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[new-ITC of AlNC　Liao　R.docx](https://mdr.nims.go.jp/filesets/945d7ab2-e8c6-4b2d-b18f-d3c19a245142/download)

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[Kongping Wu](https://orcid.org/0000-0001-5672-7610), [Meiyong Liao](https://orcid.org/0000-0003-1361-4266)

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[Mapping phonon dynamics to thermal transport            <i>via</i>            deep-learning NEMD: AlN/diamond interface engineering for GaN heat dissipation](https://mdr.nims.go.jp/datasets/4e242a51-7098-427d-8320-d4383e8e6cc9)

## Fulltext

Mapping phonon dynamics to thermal transport via deep-learning NEMD: AlN/diamond interface engineering for GaN heat dissipationKongping Wu[footnoteRef:1],†Meiyong Liao[footnoteRef:2]† Corresponding author. Tel: +86(025) 8618-8572. E-mail address: kpwu@jit.edu.cn (K. P. Wu).1School of Electronics and Information Engineering, Jinling Institute of Technology, Nanjing, Jiangsu, 211169, China2Research Center for Electronic and Optical Materials, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, JapanABSTRACTDiamond offers excellent heat sink for high power high-electron-mobility transistors (HEMTs) based on III-nitrides. However, the GaN/diamond interfaces suffer from low thermal conductance due to phonon mismatch. Although AlN interlayers can mitigate this issue, processing-induced carbon vacancies and subsurface disorder near the AlN/diamond interface ecreate a new thermal bottleneck.　In this study, we employ deep learning-enhanced non-equilibrium molecular dynamics (DL-NEMD) simulations to investigate atomic-scale thermal transport across AlN/diamond interfaces, with a particular focus on quantifying the impact of carbon vacancies. Our results reveal that the interfacial thermal conductance (ITC) of the AlN–Al/C(111) interface exhibits a non-monotonic dependence on carbon vacancy concentration. The ITC reaches a peak of 151.7 MW·m⁻²·K⁻¹ at a vacancy concentration of 2.4% due to the formation of resonant vibrational states that bridge the phonon gap and promote phonon delocalization, enabling efficient tunneling across the interface. However, beyond this optimal concentration, vacancy clustering induces destructive phonon interference, strong scattering, and severe localization effects, leading to a sharp decline in ITC. This work provides a pathway for optimizing AlN thermal bridges to achieve low thermal resistance in GaN-on-diamond devices through precise control of vacancy concentration and crystallinity.KEYWORDS: Wide band-gap semiconductors; Heat dissipation; Thermal conductivity; Interfacial thermal conductance; Non-equilibrium molecular dynamics1. IntroductionGallium nitride (GaN)-based high-electron-mobility transistors (HEMTs) have emerged as core components in next-generation power electronic systems for 5G communications [1-2] and new energy vehicles [3-4], owing to their superior high-frequency and high-voltage characteristics. However, as power density continuously escalates (>10 W/mm), the sharp temperature rise in device channels induced by self-heating effects has become a critical bottleneck constraining reliability, lifetime, and performance [5]. Conventional silicon (Si) substrates exhibit limited thermal conductivity (<150 W/m·K), failing to meet heat dissipation demands. Consequently, novel thermal management architectures must be engineered.Diamond (C), possessing the highest natural thermal conductivity (up to 2200 W•m-1K-1 at room temperature) [7], is regarded as the ultimate heat-spreading material [6]. Heterogeneous integration techniques enabling direct growth or transfer bonding of GaN devices onto diamond substrates, forming "GaN-on-diamond" structure, theoretically offer significant thermal resistance reduction and enhanced heat dissipation efficiency. Nevertheless, experimental studies reveal substantial phonon mismatch barriers at the direct GaN/C interface. The maximum phonon frequency of GaN (~22.5 THz) [8] is substantially lower than that of C (~40 THz) [9], causing strong scattering of high-frequency phonons at the interface. And thermal expansion coefficient (TEC) difference between GaN (5.6×10-6/K) [10-11] and diamond (1.0×10-6/K) [12-13] generates thermal stress, leading to interfacial microcracks or delamination. Besides, the 11.8% discrepancy in lattice constants between GaN (a = 3.189 Å) [14] and C (a = 3.567 Å) [15] induces high dislocation densities and dangling bonds at the interface. These factors collectively result in a GaN/C interfacial thermal conductance (ITC) lower than 10 MW·m-2·K-1 [16-17], constituting the primary bottleneck limiting thermal performance enhancement. To mitigate interfacial mismatch issues, aluminum nitride (AlN) has been proposed as a critical transition layer. Although a lattice mismatch of ~14.6% persists between AlN (a = 3.112 Å) [14] and diamond, this represents a significant improvement over the GaN/diamond system (11.8% → 14.6% mismatch reduction? this is increase, otherwise, this sentence can be removed). Crucially, AlN exhibits excellent lattice matching with GaN (mismatch: 2.8%), enabling high-quality coherent epitaxial interfaces (as demonstrated in mature AlGaN/GaN HEMT structures) [18]. AlN's maximum phonon frequency (~27.7 THz) [19] lies between those of GaN and diamond, theoretically serving as a "phonon spectrum adapter" to reduce interfacial phonon scattering probability. And the TEC of AlN (4.2×10-6/K) [20] provides an intermediate value between GaN and diamond, effectively buffering thermal stress. (one sentence is removed here: no reaction means poor adhesion). Numerous studies have confirmed that introducing ultra-thin AlN layers of 1-5 nm can increase the ITC of GaN/C interface by more than five times [22-23]. However, the introduction of an AlN interlayer complicates thermal transport pathways. The original direct "GaN-diamond" interface is replaced by a dual-interface system (GaN/AlN and AlN/diamond). While the GaN/AlN interface benefits from high lattice matching and mature epitaxial technology, resulting in controllable thermal resistance (~3.125 m2·K·G-1W-1) [24], the AlN/diamond interface emerges as the dominant thermal bottleneck. The thermal transport mechanisms at the AlN/diamond interface remain poorly understood [25]. Especially, chemical vapor deposition (CVD) growth or subsequent device processing (e.g., plasma etching) induces high-density carbon vacancies in the diamond subsurface regions (<5 nm). This vacancy accumulation causes significant lattice disorder or even the formation of an amorphous carbon layer. And the established models like the Diffuse Mismatch Model (DMM) and Acoustic Mismatch Model (AMM) fail to accurately describe thermal transport across amorphous/crystalline interfaces due to the inherent complexity of their atomic-scale structure and bonding mechanisms [26-27]. This limitation is particularly critical for the thermal transport at the AlN/C interface, as current research cannot meet engineering requirements. The systematic thermal characterization data of C surfaces containing defects, especially vacancy induced amorphous layers, are still scarce.In this work, non-equilibrium molecular dynamics (NEMD) simulations were employed to compute the ITC of AlN/C interfaces [28], with explicit quantification of carbon vacancy (VC) impacts. Through systematic analysis of phonon density of states (PDOS), participation ratios, and spectral decomposition, this study reveals atomic-scale phonon scattering mechanisms and transmission dynamics at defective interfaces. The study of AlN/C interfaces demonstrate AlN a critical thermal bridge that mitigates phonon mismatch at GaN/C heterojunctions, enabling ultra-low interfacial thermal resistance through vacancy concentration control and crystallinity optimization.2. Models and methods 2.1. Models The crystal structures of wurtzite AlN and cubic C were optimized using first-principles density functional theory (DFT) calculations with the Perdew-Burke-Ernzerhof (PBE) functional. The computed lattice constants for AlN (a = 3.129 Å, c = 5.419 Å) and C (a = 3.567 Å) exhibit excellent agreement with experimental values (AlN: a = 3.112 Å, c = 4.982 Å; C: a = 3.567 Å) [14-15], with deviations below 2%. Structural relaxation was performed until atomic forces converged below 10-3 eV/Å, ensuring minimal internal strain. The optimized unit cells as illustrated in Fig. 1(a) and (b), reveal characteristic tetrahedral coordination: AlN displays a hexagonal close-packed framework with alternating Al-N layers along [0 0 0 1], while C adopts a cubic lattice with sp³-hybridized C-C bonds.Fig.1 (a) Unit cell of wurtzite AlN with aluminum (grey) and nitrogen (blue) atoms, (b) C cubic structure with carbon atoms (dark grey). A rectangular unit cell was cleaved along (c) the AlN(0001) plane and (d) the C(111) plane, respectively.The AlN/C heterostructures were constructed by epitaxially aligning AlN(0 0 0 1) (Fig. 1 (c)) with low-index C surfaces. For the C(1 1 1)-oriented interface (Figs. 2(a) and (b)), the Cartesian coordinate system was defined as: z∥AlN(0 0 0 1)∥C(1 1 1), x∥AlN (1 12 0)∥C(11 0), and y∥AlN(11 0 0)∥(1 12). For the C(0 0 1)-oriented interface (Figs. 2(c) and (d)), the alignment follows: z∥AlN (0 0 0 1) ∥C(0 0 1), x∥AlN(1 12 0] ∥C(1 1 0), and y∥AlN(1 1 0 0]∥C(1 1 0).Based on the lattice orientation matching, four distinct interface configurations are possible due to the presence of both Al–C and N–C bonding scenarios at the interface. These configurations, illustrated in Figs. 2(a)-(d), are designated as: AlN-Al/C(1 1 1), AlN-N/C(1 1 1), AlN-Al/C(0 0 1), and AlN-N/C(0 0 1). Furthermore, a supercell approach was employed to construct the AlN/C heterojunction models, ensuring minimal lattice mismatch between AlN and C. For the AlN/C(1 1 1) interface, a 6×5×73 C supercell was paired with a corresponding 5×4×30 AlN supercell. The AlN/C(1 1 1) interface contains 2400 Al atoms, 2400 N atoms and 8760 C atoms. For the AlN/C(0 0 1) interface, a 5×13×42 C supercell was matched with a corresponding 4×6×30 AlN supercell. The AlN/C(0 0 1) interface comprises 2880 Al atoms, 2880 N atoms, and 10920 C atoms. Fig.2 Schematics of the (a) AlN(0 0 1)-Al/C(1 1 1) and (b) AlN(0 0 1)-N/C(1 1 1) interfaces with Al–C and N–C bonds for NEMD simulation, respectively. And the models of the (c) AlN(0 0 1)-Al/C(0 0 1) and (d) AlN(0 0 1)-N/C(0 0 1) interface with Al–C and N–C bonds for NEMD simulation, respectively.2.2. Computational methodsThe MD simulations of the AlN/C interface system were performed using the first principle method. The simulation generated “OUTCART” files containing key physical properties at various points, including atomic coordinates, interatomic forces, and total energies. Data generation, training process, and establishment of deep learning potential models are depicted in Fig. 3(a). The dpdata utility was employed within the DeePMD-kit framework to convert the raw simulation data into a format suitable for deep learning [29-30]. This processed data was then used to train a deep potential model. The specific hyperparameters utilized during the training process are detailed in Table I. Table I. The key parameters in deep learning data training Modules Keywords Parameters descriptor type se_e2_a  sel [30, 30, 30]  rcut  6.00  neuron [60, 60, 60] learning_rate type exp  decay_steps 200 loss start_pref_e   0.02  limit_pref_e 1  start_pref_f 1000  limit_pref_f  1  start_pref_v 0.1  limit_pref_v 0.1 training numb_steps  40000After the data training is completed, loss function of the root-mean-squared error (RMSE) of force (F) and energy (E) and virial (V) are plotted as a function of training steps (Fig. 3(b)), and demonstrated good convergence indicating successful model optimization. The trained deep potential model was then frozen and converted into a format compatible with the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). To enhance computational efficiency in subsequent LAMMPS simulations, the model underwent compression. Finally, the predictive accuracy and transferability of the compressed deep potential model were rigorously validated. This validation involved comparing the model's predictions against reference data obtained from first-principles calculations. The errors in predicted atomic force (F) and per-atom energy (E) and virial (V) are presented in Figs. 3(c)-3(e), respectively. The results show close agreement between the deep potential predictions and the first-principles reference values. This confirms that the developed deep potential provides a reliable description of the interatomic interactions within the AlN/C interface system.Fig. 3 (a) Workflow diagram for data generation, training, and model building. (b) Loss function of RMSE for force (F), energy (E) and virial (V), (c) Atomic force (F) and (d) Per-atom energy (E) and (e) virial (V) predicted using the deep learning potential vs. first-principles validation at AlN/C interface.Prior to computing the ITC of the AlN/C interface system, the conjugate gradient method was employed to optimize the AlN/C interface system to its energy minimum. The total energy and cross-sectional area of the relaxed interface were recorded for subsequent interfacial binding energy calculations. The ITC was determined the NEMD simulations [31-32]. A stable temperature gradient was established across the interface (325 K at the heat source, 275 K at the heat sink in Fig. 2(a)), with atomic motion constrained by fixed boundary layers.The thermal equilibration phase required 300,000 simulation steps at a timestep of 0.001 ps (1 fs), corresponding to 0.3 ns of physical time, to achieve steady-state heat flux under the imposed thermal bias. This was followed by a 4,000,000-step (4 ns) data acquisition stage for precise thermal conductance quantification. During this phase, temperature profiles across 22 discrete layers along the heat flux direction were monitored in real-time, while heat flux density (J) was extracted from thermostat energy exchange records. The temperature gradient was derived by fitting spatial temperature distribution data. The ITC was ultimately calculated according to Fourier's law [33]: ITC = J / ΔT, where ΔT represents the temperature jump across the interface, determined through linear extrapolation of temperature layers adjacent to the interfacial region. Besides, the detailed computational methodologies for interfacial phononic characteristics—including vibrational density of states (VDOS), phonon mode overlap factor (S), and phonon participation ratio (PPR)—are available in our recent work [34].3. Results and discussionA. Interfacial binding energy and the ITCAfter minimizing the energy of the AlN/C interface systems, the average spacing between interface atoms C and Al or N (dintf), interfacial binding energy (ΔEintf), and the ITC in pristine AlN/C heterostructures were calculated and listed in Table II. Based on the calculated average interatomic distance and interfacial binding energy at theAlN/C interface, the interface bonded via Al-C bonds exhibits significantly enhanced stability. This finding is consistent with our recent first-principles calculations on the characteristics of the Al2O3/diamond interface [35]. We further calculated the ITC for the AlN-Al/C(1 1 1) and AlN-Al/C(0 0 1) interfaces, both bonded via Al-C bonds. The ITC was computed via NEMD simulations. As depicted in Figs. 4(a) and 4(c), the steady-state heat flux (J) was derived from the linear slope of energy exchange between the heat source and sink. The interfacial temperature-drop ΔT (Figs. 4(b) and 4(d)) was obtained by extrapolating the linear temperature profiles in the AlN and diamond regions to the interface plane (z=0). The ITC is then given by ITC = J/ΔT. Our results indicate that the ITC of the AlN/C(1 1 1) interface (132.82 MW m-2K-1) is slightly lower than that of the AlN/C(0 0 1) interface (164.94 MW m-2K-1) as shown in Table II. Table II. Interface space (dintf), interfacial binding energy (ΔEintf), and the ITC at the calculated interface systems. Interface types ΔEintf (J/m2) dintf (Å) ITC(MWm-2K-1) AlN-Al/C(1 1 1) -10.55 2.83 132.82 AlN-N/C(1 1 1) 3.61 4.59 - AlN-Al/C(0 0 1) -13.55 2. 41  164.94 AlN-N/C(0 0 1) 4.09 3.37 -Fig. 4. At steady state, (a) Region energy vs. time and (b) z-direction temperature distribution for AlN-Al/C(1 1 1), and (c) Region energy vs. time and (d) z-direction temperature distribution for AlN-Al/C(0 0 1).B. The VC impact on the ITCThe intrinsic vacancy defects within the interface region have a significant impact on the ITC [31,36], with the VC at the AlN/diamond interface being particularly noteworthy. The VC defects are prevalent in diamond growth by chemical vapor deposition method. And probing their impact on this vulnerable interface is critical for predicting thermal stability in high-power devices. Furthermore, the AlN/C(111) interface was selected as the focus for vacancy studies based on two key considerations:　(i) Compared to the C(001) surface, the AlN/C(111) interface offers a superior lattice match, with a misfit of less than 1%. This enables the construction of smaller, computationally tractable supercells suitable for statistical sampling of vacancy configurations.(ii) The (111) surface exhibits lower bond coordination, which enhances phonon scattering effects induced by vacancies, thereby amplifying their impact on interfacial thermal transport. This combination of computational efficiency and physical sensitivity positions the AlN/C(1 1 1) interface as an ideal platform for elucidating defect-thermal transport correlations.Fig. 5. (a) Layer–resolved VDOS in the interfacial C region at the AlN-Al/C(1 1 1) interface, (b) In the interfacial C region, the number of the interface C layer starts counting from the interface.The definition of the carbon atoms in the interface region proceeded as follows. First, the total number of carbon atoms within the interfacial zone was determined, which served as the basis for subsequently setting the concentration of carbon vacancies. Following the methodology illustrated in Fig.5(a), we calculated the VDOS layer-by-layer for the carbon atoms, as presented in Fig. 5(b). Analysis of the evolution of the VDOS revealed a critical observation: the phonon density of states for carbon atoms located in the fifth atomic layer exhibited consistency with the characteristic phonon VDOS of bulk diamond. This convergence indicates that the distinct properties associated with the interface region extend only through the first four atomic layers. Consequently, the interfacial carbon region is defined as encompassing precisely four atomic layers, containing a total of 480 carbon atoms.The ITC of AlN-Al/C(1 1 1) depends on the carbon vacancy concentration (nVC ), as shown in Fig. 6. Each data point represents the mean ITC value derived from five distinct atomic configurations of carbon vacancies at identical concentrations, ensuring statistical robustness. And the horizontal line marks the ITC of the pristine interface at 132.82 MW·m-2K-1. The ITC exhibits strong dependence on nVc, increasing from 132.82 MW·m-2K-1 at vacancy-free to 151.7 MW·m-2K-1 at 2.4% vacancy concentration, then decreasing to 102.1 MW·m-2K-1 at 15% vacancy concentration. The non-monotonic thermal transport response stems from competing vacancy-mediated phonon processes: at low concentrations (nVC＜2.4%), isolated carbon vacancies enhance interfacial thermal conductance by generating resonant vibrational states that bridge spectral gaps between AlN and diamond, enabling efficient phonon tunneling. Beyond the critical 2.4% threshold, vacancy clustering triggers destructive phonon interference and creates nano-scale scattering centers, while overlapping strain fields strongly attenuate heat-carrying high-frequency phonons.Fig. 6. The ITC of the AlN/C(111) interface as a function of carbon vacancy concentration (nVC). The horizontal line indicates the ITC of the vacancy-free interface for reference. Error bars represent standard deviation derived from statistical sampling. C. The VC impact on the phonon dynamics characterizationTo elucidate the phonon transport mechanisms underlying the carbon vacancy-dependent the ITC in AlN-Al/C(1 1 1) , where peak ITC occurs at 2.4% vacancy concentration (as shown in Fig. 6) , we computed the VDOS and PPR for three representative interface configurations: pristine AlN-Al/C(1 1 1), optimal vacancy-concentration interface (nVC=2.4%), and high-degradation interface (nVC=15%). This comparative analysis is expected to establish atomic scale connections between the vibrational characteristics of interface atoms (VDOS/PPR) and the macroscopic thermal transport at the AlN/C interface, particularly providing an opportunity to understand the physical mechanism of the non-monotonic response of ITC to changes in vacancy concentration.The VDOS spectra reveal a significant evolution in interfacial phonon characteristics induced by the VC. The magenta-filled region in Figs. 7(a)-7(c) denotes the overlapping area between the VDOS of AlN and diamond. An increased overlap area indicates enhanced VDOS matching at the AlN/C interface, which facilitates interfacial phonon transmission across the AlN/C interface [37-38]. The pristine interface (in Fig. 7(a)) exhibits a pronounced phonon spectral gap between the characteristic bands of AlN (0~9 THz) and diamond (>23 THz), limiting phonon coupling. Introduction of an optimal vacancy concentration (2.4% VC, in Fig. 7(b)) generates distinct resonant vibrational states within this gap (0~9 THz), effectively bridging the spectral mismatch and enhancing overlap between the materials' vibrational spectra. This facilitates new phonon-mediated energy transfer pathways. Conversely, at high vacancy concentration (15% VC, in Fig. 7(c)), these resonant states are severely weakened, replaced by broadened intermediate-frequency defect modes (10~15 THz). Critically, the high-frequency phonon peaks characteristic of diamond (>30 THz) experience significant enhancement (>60% intensity increase), indicating strong phonon scattering due to vacancy clustering and associated strain fields.Fig. 7. Comparison of phonon properties in AlN-Al/C(1 1 1) interfaces with controlled vacancy defects. The VDOS) spectra for (a) Pristine interface, (b) Interface at optimal vacancy concentration (2.4%), (c) highly degraded interface (15% vacancies). And the corresponding PPR for (d) Pristine interface, (e) Interface at optimal vacancy concentration (2.4%), (f) highly degraded interface (15% vacancies).The PPR, quantifying the spatial delocalization of phonon modes, elucidates the mechanisms governing heat conduction. Phonons with values below the threshold of 0.4 are considered highly localized and do not contribute to thermal transport [39-40]. The pristine interface (in Fig. 7(d)) shows uniformly high PPR values (mean ~0.6), signifying predominantly propagating phonon modes across the interface. At the optimal vacancy concentration (2.4%, in Fig. 7(e)), a marked enhancement in PPR (peaking~0.8) occurs precisely within the resonant state frequency window (0~15 THz). This demonstrates that the VC-induced resonant states exhibit enhanced spatial coherence, promoting efficient phonon tunneling across the interface and directly correlating with the peak ITC. In stark contrast, the highly degraded interface (15%, in Fig. (7f)) exhibits a systematic collapse of PPR across all frequencies (mean<0.4), with values plunging to near 0.2 within the frequency range of 4 to 9 THz. This signifies extreme phonon localization, where vibrations become confined around vacancy clusters, disrupting long-range energy propagation.The combined VDOS and PPR analysis provides a complete phonon-scale explanation for the non-monotonic ITC dependence on the nVC (in Fig. 6). At low vacancy densities (<2.4%), the emergence of resonant states bridges the spectral gap, while concurrently enhancing phonon delocalization (high PPR in resonant band), enabling efficient phonon tunneling and increasing ITC. The peak ITC at 2.4% represents the optimal balance where resonant tunneling maximizes heat transfer before detrimental effects dominate. Beyond this threshold, vacancy clustering degrades phonon transport via strong high-frequency scattering (VDOS attenuation) and profound spatial localization (collapsed PPR), severely impacting dominant low-frequency modes. This synergistic action of spectral filtering (VDOS) and spatial confinement (PPR) drastically impedes phonon transmission, causing the precipitous drop in ITC at high vacancy concentrations.4. SummaryIn this work, we employed deep learning-assisted non-equilibrium molecular dynamics (DL-NEMD) simulations to investigate thermal transport across AlN/diamond interfaces for effective thermal management in GaN power devices by considering the presence of carbon vacancies (VCs). Simulations of pristine interfaces showed that the AlN–Al/C(001) interface exhibited a higher interfacial thermal conductance (ITC) of 164.94 MW·m⁻²·K⁻¹, compared to 132.82 MW·m⁻²·K⁻¹ for AlN–Al/C(111). Critically, the ITC of the AlN–Al/C(111) interface exhibited a non-monotonic dependence on VC concentration. As the VC concentration increased, the ITC rose to an optimal value of 151.7 MW·m⁻²·K⁻¹ at 2.4%, then declined sharply to 102.1 MW·m⁻²·K⁻¹ at 15%. Spectral and spatial analyses revealed that low VC concentrations promote the formation of resonant phonon states that bridge the vibrational mismatch between AlN and diamond, enhancing phonon delocalization and enabling efficient tunneling across the interface. In contrast, high VC concentrations lead to vacancy clustering, which induces strong phonon scattering and severe phonon localization, as indicated by reduced phonon participation ratios (PPR), thereby suppressing thermal transport. These findings demonstrate that the controlled introduction of carbon vacancies at the AlN/diamond interface provides an effective strategy to tune ITC and pave the way for the development of GaN-on-diamond devices with low interfacial thermal resistance. Disclosure statementNo potential conflict of interest was reported by the author.AcknowledgementsThis work is financially supported by the Science Foundation of Jinling Institute of Technology (jit-rcyj-202001). 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