Two-dimensional $\mathrm{Re}{\mathrm{S}}_2$: Solution to the unresolved queries on its structure and inter-layer coupling leading to potential optical applications

Over the last few years, $\mathrm{Re}{\mathrm{S}}_2$ has generated a myriad of unattended queries regarding its structure, the concomitant thickness-dependent electronic properties, and its apparently contrasting experimental optical response. In this paper, with elaborate first-principles investigations, using density functional theory (DFT) and time-dependent DFT, we identify the structure of $\mathrm{Re}{\mathrm{S}}_2$, which is capable of reproducing and analyzing the layer-dependent optical response. The theoretical results are further validated by an in-depth structural, chemical, optical, and optoelectronic analysis of the large-area $\mathrm{Re}{\mathrm{S}}_2$ thin films, grown by the chemical vapor deposition (CVD) process. Micro-Raman, x-ray photoelectron spectroscopy, cross-sectional transmission electron microscopy, and energy-dispersive x-ray analysis have enabled the optimization of the uniform growth of the CVD films. The correlation between the optical and electronic properties was established by static photoluminescence and excited state transient absorption measurements. Sulfur vacancy-induced localized mid-gap states render a significantly long lifetime of the excitons in these films. The ionic gel top-gated photodetectors, fabricated from the as-prepared CVD films, exhibit a large photo-response of $\sim 5$ A/W and a remarkable detectivity of $\sim {10}^{11}$ Jones. The outcome of this paper will be useful in promoting the application of vertically grown large-area films in the field of optics and opto-electronics.

Figure 1

Polyhedral coordination of octahedra (OCT) and square pyramids (SQP) for (a) S-1 with the corresponding unit cell orientation and (b) the Re4 parallelogram array along the $a$ direction (a typical Re4 parallelogram highlighted within blue ellipse); (c) the OCT polyhedral coordination for S-2 with the respective unit cell orientation and (d) the Re4 parallelogram array along the $b$ direction (highlighted within blue ellipse). Red and green are the colors used for indicating Re and S, respectively.

Figure 2

Band structure and corresponding density of states (DOS) of $\mathrm{Re}{\mathrm{S}}_2$ (S-1) (a) monolayer, (b) bilayer, (c) trilayer, and (d) bulk system. (e) Multiple polyhedral coordination of $\mathrm{Re}{\mathrm{S}}_2$ in S-1, square pyramidal (SQP) and octahedral (OCT) polyhedra have been marked by using pink and yellow circles, respectively. Right inset shows the one-dimensional (1D) OCT chain and bridging SQP structure (f) corresponding Brillouin zone and the high symmetry directions of the structure. Optical absorbances of different $\mathrm{Re}{\mathrm{S}}_2$ systems are plotted after using (g) density functional theory (DFT) and (h) time-dependent DFT (TDDFT) methodologies.

Figure 3

Layer dependence of band structure and corresponding partial density of states (PDOS) for S-2 of $\mathrm{Re}{\mathrm{S}}_2$ in 1T octahedral coordination for (a) monolayer, (b) bilayer, (c) trilayer, and (d) bulk.

Figure 4

Contribution of edge and inside Re and S atoms in the density of states (DOS) of (a) bulk, (b) monolayer, (c) bilayer, and (d) trilayer. (e) The edge and inside atoms considered in the partial density of states (PDOS).

Figure 5

Band structure and corresponding partial density of states (PDOS) of bulk $\mathrm{Re}{\mathrm{S}}_2$ (S-1) with sulfur vacancies at the (a) distorted octahedra (vacancy at OCT), (b) square pyramid (vacancy at SQP), and (c) at both polyhedral places (vacancy at both).

Figure 6

Three-dimensional (3D) Raman maps of different chemical vapor deposition (CVD) grown films at different growth temperatures: (a) $450{}^{\circ }\mathrm{C}$ (F1), (b) $650{}^{\circ }\mathrm{C}$ (F2), (c) $750{}^{\circ }\mathrm{C}$ (F3), and their corresponding (d) Raman spectra. Corresponding scanning electron microscopic images of different films for (e) $450{}^{\circ }\mathrm{C}$ (F1), (f) $650{}^{\circ }\mathrm{C}$ (F2), (g) $750{}^{\circ }\mathrm{C}$ (F3); (h) energy-dispersive x-ray (EDX) elemental map of $\mathrm{Re}{\mathrm{S}}_2$ ($650{}^{\circ }\mathrm{C}$); XPS spectra of (i) Re-$4f$ and (j) S-$2p$ electrons in different samples (F1–F3).

Figure 7

Color map of thickness of $\mathrm{Re}{\mathrm{S}}_2$ samples using an optical profilometer for growth temperatures (a) $450{}^{\circ }\mathrm{C}$ (F1), (b) $650{}^{\circ }\mathrm{C}$ (F2), and (c) $750{}^{\circ }\mathrm{C}$ (F3); corresponding height profile of systems for (d) $450{}^{\circ }\mathrm{C}$ (F1), (e) $650{}^{\circ }\mathrm{C}$ (F2), and (f) $750{}^{\circ }\mathrm{C}$ (F3); (g) cross-sectional transmission electron microscopy (TEM) images of $\mathrm{Re}{\mathrm{S}}_2$ on $\mathrm{Si}{\mathrm{O}}_2$ (F2), (g) fast Fourier transform image of $\mathrm{Re}{\mathrm{S}}_2$, (i) high-resolution TEM image of planar $\mathrm{Re}{\mathrm{S}}_2$ depicting the Re4 parallelogram, (j) high-resolution TEM image of vertical growth of $\mathrm{Re}{\mathrm{S}}_2$ showing lattice fringes corresponding to the [202] plane of S-1 (see text).

Figure 8

Room temperature photoluminescence (PL) spectra of F1, F2, and F3 ($650{}^{\circ }\mathrm{C}$) (a) at lower energy and (b) higher energy range. Kinetics for exciton decay for (c) $\mathrm{Re}{\mathrm{S}}_2$ ($450{}^{\circ }\mathrm{C}$, F1), (e) $\mathrm{Re}{\mathrm{S}}_2$ ($650{}^{\circ }\mathrm{C}$, F2), and (g) $\mathrm{Re}{\mathrm{S}}_2$ ($750{}^{\circ }\mathrm{C}$, F3). The contour plots of transient absorption (TA) measurements for (d) $\mathrm{Re}{\mathrm{S}}_2$ ($450{}^{\circ }\mathrm{C}$, F1), (f) $\mathrm{Re}{\mathrm{S}}_2$ ($650{}^{\circ }\mathrm{C}$, F2), and (h) $\mathrm{Re}{\mathrm{S}}_2$ ($750{}^{\circ }\mathrm{C}$, F3).

Figure 9

Kinetics for A-exciton decay and trap state filling for (a) F1, (b) F2, and (c) F3. Exciton signals are seen to be alive even after 1200 ps. Kinetics for B-exciton slow decay, fast decay, and trap state filling at for (d) F1, (e) F2, and (f) F3. Exciton signals are seen to be alive even after 1200 ps.

Figure 10

Phototransistor characteristics of $\mathrm{Re}{\mathrm{S}}_2$ sample F2: (a) schematic device diagram, (b) transfer characteristics in dark and illuminated conditions, (c) current vs voltage photo-response under dark and different illumination conditions, (d) photo-transistor switching characteristics with different illuminating power, (e) responsivity and detectivity with respect to the illuminated power density of light at a gate bias of 5 V, and (f) responsivity and detectivity of the system as a function of voltage.