High-mobility two-dimensional $M{A}_2{\mathrm{N}}_4$ ($M$ = Mo, W; $A$ = Si, Ge) family for transistors

The quest for functional materials for the next generation of electronics plays a pivotal role in the postsilicon era, and two-dimensional layered semiconductors are at the core of this extensive research. In this work, we demonstrate that some members of the ${MA}_2{Z}_4$ family are candidates for high-efficiency optoelectronics. Through first-principles calculations, we find that the intrinsic electron mobility of ${MA}_2{\mathrm{N}}_4$ (where $M$ = {Mo, W} and $A$ = {Si, Ge}) layer materials reaches up to ${10}^3{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$ at liquid nitrogen temperature, and decreases as the temperature rises due to the enhanced electron-phonon scattering. Interestingly, the charge transport in these materials takes place purely along the intercalated transition metal nitride layer, so the surface adsorptions (impurities) or substrate interactions have nearly no effect on the carrier mobility due to the $A$-N bilayer protection, and the high electron mobility does not depend on the thickness of the sample. These features are distinct from other two-dimensional (2D) materials, such as silicene, black phosphorus, and indium selenide, and the 2D ${MA}_2{Z}_4$ family of materials are proposed as an outstanding candidate for field effect transistors and further studies.

Figure 1

Ab initio modeling (blue) and deformation potential theory (orange) calculations of the intrinsic carrier mobility of various bidimensional materials for (a) electrons and (b) holes at room temperature, where we have also presented the corresponding experimental values (yellow) when available. We changed the color shade between the different crystal symmetry to improve readability.

Figure 2

(a), (f) Sketch of the top and lateral views of the atomic structure of monolayers ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{ZrS}}_2$, respectively, where we expanded the primitive cell to a $3\times 3$ supercell to clearly show the crystal symmetry. For 2D ${\mathrm{MoSi}}_2{\mathrm{N}}_4$, we find that the overall structure exhibits a triangular symmetry and has seven atomic layers which are named Mo, Si, and N, and N' correspond to nonequivalent nitrogen elements in the lattice, whereas monolayer ${\mathrm{ZrS}}_2$ is composed of three atomic layers which are named Zr and S, respectively. The structures were produced with vesta [54]. (b), (g) Energy bands and DOS obtained within DFT and Wannier interpolation methods for 2D ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{ZrS}}_2$ as a function of high-symmetric paths of Brillouin zone, where the Fermi energy is shifted to zero. (c), (h) PDOS as a function of electron energy for 2D ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{ZrS}}_2$, where we projected to every atomic layer as well as the atomic orbitals, respectively. Charge density distributions of (d), (i) the CBM and (e), (j) the VBM states for 2D ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{ZrS}}_2$, where we set the same isosurface value of 0.0035 $\mathrm{e}/{\mathrm{Bohr}}^3$. The isosurface is in gray and the cut due to the periodic boundary conditions appears as blue areas.

Figure 3

Electron and hole lifetimes of 2D monolayer ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{ZrS}}_2$ as a function of the absolute value of quasiparticle energy relative to the CBM or VBM, where ${\mathrm{E}}_{\mathrm{CBM}}$ and ${\mathrm{E}}_{\mathrm{VBM}}$ are the energies of conduction and valence bands extreme point, respectively.

Figure 4

The intrinsic electron mobility of (a) ${\mathrm{MoSi}}_2{\mathrm{N}}_4$, (b) ${\mathrm{WSi}}_2{\mathrm{N}}_4$, (c) ${\mathrm{MoGe}}_2{\mathrm{N}}_4$, and (d) ${\mathrm{WGe}}_2{\mathrm{N}}_4$ as a function of the number of layers $N_L$, where both ab initio simulations (blue) and deformation potential theory (orange) calculated results are presented at room temperature, respectively.

Figure 5

The electron and hole mobilities of monolayer ${\mathrm{MoSi}}_2{\mathrm{N}}_4$, ${\mathrm{WSi}}_2{\mathrm{N}}_4$, ${\mathrm{MoGe}}_2{\mathrm{N}}_4$, and ${\mathrm{WGe}}_2{\mathrm{N}}_4$ as a function of (a, b) temperature and (c, d) carrier concentration at room temperature, respectively.