Domain-size effect on the electronic properties of two-dimensional ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$

In view of the wreath of potential functionalities two-dimensional (2D) transition-metal dichalcogenides can offer, we study here tuning pathways of 2D lateral arrangements of structures. Specifically, we have systematically doped a pristine 2D ${\mathrm{MoS}}_2$ with ${\mathrm{WS}}_2$ domains of varying sizes. The resulting materials made of ${\mathrm{MoS}}_2$ with ${\mathrm{WS}}_2$ have distinct structural, electronic, and optical properties, which we analyze in detail. By including spin-orbit coupling in our quantum mechanical calculations, we were able to resolve the band structure of these lateral structures. Our analysis reveals a decrease in the band gap from ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$ to ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$. The results underline the nature and role of the $d_{z^2}$ and $d_{x^2-y^2}$ orbitals in the pristine and hybrid 2D structures, respectively, while indicating the possibility of a charge transfer from W to Mo atoms within the 2D hybrid structures. The dielectric matrix computed using the Bethe-Salpeter equation significantly affects the imaginary dielectric function and hence the absorption spectra of the lateral structures. In the end, we discuss the relevance of our work in paving a pathway for a selective tuning of the optoelectronic properties of 2D lateral heterostructures in view of optoelectronic applications.

Figure 1

Optimized geometries of the (a) pristine ${\mathrm{MoS}}_2,{\mathrm{WS}}_2$, and their lateral ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ arrangements and (b) including small ${\mathrm{WS}}_2$ domains: hexagonal-${\mathrm{WS}}_2\left({\mathrm{MoS}}_2/{\mathrm{hexWS}}_2\right)$, pyrene-${\mathrm{WS}}_2\left({\mathrm{MoS}}_2/{\mathrm{pyrWS}}_2\right)$, perylene-${\mathrm{WS}}_2\left({\mathrm{MoS}}_2/{\mathrm{peryWS}}_2\right)$, and coronene-${\mathrm{WS}}_2\left({\mathrm{MoS}}_2/{\mathrm{coroWS}}_2\right)$. The black circular regions denote the ${\mathrm{WS}}_2$ structure embedded in the ${\mathrm{MoS}}_2$ matrix. In the lower right panel, the regions corresponding to the $\left(\mathrm{coro}\text{−}1\right){\mathrm{WS}}_2,(\mathrm{coro}+5){\mathrm{WS}}_2$, and $(\mathrm{coro}+9){\mathrm{WS}}_2$ are indicated by the highlighted atoms and the respective arrows. The latter sketch the regions corresponding to the $\mathrm{coro}+5$ and $\mathrm{coro}+9$ structures (see discussion in text). The Mo, W, and, S atoms are colored in cyan, green, and yellow, respectively. The same color coding for the atoms will be used throughout.

Figure 2

Projected density of states (PDOS) for the pristine ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$ and their lateral ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$. The contributions of the valence orbitals for the Mo, W, and S atoms are shown. The arrows point to the electronic band gap with its value also shown.

Figure 3

Projected density of states (PDOS) for different ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ lateral hybrid arrangements with a varying ${\mathrm{WS}}_2$ content, as denoted by the labels. The contributions of the valence orbitals for Mo, W, and S are shown. The arrows point to the electronic band gap with its value also shown.

Figure 4

Partial charge densities of the VB and CB for the pristine ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$ and the hybrid ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$. Each panel shows a top and side view of the structures.

Figure 5

Partial charge densities of the VB and CB of the ${\mathrm{MoS}}_2/{\mathrm{hexWS}}_2,{\mathrm{MoS}}_2/{\mathrm{pyrWS}}_2,{\mathrm{MoS}}_2/{\mathrm{peryWS}}_2$, and ${\mathrm{MoS}}_2/{\mathrm{coroWS}}_2$ hybrid structures. Each panel shows a top and a side view of the structures.

Figure 6

Electronic band structures of the pristine ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$ and the hybrid ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$. The results for (a) a broader range of $k$-point directions (unit cell calculations) and (b) the $\mathrm{\Gamma }\to Y$ direction $(6\times 1\times 1$ calculations) are shown. The numbers correspond to the spin-orbit splitting energies, ${\mathrm{\Delta }}_{\text{VB/CB}}$. In (c), contributions of the $d$ orbitals on the VBM and CBM energy levels in the pristine structures and their lateral arrangements are sketched. The energy values of the VBM and CBM edges are also given.

Figure 7

The real $\mathrm{[}{\varepsilon }_1\left(\omega \right)$, top panel] and the imaginary $\mathrm{[}{\varepsilon }_2\left(\omega \right)$, bottom panel] parts of the dielectric function for the pristine ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$, and the ${\mathrm{MoS}}_2/{\mathrm{WS}}_2$ structure, as denoted by the legends.