First-principles study on the electronic properties and Schottky barrier of WC/$\mathrm{W}{\mathrm{S}}_2$ and WC/$\mathrm{WS}{\mathrm{e}}_2$ heterostructures

Within the realm of two-dimensional materials, monolayer transition metal dichalcogenide semiconductors boasting intrinsic band gaps of 1–2 eV are regarded as promising candidates for channel materials in next-generation transistors. The judicious choice of electrodes is paramount to achieving low-resistance contacts, thereby enhancing the performance of nanoelectronic devices. Therefore, the exploration of novel metal-semiconductor combinations and a comprehensive grasp of the atomistic nature of interfaces are indispensable. In this work, we present a systematic examination of vertical Moiré pattern contacts between WC and $\mathrm{W}{\mathrm{S}}_2$ or $\mathrm{WS}{\mathrm{e}}_2$, with the termination atoms (tungsten or carbon termination) being investigated through density-functional theory calculations. The Moiré pattern heterostructure is found to exhibit greater energetic favorability when compared to coherent epitaxial strain heterostructures. Our analyses encompass an in-depth exploration of the interface structure, effective potential, electron localization function, Bader charge, energy bands, and density of states within these heterostructures. These investigations reveal the formation of Schottky barriers within these systems, with the dominant carrier type and height of the Schottky barriers being under the control of the termination atoms. Metal-induced gap states formed in the interfaces give rise to a strong Fermi-level pinning. We conclude that the WC/$\mathrm{WS}{\mathrm{e}}_2$ heterostructure with carbon terminations in WC have the smallest $p$-type Schottky-barrier height of 0.08 eV among all other heterostructures considered. Transport properties are assessed using the Simmons tunneling injection model. These findings yield valuable insights that can be leveraged in the design of high-performance nanoelectronic d built upon two-dimensional materials.

Figure 1

Atomic structure of (a) δ-WC. (b) Side view and top view of (b) ML-$\mathrm{W}{\mathrm{S}}_2$ and (c) ML-$\mathrm{WS}{\mathrm{e}}_2$. The band structure of (d) ML-$\mathrm{W}{\mathrm{S}}_2$ and (e) ML-$\mathrm{WS}{\mathrm{e}}_2$.

Figure 2

WC-$m/\mathrm{W}{\mathrm{S}}_2$ coherent epitaxial strain heterostructures with AB stacking (a) and AA stacking (b). (c) Schematics showing the impact of lattice mismatch to the interface: coherent lattice constant maximizes the orbital overlap (left) while Moiré pattern prevents maximizing orbital overlap (right). Side view of Moiré pattern heterostructure: (d) WC-$c/\mathrm{W}{\mathrm{S}}_2$; (e) WC-$m/\mathrm{W}{\mathrm{S}}_2$; (f) WC-$c/\mathrm{WS}{\mathrm{e}}_2$; (g) WC-$m/\mathrm{WS}{\mathrm{e}}_2$.

Figure 3

Average effective potentials along the $z$ direction for (a) WC-$c/\mathrm{W}{\mathrm{S}}_2$; (b) WC-$m/\mathrm{W}{\mathrm{S}}_2$; (c) WC-$c/\mathrm{WS}{\mathrm{e}}_2$; (d) WC-$m/\mathrm{WS}{\mathrm{e}}_2$.

Figure 4

Electron localization functions and electron densities for (a) WC-$c/\mathrm{W}{\mathrm{S}}_2$; (b) WC-$m/\mathrm{W}{\mathrm{S}}_2$; (c) WC-$c/\mathrm{WS}{\mathrm{e}}_2$; (d) WC-$m/\mathrm{WS}{\mathrm{e}}_2$.

Figure 5

Charge density difference of heterostructures for (a) WC-$c/\mathrm{W}{\mathrm{S}}_2$; (b) WC-$m/\mathrm{W}{\mathrm{S}}_2$; (c) WC-$c/\mathrm{WS}{\mathrm{e}}_2$; (d) WC-$m/\mathrm{WS}{\mathrm{e}}_2$. The pink and cyan stand for electron accumulation and depletion, respectively. The isosurface level is $3.3\times {10}^{-3}e/{\AA }^2$.

Figure 6

The projected band structure of (a) WC-$c/\mathrm{W}{\mathrm{S}}_2$; (b) WC-$m/\mathrm{W}{\mathrm{S}}_2$; (c) WC-$c/\mathrm{WS}{\mathrm{e}}_2$; WC-$m/\mathrm{WS}{\mathrm{e}}_2$. The black lines standing for Fermi levels are set to zero. The gray curves are bands of whole heterostructures, the orange shaded “fat bands” represent the contributions from $\mathrm{W}{\mathrm{S}}_2$ or $\mathrm{WS}{\mathrm{e}}_2$, and the width of the line is proportional to the band's weight. The black dashed lines represent the CBM and VBM of heterostructures.

Figure 7

The partial density of states of (a) WC-$c/\mathrm{W}{\mathrm{S}}_2$; (b) WC-$m/\mathrm{W}{\mathrm{S}}_2$; (c) WC-$c/\mathrm{WS}{\mathrm{e}}_2$; (d) WC-$m/\mathrm{WS}{\mathrm{e}}_2$. Fermi level is set to zero. The red, blue, and black curves represent the density of states of sulfur, tungsten in semiconductor, and their summation; the gray shade stands for the metal density of states. The yellow region is the gap between VBM and Fermi level, indicating hole SBH; the green region is the gap between CBM and Fermi level describing electron SBH.

Figure 8

The data summary of vertical SBH as a function of the work function of metals. The blue and red colors represent metal/$\mathrm{W}{\mathrm{S}}_2$ heterostructures and metal/$\mathrm{WS}{\mathrm{e}}_2$ heterostructures, respectively. The square [16], star [51], triangle [52], and plus [9] data points are abstracted from references; the empty circles denote the calculations in this work. The blue and red lines depict the slope parameter for $\mathrm{W}{\mathrm{S}}_2$ and $\mathrm{WS}{\mathrm{e}}_2$, respectively. The black dashed line represents the $S=1$ for comparison.