Growth and fundamentals of bulk β-Ga₂O₃ single crystals

The Verneuil method was developed by Auguste Verneuil in 1902 and is also known as flame fusion. This process is used mainly to fabricate the gem varieties of sapphire and ruby. The steps of the operation include melting the powder material using an oxyhydrogen flame, and thereafter, the melted material crystallizes into boule (as shown in Fig. 3).

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In 1964, Chase^[17] prepared the first β-Ga₂O₃ single crystal boules using the Verneuil method. The crystals grow to the desired size by increasing the gas flow and powder feed; the obtained boules are 3/8 inch in diameter and 1 inch in length. The growth direction of the boule was mostly parallel to the crystallographic b axis. β-Ga₂O₃ has two cleavage planes (100) and (001). Thin slabs of β-Ga₂O₃ can be prepared by slitting the crystal on these planes. In addition, β-Ga₂O₃ crystals in the direction [100] have a twin plane and the majority of the crystals exhibit fine laminar twinning.

In addition, Lorenz et al.^[18] found that the Verneuil method permits a redox reaction in the growth process. β-Ga₂O₃ crystals were insulating and colorless when grown in an oxidizing condition. In contrast, crystals grown under reducing conditions were bluish. Mg- and Zr-doped β-Ga₂O₃ crystals were grown by Harwig et al.^{[19, 20]} using the same method. They demonstrated that the crystals were light blue and blue when doped with Mg and Zr, respectively^[19].

In 1955, Theurer^[21] modified the method developed by Pfann at Bell Lab for germanium, which is known as the FZ method. This method relies on moving a liquid zone through the material, and if properly seeded, a single crystal may be obtained, as shown in Fig. 4. The most prominent feature of this method is that no crucible is required, which facilitates the growth of congruent as well as incongruent melting materials.

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Villora et al.^[22] grew a single crystal β-Ga₂O₃ of approximately 1 inch in three crystallographic directions: [100], [010], and [001] (Fig. 5).

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Moreover, Zhang et al. ^[23] grew crystals with a 6-mm diameter and 20-mm length using the same method and also found that the preferred crystallographic growth direction is <010>.

The major drawback of this method is that it is difficult to prevent the liquid from collapsing. It can only be held in place by surface tension. Cracks occur in the cooling crystal owing to the stress caused by high thermal gradients.

The Czochralski method is a process of growing single crystals of metals (Pd, Pt, Ag, Au, etc.), semiconductors (Si, Ge, and GaAs), and artificial gemstones (Fig. 6).

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In 1915, Czochralski invented this method while investigating the rate of metal crystallization^[24]. The most prominent feature of this method is the growth of large boules or cylindrical ingots of a single crystal. Some scientists believe the Czochralski method is the "inverse" of the Verneuil technique. The following steps briefly describe the work process involved. High-purity material is melted within a crucible, and a seed on a rod is then immersed in the liquid. The rod is pulled upwards and rotated simultaneously.

The diameter of the crystal increased to approximately 2 inch. The growth direction is always along the <010> crystallographic direction, which is parallel to both cleavage planes (100) and (001).

The first Czochralski growth of a β-Ga₂O₃ single crystal was reported by Tomm et al.^[26]. They utilized 10% CO₂ in Ar instead of O₂ to decrease the evaporation of molten Ga₂O₃. Galazka et al.^[25] utilized similar growth conditions to grow β-Ga₂O₃ crystals. They found that the CO₂ concentration in the growth atmosphere may be used for adjusting the crystal perfection and growth stability in addition to tuning the optical and electrical properties of the crystals. Galazka et al.^[27] presented a new approach for scaling up the growth of β-Ga₂O₃ single crystals grown from the melt. They found that the desired larger crystal required a higher oxygen concentration in the growth atmosphere of up to 100 vol.%. They illustrated the growth of a cylindrical crystal with a 2-inch diameter (as shown in Fig. 7). When using an oxygen concentration between 8 and 35 vol.%

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Furthermore, the same co-workers of Galazka in 2018^[28] experimentally studied the segregation of Ce, Cr, Al-doped β-Ga₂O₃ crystals grown using the Czochralski method as well as the effect of doping on the optical properties. They observed that both the segregation and incorporation of Cr and Ce into the β-Ga₂O₃ crystals strongly depended on the O₂ concentration during the growth and on their charge state.

Intensive experiments performed by La Belle and Mlavsky^[29–31] on the growth of sapphire tubes resulted in the discovery of the edge-defined film-fed growth (EFG) technique. They observed that if the top surface of the shaper (also referred to as a die) was flat, the molten materials spread out to the edge and stopped, which implied that the melt wetted a die shaper. Hence, the diameter of the die, and not of the melt column, dictated the diameter of the filament produced (Fig. 8). Consequently, the technique was named "edge-defined film-fed growth". The major problems of this method are the geometry and the material of the die, while the major advantages of this method are the growth of a near-net shape and other complicated shapes and a higher growth rate. The growth direction was the [010] crystallographic direction, which is parallel to both the cleavage planes (100) and (001). The first successful growth of β-Ga₂O₃ single crystals using the EFG method was reported by Aida^[32] et al. wherein the rate of growth was 10 mm/h for crystal ribbons with 50-mm width, 70-cm length, and 3-mm thickness. Mu et al.^[33] grew bulk β-Ga₂O₃ single crystals having a width of 1 inch using an optimized EFG method under an Ar and 50% CO₂ atmosphere. The full width at half maximum of the X-ray rocking curve was only 43.2 arcsec, indicating high-quality single crystals.

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Kuramata et al.^[34] reported on the growth of large and high-quality β-Ga₂O₃ single crystals using the EFG method (Fig. 9(a)). They obtained a semiconductor substrate containing no twin boundaries with a diameter of up to 4 inches (Fig. 9(b)). The etch pit density revealed that the dislocation density on the ( $\bar{2}01$), (010), and (001) oriented wafers was in the order of 10³ cm⁻². Moreover, Kuramata et al.^[35] also showed the growth of large crystals of up to 6 inches by the EFG method.

Chinese scientists also used this method to grow bulk crystals, Zhang et al.^[36] grew 2-inch crystal with an atmosphere of 20% argon (Ar) and 80% carbon dioxide (CO₂) (Fig. 9(c)), and FWHM of rocking curve was only 19.06 arcsec. Our group also reported 2-inch crystal growth (Fig. 9(d) published in CCCG-18 conference) .

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The Bridgman–Stockbarger method is named after the Harvard physicist, Percy Williams Bridgman (1882–1961) and MIT physicist, Donald C. Stockbarger (1895–1952)^{[37, 38].} This method depends on the directional solidification process controlled by the movement of the crucible containing the molten to the axial temperature gradient in a vertical/horizontal furnace. Initially, the polycrystalline material is required to be melted completely in the hot zone, and then, it should be slowly cooled from the end of a seed crystal. A single crystal is gradually formed along the direction of the container length (Fig. 10).

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Part of the seed will be re-melted after contact with the melt. One feature of this method of growing β-Ga₂O₃ is the utilization of a platinum–rhodium (70%–30%) crucible^{[39, 40]}, which can weather a high oxygen concentration.

Hoshikawa et al.^[39] studied the effect of the crucible material on the shapes of the grown β-Ga₂O₃ crystals on using the vertical Bridgman (VB) method. They found that β-Ga₂O₃ single crystals were grown in the direction perpendicular to the (100) faceted plane using a seedless growth method in ambient air with a diameter of 25 mm and without adhering to the wall of the vertical cylinder crucible or a conical crucible (Fig. 11).

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Ohba et al.^[40] studied the structural defects on (100) wafers in β-Ga₂O₃ single crystals approximately 25 mm in diameter grown by directional solidification in a vertical Bridgman furnace. They observed no regions of high dislocation density near the periphery of the (100) wafers cut as cross sections from the crystal ingots. Moreover, they detected line-shaped defects that were 20–150 μm in length in the <010> direction using optical microscopy, as shown in Fig. 12. These defects are considered to be the same as those observed in the previously used EFG method.

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In summary, the crucible-free FZ and Verneuil methods facilitate the use of a high oxygen concentration and a reduced amount of residual impurities. The Czochralski method provides a large crystal size of approximately 2 inch in diameter, while the EFG method provides a 6-inch-width crystal of the highest quality.

Ga₂O₃ substrates underwent a massive breakthrough owing to their low cost and low energy consumption. The following organization chart (Fig. 13) depicts the comparison of the melt growth methods for β-Ga₂O₃ bulk single crystals.

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In addition, the best method for the mass production of substrates is the EFG method, which has a good track of the availability of large area, low defect density, high crystal quality.

A β-Ga₂O₃ crystal exhibits n-type conductivity with no intentional doping. The n-type semiconductivity is commonly attributed to oxygen vacancies, which are ionized and form donors. Therefore, it is assumed that there is a strong correlation between the conductivity of β-Ga₂O₃ crystals and oxygen vacancies. This assumption has been debated by Varley et al.^[15] who performed first-principle calculations for various impurities and oxygen vacancies in β-Ga₂O₃. Based on calculations, they suggested that the oxygen vacancy serves as a deep donor with an ionization energy of more than 1 eV and, thus, cannot contribute to n-type. They proposed that hydrogen is the probable cause of the electrical conductivity.

Zhang et al.^[23] produced β-Ga₂O₃ single crystals using the FZ method. They found that the 300-nm emission can be ascribed to the potential wells formed by acceptor clusters, and the 692-nm emission was attributed to the recombination of holes and electrons via the acceptors and donors in the vicinity.

The fabrication and characterization of Sn-doped β-Ga₂O₃ single crystals were studied by Suzuki et al.^[42] and Ueda et al.^[43] via the FZ method. High-conductivity crystals were obtained using the FZ method using Ga₂O₃ rods doped with 2–10 mol% SnO₂. The low incorporation efficiency causes a massive amount of Sn atoms to evaporate during the growth process. Ueda et al.^[43] reported that Sn-doped β-Ga₂O₃ had a blue coloration, and the value of their conductivity was 0.96 Ω⁻¹ cm⁻¹ (electrical resistivity = 1.04 Ω·cm). Suzuki et al.^[42] reported that the optimized specimen was 32 ppm. The conductivity value is 23.4 Ω⁻¹·cm⁻¹ (electrical resistivity = 4.27 × 10⁻² Ω·cm), and the carrier concentration is approximately 2.26 × 10¹⁸ cm⁻³. Zhang et al.^[23] studied the effect of Sn doping in β-Ga₂O₃ crystals prepared using the FZ method and that of the annealing process on their conductivity and optical properties. They showed that the forbidden bandwidth of β-Ga₂O₃ is influenced by Sn⁴⁺ doping. Both the absorption coefficient and conductivity increase on increasing the Sn doping. A reduction in the absorption coefficient after the annealing refers to the decrease in the free carriers. Thus, the annealed process changes the sample into an insulator. Moreover, Ohira et al.^[44] examined the effect of the annealing process on the surface morphology, electrical and optical properties of Sn-doped β-Ga₂O₃ produced using the FZ method. It was observed that these properties did not change, however the lattice parameters increased slightly after annealing at 1100 °C. Furthermore, Sn was uniformly dispersed in the β-Ga₂O₃ matrix.

VÍllora et al.^[45] obtained Si-doped β-Ga₂O₃ using the FZ method. It was found that the Si concentration is in the range of 10¹⁶–10¹⁸ cm⁻³, and the conductivity increases contentiously from 0.03 to 50 Ω⁻¹cm⁻¹. At a low doping rate, nearly all the Si is incorporated into the crystals, while at a high doping rate, the Si concentration in the crystal is approximately 5% that of the feed rod. While the mobility fluctuated around 100 cm²/V, the free carrier concentration increased by three orders of their magnitude. Therefore, the electrical conductivity depends sustainably on the main impurity. This is in agreement with the theoretical calculations^[15], which shows that the oxygen vacancies in the crystal are deep donors and can hardly contribute to the electron conductivity.

Sasaki et al.^[46] published good results on Si-ion implantation into Ga₂O₃ crystals fabricated using the FZ method. The Si concentration varies from 1 × 10¹⁹ to 1 × 10²⁰ cm⁻³ owing to the varying in the total dose from 2 × 10¹⁴ to 2 × 10¹⁵ cm⁻². The sample with a Si concentration of 5 × 10¹⁹ cm⁻³ had a resistivity of 1.4 mΩ·cm. A high electrical activation efficiency of over 60% was obtained in the samples with a Si concentration of ≤5 × 10¹⁹ cm⁻³ through the annealing process in the range of 900–1000 °C. Kuramata et al.^[34] reported the growth of Si-doped β-Ga₂O₃ bulk crystals using the EFG and FZ methods and investigated the residual impurities, controllable doping, crystal defect, and the effect of thermal annealing on the electrical properties of the β-Ga₂O₃ bulk crystals. They observed that the main residual impurity in the EFG crystals is Si and that the Si content controlled the effect donor concentration (N_d − N_a) of unintentionally doped crystals. Therefore, obtaining an intentionally n-doped crystal was found to be possible by doping with SiO₂. N_d − N_a was approximately the same as the Si concentration in the samples annealed in nitrogen, while it was independent of the Si concentration under oxygen ambient.

Zhou et al.^[47] experimentally confirmed that Nb element is a good choice to control the conductivity of β-Ga₂O₃. Nb-doped β-Ga₂O₃ crystals were grown using the FZ method, and their structure was that of monoclinic β-Ga₂O₃. The electrical resistivity decreased from 3.6 × 10² to 5.5 × 10⁻³ Ω·cm and the carrier concentration increased from 9.55 × 10¹⁶ to 1.8 × 10¹⁹ cm⁻³ on increasing the doping.

Varley et al.^[49] studied the effect of holes in many bandgap oxides and found that the holes in Ga₂O₃ can form self-trap holes with an energy of 0.53 eV. This indicates that free holes will be precarious and tend to localize as small polarons. Kananen et al.^[50] observed self-trapped holes in Ga₂O₃ using the electron paramagnetic resonance technique. These defects are thermally stable below ~80–100 K.

Onuma et al.^[51] obtained Mg-doped β-Ga₂O₃ crystals using the FZ method and found the samples' behavior to be semi-insulating with a resistivity of 6 × 10¹¹ Ω·cm for Mg concentration of 4 × 10¹⁸–2 × 10¹⁹ cm⁻³. The Blue luminescence intensity depended on the Mg doping, and there was a correlation between the intensity and the formation energy of V_o. Mg-doped β-Ga₂O₃ crystals were prepared by Galazka et al.^[27] via the CZ method in a very low range of Mg of 6–28 ppm at 100% CO₂, which indicates that Mg very efficiently compensates acceptors. Thus far, only Liu et al.^[52] have reported on N-doped β-Ga₂O₃ nanowires with a p-type electrical conductivity. As in the case of β-Ga₂O₃, p-type doped ZnO is difficult to acquire, and previous studies have stated that N acceptors are strongly compensated by intrinsic defects, and N atoms cannot be effective acceptors owing to the deep acceptor levels in the bandgap of ZnO. Dong et al.^[53] studied the compensation mechanism between N acceptors and native defects in β-Ga₂O₃ using first-principle calculations based on DFT. They found that the N dopant serves as a deep acceptor with an acceptor level of 1.33 eV above the valence band maximum, which cannot be an effective p-type dopant. In addition, the N dopant formed four types of defect complexes including oxygen and Gallium vacancies and interstitials. Kyrtsos et al.^[54] used DFT to investigate the various cation substitutional dopants in β-Ga₂O₃ for the possibility of p-type conductivity. They found that these dopants act as deep acceptor levels with ionization energies of more than 1 eV. They can also trap an extra hole at a very deep donor level, which inhibits p-type conductivity.