β-Ga₂O₃, one of the next-generation semiconductor materials with a ultrawide bandgap (4.7−4.9 eV), which is endowed with outstanding comprehensive properties. The potential performance parameters, e.g. high breakdown electric field strength of 8 MV/cm and baliga figure of merit of 3444, stimulating the vitality of different sectors of semiconductor industry^[1−6]. It is worth noting that the bulk crystals can be grown by low-cost melt methods, including the Verneuil (V), optical floating zone (OFZ), Czochralski (CZ), vertical Bridgman (VB), and edge-defined film-fed growth (EFG) methods. Among these, the EFG method is the only fully commercialized growth method to date^[7−14]. Therefore, β-Ga₂O₃ bulk single crystals are endowed with large-scale production advantages, which is the significant material support to β-Ga₂O₃-based high-voltage power, radio frequency (RF), and optoelectronics novel devices^[15−20].

In the complex growth process of single crystals, β-Ga₂O₃ exhibits evident anisotropic characteristics^[21]. It has been reported that a limited number of dangling bonds are found on the atomic-scale termination surfaces of (100) and (001) planes, resulting in a low degree of unsaturation and surface free energy^{[22, 23]}. By contrast, the (010) plane has the highest density of dangling bonds, leading to a higher degree of unsaturation and surface free energy. Consequently, the [010] growth direction has the maximum normal growth rate, the [100] direction has the minimum growth rate, and the [001] direction falls in between^{[24, 25]}. Additionally, the equilibrium state can be adjusted by the variation of interfacial free energy, which eliminates disturbances and restores stability to the growth interface^[26−28]. Thus, the stability of the solid-melt interface is heavily dependent on the regulation of interfacial energy, which can suppress the secondary nucleation phenomenon (primary cause misoriented of polycrystal) for the dynamic equilibrium of interface, and thus compared with the (100) and (001) planes, the (010) plane possesses superior stability of growth interface. As a result, in the practical growth process of β-Ga₂O₃ single crystals, the [010] orientation is chosen as the optimal or dominant pulling direction. The (100) or (001) planes are commonly used as the principal faces of single crystals. Therefore, the (010) β-Ga₂O₃ substrates can only be obtained from the growth cross-section of bulk single crystals^[9].

Currently, commercialization of the EFG method has been accomplished first among various β-Ga₂O₃ growth techniques, 4-inch diameter (001) substrates have been successfully commercialized for market, and 6-inch plates have also been demonstrated in laboratory^{[4, 8, 9, 29]}. It is worth noting that the EFG method possess the highest growth rate attributing to utilization of growth die, which is given more stable growth interface. However, the maximum specification of (010) substrates is only up to 10 × 15 mm², the reason is that (010) plane as growth cross section is limited by dimensions of die. On the other hand, 2-inch diameter β-Ga₂O₃ boules could be grown by CZ and VB methods, indicating that possibility of obtaining larger (010) substrates^{[11, 12]}. However, the inferior thermal conductivity of β-Ga₂O₃ would make heat accumulation underlying the solid-melt interface, and stable growth interface was difficultly to be realized^[4]. Furthermore, the (010) plane is perpendicular to both (100) and (001) cleavage planes, the growth cross section is accumulation area of stress, and thus cracking and collapsing phenomena are easily aroused in necking and shouldering processes of single crystal growth^[30]. Hence, compared with other substrates, the preparation process of (010) substrates is confronted with greater growth challenge. However, the (010) plane of β-Ga₂O₃ single crystals possesses the highest thermal conductivity and the fastest epitaxial growth rate, making it an ideal selection for high-power electronic devices, RF devices, high electron mobility transistors (HEMT)^{[15, 19, 31]}. However, various defects of β-Ga₂O₃ have been revealed in forward research for obtaining large-scale (010) substrates^[32−37]. The formation of dislocation spirals, dislocation climbing, and structural defects of thick-plate β-Ga₂O₃ single crystals were observed by Yao et al.^[32], larger (010) substrates could be obtained by using a thicker die in the EFG method, but severe dislocation loop of (010) substrates was also be generated. Meanwhile, nature and propagation of extended defects, e.g. high angle grain boundaries, low angle grain boundaries, polycrystalline grains, and increased misorientation of (010) principal-face β-Ga₂O₃ bulk crystals were investigated by Drew et al.^[37]. During the EFG growth process, non-dominant pulling direction (i.e., non-[010] pulling direction) might be the origin of confused defects phenomena, which severely affect the quality and limit the usable size of (010) substrates. Furthermore, the inferior stability of the solid-melt interface associated with non-dominant pulling directions can induce complex defect types, such as inclusions, dislocation pile-up group, and facet. In light of this, large-scale (010) substrates are urgently needed for the practical application of β-Ga₂O₃. To address this issue, novel technologies and fabrication methods for (010) substrates must be further developed and improved.

In this work, in order to obtain large-scale (010) β-Ga₂O₃ substrates, we utilized the non-dominant orientation of [001] as pulling direction and the (010) plane as the principal face of bulk crystals to grow high-quality, thick β-Ga₂O₃ plates using the EFG method. In this growth technique, tree-like defects (TLDs) were observed for the first time, which was a complex macroscopic defect accompanied by numerous cracks. The unusual TLDs in (010) principal-face β-Ga₂O₃ bulk crystals attracted our attention. Their morphology resembles a tree trunk with numerous branches, and they can even destroy the entire bulk crystal. This phenomenon might be induced by inappropriate growth conditions. Hence, proper growth conditions should be established for growing (010) principal-face β-Ga₂O₃ single crystals, to eliminate corresponding defects, especially the TLDs. The morphology of TLDs was characterized and analyzed by optical imaging microscope. The formation mechanism and origin of TLDs were investigated and discussed in depth. Consequently, the severe tree-like crystal growth phenomenon of (010) principal-face β-Ga₂O₃ bulk crystals was completely inhibited. Crucially, 2-inch diameter (010) principal-face β-Ga₂O₃ single crystal was successfully fabricated by the optimized EFG method. The high crystalline quality of the (010) substrate was evaluated by X-ray diffraction (XRD), back-reflection Laue diffraction system, and high-resolution X-ray diffraction (HRXRD).

The (010) principal-face β-Ga₂O₃ plate crystals were grown by the EFG method. For all plates, the [001] orientation served as the pulling direction of seed crystal, and the (010) plane was used as principal face of bulk crystals. High purity Ga₂O₃ (99.999%) and Fe₂O₃ (99.99%) powders were chosen as raw materials and placed into an iridium crucible with dimensions of Φ 90 × 45 mm². The Fe dopant concentration was approximately 5 × 10¹⁸ cm⁻³ to achieve high resistivity property. The upper surface size of iridium die was 10 × 60 mm², with a slit width of 0.3 mm. The plates were initially pulled from the top surface of die in the crucible (Fig. 1(a)), which was surrounded by RF induction heating coils operating at 7 kHz. The growth atmosphere consisted of a mixture of 98% CO₂ and 2% O₂, with a slight overpressure of up to 25 kPa to suppress dopant evaporation during crystal growth. When raw materials were heated and the melt moved up to the surface of the die through capillary action, β-Ga₂O₃ seed crystal with [001] direction would be transfer down to contact with melt. The bulk crystals were then grown through necking, shouldering, and equal-diameter processes. The pulling rate of [001] direction was limited to a range of 3−5 mm/h, which is lower than that of the conventional growth direction with [010].

The (010) principal-face macro and micro morphology of TLDs were observed by optical imaging scope and microscope (BK-POL, OPTEC), respectively. The evolution of the morphology in cross-sections perpendicular to the [001] pulling direction of TLDs was observed by scanning electron microscopy (SEM). The XRD was performed on (010) principal face single crystal to confirm the substrate orientation by Bruker D8 ADVANCE diffractometer. X-ray rocking curves were measured on (010)-oriented substrate using HRXRD D8 Discover (Bruker AXS) equipped with a crystal monochromator set for Cu Kα1 radiation (λ = 1.54056 Å). The crystal structural quality and crystallographic orientation were further demonstrated by Real-Time Back-Reflection Laue Camera System (Multiwire Laboratories, Ltd.). The typical dislocation-related etch pit density was revealed by wet etching of 85% H₃PO₄. The etching time and temperature were 90 min and 160 °C, respectively.

The optical transmittance spectra of (010)-oriented β-Ga₂O₃ substrate were recorded at room-temperature (RT) using a ultraviolet−visible−near-infrared (UV−VIS−NIR) Cary 7000 spectrophotometer (Agilent USA) in the wavelength range from 200 to 2500 nm and MWIR Fourier transform spectrophotometer NEXUS 670 (Thermo Nicolet), both of that were implemented in air conditions. The high-resistivity property was measured by a combined electrical system (Heating Furnace and Keithley 2400 Source Meter), and the temperature range was from RT−800 °C.

As shown in Fig. 1(a), the (010) principal-face β-Ga₂O₃ bulk crystals could be grown by EFG method with [001] pulling direction of seed crystal. Unfortunately, the TLDs were induced by inappropriate growth condition in our initial work, resulting to inferior crystal quality and yield of single crystals as displayed in Figs. 1(b) and 1(c). First, macroscopic morphology of TLDs was observed by optical imaging scope, obvious branching tendency of evolution process for TLDs was revealed by Fig. 1(b), showing that origin of TLDs was from the defect-free region of right to left paralleling to [001] pulling direction as indicated of lateral red arrow, and the TLDs gradually expanded to branch (longitudinal arrow) and deteriorated accompanied with bulk crystals growth process. Furthermore, enlarged surrounding of origin of local TLDs could be clearly observed in Fig. 1(c) of red rectangular block from Fig. 1(b), which was similar to an arborescent form of crystallizing, e.g. snow flakes and frost patters in nature^[38−43]. In addition, Fig. 1(d) displayed micro-morphology of TLDs of yellow rectangular block in Fig. 1(b), which was observed by optical microscope with transmissive mode, showing that terminational microstructure of TLDs developed into regular branching structure covering surface of bulk crystals, with significant TLD clusters observed in these regions.

Due to the adoption of the most optimal pulling direction during growth of single crystals, the TLDs seldom appear in the high-temperature oxide single crystal growth field, such as β-Ga₂O₃, Al₂O₃, where the solid-melt growth interface is stable and melt is pure. However, if a non-dominant orientation of single crystals is used as growth direction, such as the [001] or [100] orientation in β-Ga₂O₃, the stability of solid-melt interface was broken. Consequently, the TLDs may be induced as a means to restore a balanced state, as previously mentioned. Additionally, once the TLDs were formed in single crystals, the crystalline quality and structure would be greatly destroyed, and thus available area of crystals and production would be also confined as shown in Figs. 1(b)−1(d). Obviously, growth process of TLDs is generally coupling of both different independent processes as shown in Figs. 1(c) and 1(d), that corresponding to [001] and [100] orientations, respectively. The latent heats lying crystal bottom are not effectively released by small positive temperature gradient (from interface to crystal), the TLDs will be channel for losing heat at this moment. As a result, the relative position of height between heating coils, bottom of crucible, and surface of die was accurately modulated, an iridium lid covering crucible was introduced to growth system for symmetrical temperature gradients. The proper thermal gradient of solid-melt growth interface to [001] pulling direction was final established to overcome the TLDs of β-Ga₂O₃ single crystals, and thus (010) principal-face non-TLDs β-Ga₂O₃ single crystal was successfully fabricated by improved EFG method, as shown in Fig. 1(e), single crystal was brown resulting from Fe dopants and the maximum diameter up to 2 inches.

In order to investigate the relationship between growth interface stability of (010) principal-face β-Ga₂O₃ and evolution path of TLDs, the growth cross section was further observed by SEM. The cross-sectional morphology of TLDs at early pulling stage could be clearly observed as shown in Fig. 2(a), the relatively bright region with distinct branch structures corresponded to TLDs, with their boundaries located between a misoriented polycrystalline domain and a single crystal, accompanied by cracking and cleavage of side (100). Detailed observations were made at the edges (yellow square) of the relatively bright region in Fig. 2(a). Fig. 2(b) shows that the termination point of TLDs marked by yellow square in Fig. 2(a) permeated into deeper position of thickness of bulk crystals, and that the left and right extend paths of TLDs were further displayed by Figs. 2(c), 2(d) and 2(e), 2(f), respectively. Obvious cracking emerged from TLDs could be observed from Figs. 2(c) and 2(e), and more cleavage might be induced by extended cracking as presented in Fig. 2(f). Different from the clustering region of TLDs, Fig. 2(d) shows better surface quality in non-cracking location where only the grain boundaries are present as two-dimensional defects. Compared with TLDs of early stage in Fig. 2(a), deteriorated tendency of TLDs was revealed by Fig. 2(g) of later growth period, and the same evolutionary development could also be found in Fig. 1(b). Serious cluster of defects were commonly resulting from unstable solid−liquid growth interface. Furthermore, Figs. 2(h) and 2(i) show enlarged views of the yellow squares in Fig. 2(g), from which it can be observed that the structural quality of the bulk crystals is worse than in the early stage, with more cracking. The serious cracking defects were easily induced by improper temperature gradient, which was corresponding to the origin of TLDs. Hence, the instability of growth interface was positive correlation with deterioration of TLDs, more badly TLDs would be caused by more unstable factors of interface with proceeding of pulling bulk crystals, and that stable growth condition was vital for single crystal growth process.

The crystalline quality and orientation of (010)-oriented substrate from (010) principal-face β-Ga₂O₃ single crystal is significant for subsequent research and development of devices, which should be demonstrated by diversified measurements. As shown in Fig. 3(a), strong and sharp XRD peak of (020) was exhibited in the range of wide angle, showing consistent and pure crystalline orientation for (010) principal-face single crystal. Fig. 3(b) shows that crystalline quality of the (010)-oriented substrate was evaluated by HRXRD, high structural quality of single crystal was confirmed by the full width at half maximum (FWHM) of rocking curve with 50.4 arcsec. Moreover, the crystalline orientation and structural quality of (010) principal-face single crystal were further demonstrated by Laue diffraction system. The symmetrical, clear, and bright diffraction spots were presented in Fig. 3(c), predicating great crystal structure quality, and indexed Laue diffraction pattern and crystallographic plane of (010)-oriented substrate were also estimated, as displayed in Figs. 3(d) and 3(e), showing an impartial (010) plane of substrate. Additionally, dislocation-related etch pit density (revealed by wet etching of H₃PO₄) at the level of 10³ cm⁻² as shown in Fig. S1 of Supplementary material, showing great availability of (010)-oriented substrate. Consequently, the results of crystalline orientation and quality for Laue diffraction measurements were consistent with the XRD and HRXRD, respectively, identifying the expected crystal structure quality of (010) principal-face β-Ga₂O₃ single crystal grown by EFG method.

The optical and electrical properties of (010)-oriented β-Ga₂O₃ substrate were demonstrated for evaluating availability of related devices. As shown in Fig. 4(a), the UV−VIS−NIR optical transmittance spectra of (010)-oriented β-Ga₂O₃ was carried out at RT condition, whose transmittance was up to 83% at whole range, the phenomenon of free carrier absorption was not found at NIR. The cut-off wavelength of (010)-oriented β-Ga₂O₃ was around 271 nm, and thus the bandgap (E_g) of (010) plane was further estimated by combining Fig. 4(a) and equation of αhv=A(hv−Eg)1/2, where h, v, and A are the Planck’s constant, light frequency, and a constant, respectively. Thereby, the E_g of 4.4 eV for (010)-oriented β-Ga₂O₃ could be obtained from the inset of Fig. 4(a) through standard fitting process, which was less than the (100) and (001) planes, showing apparent anisotropy of optical property for β-Ga₂O₃. Furthermore, Fig. 4(b) shows the MWIR transmittance spectra of (010)-oriented β-Ga₂O₃, high and stable transmittance above 80% was displayed from NIR to around 6.2 μm, indicating great optical stability at whole range including UV and VIS in Fig. 4(a), and thus low free electron concentration of sample could also be predicted. Meanwhile, the temperature-dependent resistivity of (010)-oriented β-Ga₂O₃ was measured from RT to 800 °C, as shown in Fig. 4(c). Ultrahigh resistivity level of about 10¹² Ω·cm for (010)-oriented β-Ga₂O₃ was revealed at RT, and that mildly decreased with elevating of temperature. The high-resistivity property of sample might be attributed to introduction of Fe dopant, making the (010) principal-face β-Ga₂O₃ single crystal appear semi-insulting state^[44]. Moreover, the acceptor activation energy (E_a) of Fe with 0.78 eV was calculated with Arrhenius equation, as shown in Fig. 4(d). In sum, these preliminary results indicate crucial availability of large-scale (010)-oriented substrate, the (010) principal-face β-Ga₂O₃ single crystal will be a novel role in EFG method.

The TLDs of β-Ga₂O₃ single crystal was observed for the first time, resulting from the non-dominant [001] growth direction used in the EFG production process. Consequently, we investigated the macroscopic and microscopic morphology of TLDs, and the independent evolution mode and pathways of TLDs within (010) principal-face crystals were clearly observed. Meanwhile, the relationship between stability of solid−liquid interface and the formation of TLDs within growth cross-section was thoroughly demonstrated. The unstable interface front was identified as the source of these defects, which can extend into deeper regions of the bulk crystals and severely degrade crystalline quality. To address this issue, an appropriate thermal gradient at growth interface was established. The 2-inch diameter (010) principal-face β-Ga₂O₃ single crystal was successfully grown by the improved EFG method, enabling the fabrication of large-scale substrates. This advancement contributes to resolving the dilemma of β-Ga₂O₃ substrates, especially for (010)-oriented substrates. Notably, the high crystalline quality and consistent orientation of the (010) principal-face β-Ga₂O₃ single crystal were confirmed, and the optical and ultrahigh-resistivity properties were also revealed. These preliminary results showed that the crystalline quality of (010) principal-face β-Ga₂O₃ single crystal was great. In light of this work, the production of large-scale (010)-oriented substrates could be realized. The larger size of (010) principal-face β-Ga₂O₃ single crystal will be obtained in the future, proper growth parameters and temperature conditions should also be established, we will continue to investigate and report large-scale (010) principal-face β-Ga₂O₃ single crystal grown by EFG method.