Enhanced interlayer interactions in Ni-doped ${\mathrm{MoS}}_2$, and structural and electronic signatures of doping site

The crystal structure of ${\mathrm{MoS}}_2$ with strong covalent bonds in plane and weak van der Waals interactions out of plane gives rise to interesting properties for applications such as solid lubrication, optoelectronics, and catalysis, which can be enhanced by transition-metal doping. However, the mechanisms for improvement and even the structure of the doped material can be unclear, which we address with theoretical calculations. Building on our previous work on Ni doping of the bulk 2H phase, now we compare to polytypes (1H monolayer and 3R bulk), to determine favorable sites for Ni and the doping effect on structure, electronic properties, and the layer dissociation energy. The most favorable intercalation or adatom sites are tetrahedral intercalation for 3R (like 2H) and Mo atop for 1H. The relative energies indicate a possibility of phase change from 2H to 3R with substitution of Mo or S. We find structural and electronic properties that can be used to identify the doping sites, including metallic behavior in Mo-substituted 3R and 2H, and in-gap states for Mo- and S-substituted 1H, which could have interesting optoelectronic applications. We observe a large enhancement in the interlayer interactions of Ni-doped ${\mathrm{MoS}}_2$, opposite to the effect of other transition metals. For lubrication applications, this increased layer dissociation energy could be the mechanism of low wear. Our systematic study shows the effect of doping concentration and we extrapolate to the low-doping limit. This work gives insight into the previously unclear structure of Ni-doped ${\mathrm{MoS}}_2$ and how it can be detected experimentally, the relation of energy and structures of doped monolayers and bulk systems, the electronic properties under doping, and the effect of doping on interlayer interactions.

Figure 1

Structure of ${\mathrm{MoS}}_2$ polytypes with conventional unit cell marked by blue lines. Mo is gray and S is yellow. 1H is a single monolayer of ${\mathrm{MoS}}_2$ containing three atoms per unit cell, as in each layer of 2H or 3R. This work studies 1H, 2H, and 3R.

Figure 2

Different dopant sites for Ni in 2H (left) and 1H (right) ${\mathrm{MoS}}_2$ with top view (upper) and side view (lower). Sites include substitution in the Mo site or S site, tetrahedral or octahedral intercalation for bulk phases (2H and 3R), and Mo atop, S atop, and hollow adatoms for 1H (monolayer). 3R sites are similar to 2H (see detail in Fig. 4).

Figure 3

Doping formation energies from LDA for a $4\times 4\times 1$ supercell of monolayer 1H: (a) adatoms and (b) substitution under Mo-rich and S-rich conditions (which do not affect the value for adatoms). Insets show corresponding structures (side or top view).

Figure 4

Intercalation structures in 2H and 3R $4\times 4\times 1$ supercells, classified by bonding geometry and compared to adatom sites with respect to each layer. Mo- and S-atop tetrahedral sites are the most favorable for both 2H and 3R, consistent with Mo atop as the lowest-energy adatom site on 1H. Doping formation energies from LDA are shown relative to the most stable structure.

Figure 5

Doping formation energy from LDA in Ni-doped 2H-${\mathrm{MoS}}_2$ with respect to inverse of volume per Ni atom, in (a) intercalations, (b) Mo substitution (under Mo-rich conditions), and (c) S substitution (under S-rich conditions). For S-rich conditions, (b) is shifted down by 3.06 eV; for Mo-rich conditions, (c) is shifted down by 1.53 eV. $N$ is the parameter for the supercell size. Tetrahedral intercalation is favored over octahedral by a fairly constant amount. Red lines show extrapolation from the last two points (not always well converged yet) to the low-doping limit, achieved much more rapidly for the $z$-varying supercell series. (d) Energy difference per Ni atom between Ni-doped 2H and 3R structures.

Figure 6

Vertical atomic displacements (from $\mathrm{PBE}+\mathrm{GD}2$) in a $4\times 4\times 1$ supercell of Mo-substituted 2H-${\mathrm{MoS}}_2$, with planes shifted vertically to show changes clearly. Arrows point to the plotted heights of the Mo planes. Center: height of atoms with respect to pristine, indicated by dotted lines. Right: the two S planes sandwiching the Mo plane containing Ni. Most changes in height are observed close to the Ni atom.

Figure 7

Density of states for doped 2H and 1H structures, from $\mathrm{PBE}+\mathrm{GD}2$. The blue dotted curves in (a), (c), and (d) are the pristine density of states. (b) The partial density of states for 2H with Mo substitution. Around the Fermi level, we find (a) metallic behavior, (c) one in-gap state, and (d) two in-gap states.

Figure 8

Relative layer dissociation energy from $\mathrm{PBE}+\mathrm{GD}2$ in (a) 2H-${\mathrm{MoS}}_2$ and (b) 3R-${\mathrm{MoS}}_2$, for different doping sites and concentrations, showing a general increase in interlayer binding. We consider both adiabatic and relaxed structures of the doped monolayer.