Thermal transport in ion-beam-exfoliated β-Ga₂O₃ nanomembranes Open Access

Beta-gallium oxide (β-Ga₂O₃) has garnered significant attention as a highly promising material for next-generation power electronics due to its unique material properties.^1–3 With an ultra-wide bandgap of ∼4.8 eV at room temperature,^4–6 β-Ga₂O₃ exhibits an exceptionally high breakdown electric field (>8 MV/cm)⁷ and a high Baliga’s figure of merit (BFOM), enabling the development of devices capable of operating at significantly higher voltages and power densities compared to traditional wide-bandgap semiconductors such as SiC and GaN.^2,3,8 However, the relatively low thermal conductivity of β-Ga₂O₃ with a high thermal anisotropy along different crystallographic directions (∼10 to 30 W/m⋅K)^9–11 poses a challenge for thermal management, necessitating innovative solutions such as heterogeneous integration with high-thermal-conductivity substrates^12–14 or advanced heat dissipation architectures to mitigate self-heating effects and ensure device reliability.^1,15,16

To date, various fabrication techniques, including mechanical exfoliation,^17–19 heteroepitaxial growth,^20–23 and ion-cutting techniques,^24–26 have been developed to directly integrate β-Ga₂O₃ thin films onto highly thermally conductive substrates for thermal management. By selecting substrates with high thermal conductivity, such as Si, SiC, or diamond, the heat dissipation of devices based on β-Ga₂O₃ thin membranes can be improved. However, the mass production of single crystalline β-Ga₂O₃ thin films using epitaxial methods on high-conductivity substrates is still challenging. Unlike the single-crystalline nature of bulk β-Ga₂O₃ or homo-epitaxial β-Ga₂O₃, some of the hetero-epitaxial thin films resulting from direct growth are polycrystalline.^14,22,27

Ion-beam-induced exfoliation is a new advanced technique to prepare thin nanomembranes.^28,29 A high-energy ion beam is directed at the surface of (100)-oriented β-Ga₂O₃ bulk crystals, causing subsurface radiation damage and inducing a stress/strain profile in the sample.^28,29 This process leads to the exfoliation by self-rolling thin layers of β-Ga₂O₃ (also known as microtubes) from the bulk crystal. The thickness of thin layers can be controlled to some extent by adjusting the energy of the ion beam. The exfoliated microtubes are subsequently transferred to a suitable substrate, where annealing at temperatures of ∼500 °C allows the microtubes to unroll and at the same time promotes the adhesion of the resulting nanomembrane to the substrate.

Thermal transport in nanoscale films is usually assessed by various near-surface sensitive techniques ranging from femtosecond laser-based time-domain thermoreflectance (TDTR)^30,31 and the 3ω method^20,32 to Raman opto-thermal microscopy.^33,34 For the first time, we conducted a nanoscale thermal transport investigation of ion-beam-exfoliated β-Ga₂O₃ nanomembranes integrated with Si substrates using the TDTR technique. By tuning the modulation rate of the heating pump laser, we enable probing heat propagation across these nanomembranes. A semi-analytical model based on the Debye approximation was used to analyze the effect of phonon scattering from boundaries and defects on the thermal conductivity of membranes, particularly after their thermal annealing. Furthermore, non-equilibrium molecular dynamics (NEMD) simulations were performed to support our thermal boundary conductance (TBC) measured by TDTR and demonstrated that the thickness of the amorphous silicon oxide (a-SiO₂) interlayer is a key factor in significantly enhancing TBC across the β-Ga₂O₃/Si interface. The structural characterization of nanomembranes transferred to the substrate is examined by x-ray diffraction (XRD) and micro-Raman spectroscopy.

Commercially acquired bulk β-Ga₂O₃ samples from Novel Crystal Technology, Inc., with (100) orientation, were implanted at room temperature with 250 keV Cr ions with the fluence of 1 × 10¹⁴ ions/cm² and a flux of 2.5 × 10¹¹ ions cm⁻² s⁻¹. Then, the exfoliated microtubes were transferred onto Si and sapphire (c-Al₂O₃) substrates by a pick-and-place technique, using a SmartAct microgripper system, and subsequently annealed in the air at 500 °C on a conventional hot plate to unroll, yielding nanomembranes. To promote the recovery of the implantation-induced defects, the membranes were subjected to rapid thermal annealing at 1000 °C for 60 s in a N₂ atmosphere. According to our previous results in Cr-implanted, bulk β-Ga₂O₃,^28,29 this temperature allows a nearly complete recovery of the introduced defects and strain, at least at the sensitivity level of the Rutherford backscattering spectrometry in channeling mode and x-ray diffraction techniques, respectively. Moreover, a μ-Raman study on unrolled membranes annealed at 1000 °C revealed their excellent crystalline quality, comparable to a bulk crystal of the same orientation.^28,29 However, the presence of residual point defects cannot be excluded. It is important to note that, in samples transferred and annealed on top of a Si substrate, this may promote the introduction of Si in the nanomembrane by diffusion at higher temperatures. For example, Yadav et al.³⁵ report the diffusion of Si into β-Ga₂O₃ thin films deposited by pulsed laser deposition (PLD) at temperatures as low as 600 °C.

A thin heat-transducing film of Al was deposited on these membranes by DC magnetron sputtering for subsequent thermal conductivity measurements with TDTR. The thickness of the Al layer was estimated to be ∼90 nm from transient picosecond acoustic measurements, as shown in Fig. S1 of the supplementary material. The stages of thin membrane fabrication and thermal measurement are illustrated in Fig. 1(a), while the optical microscopy images of the fabricated samples before metal deposition are shown in Fig. 1(b).

The structural characterization of prepared membranes was performed by a combination of XRD and micro-Raman spectroscopy. The XRD 2θ measurements were performed using a Rigaku SmartLab diffractometer using Cu Kα1 radiation in locked-coupled mode. The diffraction patterns were recorded in the Bragg–Brentano geometry in the 2θ angular range of 20°–80° using the powder diffraction method. The Raman spectra were acquired using a Horiba LabRam spectrometer with 600 grooves/mm grating and a 532 nm single longitudinal mode excitation laser (Torus, Laser Quantum, USA) in backscattering configuration. The incident laser beam was focused on the sample surfaces down to a spot size with a diameter of ∼2 μm using a 50× microscope objective. The laser power incident on the studied samples was kept below 10 mW to prevent their local heating while maintaining a high signal-to-noise ratio for measured spectral peaks. The surface roughness and thickness of membranes transferred onto the Si substrate were characterized using atomic force microscopy (AFM). Moreover, several other methods, such as profilometry and picosecond acoustics, were implemented for cross-verification, with details provided in the supplementary material.

For the thermal transport measurements, a frequency-modulated, home-built TDTR setup was employed, the details of which are given in our previous studies.^36,37 Briefly, a Ti:sapphire mode-locked femtosecond laser (Tsunami, Spectra-Physics) at 782 nm wavelength, 80 MHz repetition rate, and 80 fs pulse duration was used as pump and probe beams. The pump beam, modulated by an electro-optic modulator over 1.3–10 MHz, thermally excited the samples and controlled the heat penetration depth $Dth=kπCvf$⁠, where k is the thermal conductivity, C_v is the volumetric specific heat, and f is the pump modulation frequency. The probe beam was optically scan-delayed by a motorized delay stage and then detected by a photodetector connected to a radio frequency lock-in amplifier. Both laser beams were focused on the sample surface by a 10× objective lens, resulting in the 1/e² laser spot diameter of ∼11 μm, which is substantially larger than heat diffusion lengths, enabling measurements of only cross-plane thermal conductivity. In addition, the laser spot was positioned primarily near the center of the samples, away from the edges, to minimize any potential thermal bypass effects. Although the lateral heat spreading in the Al transducer was less than 1 μm and the steady-state temperature rise remained below 5 K, this careful positioning ensured that heat conduction was confined to the intended measurement area. The measured time-delayed signal of the ratio of in-phase to out-of-phase voltage (−V_in/V_out) at a picosecond temporal scale was fitted with a thermal diffusion model to extract the thermal conductivity (k) of the studied β-Ga₂O₃ membrane samples along with thermal boundary conductance (TBC) across the interface between the Al layer and the β-Ga₂O₃ membrane (TBC_1), and the TBC between the β-Ga₂O₃ membrane and the Si substrate (TBC_2).³⁸ The sensitivity analysis of measuring these quantities is given in Fig. S2 of the supplementary material. The presence of a SiO₂ layer with a thickness of about 8 nm on the Si substrate (i.e., in an area not covered with a membrane) was confirmed using ellipsometry, as shown in Fig. S3 of the supplementary material. As such, this layer was considered in the model, in particular in the NEMD results shown later in Sec. III C, and its thermal properties were taken from Ref. 39.

The NEMD modeling was employed to calculate the thermal boundary conductance (TBC) of the β-Ga₂O₃/Si interface with an intermediate a-SiO₂ interfacial layer, which acts as a bridge between β-Ga₂O₃ and Si vibrational modes. NEMD simulations were implemented in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code.⁴¹ The main heat carriers in amorphous materials are localized vibrational modes, which open new channels for thermal transport.^42,43 Both β-Ga₂O₃ and Si were oriented perpendicular to the (100) surface. The cross section of supercell size was 13.7 × 10.3 nm² with a maximum lattice mismatch of 1.3% between the β-Ga₂O₃ nanomembrane and the Si substrate. The thickness of both β-Ga₂O₃ and Si along the heat flux direction was selected to be 10 nm, and the thickness of a-SiO₂ was set at 3 and 5 nm. After equilibration at 300 K with a time step of 1 fs, a heat flux across the supercell was applied for 400 ps until a non-equilibrium steady state was reached. The temperature profile data were then averaged over the next 1000 ps. In the direction of the heat flux, both edges of the simulation box were fixed, and for in-plane directions, boundary conditions were periodic. Heat source/sink regions were placed next to the fixed walls. The microcanonical ensemble (NVE) was applied to all atoms in the simulation box. A Langevin thermostat was used to control temperatures of the heat source (350 K) and sink (250 K) regions. Finally, the TBC was calculated as G = Q/(SΔT), where Q is the heat flux, S is the cross-sectional area, and ΔT is the temperature drop across the interfacial layer. We used a Born–Mayer–Huggins type interatomic potential^44,45 for simulating the pairwise atom interaction of β-Ga₂O₃, which has been proven to reproduce thermal properties.^44,45 For crystalline Si and a-SiO_2, the Tersoff-type potential was used, which has been widely used in thermal transport studies of these materials.^46–48 Interactions of β-Ga₂O₃ with Si and SiO₂ were described with the Lennard-Jones potential, which has been used for TBC simulations with various interfaces.⁴⁹ 

To accurately determine the membrane thickness, we employed several measuring techniques. Initially, AFM measurements were conducted, and Fig. 2(a) presents an AFM image of a single membrane. The corresponding AFM thickness scans, shown in Fig. 2(b), reveal a uniform thickness of ∼340 nm, with a typical variation of ±5% across the sample. To cross-validate these measurements, we performed an optical profilometry analysis as shown in Fig. S4 (supplementary material). The results of both AFM and profilometry show excellent agreement within the uncertainties. In Fig. 2(a), it is possible to notice the presence of a crack, which is parallel to the [010] direction, in agreement with the crystalline habit of the crystals and the (100) easy-cleavage plane.⁵⁰ The fact that the membrane shows regions appearing with different colors in the AFM images suggests that its adhesion to the Si substrate is not homogeneous, highlighting the need for interface engineering and optimization in the context of applications.

For subsequent TDTR analysis, the thicknesses of samples 1, 2, and 3 were 350 ± 17 nm, 366 ± 18 nm, and 341 ± 17 nm, respectively. In addition, another membrane was prepared on an alternative substrate, such as sapphire, labeled sample 4 (S4). The thickness of S4 was estimated to be around 340 nm from the picosecond acoustics signal, as shown in Fig. S5 (a) of the supplementary material, which is in excellent agreement with the thicknesses of samples transferred onto Si substrates. It is important to highlight that these membrane thicknesses are greater than the ion penetration depth of ∼200 nm, according to the Stopping and Range of Ions in Matter (SRIM) simulation presented in Fig. S6 of the supplementary material. According to Esteves et al.,²⁸ this confirms that the implanted region remains inside the nanomembranes. In fact, the defect and strain profiles introduced by 250 keV Cr implantation in bulk samples were shown to be in great agreement with those simulations, thus suggesting that the Cr profile will also be well-described by those results. Notably, the similarity between the thicknesses of the different nanomembranes also highlights an important aspect of the ion-beam-assisted exfoliation method when compared to conventional mechanical exfoliation methods. In particular, our results show that it is possible to obtain membranes with a more controlled thickness within a given uncertainty interval, which, for 250 keV Cr ions, is compatible with the one previously reported by Esteves et al.²⁸ 

To estimate the root-mean-square (RMS) surface roughness, an AFM surface scan over a 5 × 5 μm area was taken at a scan frequency of 0.2 Hz [Fig. 2(c)], with an RMS value of ∼2 nm, to achieve reasonable accuracy of TDTR measurements.

The results of the XRD are shown in Fig. 3(a). It is worth noting that for XRD measurements, the samples were already coated with a 90 nm Al layer. Therefore, to exclude any overlapping peaks from β-Ga₂O₃, we separately deposited another Al layer on a pure Si substrate, as shown in Fig. 3(a). The XRD results show the characteristic peaks of β-Ga₂O₃ at ∼30° and 45°, corresponding to the 400 and 600 reflections of β-Ga₂O₃, respectively. Figure 3(b) shows the results of Raman measurements, where the β-Ga₂O₃ nanomembrane shows distinctive Raman modes, which are in line with previous reports in Ref. 51. There is a strong peak at 520 cm⁻¹ associated with the long wavelength transverse optical phonon (TO) of the Si substrate. In addition, we also see other phonon modes of Si, such as two transverse acoustic phonons (2TA ∼300 cm⁻¹), longitudinal acoustic plus transverse acoustic phonon (LA+TA ∼425 cm⁻¹), optical plus acoustic phonon (O+A ∼600–700 cm⁻¹), and two optical phonons (2LO ∼800 cm⁻¹).⁵² 

The results of the extracted thermal conductivity of the β-Ga₂O₃ nanomembrane as a function of the modulation frequency are given in Fig. 4(a) for sample 1. The results show no frequency-dependent thermal conductivity behavior, and the thermal conductivity remains around 5 W/m⋅K across different thermal penetration depths, suggesting that, although the ion range is lower than the membrane thickness, defect concentrations are approximately uniform after the annealing in β-Ga₂O₃ nanomembranes. Moreover, the thermal conductivity of three different membranes of β-Ga₂O₃ on Si substrate is also given in Fig. 4(b) with quite similar values around 5 W/m⋅K, demonstrating the uniform quality of the obtained nanomembranes. The thermal conductivity of a membrane on a sapphire substrate (S4) shows a slightly lower value than that of the membranes on Si substrates, which may be attributed to size effects or slight differences in substrate interactions. However, these results are less than half the value of the bulk thermal conductivity of the same-oriented β-Ga₂O₃,^9,10 as shown in Fig. 4(b). This reduction is expected due to phonon-boundary scattering and is probably due to residual irradiation-induced defects or strain, which will be discussed later. Figure 4(c) summarizes the thickness-dependent thermal conductivity of β-Ga₂O₃ thin films from the literature fabricated by different methods, including mechanical exfoliation,^17–19 PLD,²⁰ MBE,²² MOCVD,²³ ion cutting,^24,25 and the current work. The figure shows strong thickness dependence on thermal conductivity as it increases with thin film thickness. This is related to the fact that the phonon mean free path (MFP) in β-Ga₂O₃ spans from several nm to 1 μm;⁵³ therefore, thin films with thicknesses below 1 μm, such as in this work, will be mostly affected by phonon-boundary scattering. This corresponds well with the Debye model depicted as a red dashed line in Fig. 4(c), where phonon-boundary scattering dominates Umklapp phonon–phonon scattering. However, the results of the current work are lower than the Debye model and several previously reported experimental values in the same thickness range, which may be related to residual ion-induced defects or strain induced by thermal annealing. Defects formed during the rolling and unrolling of the nanomembrane as well as Si diffusion³⁵ from the substrate may also play a role; however, our preliminary results showing similar thermal conductivity values for membranes on top of a sapphire substrate [see Fig. 4(b)] suggest that the Si diffusion is likely not the key factor for the low measured conductivities.

As mentioned above, a two-step thermal annealing process was employed to fabricate these samples. First, post-irradiation annealing at 500 °C was conducted to unfold the microtubes into flat membranes, driven by strain relaxation.²⁸ Subsequently, the samples were heated to 1000 °C to facilitate crystal lattice recovery. Prior studies have demonstrated that for an ion fluence of 5 × 10¹³ ions/cm², near-complete structural recovery was achieved, as confirmed by XRD and RBS-C experiments.²⁸ However, several other studies indicate that post-implantation thermal annealing at ∼1000 °C is often insufficient to fully restore crystallinity in high-dose implanted samples.^54–57 Moreover, the formation of extended defects, including dislocations, voids, and defect clusters, has been reported under similar annealing conditions.^54–57 

Tadjer et al.⁵⁵ found that while Si-implanted β-Ga₂O₃ with fluences ranging from 1 × 10¹⁴ to 3 × 10¹⁴ ions/cm² exhibited near-complete lattice recovery at 1150 °C, Sn-induced defects persisted, leading to tensile strain and preventing full defect removal. Similarly, Peres et al.⁵⁴ observed that post-implantation annealing of Eu-doped β-Ga₂O₃ at a fluence of 1 × 10¹⁵ ions/cm² resulted in the formation of impurity-defect clusters, where Eu atoms and defects mutually stabilized each other. Furthermore, Wong et al.⁵⁸ demonstrated that Mg implantation in β-Ga₂O₃ led to the formation of defect clusters, in contrast to N implantation, which exhibited less structural damage. In addition, the high diffusivity of Mg dopants caused a significant reduction in the net local acceptor concentration.⁵⁸ 

Such defect clusters can substantially impact the restoration of thermal conductivity, as we previously demonstrated for Bi-irradiated ZnO.⁵⁹ To achieve better convergence of our experimental results with the Debye model, we introduced an additional phonon-defect scattering term, resulting in the blue dotted line displayed in Fig. 4(c). The estimated scattering cross section (Γ_i) was ∼0.13, closely aligning with heat conductivity values reported for 140 nm-thick β-Ga₂O₃ films fabricated by the ion-cutting technique.²⁴ 

Figure 5(a) presents the measured TBC for different β-Ga₂O₃ membranes. As illustrated in the inset, two distinct TBC values are considered: TBC_1, representing the conductance between the Al transducer layer and β-Ga₂O₃, extracted at a modulation frequency of 10 MHz, and TBC_2, corresponding to the interface across the β-Ga₂O₃/native SiO₂ layer/Si substrate, measured at 1.3 MHz. Despite the uniform thermal conductivity of the membranes, TBC_1 exhibits significant variation (40–70 MW/m²⋅K), which is likely influenced by differences in surface conditions following ion irradiation and annealing. Notably, no specialized surface treatment was performed prior to Al deposition, which could contribute to this variation. Previous studies have demonstrated that post-irradiation surface cleaning techniques, such as plasma treatment and ultra-high vacuum (UHV) cleaning, can substantially improve TBC at interfaces, as observed in Al/SiO₂/Si⁶⁰ and Al/GaN⁶¹ systems, respectively.

Figure 5(a) also presents the measured TBC across the β-Ga₂O₃/native SiO₂/Si interface (TBC_2). However, due to poor adhesion between the β-Ga₂O₃ membrane and the substrate, as evidenced by transient picosecond acoustic measurements in Fig. 5(b), TBC extraction was only feasible for sample 1. The sharp initial peak observed at ∼28 ps corresponds to the acoustic echo from the Al/β-Ga₂O₃ interface. Following this, periodic oscillations appear in all three samples, signifying the acoustic echo from the β-Ga₂O₃/Si interface. Notably, the amplitude and periodicity of these oscillations vary among the samples, suggesting differences in film thickness and interfacial quality. Sample 1 exhibits relatively good adhesion, while samples 2 and 3 show more pronounced oscillations, implying stronger acoustic echoes, possibly caused by higher interfacial roughness or residual defects. The obtained TBC value of sample 1 is comparable to previously reported values for van der Waals-bonded β-Ga₂O₃/diamond¹⁷ and mechanically exfoliated and bonded β-Ga₂O₃/quartz interfaces.¹⁸ 

Figure 6 presents the results of NEMD simulations for the TBC at the β-Ga₂O₃/Si interface, both with and without an intermediate a-SiO₂ layer. The simulated TBC of 47.3 MW/m²⋅K for the direct β-Ga₂O₃/Si interface closely aligns with our experimentally measured values. As shown in Figs. 6(b) and 6(c), introducing a thin a-SiO₂ interlayer reduces the temperature difference between β-Ga₂O₃ and Si, leading to a significant increase in overall TBC. Although amorphous interlayers are often associated with decreased TBCs, recent studies have demonstrated that, in certain material systems, they can enhance phonon transport across highly mismatched interfaces.^{25,49,62–66} The primary mechanism responsible for this improvement is the bridging of the acoustic mismatch, where the amorphous layer serves as an intermediate medium that partially matches the vibrational spectra of the thin film and substrate, thereby reducing phonon reflections.

We analyzed the phonon density of states (PDOS) at the interface (obtained from the Fourier transform of the velocity autocorrelation function) to better understand this phenomenon, as illustrated in Fig. 7. In the direct β-Ga₂O₃/Si interface, a significant spectral mismatch is observed, particularly at higher frequencies (>20 THz), where β-Ga₂O₃ exhibits broader phonon distributions compared to Si. This mismatch leads to a weak phonon coupling, which limits the TBC. However, introducing a 3 nm a-SiO₂ layer partially mitigates this issue by enabling phonon spectral overlap above 20 THz, as indicated by PDOS contributions from a-SiO₂ that overlap with both β-Ga₂O₃ and Si. Further increasing the a-SiO₂ thickness to 5 nm amplifies this effect, with the PDOS of a-SiO₂ becoming more pronounced and filling the spectral gap between β-Ga₂O₃ and Si more effectively. Despite this improved vibrational coupling, Fig. 6(c) reveals that the simulated TBC for a 5 nm a-SiO₂ layer is lower than that of the 3 nm layer. This reduction is likely due to increased phonon scattering within the interfacial layer, as a-SiO₂ is highly disordered and introduces strong phonon scattering.⁶² As the thickness increases from 3 to 5 nm, the probability of multiple scattering events before phonons reach the next interface also increases, thereby adding additional thermal resistance and reducing overall TBC.⁶² 

Recent studies support this observation. Xu et al.⁶⁶ reported a record-low TBR of 8.3 m² K/GW (∼120 MW/m²⋅K in terms of TBC) at the GaN/diamond interface using a 2.5 nm amorphous SiO_x interlayer. However, their study demonstrated that TBR is extremely sensitive to interlayer thickness, as a 2.8 nm increase in SiO_x thickness led to a substantial rise in TBR from 8.3 to 34 m² K/GW, corresponding to a decrease in TBC from ∼120 to ∼29 MW/m²⋅K.⁶⁶ This drastic variation was attributed to an increased interfacial vibrational frequency mismatch, particularly at the diamond/SiO_x interface, which suppressed phonon transmission, especially for low-frequency phonons. A similar trend was observed by Cheng et al.,⁶⁵ where the TBC of GaN/diamond interfaces decreased from 90 to 50 MW/m²⋅K when the interlayer thickness increased from 4 to 10 nm, respectively.

The highest NEMD-simulated TBC in this work was obtained for a 3 nm a-SiO₂ layer. However, the experimentally measured TBC (∼35 MW/m²⋅K) for the β-Ga₂O₃/Si interface remains significantly lower than the highest modeled value of 111 MW/m²⋅K for a 3 nm a-SiO₂ layer, which can be primarily attributed to the thickness and structural properties of the native SiO₂ interlayer in the system. While the estimated native SiO₂ thickness is ∼8 nm, the actual interfacial region may be even larger due to the presence of diffusion regions at both β-Ga₂O₃/SiO₂ and SiO₂/Si interfaces. As discussed above, increasing the thickness of an amorphous interlayer enhances phonon scattering and reduces phonon transmission efficiency across the interface. In addition, the native oxide layer may exhibit inhomogeneities, interface roughness, or structural defects, which further suppress phonon transport. Another possible contributing factor is interfacial bonding quality, as a poorly bonded membrane or an abrupt interface can significantly reduce TBC compared to an atomically smooth interface used in simulations. Therefore, implementing advanced surface cleaning methods such as reactive plasma cleaning⁶⁷ or etching to effectively remove surface contaminations and control the native oxide layer on the substrate prior to membrane transfer, coupled with innovative clean transfer techniques,⁶⁸ offers a promising route to enhance interface quality and, consequently, to improve the TBC. However, this is the subject of future work.

Overall, these findings emphasize the potential of amorphous interlayers for engineering thermal transport across various material interfaces. However, the effectiveness of this approach is highly dependent on interlayer thickness, phonon frequency distribution, and interfacial bonding strength, making precise control over the amorphous phase crucial for optimizing thermal transport in nanoscale electronic devices.

This work investigated the thermal transport properties of β-Ga₂O₃ nanomembranes fabricated via a novel ion-beam exfoliation technique. Chromium ion implantation induced a distribution of stress and strain, leading to the formation of rolled-up microtubes on the surface of a (100)-oriented β-Ga₂O₃ single crystal. Subsequent thermal annealing caused the microtubes to unroll, resulting in high-quality, single-crystalline nanomembranes that were successfully transferred onto Si substrates.

TDTR measurements revealed that the nanomembranes exhibited a consistent thermal conductivity of ∼5 W/m⋅K across multiple samples, demonstrating their uniformity and structural consistency. A Debye-based thermal transport model was employed to interpret the experimental results, considering phonon scattering from film boundaries as well as the potential formation of extended defects, such as dislocations and defect clusters, after thermal annealing.

To further investigate TBC at the β-Ga₂O₃/Si interface, NEMD simulations were performed, highlighting the critical role of the a-SiO₂ interlayer in mediating interfacial phonon transport. The highest TBC was achieved with a 3 nm a-SiO₂ interlayer, which effectively mitigated the phonon mismatch between β-Ga₂O₃ and Si. However, as the a-SiO₂ thickness increased, TBC decreased, primarily due to enhanced phonon scattering within the interlayer. This finding emphasizes the importance of precise control over interlayer thickness, interfacial bonding strength, and spectral phonon distribution to optimize heat dissipation.

This study contributes to the advancement of β-Ga₂O₃-based power electronics, offering strategies for improved thermal management through defect engineering and interfacial modifications.

The supplementary material includes the details of the data analysis.

This work was supported by Grant Nos. AP19577063 and AP19679332 from the Kazakhstan Ministry of Science and Higher Education; Grant No. 111024CRP2003 via the Collaborative Research Program (CRP); and Grant No. 20122022FD4130 via the Faculty Development Competitive Research Grants Program (FDCRGP) of Nazarbayev University. The authors acknowledge the financial support from the Portuguese Foundation for Science and Technology (FCT) via the IonProGO project (Grant No. 2022.05329.PTDC, http://doi.org/10.54499/2022.05329.PTDC) and the INESC MN Research Unit funding (Grant No. UID/05367/2020) through Pluriannual BASE and PROGRAMATICO financing. D.M.E. thanks FCT for his Ph.D. (Grant No. 2022.09585.BD). The implantations were performed under proposal 26001 of the Re-Made@ARI project (https://doi.org/10.3030/101058414), funded by the European Union as part of the Horizon Europe call HORIZON-INFRA-2021-SERV-01 under Grant Agreement No. 101058414 and co-funded by UK Research and Innovation (UKRI) under the UK government’s Horizon Europe funding guarantee (Grant No. 10039728) and by the Swiss State Secretariat for Education, Research and Innovation (SERI) under Contract No. 22.00187. Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the UK Science and Technology Facilities Council or the Swiss State Secretariat for Education, Research, and Innovation (SERI). Neither the European Union nor the granting authorities can be held responsible for them.

The authors have no conflicts to disclose.

Azat Abdullaev: Conceptualization (lead); Data curation (lead); Funding acquisition (equal); Investigation (lead); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (lead). Lyazzat Mukhangaliyeva: Formal analysis (equal); Investigation (equal); Validation (equal); Visualization (equal). Kairolla Sekerbayev: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (lead). Duarte M. Esteves: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Miguel C. Pedro: Formal analysis (equal); Investigation (equal); Validation (equal). Luis C. Alves: Formal analysis (equal); Investigation (equal); Validation (equal). Katharina Lorenz: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Marco Peres: Formal analysis (equal); Investigation (equal); Validation (equal); Writing – review & editing (equal). Zhandos Utegulov: Conceptualization (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.