Hybrid density functional study of structural and electronic properties of functionalized Ti${}_{n+1}{X}_n$ ($X=\mathrm{C}$, N) monolayers

Density functional theory simulations with conventional (PBE) and hybrid (HSE06) functionals were performed to investigate the structural and electronic properties of MXene monolayers, ${\mathrm{Ti}}_{n+1}{\mathrm{C}}_n$ and ${\mathrm{Ti}}_{n+1}{\mathrm{N}}_n$ ($n=1$–9) with surfaces terminated by O, F, H, and OH groups. We find that PBE and HSE06 give similar results. Without functional groups, MXenes have magnetically ordered ground states. All the studied materials are metallic except for ${\mathrm{Ti}}_2{\mathrm{CO}}_2$, which we predict to be semiconducting. The calculated density of states at the Fermi level of the thicker MXenes ($n⩾5$) is much higher than for thin MXenes, indicating that properties such as electronic conductivity and surface chemistry will be different. In general, the carbides and nitrides behave differently with the same functional groups.

Figure 1

(a) Crystal structure of layered ${\mathrm{M}}_3{\mathrm{AX}}_2$ solid phase. The ${\mathrm{M}}_3{\mathrm{X}}_2$ and A layer are stacked in a zigzag formation. (b) and (c) Side and top views of ${\mathrm{M}}_3{\mathrm{X}}_2$ monolayer.

Figure 2

Structure configurations of functionalized MXenes with different arrangements of the surface atoms: side views of (a) I-${\mathrm{Ti}}_4{\mathrm{X}}_3{\mathrm{T}}_2$, (b) II-${\mathrm{Ti}}_4{\mathrm{X}}_3{\mathrm{T}}_2$, and (c) III-${\mathrm{Ti}}_4{\mathrm{X}}_3{\mathrm{T}}_2$; (d) and (e) top views of I-${\mathrm{Ti}}_4{\mathrm{X}}_3{\mathrm{T}}_2$ and II-${\mathrm{Ti}}_4{\mathrm{X}}_3{\mathrm{T}}_2$. Since configuration III is a mixture of I and II, the top view of III is not shown.

Figure 3

Evolution of total magnetic moment of pure carbide (black line) and nitride (red line) monolayers as a function of layer thickness. Carbides and nitrides behave differently.

Figure 4

(a) and (b) Band structures of ${\mathrm{Ti}}_2{\mathrm{C}}_{}{\mathrm{T}}_2$ and ${\mathrm{Ti}}_2{\mathrm{N}}_{}{\mathrm{T}}_2$, and related MXenes and MAX phases. The HSE06 results are similar to PBE results, with modest changes to the band structures. The band gap of ${\mathrm{Ti}}_2{\mathrm{C}}_{}{\mathrm{O}}_2$ is widened by HSE06.

Figure 5

(a) and (b) Partial density of states of ${\mathrm{Ti}}_2{\mathrm{C}}_{}{\mathrm{T}}_2$ and ${\mathrm{Ti}}_2{\mathrm{N}}_{}{\mathrm{T}}_2$, and related MXenes and MAX phase computed using the HSE06 functional.

Figure 6

Partial density of states of ${\mathrm{Ti}}_{n+1}{\mathrm{C}}_n{\mathrm{O}}_2$ up to $n=4$ computed using the HSE06 functional.

Figure 7

(a) and (b) Partial density of states of ${\mathrm{Ti}}_{n+1}{\mathrm{C}}_n{\mathrm{F}}_2$ and ${\mathrm{Ti}}_{n+1}{\mathrm{N}}_n{\mathrm{F}}_2$, compared with bulk TiC and TiN phase, computed using the HSE06 functional.

Figure 8

(a) and (b) Band structures of ${Ti}_{n+1}{\mathrm{C}}_n{\mathrm{F}}_2$ and ${\mathrm{Ti}}_{n+1}{\mathrm{N}}_n{\mathrm{F}}_2$ at $n=1$, 3, 5, 7, and 9 computed using the HSE06 functional. Clearly, there are more bands forming near the Fermi level with increased $n$.