Matryoshka phonon twinning in α-GaN

Gallium nitride (GaN) is a prominent third-generation power semiconductor, valued for its wide bandgap, high thermal conductivity (reportedly 230 W m⁻¹ K⁻¹ at room temperature), and high-temperature stability. Miniaturization of high-power electronics necessitates a deeper understanding of α-GaN's thermodynamics. However, existing knowledge on its phonon dynamics is limited, particularly regarding phonon scattering processes and temperature effects. Experimental measurements of its phonon dispersion relation are primarily limited to ambient conditions. Furthermore, the anisotropic thermal transport of α-GaN along the a- (in-plane) and c-axis (out-of-plane) directions remains a subject of debate due to challenges in experimental measurements and computational modeling. A comprehensive understanding of phonon dynamics is vital for exploring thermal transport and other thermodynamic properties of GaN. Phonon topology engineering is a key strategy for manipulating thermal properties, alongside techniques like doping, creating solid solutions, isotopic engineering, and nanostructuring. Exotic phonon dispersion topologies, such as crossing/anti-crossing behaviors, bunched acoustic phonons, and dispersion waterfalls, can lead to unique properties like low thermal conductivity, negative thermal expansion, and anomalous phase transitions. Recent research highlights the role of local phonon dispersion nesting in augmenting three-phonon scattering, amplifying anharmonicity, and suppressing lattice thermal transport. This study aims to address the knowledge gap by investigating the phonon dynamics of α-GaN and its impact on thermal transport.

Previous research on GaN's thermal properties has yielded varying results regarding its anisotropic thermal conductivity. Some studies suggest higher in-plane thermal conductivity, while others indicate the opposite. These discrepancies stem from the challenges in accurately measuring anisotropic thermal conductivity and in computational modeling. The existing literature also highlights the influence of factors like doping and crystal defects on the thermal conductivity of GaN. However, a comprehensive understanding of the underlying phonon dynamics and their relation to anisotropic thermal transport remains elusive. Existing experimental data on phonon dispersion relations are primarily limited to ambient conditions, with limited exploration of phonon scattering processes and temperature effects. This study builds upon these existing works by focusing on the detailed analysis of phonon dynamics to explain the anisotropic thermal conductivity of α-GaN.

This research employed a multi-pronged approach combining inelastic X-ray scattering (IXS), inelastic neutron scattering (INS), and first-principles calculations. High-quality GaN single crystals, grown using a hydride vapor phase epitaxy (HVPE)-based method with low dislocation density (<1 × 10⁷ cm⁻²), were used for the experimental measurements. The IXS experiments, performed at the Advanced Photon Source (APS), measured phonon dispersions at 50, 175, and 300 K using an incident photon energy of ~23.7 keV. The INS measurements, conducted at the Spallation Neutron Source (SNS), provided data on the full phonon lattice dynamics at 14, 50, 300, and 630 K using an incident energy of 50 meV. First-principles calculations based on density functional theory (DFT), using the Vienna Ab Initio Simulation Package (VASP), were performed to complement the experimental data and provide theoretical insights into the phonon behavior. The experimental data were analyzed using a damped-harmonic-oscillator model to extract phonon linewidths and scattering rates. The DFT calculations provided phonon dispersion surfaces and allowed for visualization of the Matryoshka-like phonon twinning behavior. The phonon linewidths, obtained from both IXS and INS data, were used to assess the anharmonic scattering rates and their relationship to the Matryoshka phonon twinning. The temperature dependence of phonon energy was analyzed to determine anharmonicity. The anisotropic thermal conductivity was discussed in relation to the measured phonon lifetimes and group velocities.

The study revealed a novel Matryoshka-like phonon dispersion twinning in α-GaN throughout the basal plane of the Brillouin zone (BZ). This behavior was observed in both IXS and INS data and confirmed by first-principles calculations. The twinning involves nested optical and acoustic phonon branches, creating abundant three-phonon scattering channels. This significantly enhances anharmonicity and shortens the lifetimes of the affected phonon modes by more than 50%, as evidenced by the significantly broader phonon linewidths (around 2.3, 2, and 1.3 meV for Arc, TA₂, and other in-plane branches, respectively, compared to approximately 1.5 and 1.2 meV for out-of-plane branches at 300K). The analysis of phonon group velocities showed only minor anisotropy along different crystallographic directions. The strong in-plane phonon scattering stemming from the Matryoshka twinning leads to a reduction in the in-plane thermal conductivity, thus contributing substantially to the anisotropic thermal conductivity observed in α-GaN. The temperature dependence of phonon energy, showing moderate anharmonicity, indicates that the large linewidths are primarily due to the increased phase space for scattering provided by the Matryoshka twinning. The findings were consistent across different experimental techniques (IXS, INS, and Raman spectroscopy), supporting the robustness of the conclusions. The study provides quantitative estimations of the impact of the twinning on the thermal conductivity, suggesting it is a dominant factor in the material's anisotropy.

The discovery of Matryoshka phonon twinning in α-GaN provides a new understanding of its anisotropic thermal conductivity. The significant enhancement of three-phonon scattering due to this unique phonon topology explains the reduced in-plane thermal transport, resolving some of the discrepancies in previous studies. The relatively small anisotropy observed in phonon group velocities indicates that the observed anisotropy in thermal conductivity is predominantly a result of the phonon scattering rate differences induced by the twinning. This finding is significant for thermal management applications, as it provides a mechanism for controlling thermal transport by engineering the phonon topology. The results highlight the importance of considering phonon topology beyond simply the harmonic approximation in understanding thermal transport in semiconductors.

This research demonstrates the existence of Matryoshka phonon twinning in α-GaN, a phenomenon that significantly impacts its thermal conductivity. The increased three-phonon scattering resulting from this topology leads to a substantial reduction in in-plane thermal transport. Future research could explore strategies for manipulating this twinning through phonon engineering techniques, such as strain or doping, potentially enhancing in-plane thermal transport for improved thermal management in high-power electronic devices. The findings also suggest that similar phonon topology engineering could be beneficial in other materials where controlling lattice thermal transport is critical.

The study focuses primarily on high-quality, low-defect GaN single crystals. The findings might not be directly transferable to polycrystalline GaN or GaN with high defect densities. The analysis of thermal conductivity is based on estimates derived from phonon lifetimes and group velocities, rather than direct experimental measurements of thermal conductivity, introducing some level of uncertainty. Further work involving direct measurements of anisotropic thermal conductivity at various temperatures would help to validate these estimations.