Mo-Polar 5|7 Defects in MoS2

• Mo-Polar 5|7 defects are tilt grain-boundary dislocation cores in monolayer MoS2, formed by a shared Mo–Mo edge between a pentagon and a heptagon.
• Their structure is characterized by an elongated Mo–Mo bond (~2.35 Å) and precise geometric parameters that differentiate them from the pristine lattice.
• Under Mo-rich growth conditions, these defects appear in over 95% of grain boundaries, significantly affecting photoluminescence by reducing non-radiative recombination.

Searching arXiv for the specified paper to ground the article in the cited source. I’ll look up the paper on arXiv now. Mo-polar 5|7 defects are tilt-grain-boundary dislocation cores in monolayer MoS$_2$ in which a pentagon and a heptagon share a Mo–Mo homoelemental edge, corresponding to the Mo-polar variant with $\Phi \approx 0^\circ$. In Choi et al., these defects are identified as the thermodynamically favored grain-boundary structure under a Mo-rich local chemical environment established during vapor-liquid-solid growth with sodium molybdate liquid alloys; under those conditions, their yield exceeds 95%, and their presence correlates with photoluminescence behavior distinct from films containing abundant S 5|7 defects formed in vapor-solid-solid growth (Choi et al., 30 Jul 2025).

1. Atomic configuration and local geometry

At the level of the reconstructed lattice, a 5|7 defect consists of one pentagon sharing an edge with one heptagon. In the Mo-polar form, the shared edge is a Mo–Mo bridge. The Mo-only top-view sketch reported by Choi et al. places this bridge between Mo2 and Mo1, with the pentagon traced by Mo1–Mo2–Mo3–Mo4–Mo5 and the adjacent heptagon by Mo2–Mo1–Mo6–Mo7–… . The surrounding S atoms occupy the usual positions above and below the Mo plane associated with trigonal prismatic coordination in monolayer MoS$_2$ (Choi et al., 30 Jul 2025).

The local geometry was quantified over 150 defects in vapor-liquid-solid-grown films. The shared Mo–Mo bond length is reported as $d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$ Å. The surrounding hexagon–hexagon Mo–S bonds are approximately $1.83$ Å, and the average outer angle at the 5|7 core is $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$. These values distinguish the defect core from the unreconstructed host lattice and indicate that the homoelemental bridge is structurally elongated relative to the ordinary coordination environment. A plausible implication is that the defect core is both geometrically identifiable in STEM and chemically sensitive to the growth environment.

2. Crystallography of tilt grain boundaries

The relevant crystallographic parameter is the tilt-boundary misorientation $\theta_t$, defined as the in-plane rotation between the zig-zag axes of two MoS$_2$ grains. Choi et al. illustrate a grain boundary with $\theta_t \approx 20^\circ$ in the main text and report Mo-polar 5|7 defects for all $\theta_t$ up to approximately $\Phi \approx 0^\circ$0 in vapor-liquid-solid growth (Choi et al., 30 Jul 2025).

Accommodation of misorientation follows the tilt-boundary relation

$\Phi \approx 0^\circ$1

where $\Phi \approx 0^\circ$2 is the spacing between dislocations and $\Phi \approx 0^\circ$3 is the Burgers vector. For Mo5|7 with $\Phi \approx 0^\circ$4 aligned to the armchair direction, $\Phi \approx 0^\circ$5. Experimentally, $\Phi \approx 0^\circ$6 decreases monotonically with increasing $\Phi \approx 0^\circ$7, consistent with the AC-GB theoretical line. This places Mo-polar 5|7 defects within the conventional Read–Shockley description of low- to intermediate-angle tilt boundaries, rather than treating them as isolated irregular reconstructions.

3. Thermodynamic preference and growth selectivity

The thermodynamic analysis is expressed through the grain-boundary formation energy per unit length,

$\Phi \approx 0^\circ$8

where $\Phi \approx 0^\circ$9 is the total DFT energy of the supercell containing the grain boundary, $_2$0 and $_2$1 are the excess numbers of Mo and S atoms relative to pristine MoS$_2$2, $_2$3 and $_2$4 are their chemical potentials, and $_2$5 is the grain-boundary length in the cell. In the PBE-GGA loop-model calculations, the Mo-rich limit at $_2$6 eV gives $_2$7 eV/Å and $_2$8 eV/Å; at the S-rich limit, $_2$9 eV, the S-polar core becomes lower in energy (Choi et al., 30 Jul 2025).

The reported synthesis conditions align with that thermodynamic landscape. The substrate is soda-lime glass, for which a Na–Mo–O alloy forms above a eutectic temperature of approximately $d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$0. Growth is performed at $d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$1, above that eutectic point, yielding liquid Na–Mo–O with approximately 20 mol% Mo. The precursors are Mo(CO)$d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$2 and (C$d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$3H$d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$4)$d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$5S in an Ar/H$d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$6 carrier at total pressure $d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$7 Torr, with $d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$8 Torr and $d_{\mathrm{Mo-Mo}} = (2.35 \pm 0.08)$9 Torr. Although the vapor is nominally S-rich, the liquid alloy is reported to maintain a Mo-rich local chemical potential during growth. STEM statistics over 150 defects on several grain-boundary segments show Mo-polar 5|7 defects at more than 95% of sites in vapor-liquid-solid-grown films, in contrast to an approximately 60:40 mixed 5|7 population in vapor-solid-solid growth. This suggests that the liquid alloy acts not merely as a transport medium but as a local chemical-potential reservoir that selects the thermodynamic boundary core.

4. First-principles description and electronic structure

The first-principles calculations in Choi et al. use VASP 5.4.4 with PAW pseudopotentials for Mo$1.83$0 and S, and the PBE generalized-gradient approximation for exchange–correlation. The supercell is a $1.83$1 monolayer slab with vacuum of at least $1.83$2 Å. Geometry relaxation uses a $1.83$3-only $1.83$4-point mesh and a force convergence criterion below $1.83$5 eV/Å, while density of states calculations use a $1.83$6 Monkhorst–Pack grid. The plane-wave cutoff is $1.83$7 eV (Choi et al., 30 Jul 2025).

For an isolated Mo5|7 loop, the computed band and density-of-states structure shows deep-level states approximately $1.83$8–$1.83$9 eV below the conduction-band minimum and no shallow in-gap donor states. The paper therefore concludes that Mo5|7 cores themselves do not contribute free carriers. The same section also characterizes the Mo–Mo bond as relatively weak, with large bond length and low coordination, and links that feature to defect mobility under catalysis while maintaining electronic inertness with respect to $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$0-doping. Within the framework of the reported calculations, Mo-polar 5|7 defects are thus structurally active growth intermediates but electronically passive as isolated defects.

5. Optical response and non-radiative pathways

The optical distinction between Mo-polar and S-polar grain-boundary environments is established through photoluminescence measurements. PL mapping around a $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$1 grain boundary was performed with 1.88 eV excitation at approximately $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$2 W/cm$\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$3, at 120 K in vacuum. For vapor-liquid-solid-grown films containing Mo5|7 grain boundaries, the grain-boundary PL intensity is approximately equal to that of the grain interior, indicating no quenching. For vapor-solid-solid-grown films containing mixed or S5|7 defects, the grain-boundary PL is red-shifted by approximately 10 meV and its intensity is suppressed by approximately 55% relative to the grain interior (Choi et al., 30 Jul 2025).

Over a $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$4 $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$5m$\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$6 area, the global PL trion/exciton weight ratio is reported as $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$7 for the vapor-liquid-solid film and $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$8 for the vapor-solid-solid film. Using the three-level model cited in the paper, these values correspond to electron densities of approximately $\beta_{\mathrm{Mo5|7}} \approx 126.8^\circ$9 cm$\theta_t$0 and $\theta_t$1 cm$\theta_t$2, respectively. The higher PL yield of the vapor-liquid-solid film is attributed to suppression of non-radiative recombination via donor-type traps associated with adsorbed Na on S 5|7 defects. In this interpretation, the decisive variable is not merely carrier density but whether the defect-plus-adsorbate complex leaves free electrons in the lattice and thereby promotes non-radiative charged-exciton decay.

6. Relation to S-polar 5|7 defects and broader significance

Under vapor-solid-solid growth on alkali-free glass, the local chemical potential fluctuates and the boundary is described as kinetically “zipped-up,” producing a mixture of $\theta_t$3 Mo5|7 and $\theta_t$4 S5|7 cores. S-polar 5|7 defects are thermodynamically favored only at high $\theta_t$5, but in vapor-solid-solid growth they appear as kinetic survivors when Mo is locally depleted. At $\theta_t$6, the reported formation energy is $\theta_t$7 eV/Å, only slightly below that of Mo5|7 under those conditions. An isolated S5|7 defect also produces deep mid-gap states, but its behavior changes in the presence of Na (Choi et al., 30 Jul 2025).

All four major defect types discussed in the paper—Mo5|7, Mo6|8, S4|6, and S5|7—bind Na strongly, and each core can adsorb up to two Na adatoms. For two Na atoms per core, the calculated Fermi-level shifts differ sharply between Mo5|7 and S5|7. In Mo5|7 + 2Na, $\theta_t$8 eV and remains below the conduction-band minimum, implying that donated electrons are trapped in deep levels. In S5|7 + 2Na, $\theta_t$9 lies inside the conduction band, so at least one donated electron remains free in the MoS$_2$0 lattice. The paper therefore identifies only S5|7 defects as effective donor centers, leading to excess free electrons and efficient negative-trion formation that quenches PL at vapor-solid-solid grain boundaries. By contrast, Mo5|7 defects can bind Na while still trapping the donated charge and avoiding free-carrier doping. Choi et al. generalize this result by stating that catalytic liquid alloys can aid in determining a type of atomic defect even in various polycrystalline 2D films, thereby providing a technical clue for property engineering. A plausible implication is that grain-boundary defect polarity can be treated as an overview-controlled variable rather than a fixed consequence of lattice misorientation alone.