1L-MoS₂ Circular Islands: Growth & Device Prospects

• 1L-MoS₂ circular islands are monolayer domains with a distinct circular shape, featuring a highly crystalline, defect-poor core and a defective, grain-boundary-rich periphery.
• Their growth via CVD is precisely controlled by sulfur dosing, which linearly modulates island diameter and influences radial inhomogeneity in optical and electronic properties.
• These islands offer promising avenues for advanced optoelectronic devices, cryptographic primitives, and spatial sensors due to their tunable structure and superior core performance.

Monolayer molybdenum disulfide (1L-MoS₂) circular islands are single-atomic-layer domains of MoS₂ adopting a highly circular morphology, formed spontaneously on SiO₂/Si substrates during chemical vapor deposition (CVD) growth. This morphology contrasts with the more common triangular or hexagonal shapes observed in other CVD regimes and presents unique structural, optical, and electronic properties. These circular islands—often ranging from a few to several hundred micrometers in diameter—exhibit a distinct radial inhomogeneity, with a defect-poor, highly crystalline core and a periphery characterized by increased defect density, grain boundary networks, and misorientations. Their precise synthesis, tunable size, and inhomogeneous yet size-controlled structure position them as promising material platforms for novel device architectures, advanced optoelectronic applications, and physical unclonable function (PUF) primitives.

1. Chemical Vapor Deposition Growth Mechanisms and Parameters

The growth of 1L-MoS₂ circular islands is conducted via CVD using high-purity (5N) MoO₃ and sulfur powders. A standard protocol involves the placement of 6 mg MoO₃ in an alumina boat at the furnace's hot zone, with the SiO₂/Si substrates directly deployed on the boat after rigorous solvent cleaning (trichloroethylene, acetone, isopropanol; 10 min ultrasonic each) and N₂ drying. No seeding layers are introduced. Sulfur powder is positioned ∼18 cm upstream, and the process gas is Ar at 7 sccm. The temperature ramps to 700 °C and is held for 10 minutes, followed by natural cooling. Key growth result: the sole experimentally variable parameter, the sulfur mass, directly determines the lateral size of the islands. Increasing sulfur from 350 mg to 450 mg monotonically increases typical diameters from ∼70 μm to ≈250 μm (Patra et al., 4 Jan 2026).

In contrast, multilayer “island” speckles—typically sub-10 μm—can be induced on continuous monolayers under alternate conditions: higher overall growth temperature (850 °C), different substrate positioning, and variable exposure to sulfur vapor. In these systems, the Avrami exponent n≈2 indicates classical 2D disk-shaped surface-diffusion-limited growth (Alharbi et al., 2017).

Growth Parameter	Circular Islands (1L-MoS₂) (Patra et al., 4 Jan 2026)	Multilayer Speckles (Alharbi et al., 2017)
Substrate	SiO₂/Si, no seeding	SiO₂/Si (p⁺, 285 nm oxide)
MoO₃	6 mg (hot zone)	6 mg
S	350–450 mg (upstream, ∼18 cm)	≈100 mg (varies by design)
Carrier Gas	Ar, 7 sccm	N₂, 10 sccm
Furnace Temperature	700 °C	850 °C
Growth Time	10 min (hold)	Tuned for target 1L:multilayer area
Cooling	Natural	Natural

2. Nucleation, Morphological Evolution, and Structure

Optical and atomic force microscopy reveal these islands consistently nucleate about a heterogeneous central site, marked by a local dark spot attributed to residual precursor. Their measured thickness (~0.85 nm, AFM) confirms their monolayer character. Transmission electron microscopy (TEM) and selected-area electron diffraction (SAED) delineate contrasting structural zones: the internal region exhibits single-crystal hexagonal diffraction over hundreds of nanometers, while the peripheral rim displays multiple rotated MoS₂ hexagons with twist angles up to 26°, corresponding to domains with abundant grain boundaries and misorientations.

This translates into a radial gradient: a defect-sparse, single-domain core surrounded by a granular, highly defective periphery where secondary multilayer spots and filamentary chains are frequently observed. The morphological transformation from intrinsic hexagonal symmetry to an almost perfect circle is governed by the energetics:

• Total energy: $$E_{\text{total}} = E_{\text{strain}} + E_{\text{edge}}$$
• Strain energy: $E_{\text{strain}} = \frac{1}{2} Y \varepsilon^2 A$
• Edge energy: $E_{\text{edge}} = \gamma L$

where $Y$ is the 2D Young’s modulus (~180 N/m), $\varepsilon$ the thermally induced mismatch strain ($\sim -5\times10^{-3}$), $A$ the island area, perimeter $L$, and boundary tension $\gamma \sim 0.5\ \text{eV/nm}$ (Patra et al., 4 Jan 2026). After growth, cooling induces tensile strain ($\alpha_{\text{sub}} \ll \alpha_{\text{MoS}_2}$), which is relieved by grain boundary formation and corner rounding, resulting in circular geometry and radial defect grading.

3. Optical and Electronic Properties

Photoluminescence (PL) mapping at 532 nm shows marked spatial inhomogeneity: the interiors of the islands emit at ≈3–4× the intensity of their edges. The central PL peak is at 1.87 eV; at the rim, the peak red-shifts by ~20 meV and decreases ~40% in intensity, a signature of increased nonradiative recombination associated with peripheral grain boundaries and secondary multilayers.

Field-effect transistor (FET) fabrication on transferred islands demonstrates superior performance in the core region: room-temperature field-effect mobility in the interior reaches μ_int ≈ 0.25 cm² V⁻¹ s⁻¹, >2× the rim value (μ_edge ≈ 0.10 cm² V⁻¹ s⁻¹). Threshold voltages differ (–21 V vs. –15 V), but extracted carrier densities remain essentially uniform (n_int ≈ 1.4×10¹² cm⁻², n_edge ≈ 1.0×10¹² cm⁻²), isolating the mobility variation as the key factor in the conductivity profile (Patra et al., 4 Jan 2026).

In related multilayer speckle systems, the integrated PL response is nearly extinguished in bilayer regions (factor ∼0.1 reduction at 50% area coverage), and the spectral A-exciton peak exhibits a consistent red shift with increasing local thickness (Alharbi et al., 2017).

4. Growth Kinetics, Size Control, and Statistical Description

Diameter scaling with sulfur mass is nearly linear: increasing sulfur increases S vapor pressure and the lateral growth window before edge saturation. The precise, empirical control in the protocol enables reproducible production of perfectly circular disks spanning tens to hundreds of microns, uniquely without a seeding layer (Patra et al., 4 Jan 2026). In multilayer speckle systems, island size and areal density are determined by growth time and substrate position, with the Avrami growth law ($f(t) = 1 – \exp(–k t^n),\ n \approx 2$) capturing the kinetics. High-throughput runs yield consistent island spatial statistics, with a Clark–Evans ratio $R \simeq 1$, confirming complete spatial randomness (CSR) over a wide range of pixel sizes and target coverages (Alharbi et al., 2017).

Size and morphology quantification may involve measurement of equivalent circle diameters, aspect ratio, and circularity ($4\pi \cdot \text{area}/\text{perimeter}^2$), with values approaching unity in the case of the perfectly circular islands.

5. Thermodynamic and Structural Drivers of Circularity

The explicit thermodynamic competition that dictates the emergence of circular shapes involves both edge and strain energy. After cooling by ΔT ≈ 675 K:

• Strain energy per area: $$(1/2)\,Y \varepsilon^2 \sim 0.23\ \text{J}\,\mathrm{m}^{-2}$$
• Edge energy per length: $\gamma \sim 0.5~\text{eV/nm}$ ($\sim0.8\ \text{J/m}$)

The process “carves” grain boundaries at corners of the original hexagon and facilitates reorientation (twisting) of peripheral grains, reducing overall perimeter at a modest cost in strain. These rearrangements lead to a central, large-grained, low-defect structure, and an outer shell with high-angle grain boundaries and plentiful defects—a unique fingerprint of the relaxation pathway available to 1L-MoS₂ under these synthetic conditions (Patra et al., 4 Jan 2026). In multilayer speckle systems, growth is dominated by random nucleation/yield and surface diffusion, producing smaller, circular islands overlaying a monolayer background (Alharbi et al., 2017).

6. Applications, Device Prospects, and Implications

The emergence of large-area, defect-graded, monolayer MoS₂ disks is significant for several device paradigms. Their symmetry and high-quality interiors suit them for integration into circular VLSI interconnect architectures, potentially reducing parasitic capacitance and achieving more uniform thermal profiles. Radially arrayed photonic crystals, symmetric sensor platforms, and spatially structured photonic–plasmonic hybrids are direct beneficiaries, leveraging the spatial emission/transport inhomogeneity for functional device gradients.

A major application direction, documented in the context of multilayer speckle films, is in cryptographic primitives where the photoluminescence readout encodes physical randomness suitable for device authentication and anti-counterfeiting. The Clark–Evans spatial randomness is critical for these use cases (Alharbi et al., 2017).

A plausible implication is that the defect-graded structure—emissive cores and scattering-rich rims—offers new opportunities for spatially multiplexed sensing and quantum optoelectronic devices requiring localized single-crystal domains embedded in a less-perfect host, as well as for exploration of grain boundary physics in 2D materials at controlled spatial scales.

7. Reproducibility and Control Protocols

The detailed published protocols allow for reproducible synthesis of 1L-MoS₂ circular islands with controllable diameter and defect profile. The island growth is highly robust to process variations, provided sulfur dosing and substrate placement are carefully managed. The absence of seeding layers or surface activation is notable, simplifying integration with existing device processing flows.

For multilayer speckle films, the Avrami/exponential model for coverage and Clark–Evans test for spatial randomness offer standardized metrics for reproducibility, ensuring reliable translation between research efforts and potential commercial processes.

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Key source publications: "Spontaneous growth of perfectly circular domains of MoS₂ monolayers using chemical vapour deposition technique" (Patra et al., 4 Jan 2026), "Physical cryptographic primitives by chemical vapor deposition of layered MoS2" (Alharbi et al., 2017).