Unusually high thermal conductivity in suspended monolayer MoSi₂N₄

Heat dissipation is a critical challenge in modern miniaturized, high-power-density electronics. High carrier mobility combined with high in-plane thermal conductivity is desired for electronic and optoelectronic device channels. Two-dimensional van der Waals semiconductors, with dangling-bond-free surfaces and minimal mobility variation with thickness, offer advantages over bulk semiconductors like silicon. Slack’s criteria posit that high thermal conductivity materials have low average atomic mass, strong bonds, simple crystal structures, and low anharmonicity, favoring crystals with few atoms per unit cell. Graphene and hexagonal BN exemplify this. However, common 2D semiconductors (TMDCs) typically have thermal conductivity <100 W·m⁻¹·K⁻¹. Monolayer MoSi₂N₄, an artificial 2D semiconductor composed of a MoN₂ layer sandwiched between two Si–N bilayers, has been predicted to possess high mobility and high thermal conductivity simultaneously, potentially deviating from Slack’s simple-structure criterion. This study aims to experimentally determine the intrinsic in-plane thermal conductivity of suspended monolayer MoSi₂N₄ and elucidate its microscopic origins.

Prior work established extreme in-plane thermal conductivity in graphene (~5300 W·m⁻¹·K⁻¹) and monolayer h-BN (~751 W·m⁻¹·K⁻¹), though they are semi-metal and insulator, respectively. In contrast, 2D semiconductors such as MoS₂, WS₂, MoSe₂, WSe₂, and black phosphorus generally exhibit thermal conductivities below silicon (~142 W·m⁻¹·K⁻¹), commonly <100 W·m⁻¹·K⁻¹, attributed to complex unit cells, heavier mass, and weaker bonding. Slack’s criteria emphasize few atoms per unit cell, strong bonding, light elements, and low anharmonicity as prerequisites for high thermal conductivity. Monolayer MoSi₂N₄ (bandgap ~1.94 eV) has been predicted to have high in-plane thermal conductivity (~224–439 W·m⁻¹·K⁻¹ at room temperature) alongside high carrier mobility and other notable properties (e.g., strong exciton–phonon coupling, piezoelectricity). These predictions motivate experimental validation and mechanistic understanding beyond Slack’s simple descriptor set.

Material synthesis: Monolayer MoSi₂N₄ was grown by chemical vapor deposition (CVD) on Cu/Mo bilayer foils. The Cu/Mo substrate was heated to 1090 °C (H₂, 200 sccm), then dropped to 1065 °C; NH₃ (3 sccm) provided nitrogen and quartz served as the silicon source. Growth for 1.5 h yielded triangular monolayer crystals (>20 µm); >3 h produced films. Transfer used PMMA support, Cu etching in 0.15 M (NH₄)₂S₂O₈, and placement onto target substrates (e.g., through-hole Au/SiO₂/Si, SiO₂/Si, quartz, TEM grids); PMMA was removed in acetone. Structural and optical characterization: Optical microscopy, AFM, SEM, and TEM/STEM (including SAED, HAADF, IDPC, dDPC) confirmed monolayer thickness (~1.2 nm by AFM) and layered structure with measured interlayer spacing 1.07 nm, adopted as monolayer thickness h. Monolayer films on quartz were used to measure optical transmittance; at 532 nm the transmittance was 94.48%, giving optical absorption coefficient α = 5.52% (reflectance neglected as in graphene and monolayer h-BN analogies). Optothermal Raman measurements: To isolate in-plane heat conduction, MoSi₂N₄ was suspended over through-holes (3–6 µm diameter) in Au-coated (100 nm) SiO₂/Si substrates; Au acted as a heat sink to improve interfacial thermal conductance. Measurements were conducted in vacuum to eliminate convection; nitrogen environment was also tested for comparison. A 532 nm laser (spot ~1.18 µm with 50×, NA 0.55) excited Raman signals collected by confocal micro-Raman with in-situ heating stages. COMSOL simulations supported that a 6 µm hole with a ~1.18 µm laser spot ensures the edge temperature remains near ambient, satisfying radial in-plane heat flow assumptions. Raman peak positions were extracted using Voigt fitting to account for instrumental broadening. Among four principal modes (SN₁ ~290 cm⁻¹, MSN ~350 cm⁻¹, MN ~632 cm⁻¹, SN₂ ~695 cm⁻¹), SN₁ showed the largest temperature and power sensitivity and was used as the thermometer. Temperature-dependent Raman (293–573 K, laser 200 µW) and laser power-dependent Raman (0.13–3.00 mW) on suspended monolayers provided: first-order temperature coefficient χ = −0.01169 ± 0.00069 cm⁻¹/K and power-dependent slope δω/δP = −0.55471 ± 0.01978 cm⁻¹/mW. Thermal conductivity κ was extracted using the optothermal Raman formalism with α, h = 1.07 nm, χ, and δω/δP. Reproducibility and geometric dependence: Measurements were performed across hole diameters (3–6 µm) showing increasing κ with larger holes and convergence at 6 µm, consistent with excitation of longer mean free path phonons. Ten samples from different batches were measured in vacuum to obtain an average and dispersion. A nitrogen environment test assessed convection effects. First-principles calculations: Density functional theory (VASP, PAW, GGA-PBE; cutoff 500 eV; 15×15×1 k-mesh; 20 Å vacuum; energy/force convergence 10⁻⁵ eV/10⁻³ eV·Å⁻¹) was used to relax structures (MoSi₂N₄ and Si₂N₂). Phonon dispersions and 2nd-order IFCs were obtained via finite displacements in Phonopy; 3rd-order IFCs were computed with the thirdorder package using a 4×4×1 supercell (112 atoms) and 3×3×1 k-mesh. Lattice thermal conductivities were computed by solving the phonon BTE in ShengBTE, with convergence-tested q-grids (MoSi₂N₄: 111×111×1, cutoff distance of 8 atoms; Si₂N₂: 121×121×1, cutoff 9 atoms). Born effective charges and dielectric constants were included. Debye temperature and Grüneisen parameter were calculated, and a scaling analysis using M⁶θ³/γ² was performed across various 2D semiconductors.

• Experimental room-temperature in-plane thermal conductivity of suspended monolayer MoSi₂N₄: κ = 173.03 ± 4.04 W·m⁻¹·K⁻¹ (vacuum), using α = 5.52%, h = 1.07 nm, χ = −0.01169 ± 0.00069 cm⁻¹/K, δω/δP = −0.55471 ± 0.01978 cm⁻¹/mW.
• Across 10 monolayer samples (vacuum), average κ = 171.32 ± 10.86 W·m⁻¹·K⁻¹.
• In nitrogen gas environment, κ extracted as 227.05 ± 4.32 W·m⁻¹·K⁻¹, indicating that convection can inflate apparent thermal conductivity; vacuum is necessary for intrinsic values.
• κ increases with hole diameter (3→6 µm) and converges near 6 µm, consistent with inclusion of low-frequency phonons with larger mean free paths.
• Measured κ is much higher than silicon (~142 W·m⁻¹·K⁻¹) and known 2D semiconductors (typically <100 W·m⁻¹·K⁻¹ such as MoS₂, WS₂, MoSe₂, WSe₂, black phosphorus, Bi₂O₂Se).
• First-principles phonon transport reveals: Debye temperature θ ≈ 436.45 K and Grüneisen parameter γ ≈ 0.77 at 300 K; these values, together with strong bonding (high Young’s modulus), underpin the high κ.
• Scaling analysis across 2D semiconductors shows κ positively correlates with M⁶θ³/γ²; MoSi₂N₄ has the highest scaling parameter among surveyed materials, consistent with its high κ.
• Phonon dispersion: 21 branches (3 acoustic + 18 optical). In addition to acoustic modes, two lowest optical branches have large slopes in the long-wavelength limit (group velocities >10 km·s⁻¹ below ~15 THz) and significantly contribute to κ; these modes are dominated by the outer Si–N bilayers (atomic contributions: Mo 0%, Si 66.2%, N₁ 1.2%, N₂ 32.7%).
• Calculated lattice thermal conductivities (BTE): MoSi₂N₄ ~492.7 W·m⁻¹·K⁻¹ at 300 K; Si₂N₂ ~819.5 W·m⁻¹·K⁻¹, both decreasing with temperature.
• The strong role of outer Si–N bilayers explains the unusually high κ despite a complex unit cell (N = 7), deviating from Slack’s simple-structure criterion.

The experimental demonstration of κ ~173 W·m⁻¹·K⁻¹ in suspended monolayer MoSi₂N₄ validates predictions that this 2D semiconductor can combine high mobility with efficient heat transport, a desirable combination for device channels. The result challenges the traditional interpretation of Slack’s criteria by showing that complex unit cells do not preclude high κ when strong bonding yields high Young’s modulus, high Debye temperature, low anharmonicity (low γ), and significant contributions from low-lying optical modes with high group velocities. Scaling by M⁶θ³/γ² rationalizes cross-material trends and places MoSi₂N₄ at the top among 2D semiconductors studied. The dominant contribution of the outer Si–N bilayers to phonon group velocities and κ provides a structural design principle: engineering strong, stiff outer layers can offset the detrimental effects of structural complexity. The measured κ is lower than first-principles values (~493 W·m⁻¹·K⁻¹ at 300 K), which the authors attribute to real-sample imperfections (point defects, especially N₂ vacancies, and wrinkles) that enhance phonon scattering, as well as to experimental factors such as convection in non-vacuum environments. The findings establish MoSi₂N₄ as a benchmark 2D semiconductor for thermal management and guide the design of layered materials with tailored phonon transport.

This work experimentally establishes that suspended monolayer MoSi₂N₄ exhibits unusually high in-plane thermal conductivity (~173 W·m⁻¹·K⁻¹ at room temperature), surpassing silicon and typical 2D semiconductors. First-principles analyses link the high κ to a high Debye temperature and low Grüneisen parameter derived from strong Si–N bonding and high Young’s modulus, with significant contributions from low-frequency optical modes dominated by outer Si–N bilayers. The study provides a clear design insight: strong, stiff outer layers can enable high lattice thermal conductivity even in complex 2D semiconductors. Future research should focus on wafer-scale growth of high-quality, defect- and wrinkle-free monolayer MoSi₂N₄ and related MA₂Z₄ materials, improved defect control, and device-level integration to fully exploit their combined thermal and electronic advantages.

The experimentally measured thermal conductivity is lower than first-principles predictions, primarily due to real-sample imperfections: thermodynamic point defects (notably nitrogen vacancies, with N₂ vacancies strongly scattering high-frequency phonons) and wrinkles causing out-of-plane torsional deformation and phonon localization. Environmental effects such as heat convection in gas environments (e.g., nitrogen) can overestimate κ; thus, vacuum conditions are necessary. Geometric constraints (hole size relative to laser spot) can bias extraction if not properly designed, though simulations and experiments indicate convergence at 6 µm holes. Residual uncertainties arise from assumptions like negligible reflectance in α determination and using interlayer spacing (1.07 nm) as monolayer thickness.