single layer is dynamically stable, as indicated by the phonon spectrum. The electronic band diagram of the Janus structure shows that an ${\mathrm{In}}_2\mathrm{SSe}$ single layer is a direct band gap semiconductor, in contrast to its analogs, InS and InSe single layers, which are indirect band gap semiconductors. Nevertheless, it is found that the strain effect on electronic properties of the InS and InSe single layers designates the electronic structure of the Janus single layer. A rough model for the construction of the electronic band diagram of the Janus structures is discussed, and it is indicated that the difference in work functions of chalcogenide sides in the Janus structure determines the construction of the electronic structure. It is found that the Janus structure is a robust direct gap semiconductor under tolerable strain; for that reason, the Janus ${\mathrm{In}}_2\mathrm{SSe}$ single layer is a candidate for optoelectronic nanodevice applications.

Figure 1

(a) Top (perspective) and side views of the geometric structure of the Janus ${\mathrm{In}}_2\mathrm{SSe}$ single layer. Purple, yellow, and green balls show In, S, and Se atoms, respectively. (b) Phonon band diagram of the Janus ${\mathrm{In}}_2\mathrm{SSe}$ single layer. (c) Pathway to synthesizing the Janus structure. $\mathrm{\Delta }$ indicates the total-energy difference between the final energy (Janus ${\mathrm{In}}_2\mathrm{SSe})$ and initial energy (InSe/InS) of single-layer structures.

Figure 2

The electronic band structure of (a) InSe, (b) InS single layers, and (c) Janus ${\mathrm{In}}_2\mathrm{SSe}$. The electronic band structure of strained (d) InSe and (e) InS single layers. The Fermi level is set to zero, and for better projection, an energy range between 0 and 2.5 eV is scissored in the $y$ axis. (f) The electronic band structures' superposition of strained InS and InSe; however, the Fermi level of InS is shifted due to the vacuum level.

Figure 3

Strain-dependent electronic band diagram of the Janus ${\mathrm{In}}_2\mathrm{SSe}$ structure along the (a) biaxial, (b) zigzag, and (c) armchair directions. The Fermi level is set to zero, and for better projection, an energy range between 0 and 2.5 eV is scissored in the $y$ axis. Strain-dependent band gap crossovers along the (d) biaxial (e) zigzag (f) armchair directions.

Figure 4

Band-decomposed charge densities (side view and top view) of the valence-band edge and conduction-band edge of the Janus ${\mathrm{In}}_2\mathrm{SSe}$ single layer under biaxial strain. The isosurface level was taken to be $1.15\times {10}^{-5}$ electrons/${\AA }^3$.