Introduction Gallium oxide crystal phase is widely used, and the metastable phase can be only obtained by means of epitaxy. Selecting suitable growth methods and improving the heteroepitaxy level are still the problems that the academic circles have been discussing. The mist chemical vapour deposition (Mist-CVD) method does not require a vacuum system, which is safe, economical, simple and controllable, demonstrating a potential application for metastable phase growth of gallium oxide. The level of heterogeneous epitaxy of various crystalline phases of gallium oxide still needs to be further improved. For instance, there is still a problem of mixing phases during the growth process, which leads to a difficulty of regulating the crystalline phases. In terms of the nucleation mechanism, there is a lack of process-specific research and explanatory notes. In this paper, the most suitable growth intervals of Ga2O3 crystalline phases on sapphire substrates were explored in a vertical mist chemical vapour deposition epitaxy furnace. The relationships among Ga2O3 crystal phase modulation, crystalline quality, growth rate and growth process parameters, as well as the optimisation of surface morphology by annealing were investigated respectively. The nucleation mechanism of the films and the precursor droplet motion law of Mist-CVD were analyzed, and the experimental results were discussed.Methods Heterogeneous epitaxial Ga2O3 films were prepared by the Mist-CVD method in a vertical mist chemical vapour deposition epitaxy furnace with a 2-inch commercial sapphire substrate. Gallium acetylacetonate (Ga(acac)3) aqueous solution was used as a precursor for Ga and O at 0.05 mol/L, and 1.5% HCl was used as a co-solvent. High-purity Ar (99.999%) was used as a carrier gas with Ar flow rate of 2 250 mL/min and growth pressure of 101.325 kPa, respectively, and O2 was used as a dilution gas. The growth parameters were adjusted in the growth temperature range from 600 ℃ to 750 ℃ and O2 flow rate from 225 mL/min to 600 mL/min for 1 h.A model D8-ADVANCE X-ray diffractometer (XRD) was used to determine the crystal structure. The elemental composition and content of the epitaxial layer surfaces were determined using a model ESCALAB-250 X-ray photoelectron spectrometer (XPS). In addition, the cross-sectional image and thickness of the Ga2O3 epitaxial layer were characterized by a model S-4800 scanning electron microscope (SEM). The AFM images and root-mean-square (RMS) surface roughness of Ga2O3 epitaxial layers were analyzed by a model ICON-type atomic force microscope (AFM). A LAMBDA-950 UV-Vis spectrophotometer (UV-Vis) was used to characterize the transmittance of the samples and calculate the forbidden band width.Results and discussion Based on the XRD analysis on the crystal structure of the epitaxial films of gallium oxide at 600-750 ℃, there exist α and ε mixed phases at 600-700 ℃, and the film diffraction peaks are weak with no obvious selective orientation. This is due to the higher lattice matching of the α phase to the c-plane sapphire substrate, which is more easily induced to grow on the sapphire substrate at low temperatures and stabilised under lattice mismatch strain. The ε-pure phase is grown at 750 ℃ with a selective orientation. The crystalline phase of gallium oxide at higher temperatures is not explored, and pure phase films of β-Ga2O3 are expected to be obtained at higher growth temperatures due to the limitations of the current epitaxial furnace equipment with a maximum set temperature of 750 ℃.ε-Ga2O3 pure phase is generated at different oxygen flow rates. However, the half-height width of the diffraction peaks of the films appears at a lower level of 0.141° and 0.150° for oxygen flow rates at 225-250 mL/min. When the oxygen flow rate exceeds 400 mL/min, the half-height widths of the samples become larger, i.e., 0.178°, 0.162° and 0.162°, respectively, and the crystalline quality of the films decreases, but the overall crystalline quality of ε-Ga2O3 is better. Based on the analysis on the cross-section of the film thickness by SEM, the growth rate of the film firstly increases and then decreases with the increase of the oxygen flow rate, reaching a growth rate of 3 μm/h at 250 mL/min and 400 mL/min. A higher growth rate can be obtained at 250-400 mL/min.For the ε-Ga2O3 samples grown at 750 ℃, the surface of the ε-Ga2O3 sample shows a cluster with coarser particles and a cloudy morphological features, and its surface roughness is 10.8 nm. From the 3D stereogram, the surface morphology shows multiple bulge-like or hill-like bumps, and the height of the surface bumps is between 50 nm and 100 nm, and its overall height is larger than the grain size of the film, indicating that the epitaxial film grows in accordance with the three-dimensional island-like growth mode. The β-Ga2O3 sample after annealing at 900 ℃ is similarly characterized by AFM. The surface roughness of the thin film of β-Ga2O3 samples decreases as RMS=5.42 nm, and the grain size becomes larger, ranging from 50 nm to 80 nm. At high temperatures, the height of the surface bumps is between 5 nm and 30 nm, which is smaller than the grain size, showing that the film densities increase at high temperatures.Conclusions Pure phase films of ε-Ga2O3 were obtained at 750 ℃ in a three-dimensional island growth pattern with a high surface roughness of 10.8 nm at low temperatures. The growth rate of the film of ε-Ga2O3 at an oxygen flow rate of 225 mL/min was 1 μm/h with a half-height width of 0.141°. The growth rate of the film increased to 3 μm/h with increasing the oxygen flow rate, and the film was still in the pure phase of ε-Ga2O3. However, the crystalline quality of ε-Ga2O3 was not improved, while rather deteriorated due to the high oxygen flow rate. β-Ga2O3 pure-phase thin films were obtained after annealing at 900 ℃, and the surface morphology was further optimized with a reduced roughness of only 5.42 nm. The pure crystalline phases of Ga2O3 with a considerable thickness could be prepared by a low-cost mist chemical vapor deposition method in a Mist-CVD equipment.