Carrier Distribution Control in van der Waals Heterostructures of ${\mathrm{Mo}\mathrm{S}}_2$ and ${\mathrm{WS}}_2$ by Field-Induced Band-Edge Engineering

The electronic properties of van der Waals heterostructures composed of ${\mathrm{Mo}\mathrm{S}}_2$ and ${\mathrm{WS}}_2$ under a perpendicular electric field are studied in terms of field strength, electron doping concentration, and interlayer stacking arrangement based on the density-functional theory. The calculation results show that accumulated carrier distribution can be controlled by tuning the field direction, field strength, and doping concentration. The electron is localized on the ${\mathrm{Mo}\mathrm{S}}_2$ layer on the positively charged electrode side under a strong positive field with a low doping concentration, whereas they are extended throughout both the ${\mathrm{Mo}\mathrm{S}}_2$ and ${\mathrm{WS}}_2$ layers under a strong negative field. Stacking misorientation between the layers further enhances the electron localization under a positive field and delocalization under a strong negative field. The stacking arrangement and electric field allow additional tuning of the electronic properties of van der Waals heterostructures.

Figure 1

(a) A structural model of a dual-gate field-effect transistor of ${\mathrm{Mo}\mathrm{S}}_2$/${\mathrm{WS}}_2$ van der Waals heterostructures with (b) AB and (c) twisted interlayer stacking arrangements. The gray rectangles denote the top- and bottom-gate electrodes with infinite permittivity. $V_T$ and $V_B$ are the top- and bottom-gate voltages, respectively, which determine the electrostatic potentials of the top gate, ${\varphi }_T$, and the bottom gate, ${\varphi }_B$, respectively. The purple, gray, and yellow circles indicate $\mathrm{Mo}$, $\mathrm{W}$, and $\mathrm{S}$ atoms, respectively. The blue dotted rectangles denote the lateral unit cell of the ${\mathrm{Mo}\mathrm{S}}_2$/${\mathrm{WS}}_2$ heterostructures.

Figure 2

The accumulated electron distribution as a function of the $z$ axis of a van der Waals heterostructure consisting of ${\mathrm{Mo}\mathrm{S}}_2$ and ${\mathrm{WS}}_2$ with an AB stacking structure under strong ($\pm 1.0\mathrm{V/nm}$), weak ($\pm 0.1$ V/nm), and zero electric fields with high (${10}^{14}$/${\mathrm{cm}}^2$) and low (${10}^{13}$/${\mathrm{cm}}^2$) doping concentrations. Positive and negative values correspond to the regions where electron accumulation and depression occur, respectively. The numerical values above each panel indicate the carrier ratio accommodated in the ${\mathrm{WS}}_2$ and ${\mathrm{Mo}\mathrm{S}}_2$ layers. The gray points denote atomic positions. In each panel, the left- and right-hand sets of three points correspond to ${\mathrm{WS}}_2$ and ${\mathrm{Mo}\mathrm{S}}_2$ layers, respectively.

Figure 3

The accumulated electron distribution as a function of the $z$ axis of the van der Waals heterostructure consisting of ${\mathrm{Mo}\mathrm{S}}_2$ and ${\mathrm{WS}}_2$ with a twisted stacking structure under strong ($\pm 1.0$ V/nm), weak ($\pm 0.1$ V/nm), and zero electric fields with high (${10}^{14}$/${\mathrm{cm}}^2$) and low (${10}^{13}$/${\mathrm{cm}}^2$) doping concentrations. Positive and negative values correspond to the regions where electron accumulation and depression occur, respectively. The numerical values above each panel indicate the carrier ratio accommodated in ${\mathrm{WS}}_2$ and ${\mathrm{Mo}\mathrm{S}}_2$ layers. The gray points denote atomic positions. In each panel, the left- and right-hand sets of three points correspond with ${\mathrm{WS}}_2$ and ${\mathrm{Mo}\mathrm{S}}_2$ layers, respectively.

Figure 4

The energy diagram of the electronic states near the band gap of the ${\mathrm{Mo}\mathrm{S}}_2$/${\mathrm{WS}}_2$ van der Waals heterostructure with (a) AB and (b) twisted stacking structures under strong negative and positive electric fields. The band edges of the heterostructures under the zero electric field are also listed in each figure. The purple, gray, and orange levels indicate the electron states localized on the ${\mathrm{Mo}\mathrm{S}}_2$ layer at the K point, localized on the ${\mathrm{WS}}_2$ layer at the K point, and distributed on both layers at the $\mathrm{\Gamma }$ points or the middle of the K-$\mathrm{\Gamma }$ line, respectively. CBE and VBE indicate conduction and valence band edges, respectively.

Figure 5

Isosurfaces and contour plots of the squared wave function of the conduction-band edge of ${\mathrm{Mo}\mathrm{S}}_2$/${\mathrm{WS}}_2$ van der Waals heterostructures with AB stacking under strong (a) negative and (b) positive electric fields and with the twisted stacking arrangement under strong (c) negative and (d) positive electric fields. The purple, gray, and yellow circles indicate $\mathrm{Mo}$, $\mathrm{W}$, and $\mathrm{S}$ atoms, respectively. The gray dotted rectangles denote the lateral unit cell of ${\mathrm{Mo}\mathrm{S}}_2$/${\mathrm{WS}}_2$ van der Waals heterostructures.