🔬 applied physics

Low cross-plane thermal conductivity of $\kappa$ -Ga $_2$ O $_3$ thin films

This study experimentally demonstrates that $\kappa$ -Ga $_2$ O $_3$ thin films exhibit low cross-plane thermal conductivity (1.83–2.26 W/m $\cdot$ K) that is weakly dependent on thickness but decreases with temperature, a behavior attributed to the material's complex crystal structure and supported by first-principles calculations, highlighting the need for advanced thermal management in $\kappa$ -Ga $_2$ O $_3$ -based devices.

Original author: Seungwon Park, Jingyu Tang, Minsung An, Alan J. H. McGaughey, Lisa M. Porter, Robert F. Davis, Jonathan A. Malen

Published 2026-11-05

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CC BY 4.0

Original author: Seungwon Park, Jingyu Tang, Minsung An, Alan J. H. McGaughey, Lisa M. Porter, Robert F. Davis, Jonathan A. Malen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

Heat is a relentless traveler. In the solid materials that make up our electronics, it moves not as a fluid, but as a wave of vibration traveling through the atomic lattice. When a device works, it generates this heat, and if the material cannot carry that energy away quickly enough, the device overheats and fails. For decades, engineers have relied on a specific family of materials called semiconductors to power everything from power grids to radio signals. Among these, gallium oxide has emerged as a promising candidate because it can withstand high voltages and operate in extreme environments. However, like many materials in this class, it struggles to shed heat efficiently. The challenge is not just about the material itself, but about how it is built. When scientists grow these materials into thin layers for use in tiny electronic components, the way heat moves through them changes. It becomes a game of scale, where the thickness of the layer and the specific arrangement of its atoms dictate whether the heat flows freely or gets stuck.

A team of researchers at Carnegie Mellon University has turned its attention to a specific, less common version of gallium oxide known as kappa-gallium oxide. While the more common form of this material is already known to be a poor conductor of heat, this particular version is unique because its atomic structure lacks a specific type of symmetry found in others. This missing symmetry gives it special electrical properties that could be useful for creating high-frequency radio devices and advanced sensors. But before these devices can be built, scientists needed to know a critical question: how well does this specific material conduct heat when it is made into a thin film? The answer would determine if the material could survive the intense heat generated during operation or if it would require a completely new approach to cooling.

To find the answer, the researchers grew six different samples of this material on a sapphire base, creating films that ranged from very thin at 159 nanometers to thicker at 689 nanometers. They then used a precise, non-contact method to measure how heat traveled through these layers. By shining a laser to heat a tiny spot on the surface and a second laser to watch how the surface cooled down, they could map the flow of thermal energy. The results were clear and somewhat surprising. The material proved to be a very poor conductor of heat, with values ranging from roughly 1.8 to 2.3 watts per meter-kelvin. To put this in perspective, this is significantly lower than other common semiconductors used in high-power electronics, which can conduct heat many times better.

What made the discovery particularly interesting was how the thickness of the film affected the results. In many materials, making a film thicker allows heat to flow more easily because there are fewer boundaries for the heat-carrying vibrations to hit. In these films, the researchers saw a slight increase in conductivity as the films got thicker, but the change was very small. This told them that the heat was not being blocked by the edges of the film, but rather by the material itself. The vibrations that carry heat were getting scattered and slowed down by the complex, messy arrangement of atoms inside the kappa-gallium oxide. The atoms in this structure are arranged in a way that creates a lot of internal friction for these vibrations, causing them to lose energy quickly before they can travel far.

The team also tested how the material behaved as it got hotter, measuring the films at temperatures rising from room temperature up to 400 Kelvin. As expected, the ability to conduct heat dropped as the temperature rose. This is because the atoms vibrate more violently at higher temperatures, causing them to collide with each other more often and disrupt the flow of heat. This effect was even more pronounced in the thicker films. In the thinnest films, the constant hitting of the film's boundaries helped mask some of this temperature sensitivity, but the overall trend remained the same: the material becomes less efficient at moving heat as it gets hotter.

By comparing their measurements with detailed computer simulations, the researchers confirmed that their findings were consistent with the laws of physics governing these atomic structures. The simulations showed that the complex, distorted shape of the atomic groups in this material naturally leads to slow-moving heat waves and frequent collisions. This explains why the material performs so poorly at conducting heat compared to its cousins in the gallium oxide family. The study concludes that while this material holds great promise for its electrical capabilities, its thermal limitations are a significant hurdle. If engineers wish to use it in future devices, they will likely need to pair it with other materials that can act as a heat sink, or find new ways to manage the heat that builds up, ensuring that the device does not cook itself from the inside out.

Technical Summary: Low Cross-Plane Thermal Conductivity of κ-Ga2O3 Thin Films

Problem Statement
Gallium oxide (Ga2O3) is an ultra-wide bandgap semiconductor existing in four polymorphs (α, β, γ, and κ). While the κ-phase offers unique advantages for radio frequency (RF) resonators and high electron mobility transistors (HEMTs) due to its lack of inversion symmetry, spontaneous polarization, and piezoelectric behavior, its thermal management potential remains unquantified. Previous literature has established that β-Ga2O3 possesses relatively low thermal conductivity compared to other wide bandgap semiconductors like GaN and AlN, posing challenges for heat dissipation in power and RF devices. However, extensive experimental data on the thermal conductivity of κ-Ga2O3, particularly regarding its dependence on film thickness and temperature, has been lacking. Understanding these thermal properties is critical for mitigating self-heating in κ-Ga2O3-based electronic devices.

Methodology
The study employed Frequency-Domain Thermoreflectance (FDTR), a non-contact optical technique, to measure the cross-plane thermal conductivity of (001) κ-Ga2O3 thin films.

Sample Preparation: Six κ-Ga2O3 films with thicknesses ranging from 159 nm to 689 nm were grown on c-plane sapphire substrates via metal-organic chemical vapor deposition (MOCVD) at 530 °C. Structural characterization via High-Resolution X-ray Diffraction (HR-XRD) and Atomic Force Microscopy (AFM) confirmed phase purity (with a thin transition layer of mixed β/γ phases at the interface) and consistent crystallinity across samples.
Measurement Protocol: A 5 nm Cr adhesion layer and a 65 nm Au transducer were deposited on the films. FDTR measurements were conducted using a 515 nm pump laser and a 532 nm probe laser across modulation frequencies from 100 kHz to 5 MHz.
Data Analysis: Thermal conductivity ( $k$ ) and interfacial thermal boundary conductances ( $G$ ) were extracted by fitting the measured phase lag to an analytical solution. Bayesian Parameter Estimation (BPE) was utilized to determine uncertainties, incorporating Gaussian priors for externally determined parameters (volumetric heat capacity and laser spot radius) and uniform priors for fitting parameters ( $k$ and $G$ ).
Theoretical Support: First-principles-based calculations using the phonon Boltzmann transport equation were performed to predict size-dependent thermal conductivity, incorporating both phonon-phonon and phonon-boundary scattering via the Matthiessen rule.

Key Results

Thickness Dependence: The measured cross-plane thermal conductivity of κ-Ga2O3 increased from $1.83^{+0.19}_{-0.18}$ W/m·K to $2.26^{+0.35}_{-0.40}$ W/m·K as film thickness increased from 159 nm to 689 nm. This weak thickness dependence suggests that the majority of intrinsic phonon mean free paths (MFPs) are smaller than the investigated film thicknesses, meaning heat transport is not significantly limited by boundary scattering.
Comparison with Polymorphs: At comparable thicknesses, the measured κ-Ga2O3 films exhibited lower cross-plane thermal conductivity values than experimentally measured α-, β-, and γ-Ga2O3 polymorphs.
Temperature Dependence: Measurements from 293 K to 400 K revealed a decrease in thermal conductivity with increasing temperature for both film thicknesses, attributed to enhanced phonon-phonon scattering. The 689 nm film showed a stronger temperature dependence ( $n \approx 0.93$ ) compared to the 159 nm film ( $n \approx 0.23$ ), where phonon-boundary scattering suppresses the temperature sensitivity.
Theory-Experiment Agreement: First-principles calculations captured the trend of increasing thermal conductivity with thickness. The experimental values were, on average, 12% lower than the calculations, a discrepancy the authors attribute to internal defects and the presence of the transition layer containing other Ga2O3 phases.

Significance and Claims
The paper establishes that κ-Ga2O3 possesses intrinsically low thermal conductivity, which is further reduced by its complex crystal structure. The authors attribute this low conductivity to:

Structural Complexity: The κ-phase exhibits more distorted Ga-O polyhedra and a broader distribution of bond lengths compared to α- and β-phases, leading to lower average bond stiffness.
Reduced Group Velocities: The complex structure results in lower phonon group velocities.
Enhanced Anharmonicity: Larger third-order force constants and Grüneisen parameters indicate stronger phonon-phonon scattering.
Localized Modes: A lower phonon participation ratio suggests a larger fraction of vibrational modes are spatially localized, contributing weakly to thermal transport.

The authors conclude that because heat transport in κ-Ga2O3 is predominantly limited by intrinsically short phonon MFPs rather than boundary scattering, increasing film thickness offers limited improvement in thermal management. Consequently, effective thermal management for κ-Ga2O3-based devices will likely require strategies such as integration with high-thermal-conductivity substrates (e.g., diamond or SiC) or engineered composite stacks, rather than relying on the material's intrinsic thermal properties.

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