Two-dimensional ferromagnet/semiconductor transition metal dichalcogenide contacts: $p$-type Schottky barrier and spin-injection control

We study the ferromagnet/semiconductor contacts formed by transition metal dichalcogenide monolayers, focusing on semiconducting MoS${}_2$ and WS${}_2$ and ferromagnetic VS${}_2$. We investigate the degree of $p$-type doping and demonstrate tuning of the Schottky barrier height by vertical compressive pressure. An analytical model is presented for the barrier heights that accurately describes the numerical findings and is expected to be of general validity for all transition metal dichalcogenide metal/semiconductor contacts. Furthermore, magnetic proximity effects induce a 100% spin polarization at the Fermi level in the semiconductor where the spin splitting increases up to 0.70 eV for increasing pressure.

Figure 1

Spin polarized band structures of (a) $h$VS${}_2$ and (b) $t$VS${}_2$. Red and blue lines correspond to the spin majority and minority bands, respectively.

Figure 2

Binding energy per interface metal atom as a function of the interface separation ($D$) in (a) $h$VS${}_2$/MoS${}_2$, (b) $h$VS${}_2$/WS${}_2$, and (c) $t$VS${}_2$/MoS${}_2$. The equilibrium positions are indicated by stars. (d) Side views of the nonequivalent configurations of $h$VS${}_2$/MoS${}_2$ and $t$VS${}_2$/MoS${}_2$. Yellow, gray, and red balls represent S, Mo, and V atoms, respectively.

Figure 3

Spin polarized partial density of states for VS${}_2$, MoS${}_2$, and WS${}_2$ in $h$VS${}_2$/MoS${}_2$-AA and $h$VS${}_2$/WS${}_2$-AA for (a), (c) an interface separation of 2.4 Å and (b), (d) the equilibrium position. In (b) and (d) the $p$-type Schottky barrier heights (Φ_B,p) are indicated.

Figure 4

Spin polarized band structures of $h$VS${}_2$/MoS${}_2$-AB for (a) $D$ = 2.4 Å, (b) the equilibrium position, and (c) $t$VS${}_2$/MoS${}_2$-fcc-II at the equilibrium position. The MoS${}_2$ derived conduction and valence bands in the hybrid systems are indicated by white dotted curves. (d) Band-gap variation (black) and spin splitting at the Γ point (red) of MoS${}_2$ and WS${}_2$ as a function of the interface separation from $D$ = 2.4 Å to the respective equilibrium position.

Figure 5

(a) Plane-averaged difference of the electron density, Δρ($z$), for $h$VS${}_2$/MoS${}_2$-AB at the equilibrium position. The positions of the atoms are indicated, $q$ is the charge transfer, and $M_V$ is the magnetic moment of the V atom. (b) $q$ (black) and $M_V$ variation (Δ$M_V$, blue) as a function of the interface separation in $h$VS${}_2$/MoS${}_2$-AB.

Figure 6

(a) Schematic diagram of the Schottky barrier formation. (b) Schottky barrier height as a function of the vertical compressive pressure in $h$VS${}_2$/MoS${}_2$-AB (circles) and $t$VS${}_2$/MoS${}_2$-fcc-II (squares). The lines represent the results obtained from Eq. (3). (c) Interface dipole (${\mu }_{\mathrm{IS}}$) and (d) MoS${}_2$ VBM upshift (Δ) as a function of $D$ from 2.4 Å to the respective equilibrium positions.