Introduction

As a well-known wide bandgap semiconductor, gallium nitride (GaN) has been widely used in photonic and electronic devices such as light-emitting diodes (LEDs), laser diodes, UV photodetectors, field effect transistors (FETs), and ultrahigh power switches1,2,3,4,5,6. The growth and applications of GaN are mainly based on its tetrahedral-coordinated three-dimensional (3D) form7,8,9,10,11. It has been predicted that GaN will reconstruct into a buckled two-dimensional (2D) graphitic structure when its thickness is reduced to a few atomic layers12,13,14,15. In previous work, migration-enhanced encapsulated growth (MEEG) was reported to achieve buckled 2D GaN by using epitaxial graphene16. The requirements of GaN-based nanodevices, such as FETs and nanosensors, ask for knowledge of 2D GaN17,18, and this aspect is not yet sufficiently understood. Thermal management is of great significance in optimizing the performance of GaN-based devices. Phonon transport greatly influences the thermal conductivity of semiconductors19,20,21. Therefore, understanding the phonon behaviors of buckled 2D GaN is crucial to the thermal management of GaN-based devices at the nanoscale. Unfortunately, the study of the phonon behaviors of 2D GaN remains limited to theoretical calculations22,23,24. Buckled 2D GaN is embedded in the sample with a thickness of only a few atomic layers, making experimental characterization difficult. Therefore, the phonon dispersion of buckled 2D GaN has never been experimentally reported due to the limitations of traditional spectral measurement methods in terms of spatial resolution and spectral range.

Recent advancements in high-energy-resolution electron energy loss spectroscopy (EELS) and scanning transmission electron microscopy (STEM) have enabled the achievement of electron probes with atomic spatial resolution and energy resolution below 10 meV25,26,27,28,29,30,31,32,33,34,35. Thus, the acoustic and optical phonons excited in buckled 2D GaN can be distinguished. The phonon peaks of buckled 2D GaN were extracted from EELS experiments at on-axis and off-axis geometries. The comparison of the phonon peaks between buckled 2D GaN and bulk GaN shows a shift in the peak positions of the optical phonons. Here “bulk GaN” refers to tetrahedral-coordinated 3D GaN. Furthermore, the phonon dispersion of buckled 2D GaN under a specific momentum path was measured via the four-dimensional EELS (4D-EELS) technique. Buckled 2D GaN has a larger energy gap between its optical and acoustic phonon branches compared to bulk GaN. This larger gap is one of the key factors that contribute to the anomalous thermal conductivity of 2D GaN22. Our experimental results of phonon dispersion agree well with the numerical calculations. These findings on phonon behaviors and phonon band gap demonstrate that buckled 2D GaN can play an important role in the thermal management of GaN-based devices. Our methods for detecting phonon dispersion enrich the understanding of buckled 2D GaN and the thermal engineering of GaN-based devices.

Results

EELS setup and structural analysis of buckled 2D GaN

STEM-EELS experiments are performed on a Nion U-HERMES200 microscope. High-energy electrons are emitted from the electron gun and are focused at a diameter of ~0.1 nm. When interacting with the sample, the electrons excite phonons inside the sample and lose a small amount of energy (tens of meV). The energy loss signal is recorded by the spectrometer and EELS detector, allowing the phonon signal to be extracted. In addition, the electrons with high momentum transfer are collected by an annular detector at a high angle, enabling the acquisition of high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of the sample at an atomic spatial resolution. Thus, the localized phonon modes in a specific region of the sample can be studied. Moreover, electrons with a specific momentum transfer can be collected by placing apertures on the diffraction plane. EELS measurements can be performed at on-axis or off-axis geometries. The difference between these two geometries is whether the electron collection area is at the center of the diffraction plane. Furthermore, if the round aperture is replaced with a slot aperture, we can obtain the EELS signal along the momentum path corresponding to the position and direction of the slot. Therefore, the phonon dispersion can be directly extracted. This technique is named 4D-EELS36,37,38.

The buckled 2D GaN sample was grown by using metal-organic chemical vapor deposition (MOCVD). A sketch of the sample structure is shown in Fig. S1a. Epitaxial graphene was grown on a 4H-SiC substrate via silicon sublimation. Then, an AlN layer with a thickness of ~170 nm was grown on the graphene. Finally, bulk GaN was grown on top of the AlN layer. A cross-sectional HAADF-STEM image of the sample is shown in Fig. S1b. A magnified HAADF-STEM image of the sample area between the AlN and 4H-SiC layers is shown in Fig. 1a. The zone axis of the HAADF-STEM image is \([11\bar{2}0]\). As mentioned above, graphene is located between the AlN and 4H-SiC layers. However, another layer with a bright contrast is observed between graphene and 4H-SiC, as shown in Fig. 1a. To clarify the elemental composition of the bright layer, we performed energy dispersive spectroscopy (EDS) on the area shown in Fig. 1a. Figure 1b, c shows the elemental mapping of Ga and N, respectively. Both the Ga and N signals appear at the position of the bright layer. In addition, Fig. S2 shows the elemental mapping of C, Al, and Si in the same area. The signals of C, Al, or Si are not detected at the position of the bright layer. Thus, the layer is composed of Ga and N. Core-loss EELS was performed for elemental analysis. The results are shown in Fig. S3. The L edge signal of Ga in buckled 2D GaN is presented in Fig. S3a, and the K edge signal of N in buckled 2D GaN is shown in Fig. S3b. In addition, the near-edge structures of Ga and N were compared between bulk GaN and buckled 2D GaN. The core-loss EELS peaks of buckled 2D GaN are weaker and flatter than those of bulk GaN, indicating differences in elemental coordination and atomic structure. Figure 1b also shows that the Ga signal appears in the region of AlN. This result indicates that the formation of the GaN layer results from the permeation of the top bulk GaN. As shown in Fig. S1, the 170-nm-thick AlN layer exhibits a columnar structure. During the growth of the top GaN layer, the Ga and N atoms migrate through the boundaries of the AlN columns and the damaged regions of graphene and form a GaN layer on the 4H-SiC substrate. Notably, this kind of GaN layer does not continuously form over the entire wafer.

Fig. 1: Atomic structure of buckled 2D GaN.
figure 1

a HAADF-STEM image of the sample area around the buckled 2D GaN. b–c Elemental EDS mapping of Ga (b) and N (c) corresponding to the area in (a). d iDPC-STEM image of the atomic structure of buckled 2D GaN at the \([11\bar{2}0]\) zone axis. The scanning area is marked by the red dashed box in (a). The atomic structure of buckled 2D GaN is marked with balls in different colors. The green dashed box indicates the area used for EELS measurements shown in Fig. 2.

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To clarify the atomic structure of the thin GaN layer, we performed integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM) measurements on the area marked by the red dashed box in Fig. 1a. The results are shown in Fig. 1d. The experimental iDPC image agrees well with the simulated image shown in the inset of Fig. S439. The iDPC technique enables simultaneous visualization of both heavy and light atoms40, which makes it easy to distinguish the positions of N atoms. The corresponding HAADF-STEM image is shown in Fig. S5a, where only the heavy Ga atoms are visible in buckled 2D GaN layers. Several layers of AlN can be found on the top of Fig. 1d. Under the region of AlN, two layers of graphene can be distinguished. At the bottom of Fig. 1d, the atomic structure of 4H-SiC can be clearly recognized. The atomic positions of the Si and C atoms are marked by yellow and grey balls, respectively. Between the regions of graphene and 4H-SiC, the two atomic layers correspond to the bright GaN layer shown in Fig. 1a. By assigning the symbols of the Ga atoms (pink balls) and N atoms (blue balls) to the atoms distinguished in Fig. 1d, we can see that the upper layer has an approximate hexagonal honeycomb structure, with the exception that the Ga and N atoms are not strictly on the same plane. The distance between the upper N atoms and lower Ga atoms is ~0.5 Å. The lower layer is bonded to the upper layer and the 4H-SiC substrate. The distance between the two GaN layers is ~2.9 Å. The lattice constant of the GaN layers can also be extracted from the iDPC-STEM image, where the lattice constant a is ~3.1 Å. This lattice constant matches that of the 4H-SiC substrate. The two-layer buckled structure exhibits R3m symmetry and shows nearly the same atomic structure as previously reported for buckled 2D GaN16. The subtle difference between the structure in our sample and that of the reported buckled 2D GaN is reflected in the relative orientations of the two atomic layers. We attribute the structural differences to variations in the substrates, i.e., the 4H-SiC substrate we used rather than the 6H-SiC substrate used in a previous report16. In addition, the atomic structure of buckled 2D GaN at the \([10\bar{1}0]\) zone axis is also captured and shown in Fig. S5c. The captured atomic structures at both zone axes agree well with the simulated images in Fig. S5b, d, which are calculated based on our established atomic model. The distance between atomic columns is closer at the \([10\bar{1}0]\) zone axis, making it more difficult to distinguish the positions of light atoms. Therefore, the \([11\bar{2}0]\) zone axis is preferable for displaying the atomic structure of buckled 2D GaN. Through our elemental and structural analysis, we classified the GaN layers in our sample as buckled 2D GaN.

On-axis and off-axis EELS measurements of buckled 2D GaN

To study the phonon behaviors of buckled 2D GaN, we performed on-axis and off-axis EELS measurements on the local area (marked by the green dashed box in Fig. 1d) to extract the phonon signals with a specific momentum. The results are shown in Fig. 2. Figure 2a shows the on-axis and off-axis geometries that we used in this study. With a collection semiangle of 25 mrad, the electron beam is moved away from the center of the round aperture by ~30 mrad to satisfy off-axis geometry41. The schematic of EELS aperture placement at off-axis geometry is shown in Fig. S7. Maps of vibrational peaks are extracted from EELS data after normalization, zero-loss peak (ZLP) subtraction, and deconvolution (see Methods for details). By integrating the EELS maps over the detecting area, we obtain the EELS line profiles. Figure 2b, d shows the on-axis and off-axis EELS line profiles, respectively. The EELS line profiles contain four different regions from left to right, which correspond to AlN, graphene, buckled 2D GaN, and 4H-SiC, respectively. These regions are marked and separated by black dashed lines in Fig. 2b, d. The positions for extracting the EELS spectra of buckled 2D GaN are marked by orange triangles under the line profiles. The EELS signals of buckled 2D GaN appear to be a transition between the EELS signals of AlN/graphene and SiC. The phonon signals of bulk GaN were also extracted by EELS and are shown in Fig. S6. The phonon peaks of bulk GaN are consistent with those reported in the literature42,43. In addition, the thickness variations between buckled 2D and bulk GaN in our sample are on the order of a few nanometers, which is normal in a focused ion beam (FIB) sample. This minor thickness discrepancy does not influence the positions of EELS peaks44. Then, we compare the phonon excitations of bulk GaN and buckled 2D GaN at on-axis and off-axis geometries, respectively. The results are shown in Fig. 2c, e, respectively.

Fig. 2: On-axis and off-axis EELS measurements of buckled 2D GaN.
figure 2

a Schematic diagram of the on-axis and off-axis geometries used in this study. b EELS line profile of buckled 2D GaN at on-axis geometry. The detecting area is marked by the green dashed box in Fig. 1d. Each layer is separated with black dashed lines. The line profile is obtained by integrating the EELS map in the detecting area. The position where the EELS spectra of buckled 2D GaN in (c) are extracted is marked by an orange triangle. c EELS spectra of bulk and buckled 2D GaN at on-axis geometry. The signals were extracted from Fig. S6b and (b). d EELS line profile of buckled 2D GaN at off-axis geometry. The detecting area is the same as that in (b). Each layer is separated with black dashed lines. The position where the EELS spectra of buckled 2D GaN in (e) are extracted is marked by an orange triangle. e EELS spectra of bulk and buckled 2D GaN at off-axis geometry. The signals were extracted from Fig. S6d and (d). The intensities are in log scale.

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At on-axis geometry, we found that buckled 2D GaN exhibits three dominant EELS peaks at ~40, 70, and 110 meV. In comparison, bulk GaN shows EELS peaks at ~20, 40, and 80 meV. To clarify the vibrational nature exhibited in those EELS peaks, we measured the EELS spectra of bulk GaN and buckled 2D GaN at off-axis geometry, and the results are shown in Fig. 2e. Buckled 2D GaN exhibits EELS peaks at ~20, 30, and 110 meV at off-axis geometry. The EELS peaks of bulk GaN at off-axis geometry basically remain at the same positions as those at on-axis geometry, with the exception of the EELS peak at ~80 meV that splits into two overlapping peaks. In comparison to the phonon dispersion of bulk GaN, the EELS peaks below 40 meV result from the acoustic phonons. The EELS peak at 70 meV for buckled 2D GaN at on-axis geometry also appears in the EELS spectra of 4H-SiC, as shown in Figs. 2b and S8. We labeled this peak of 4H-SiC as the 610 cm−1 acoustic phonon mode45. The 70 meV EELS peak of buckled 2D GaN is attributed to the delocalized phonon signals of the adjacent 4H-SiC. The EELS signals extracted from the off-axis geometry are more localized and can help to avoid the delocalized signals41,46. EELS spectra of 4H-SiC at on-axis and off-axis geometries are extracted from Fig. 2b, d and shown in Fig. S8 to compare with buckled 2D GaN. It can be found that the EELS peak at 70 meV for buckled 2D GaN at on-axis geometry vanishes at off-axis geometry. Moreover, peaks at ~80 meV for bulk GaN are classified as optical phonons. However, for buckled 2D GaN, those phonons move to ~110 meV. The blueshift of the optical phonons is the major difference in phonon excitation between buckled 2D GaN and bulk GaN.

Calculations and experimental measurements of the phonon dispersion of buckled 2D GaN

On-axis and off-axis EELS measurements only extract the phonon information at a single “point” in momentum space. To fully understand phonon behaviors, we need to measure the phonon dispersion of buckled 2D GaN. We initially calculated the phonon dispersion curves by using Quantum ESPRESSO47,48 for the bulk GaN, free-standing planar 2D GaN, and buckled 2D GaN, and the calculated results are shown in Fig. 3. Figure 3a, c, e shows the typical atomic structures of bulk GaN, planar 2D GaN, and buckled 2D GaN, respectively. The structures of bulk GaN and planar 2D GaN in Fig. 3a, c are plotted in two orthogonal directions, respectively. In comparison to bulk GaN, planar 2D GaN reconstructs in the [0001] direction and all atoms are on the same interface. This intuitively demonstrates why the structure is labeled as “two-dimensional” GaN. The two-layer buckled structure of 2D GaN is believed to be more stable than the planar structure16. As shown in Fig. 3e, this two-layer GaN structure grown on the 4H-SiC substrate effectively explains the structure shown in Fig. 1d. The phonon dispersions of bulk GaN, planar 2D GaN, and buckled 2D GaN are shown in Fig. 3b, d, and f, respectively. As shown in Fig. 3b, d, planar 2D GaN has blueshifted optical phonon branches compared with those of bulk GaN. The optical phonon branches of bulk GaN lie in the energy range of ~60–90 meV, while they shift to 90–110 meV for planar 2D GaN. The energy ranges of the acoustic phonons remain the same for both structures. Thus, the energy gap between the acoustic and optical phonon branches is ~20 meV greater for planar 2D GaN with respect to bulk GaN. The phonon dispersion for the buckled 2D GaN structure was also calculated and projected onto the (0001) interface. The results are shown in Fig. 3f. The three color channels represent the squared norm of the vibrational eigenvectors for the upper layer of buckled 2D GaN (cyan), the lower layer of buckled 2D GaN (yellow), and 4H-SiC (magenta), respectively. Phonon dispersions of the upper layer of the buckled 2D GaN, the lower layer of the buckled 2D GaN, and the 4H-SiC are shown in Fig. S9, respectively. The projected phonon dispersions are highly localized in buckled 2D GaN. The energy ranges of optical and acoustic phonon branches in the upper and lower buckled 2D GaN layers are similar to those in planar 2D GaN. These energy ranges of optical and acoustic phonon branches are different from those of 4H-SiC. Therefore, the larger phonon band gap of buckled 2D GaN results from its two-dimensional nature rather than the modulation of the substrate.

Fig. 3: Calculated phonon dispersions of bulk GaN and 2D GaN.
figure 3

a Atomic structure of the bulk GaN used for calculation. b Calculated phonon dispersion for the bulk GaN. c Atomic structure of the free-standing planar 2D GaN. d Calculated phonon dispersion for the free-standing planar 2D GaN. e Atomic structure of the buckled 2D GaN in our sample. f Calculated phonon dispersion of the model in (e), projected onto the (0001) interface. Three color channels represent the squared norms of the vibration eigenvectors: cyan for the upper layer of the buckled 2D GaN, yellow for the lower layer of the buckled 2D GaN, and magenta for the 4H-SiC, respectively. Phonon dispersions of the upper layer of the buckled 2D GaN, the lower layer of the buckled 2D GaN, and the 4H-SiC are shown in Fig. S9, respectively.

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Finally, we performed 4D-EELS measurements on our sample to directly determine the phonon dispersion of buckled 2D GaN. Figure 4a shows a schematic of the EELS slot aperture displacement used in the experimental setup of 4D-EELS. The slot aperture was placed away from the transmission spot for better contrast of the signal. Since the buckled 2D GaN is spatially constrained along the c axis, we consider only the in-plane phonon dispersion. Therefore, as shown in Fig. 4a, the green rectangle indicates the available momentum path at the [\(11\bar{2}0\)] zone axis. This \(\Gamma -{{\rm M}}\) momentum path is sufficient to reveal the differences in the phonon bandgap between bulk and buckled 2D GaN. Figure 4a shows the diffraction pattern calculated for ideal bulk GaN at the \([11\bar{2}0]\) zone axis. For buckled 2D GaN, the diffraction pattern becomes closer at the direction perpendicular to the \(\Gamma -{{\rm M}}\) path due to its spatial confinement along the c axis. Therefore, the slot displacement shown in Fig. 4a remains valid. After the slot aperture was displaced, the phonon signals along that path were extracted, and these signals were exactly the phonon dispersion. The results for buckled 2D GaN are shown in Fig. 4e. Although not every single branch could be clearly distinguished due to the lack of energy resolution, the main optical and acoustic phonon branches could be effectively clarified. In comparison, the 4D-EELS results for bulk GaN were also extracted and are shown in Fig. 4b. The calculated phonon dispersion of bulk GaN is marked by white lines in Fig. 4b. The calculated projected phonon dispersion for the two-layer buckled 2D GaN is shown in Fig. 4d. Both experimental results agreed well with the calculated phonon dispersion. In addition, based on the calculated phonon dispersion, simulations of 4D-EELS can be performed. The results for bulk GaN and buckled 2D GaN are shown in Fig. 4c and f, respectively. For both bulk GaN and buckled 2D GaN, the calculated, experimental, and simulated results agreed with each other on the energy ranges of optical and acoustic phonon branches. From the 4D-EELS results, we determine that the energy gap between the acoustic and optical phonon branches is ~20 meV for bulk GaN, whereas buckled 2D GaN exhibits a larger phonon band gap of ~40 meV.

Fig. 4: Phonon dispersions of bulk GaN and buckled 2D GaN extracted using 4D-EELS.
figure 4

a Schematic of the EELS slot aperture displacement used in the experimental setup of 4D-EELS. The bright spots show the diffraction pattern of the sample at the \([11\bar{2}0]\) zone axis. The brightest spot is the transmission spot. The green rectangle marks the slot aperture, which corresponds to the momentum path \(\Gamma -{{\rm M}}\). b Phonon dispersion of bulk GaN extracted using 4D-EELS. The calculated phonon dispersion of bulk GaN is indicated by white lines. c 4D-EELS simulation results for bulk GaN, based on the calculated phonon dispersion in Fig. 3b. The calculated phonon dispersion of bulk GaN is also indicated by white lines. d Calculated phonon dispersion projected onto the buckled 2D GaN. This is the sum of the squared norms of the vibration eigenvectors from the upper and lower layers of the buckled 2D GaN, corresponding to the cyan and yellow channels in Fig. 3f. e Phonon dispersion of the buckled 2D GaN extracted using 4D-EELS. f 4D-EELS simulation results for buckled 2D GaN, based on the calculated phonon dispersion in Fig. 3f.

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Due to the energy conservation law, the increased energy gap inhibits the phonon-scattering process between the optical and acoustic phonons. This increases the lifetime of the optical phonons. The longitudinal optical (LO) phonons of 2D GaN have been reported to play a major role in the thermal conductivity when the temperature increases. The increased lifetime of the optical phonons is one of the factors that causes the thermal conductivity to decrease more slowly with increasing temperature with respect to the traditional \(\kappa \sim 1/T\) relation22. Therefore, buckled 2D GaN can aid in the fundamental understanding of the phonon transport of 2D materials, providing insights for the design of nanoelectronic devices with considerations for thermal management.

Discussion

In summary, we fabricated a two-dimensional buckled GaN layer on a 4H-SiC substrate. Using an electron microscope with high spatial and energy resolution, we investigated the phonon behaviors of buckled 2D GaN. By performing on-axis and off-axis EELS measurements, we extracted the phonon signals of buckled 2D GaN in the energy range of 20–120 meV. In comparison to that of bulk GaN, the optical phonons of buckled 2D GaN are blueshifted from ~80 to 110 meV. The 4D-EELS measurements revealed the phonon dispersion of buckled 2D GaN along a specific momentum path. The phonon band gap between the acoustic and optical phonon branches of buckled 2D GaN is ~40 meV. This value is larger than the ~20 meV phonon band gap of the bulk GaN. The experimental results of the phonon dispersion agree well with our numerical calculations. Our work experimentally demonstrates the phonon behaviors of buckled 2D GaN. The techniques used to extract phonon signals and dispersion via EELS can also be applied to study other spatially confined structures. Our investigation of the phonon behaviors of buckled 2D GaN significantly contributes to high-performance thermal management in nano- and optoelectronics.

Methods

Sample preparation

The GaN films were obtained following an AlN buffer layer on graphene/SiC substrates by metal-organic chemical vapor deposition (MOCVD). The AlN buffer layer grown on graphene was polycrystalline. As shown in Fig. S1, a columnar structure was found in the AlN layer. The Ga and N atoms migrated through the boundaries of AlN columns and the damaged regions of graphene during the growth of GaN, and then formed a buckled 2D GaN layer on the 4H-SiC substrate.

Characterization of the structure and composition of buckled 2D GaN

The cross-sectional TEM sample was prepared with a ThermoFisher Helios G4 UX FIB49,50. Atomic resolution structural analysis was conducted by an aberration-corrected transmission electron microscope operated at 300 kV (Thermo Fisher Scientific Titan Cubed Themis G2). The convergence semiangle was 30 mrad for the iDPC and HAADF-STEM imaging, and the collection semiangles were 4–21 mrad for the iDPC-STEM imaging and 39–200 mrad for the HAADF-STEM imaging.

EELS data acquisition

A Nion U-HERMES200 microscope equipped with a monochromator and aberration correctors was used to acquire the EELS data and HAADF-STEM image at 60 kV. Three-dimensional EELS datasets were acquired with a convergence semiangle α of 20 mrad and a collection semiangle β of 25 mrad. For the off-axis datasets, the central diffraction spot was displaced away from the EELS aperture, as shown in Figs. 2a and S7. The energy resolution of EELS was ~10 meV. To achieve a high signal-to-noise ratio, we selected acquisition times of 400–800 ms per pixel and ~30 min for each dataset in total.

Four-dimensional EELS datasets were acquired with a 3 mrad convergence semiangle. A slot aperture with an aspect ratio of 16:1 was placed along the \(\Gamma -{{\rm M}}-\Gamma\) line. To avoid the strong central diffraction spot and enhance the signal-to-background ratio, the slot aperture was displaced by a reciprocal lattice vector (Fig. 4a). The acquisition time was 15 seconds per pixel and ~40 min for each dataset in total. The energy resolution was ~20 meV.

EELS data processing

All EELS spectra were processed by MATLAB code written by Ruishi Qi37. The raw EELS spectra were initially aligned by their normalized cross-section. Then, block-matching and 3D filtering (BM3D) algorithms were applied to remove the Gaussian noise51,52.

For 3D-EELS datasets, the signals were first normalized by the ZLP intensity. We fitted the spectra to a Pearson function in two energy windows. This approach allowed us to remove the ZLP. As a result, the signals showed several energy loss peaks. Lucy–Richardson deconvolution was employed to reduce the broadening effect caused by finite energy resolution while taking the elastic peak as the point spread function.

For the 4D-EELS datasets, a correction for the statistical factor was performed following the literature53. This process suppressed the low-energy peaks because they had a higher occupation number. After the correction, the ZLP was automatically extremely small and could be neglected.

Ab initio calculations

Phonon dispersion calculations were performed using Quantum ESPRESSO47,48 with the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional and the projector augmented wave (PAW) pseudopotentials. The kinetic energy cut-off is 70 Rydbergs (Ry) for the wavefunctions and 350 Ry for the charge density and potential. The cell parameters of the bulk GaN model are a = 3.22 Å and c = 5.24 Å. The cell parameter of the planar 2D GaN model is a = 3.22 Å. The buckled 2D GaN model consists of 2 layers of GaN connected to 4 layers of SiC (13 atoms in one hexagonal unit cell with cell parameters a = 3.13 Å and c = 14.32 Å, as shown in Fig. 3e). Thick vacuum regions (15 Å) are added along the c axis to the cells of planar and buckled 2D GaN model, respectively. All structures were optimized under hexagonal symmetry until the energy converged to 10−5 Ry and the residual force was below 10−4 Ry per Bohr on every atom. A Monkhorst–Pack grid of 21 × 21 × 21 is used for bulk GaN, while the grid of 21 × 21 × 1 is used for planar 2D GaN. A sparser Monkhorst–Pack grid of 6 × 6 × 1 is used for buckled 2D GaN. The phonon dispersion of bulk GaN was calculated by interpolating the dynamical matrix on a 4 × 4 × 4 q-mesh. The phonon dispersions of planar and buckled 2D GaN were calculated by interpolating the dynamical matrices on a 6 × 6 × 1 q-mesh. The 4D-EELS simulation results are obtained based on the calculated phonon dispersion and eigenvectors. The 4D-EELS simulations were performed using the MATLAB code written by Ruishi Qi and Peng Gao37.