Matryoshka phonon twinning in α-GaN

Gallium nitride (GaN) is a key third-generation power semiconductor with high thermal conductivity and wide bandgap, enabling high power density and temperature stability. Despite its technological importance, critical aspects of its phonon dynamics remain insufficiently understood. Prior experimental phonon dispersion measurements for α-GaN (wurtzite) were largely limited to ambient conditions, with phonon scattering processes and temperature effects mostly unexplored. Additionally, anisotropy of thermal transport between in-plane (a-axis) and out-of-plane (c-axis) directions remains controversial due to challenges in both measurements and calculations. This study aims to provide a comprehensive understanding of α-GaN phonon dynamics, focusing on identifying dispersion features that govern anharmonic scattering and their impact on anisotropic thermal conductivity, by combining inelastic X-ray and neutron scattering with first-principles calculations.

Thermal conductivity of GaN has been widely reported around ~230 W m−1 K−1 at room temperature, with dependence on dislocation density and impurities. Previous IXS and INS studies provided phonon dispersion and density of states but lacked comprehensive temperature-dependent scattering information. Anisotropy in thermal conductivity has been debated; recent theoretical works suggest in-plane conductivity is slightly lower than out-of-plane with ~12–14% anisotropy. Beyond GaN, literature shows that exotic phonon topology (e.g., crossing/anti-crossing, acoustic bunching, waterfall effect) can strongly affect thermodynamic properties, and dispersion nesting has been linked to enhanced three-phonon scattering and reduced thermal conductivity in materials like SnTe, PbTe, and CuCl. These insights motivate examining whether similar topological features exist in α-GaN and how they influence scattering and transport.

• Samples: High-quality, undoped n-type α-GaN single crystals grown by HVPE (MTI Corp.), with low dislocation density (<1×10^7 cm−2). Crystalline quality verified by X-ray and neutron diffraction (XRD FWHM at (002): 0.10 ± 0.02°).
• Inelastic X-ray scattering (IXS): Conducted at APS 30-ID-C (HERIX) at 50, 175, 300 K. Incident energy ~23.7 keV; energy resolution ΔE = 1.2 meV; momentum resolution 0.65 nm−1. Reflection geometry, constant-Q scans. Orientation defined using Bragg peaks (400), (004), (005), (220). A 250 μm thick single crystal mounted in a cryostat.
• Inelastic neutron scattering (INS): Performed on ARCS (SNS, ORNL) with Ei = 50 meV, Fermi chopper 420 Hz; elastic energy resolution ~2 meV. Measurements at 14, 50, 300, 630 K with [110] vertical, rotations covering in-plane and out-of-plane phonons. Data normalized to incident flux; detector efficiency corrected using vanadium standard. Data reduction with Mantid.
• Spectral analysis: INS spectra converted to dynamical susceptibility χ″(Q,E) = S(Q,E)/(n(E)+1). Fits used a damped-harmonic-oscillator model S(ω) ∝ [1+n(ω)] (γω)/πM /[(ω−ω0)^2+(γω)^2]. Phonon energies and linewidths extracted with deconvolution of instrument energy and momentum resolutions to mitigate slope effects.
• Raman spectroscopy: Zone-center (Γ-point) measurements provided linewidth at the I-point for the Arc branch.
• First-principles calculations: DFT (VASP) with LDA and PAW (Ga: 4s^2 4p^1; N: 2s^2 2p^3), plane-wave cutoff 600 eV, k/q-mesh 7×7×5, energy convergence 1×10^−8 eV, force convergence 10^−3 eV/Å. Fully relaxed structure (a=b=3.188 Å, c=5.190 Å). Harmonic phonons computed via Phonopy using a 4×4×3 supercell (192 atoms). Comparison with experiments across BZ; construction of dispersion surfaces and in-plane projections. Temperature-dependent energy of Arc mode at q=0.1 (Γ–M) fitted with ωA(T)=ωA(0)−A[1+2/(e^{θD/T}−1)].

• Discovery of in-plane Matryoshka-like phonon dispersion twinning in α-GaN: two nested, nearly parallel branches across the basal plane—TA2 (lower) and an upper Arc branch (LEO at low q transitioning to LA at higher q). Energy offset is ~16 meV along Γ–M and ~15 meV along Γ–K.
• Nesting observed by both IXS (selected high-symmetry directions) and INS (2D slices across BZ), and reproduced by DFT χ″(Q,E) and dispersion surface calculations. Volume and cross-section views of χ″(Q,E) show twinning throughout the basal plane.
• Physical origin: Large ionic radius mismatch between N (0.75 Å) and Ga (1.62 Å), and the presence of two [GaN4] tetrahedra along c-axis causing TA branch folding from the A-point and producing a low-energy Arc at Γ.
• Enhanced three-phonon phase space: The nested topology opens abundant acoustic–optical emission channels (e.g., Arc phonon decays into Arc+TA2 within basal plane), significantly enlarging the scattering phase space in the 20–40 meV (~5–10 THz) range.
• Linewidths and lifetimes: At 300 K, phonon linewidths are anomalously large on TA2 and Arc branches—IXS shows many modes between 0.5–1.5 meV, but TA2 and Arc modes are much broader (roughly double some others). INS-derived linewidths: in-plane Arc ~2.3 meV, TA2 ~2.0 meV, other in-plane branches ~1.3 meV; out-of-plane HEO ~1.5 meV, other out-of-plane branches (LEO, TA, LA) ~1.2 meV. These imply >50% reduction in lifetimes for TA2 and high-q LA relative to counterparts.
• Anharmonicity assessment: Temperature dependence of Arc mode at q=0.1 (Γ–M) shows moderate anharmonicity below Debye temperature (~636 K). Experimental mode Grüneisen parameters are moderately larger than calculated volumetric values; frozen-phonon potentials slightly non-harmonic. Thus, linewidth enhancement is dominated by expanded phase space from Matryoshka twinning rather than unusually strong third-order potentials.
• Group velocities: Experimentally extracted acoustic group velocities show minor anisotropy: along Γ–A are slightly larger than in-plane (e.g., LA: 8403, 8290, 8087 m/s at 14, 50, 300 K along Γ–A vs 8319, 8149, 8015 m/s along Γ–M). Differences (≤~4%) are too small to account for strong thermal conductivity anisotropy.
• Impact on thermal conductivity anisotropy: Assuming similar group velocities in- and out-of-plane, Eq. κ=Σ C v^2 τ together with measured linewidths suggests in-plane contributions by TA1/LA, TA2, and Arc (TO) branches are roughly 8%, 40%, and 48% lower, respectively, than out-of-plane, indicating Matryoshka twinning substantially suppresses in-plane thermal transport and drives anisotropy, particularly above θD when phonon-phonon scattering dominates.

The comprehensive IXS/INS measurements and DFT reveal a basal-plane-wide Matryoshka twinning between TA2 and the Arc (LEO/LA) branches in α-GaN. This topology generates extensive acoustic–optical three-phonon emission channels, markedly increasing the scattering phase space and broadening phonon linewidths for the nested modes, which correspond to significantly reduced lifetimes. Since acoustic and low-energy optical modes dominate thermal conduction, these enhanced scattering rates directly suppress in-plane thermal conductivity. The nearly isotropic group velocities indicate that anisotropy arises primarily from lifetime differences induced by the twinning, thereby addressing prior controversies regarding the origin of the in-plane vs out-of-plane thermal conductivity difference. These findings highlight phonon topology as a key lever for thermal transport control and suggest that targeted engineering (e.g., strain, doping) to modulate the nesting could tune anisotropy and overall heat dissipation in GaN-based power electronics.

Using complementary inelastic X-ray and neutron scattering and first-principles calculations, the study identifies a Matryoshka-like phonon dispersion twinning across the basal plane of α-GaN. This topology substantially expands three-phonon scattering channels, producing anomalously large linewidths and >50% reductions in phonon lifetimes for nested modes, thereby suppressing in-plane thermal conductivity and enhancing thermal transport anisotropy, despite relatively isotropic acoustic group velocities. These insights establish anomalous phonon topology as a central mechanism governing thermal transport in α-GaN and suggest that engineering strategies (e.g., strain, doping) to suppress or amplify twinning could be used to optimize thermal management in GaN and related semiconductors for electronics, thermoelectrics, and thermal barrier applications. Future work could quantify the influence of four-phonon processes, perform direct thermal conductivity measurements under controlled strain/doping to validate tunability, and extend topology-based engineering to other materials systems.

• Phonon linewidths from IXS, INS, and Raman differ due to distinct instrument resolution functions; comparisons are most reliable within a single technique. INS energy resolution (~2 meV at elastic line) limits precision for narrow modes; Raman probes only Γ-point modes.
• Estimates of thermal conductivity anisotropy rely on assuming similar group velocities between in-plane and out-of-plane branches and using linewidth-derived lifetimes, rather than full iterative solutions including all scattering processes.
• The analysis primarily attributes enhanced scattering to increased phase space from twinning and considers moderate third-order anharmonicity; potential contributions from higher-order (e.g., four-phonon) processes are not explicitly quantified in this work.
• Experimental nesting visualization along non-high-symmetry directions relies on cuts and projections; some regions have weaker scattering intensity due to structure factors, and multiple scattering artifacts were noted in specific slices.