Temperature dependence of liquid-gallium ordering on the surface of epitaxially grown GaN

The three-dimensional ordering of the gallium (Ga) adlayers on GaN(0001) and (000 1¯ ) surfaces was probed using in situ X-ray scattering under MBE conditions. An ordered bilayer of Ga forms on GaN(0001) but the ordering decreases at substrate temperatures of <450 °C, consistent with the mechanism of non-equilibrium epitaxial growth. Monolayer Ga that forms on GaN(000 1¯ ) is laterally disordered and has no temperature dependence, along with droplets of excess Ga. The vertical and lateral B-factors for each Ga layer were confirmed using first-principles molecular dynamics calculations.

The three-dimensional ordering of the gallium (Ga) adlayers on GaN(0001) and (0001 ¯) surfaces was probed using in situ X-ray scattering under MBE conditions.An ordered bilayer of Ga forms on GaN(0001) but the ordering decreases at substrate temperatures of <450 °C, consistent with the mechanism of non-equilibrium epitaxial growth.Monolayer Ga that forms on GaN(0001 ¯) is laterally disordered and has no temperature dependence, along with droplets of excess Ga.The vertical and lateral B-factors for each Ga layer were confirmed using first-principles molecular dynamics calculations.© 2024 The Author(s).][8][9][10][11][12][13] In this context, interfacial liquid rearrangement can be observed even during epitaxial (i.e. noneqilibrium) growth, such as during MBE and chemical vapor deposition.Especially, for MBE-grown GaN, coverage of the growth surface by molten metal (e.g.liquid Ga on GaN) is crucial for regularly incorporating N atoms into the crystals and obtaining smooth, high-quality nitride films.14) Therefore, growth parameters that include the substrate temperature or III/V ratio need to be carefully controlled to maintain liquid Ga on the GaN surface.Although extensive theoretical studies have been performed to predict the interfacial structure of liquid Ga/GaN, [15][16][17][18][19] the observation of Ga ordering at the atomic scale is limited because of the lack of appropriate characterization tools.In situ X-ray crystal truncation rod (CTR) scattering is a powerful tool for determining surface or interfacial atomic structures.6,[20][21][22][23][24] Although Ga ordering has been observed in high-temperature and high-pressure GaN(0001) bulk crystals, 6) there are no reports on the growth temperature dependence of Ga ordering under epitaxial growth conditions because of the lack of accessible experimental equipment.
In this study, we employed a surface X-ray diffractometer with MBE apparatus (MBE-XRD system) 25,26) and measured in situ X-ray scattering to probe liquid Ga on GaN(0001) and (0001 ¯) surfaces under MBE conditions because the crystal growth conditions and crystallinity differ greatly when the polarity of the GaN substrate used for growth differs.Analysis of the obtained data revealed that although liquid Ga undoubtedly formed an ordered structure consistent with the bilayer on GaN(0001) model.The extent of this ordering decreased at temperatures below 450 °C.In contrast, liquid Ga on GaN(0001 ¯) was found to be laterally disordered and does not exhibit temperature dependence.The experimental results were verified by first-principles molecular dynamics (MD) calculations of the dynamic mobility of Ga atoms on GaN(0001) and (0001 ¯).
All measurements were performed at the SPring-8 BL11XU beamline using the MBE-XRD system with a radio-frequency nitrogen plasma source. 25,26)A hydride vapor-phase epitaxially grown GaN(0001) or (0001 ¯) substrate fixed using a molybdenum holder was introduced into the MBE chamber.The buffer layers were grown at 650 °C to allow an atomically flat GaN surface.In situ measurements of CTR scattering and reflection high-energy electron diffraction (RHEED) intensities were performed before, during, and after supplying Ga to the GaN surface at substrate temperatures of 320 °C-600 °C for GaN(0001) and 340 °C-640 °C for GaN(0001 ¯).The evolution of RHEED intensity was employed to check the status of Ga coverage on the GaN surface, allowing the CTR intensity profiles to be obtained along the surface-normal direction.The X-ray energy and beam size were 20 keV and 0.1 × 0.1 mm 2 , respectively.The distance between the sample and the PILATUS-100K two-dimensional X-ray detector (Dectris) was 700 mm, corresponding to an angular resolution of 0.0141°per pixel.First-principles MD simulations were performed using STATE-SENRI software 27) based on density functional theory with norm-conserving/ultra-soft pseudopotentials and a plane-wave basis set.Time-dependent diffusion coefficients were simulated in the x, y, and z directions.For comparison with the experimental results, we varied the substrate orientation [GaN(0001) or (0001 ¯)] and temperature (727 °C or 327 °C).
Figures 1(a) and 1(b) depict the effect of Ga supply on the CTR profiles along 00 and 01 rods measured at 600 °C-GaN (0001) and 640 °C-GaN(0001 ¯), respectively.Simulated profiles were obtained based on X-ray scattering theory (see the Supplemental Materials for details).The threedimensional atomic coordinates, Ga coverage, and anisotropic B-factor (temperature factor) in each surface layer were determined as fitting parameters for the least-squares method.The initial GaN(0001) surface before the Ga supply comprised a 0.3 Ga monolayer (ML; denoted Layer 1)/0.6 Ga ML (denoted Layer 0) on the N-terminated GaN(0001). 28)When Ga was supplied to the initial surface, the RHEED intensity decreased with increasing supply time and then became saturated.The CTR profiles after the Ga supply were recorded when the RHEED intensity was at the saturation stage, ensuring that a sufficient amount of Ga existed on the surface.The structures of Ga ordering, corresponding to the 2 ML stable interfacial structure comprising Layers 1 and 2, which agrees well with the bilayer model. 18)Excess Ga atoms over 2 ML are expected to form droplets on Layer 2. The vertical and lateral fluctuations (B-factor) in each layer were estimated by analyzing the 00-and 01-rod profiles, respectively.Unlike the 00-rod profiles, the 01-rod profiles, which reveals lateral disordering, did not show the characteristic modulation associated with three-dimensional ordering. 28)nalysis of the 00-rod profile of GaN(0001 ¯) indicated that the initial surface comprised 0.9 Ga ML [Layer 0]/0.4Ga ML [Layer 1] on the N-terminated substrate, with similar lattice distances of 2.0 Å.Several surface structures, such as 1 × 1, 3 × 3, 6 × 6, and c(6 × 12), have been suggested, depending on the Ga/N atomic ratio and temperature. 15,29)The RHEED patterns and observation of other high-index structures at a relatively low temperature (<300 °C) suggested that our surface was most likely the 1 × 1 type. 29,30)The CTR profiles for the 00-rod were slightly different after Ga supply owing to a slight reduction in coverage (0.9 to 0.8 ML) for Layer 0, as illustrated in Fig. 1(b).The RHEED intensity decreased during Ga supply, unambiguously indicating that the Ga atoms deposited on the surface did not entirely contribute to the adlayer formation and slightly reduced the original ordering.Therefore, the Ga atoms supplied to GaN (0001 ¯) are immediately converted to droplets on Layer 1 without the formation of Layer 2, consistent with the monolayer model. 15)The very small effect of Ga supply on the 01-rod profile evident in Fig. 1(b) supports the formation of droplets on Layer 1, which continued to be laterally disordered.
The dependence of Ga ordering on the substrate temperature was examined for both GaN(0001) and GaN(0001 ¯) substrates by performing 00-and 01-rod measurements at different temperatures.The results in Fig. 2 show only the typical results of the 00-rod scan for Ga-supplied GaN(0001).This is because clear temperature dependence was not observed in the case of the Ga-supplied GaN(0001 ¯).By fitting the scans, the temperature-dependent lattice distances, Ga coverage, and vertical and lateral B-factors for Layers 0-2 were evaluated, as shown in Figs.3(a)-3(c).Notably, the lattice distances remained almost unchanged, whereas the coverage of Layer 2 gradually decreased to 0.6 ML at 320 °C, and that of Layers 0 and 1 remained at ∼1 ML.The surplus Ga (more than 3 MLs) was supplied to the surface.Thus, the decrease in coverage indicated that some of the Ga atoms did not join the ordered layers and most likely formed droplets, resulting in an incomplete bilayer with disordered Ga atoms.This thermal behavior at low temperatures as observed under MBE conditions, but not during bulk growth. 6)The vertical B-factor of Layer 2 also decreased with decreasing temperature and approached those of Layers 1 and 0, which were close to that of ideal bulk GaN (∼2 Å 2 ).The B-factor estimated from the 00-rod profiles reflected a thermally driven deviation from the original atomic position along the surface-normal direction. 31)Therefore, it is likely that the mobility of Ga atoms progressively decreases and approaches the ideal value with decreasing temperature.In contrast, the lateral B-factor of Layer 2 was ∼50 Å 2 without a clear temperature dependence.These findings suggest that a fluid- 025502-2 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd like lateral disorder weakens the effect of temperature dependency compared to that in the vertical direction.The lower temperature 00-rod profiles of Ga-supplied GaN(0001 ¯) did not indicate a specific change for Layer 1.Therefore, the influence of temperature on Layer 2 of GaN(0001) was ascribed to the lower binding strength between Layers 2 and 1.
The thermal behavior of the Ga bilayer on GaN(0001) was compared with that of the Ga monolayer on GaN(0001 ¯) by recording the 00-and 01-rod profiles at different temperatures and extracting the total coverage before and after Ga supply.The temperature-dependent increase in the total coverage upon Ga supply was used as an indicator of the number of Ga atoms that formed ordered layers rather than droplets [Fig.3(d)].The ordering of the Ga bilayer (red circles) gradually weakened with decreasing temperature, reflecting the concomitant decrease in the coverage of Layer 2 [Fig.3(b)].Thus, the Ga bilayer on GaN(0001) was thermally unstable below ∼450 °C.As mentioned above, the Ga monolayer on GaN(0001 ¯) was not affected by temperature (blue circles), which resulted in an unstable fully covered monolayer structure on GaN(0001 ¯).
Although the bilayer and monolayer structures on GaN (0001) and (0001 ¯), respectively, are consistent with theoretical models, there was no evidence to confirm the estimated coverage, B-factor, or thermal behavior.Therefore, the dynamic atomic movement was simulated using first-principles MD, which is more suitable for this purpose than conventional static simulations.Figures 4(a    supplemental movies) and the obtained average diffusion coefficients, which reflect the mobility of the Ga atoms along the x-y (lateral) and z (vertical) directions.In the case of the bilayer on GaN(0001), the vertical diffusion coefficient was smaller than the lateral diffusion coefficient, consistent with the larger extent of lateral disordering compared with that in the surface-normal direction [Fig.3(c)].Moreover, the lateral diffusion coefficients observed for Layer 2 exceed those of Layer 1, consistent with the weaker ordering of the outer layer compared to the inner layer.For the monolayer on GaN(0001 ¯), the diffusion coefficients of Layer 1 were much larger than those of Layer 0, which agrees with the disordering of Ga atoms and the larger B-factor of Layer 1 (refer to Supplemental Material for details).The coefficients obtained at 327 °C were clearly lower than those obtained at 727 °C, indicating a decrease in the vertical B-factor of Layer 2 with decreasing temperature [Fig.3(c)].However, this thermodynamic simulation did not predict the decrease in coverage shown in Figs.3(b) and 3(d).This indicated certain limitations at low temperatures, which highlights the need for kinetics information.Ga disordering on low-temperature GaN(0001) [Fig.3(d)] can be interpreted from a kinetic viewpoint.At low temperatures, the formation of surface roughness or droplets dominates the corresponding thermodynamics because of the low surface migration of Ga atoms.Previous reports on the crystal growth of GaN revealed that high-temperature growth (>650 °C) affords high-quality atomically flat GaN films because of the surfactant effect of the Ga bilayer. 34,35)However, this growth regime disappears at lower temperatures and the film quality deteriorates. 14)Ga disordering at low temperatures likely reflects the actual growth mechanism and is the main reason for the deterioration in film quality.In contrast to the case of GaN(0001), the growth of high-quality films on GaN(0001 ¯) requires more Ga-rich conditions, as surface roughening and deep pit formation are observed under less Ga-rich conditions (Ga/N ≈ 1.2). 36)This difference is arguably related to the highly disordered monolayers observed experimentally.Growth temperatures >780 °C are suitable for the step-flow GaN growth on GaN(0001 ¯). 37)Such high temperatures are expected to favor the formation of an ordered monolayer, which was not observed in this study.
In situ X-ray scattering measurements were used to characterize the GaN(0001) and (0001 ¯) surfaces before and after Ga supply under MBE conditions.Liquid Ga formed a bilayer structure on GaN(0001), which is consistent with the theoretical model.However, this ordering is lost at lower temperatures (<∼450 °C).The Ga atoms adsorbed on the GaN(0001 ¯) surface were significantly disordered in the investigated temperature range (340 °C-640 °C).First-principles MD simulations validated the experimental results and confirmed the high lateral and vertical mobility of Ga atoms at 727 °C.For both surfaces, the observed Ga (dis)ordering within a few monolayers was expected to determine the actual crystal quality and underlying growth mechanism.The collective findings of this study enrich the understanding of the interfacial characteristics of liquid Ga/GaN and provide technical insights into the control of the epitaxial growth of nitrides.). 32,33)5502-4 © 2024 The Author(s).Published on behalf of The Japan Society of Applied Physics by IOP Publishing Ltd

Fig. 1 .
Fig. 1.Measured (filled circles) and simulated (solid lines) CTR profiles obtained before (blue) and after (brown) Ga supply along 00 and 01 rods on (a) GaN (0001) at 600 °C and (b) GaN(0001 ¯) at 640 °C.Each structure of Ga ordering after Ga supply is illustrated based on the obtained lattice distances, coverages, and B-factors.The arrow lengths in each adlayer express the relative magnitudes of the vertical and lateral B-factors based on obtained results.The B-factors in the outer layer/along the lateral direction are larger than those in the inner layers/along the vertical direction.
) and 4(b) summarize the representative atomic arrangements (refer to

Fig. 3 .
Fig. 3. Effect of substrate temperature on the Ga adlayer.(a) Lattice distance, (b) coverage, and (c) lateral and vertical DW factors of Layers 0-2 were obtained by analyzing the 00-and 01-rod profiles of GaN(0001).(d) Percentage increase in total coverage with Ga supply.The full coverage of each layer (0-2) corresponds to a 100% increase in the total coverage.The maximum theoretical increases in total coverage are 300% for GaN(0001)and 200% for (0001 ¯).

Fig. 4 .
Fig. 4. (a) Simulated cross-sectional atomic arrangements for three situations at 0-10 ps.The outer layers exhibit a similar extent of lateral disorder to the melt.(b) Average diffusion coefficients in lateral (average of x and y) and vertical (z) directions for each layer.The horizontal line indicates the diffusion coefficient of the Ga melt (9 × 10 −9 m 2 s −1 ).32,33)