Two inch diameter, highly conducting bulk β-Ga₂O₃ single crystals grown by the Czochralski method

β-Ga₂O₃ with its unique combination of great electrical and optical properties is considered to be a future material in high power electronics and UV optoelectronics. This is the result of a large bandgap of 4.85 eV¹ and a high theoretical breakdown field of 8 MV/cm.² Indeed, in the last decade, there has been a significant and substantial β-Ga₂O₃ development in terms of the growth of bulk crystals, e.g., Refs. 3–12, and thin films, e.g., Refs. 13–23, as well as various device demonstrators, e.g., Refs. 2 and 24–32. Remarkable research on the above-mentioned aspects of β-Ga₂O₃ has been summarized in a number of review articles and books.^33–47 Particular attention is paid to high power switching devices that are economical and environmentally friendly. These requirements can potentially be met by β-Ga₂O₃-based Schottky barrier diodes (SBDs) and field effect transistors (FETs).

In β-Ga₂O₃-based SBDs and FETs in the vertical configuration, which can switch higher voltages as compared to the lateral configuration (due to better exploitation of the breakdown field), the substrate functions as an electrode for an epitaxial drift layer; therefore, it should have high conductivity represented by the free electron concentration > 10¹⁸ cm⁻³ and resistivity on the order of 10⁻² Ω cm. The substrates should also be of high structural quality to get high quality epitaxial films (drift layers) thereon, as structural defects have an impact on the electrical properties of the films and operation of the electronic devices, such as SBDs.^48–51 

Availability of large wafers, minimum 2 in. diameter, is required for device fabrication at the industrial level. Indeed, 2 and 4 in. diameter wafers of β-Ga₂O₃ have been commercialized,⁵² and 6 in. diameter wafers were demonstrated⁵³ with the use of the EFG method. So far, large diameter wafers, both electrically conducting and semi-insulating, can be fabricated with orientations $(2¯01)$ and (001); however, other orientations are available in smaller sizes, e.g., the size of (010) wafers is limited by the cross section of the EFG-grown crystal slabs, and it is 10 × 15 mm².⁵² On the other hand, 2 in. diameter (010)-oriented wafers can be prepared from 2 in. diameter cylindrical crystals grown by the Czochralski^{5,6,8,9,36,47,54,55} and Bridgman¹² methods. Such wafer orientation showed the highest growth rate (due to strong bonds to the surface) of homoepitaxial thin films grown by the Molecular Beam Epitaxy.^19,21,56 Although electrically insulating or semi-insulating β-Ga₂O₃ crystals of 2 in. diameter can be grown by the Czochralski method as long cylinders (> 2 in.),^6,8,47 highly conducting crystals encounter length limitation due to free carrier absorption.^5,8,47,54,57

In this report, we highlight the capability of growing 2 in. diameter, highly conducting bulk β-Ga₂O₃ single crystals grown by the Czochralski method, including their basic structural quality and electrical properties that are suitable for electronic device fabrication in the vertical configuration.

Details of the growth of bulk β-Ga₂O₃ single crystals by the Czochralski method with the use of inductively heated Ir crucibles, including thermodynamics and free carrier absorption issues, as well as different doping we have already reported in numerous articles.^{5–8,55,57–59} Here, the initial Si concentration in the starting material was 0.15–0.2 mol. %, which is sufficient to induce the free electron concentration (n_e) in the crystals of 10¹⁸–10¹⁹ cm⁻³. Some of the crystals were also co-doped with Al at initial concentrations in the starting material of 1, 2.5, and 5 mol. % to enlarge the bandgap. The equilibrium segregation coefficient for Si and Al in the Ga₂O₃ melt is about 0.1 and 1.1, respectively.⁷ The oxygen concentration in the growth atmosphere, necessary to minimize the formation of elemental Ga in the melt, was between 14 and 20 vol.%. The growth and rotation rates were 1.5 mm/h and 5 rpm, while the growth direction was parallel to the ⟨010⟩ crystallographic direction.

As stated above, we could easily reach a cylinder length exceeding 2 in. for 2 in. diameter, semi-insulating β-Ga₂O₃ crystals (Mg-doped). The situation drastically changes in the case of highly electrically conducting crystals, where the free carrier absorption has a huge impact on the growth stability. Shortly, latent heat of crystallization, which is dissipated away through a growing crystal via radiation in the near-infrared (NIR) region, is absorbed by the free electrons and cannot be easily removed from the crystal. After reaching a certain length, heat accumulation rate exceeds the heat dissipation rate and the temperature near the growth interface increases. Once it reaches the melting point of Ga₂O₃, there is an interface inversion from convex (stable) to concave (unstable). The crystal cannot grow vertically as a cylinder any longer, and it forms a corkscrew (spiral) with windings extending beyond the cylinder. Such configuration enables easy heat dissipation (small thickness of the windings facing higher temperature gradients). Generally, the spiral formation in high-melting point oxides (>1600 °C, when radiative heat transport dominates over conductive one) grown by the Czochralski method is a known phenomenon that arises from the heat absorption caused by one or more absorption bands.^60–63 The symmetry breaking and consequently spiral formation after interface inversion (highly unstable growth environment) may have different triggers, such as non-uniform temperature gradients around the interface, melt flow instability (baroclinic or Marangoni), and asymmetry of thermal conductivity across the interface, faceting. In the case of β-Ga₂O₃ crystals, the heat absorption is caused by free electrons, which is continuum over the NIR spectral region. Detailed discussion on the spiral formation during growth of β-Ga₂O₃ crystals by the Czochralski method is available elsewhere.^{5,47,54,55,58}

This is why highly conducting bulk β-Ga₂O₃ crystals grown by the Czochralski method are relatively short, typically about 2 cm for both 2 cm⁵⁷ and 2 in. diameter crystals shown in Fig. 1(a). Although Al co-doping (5 mol. %) increased the cylinder length of 2 cm diameter crystals by about 50%,⁵⁷ this is not the case for 2 in. diameter crystals [Fig. 1(b)], due to much larger optical thickness of the former. Also, higher O₂ concentration in the growth atmosphere [Fig. 1(c)] did not increase the cylinder length, which is still about 2 cm. Applying He in the growth atmosphere,⁶⁴ which has a high thermal conductivity, increased the crystal length to 2.5 cm [Fig. 1(d)]. In each case, the cylinder length is sufficient to fabricate a number of highly conducting 1 or 2 in. diameter (010)-oriented wafers.

Most of the Si-doped crystals (only a few are shown in Fig. 1) were twin- and grain-free, others had 1 or 2 twins parallel to the {100} plane. Occasionally, small polycrystalline grains occurred. The blue coloration of the crystals is the result of the free carrier absorption that extends into the red part of the visible spectrum. This can be recognized from transmittance spectra reported elsewhere.^5,47,57

The primary wafer orientation for homoepitaxial growth by MOVPE, prepared from Czochralski-grown bulk β-Ga₂O₃ crystals, is (100) with an offcut of 2°–6° toward the $001¯$ direction (Fig. 2) to avoid the formation of twin lamellae and achieve step flow growth mode by MOVPE as described in detail by Schewski et al.,^14,65 Fiedler et al.,⁶⁶ Bin Anooz et al.,^15,67,68 and Chou et al.¹⁶ After surface treatment of the fabricated wafers, first by a wet chemical etching step with phosphoric acid to remove the damage layer resulting from polishing followed by an annealing step in O₂ at 900 °C for 60 min, the RMS roughness was typically between 150 and 200 pm¹⁵ also shown in Fig. 2.

Such heat treatment to obtain epi-ready wafers does not affect their electrical properties. We observed, through annealing experiments depicted in Fig. 3, an increase in the resistivity by more than one order of magnitude only after annealing in the oxidizing atmosphere (air) at minimum 1000 °C for at least several hours (here 20 h). This is valid for both 2 cm and 2 in. diameter and for both Si- and Si+Al-doped crystals, which all show the same trend. In Ref. 5, we reported that in the case of undoped β-Ga₂O₃ crystals (free electron concentration, n_e < 10¹⁸ cm⁻³) annealing at high temperatures (≥1200 °C) creates a thin electrically insulating layer on a sample surface, while the bulk conductivity decreases by about an order of magnitude. The latter is due to hydrogen removal that have a high contribution in the electrical conductivity, as we reported elsewhere.⁷ Here, by intentional doping with Si, such insulating layer was rather not formed upon annealing, or it was thinner than the Ohmic contact thickness for Hall effect measurements. The increase in the resistivity after annealing at high temperatures is due to a decrease in the free electron concentration associated with hydrogen removal at high temperatures (acting as a shallow donor) and next by compensation of a portion of Si by gallium vacancies (acting as deep acceptors), the concentration of which increase with oxygen partial pressure during growth.⁶⁹ The resistivity of all, highly conducting crystals studied here, remains substantially intact for annealing temperatures below 1000 °C. This means that neither the surface heat treatment nor the growth temperature by MOVPE (<850 °C) will affect the electrical properties of highly conducting Si-doped β-Ga₂O₃ wafers.

Figure 4(a) shows x-ray rocking curves of Si-doped β-Ga₂O₃ (100) samples as-cleaved from 3 different, 2 in. diameter, Si-doped β-Ga₂O₃ crystals. Full widths at half maximum (FWHM) values, even below 20 arc sec, indicate the capability of obtaining high structural quality samples or wafers for epitaxy. They do not show shoulders that would indicate the presence of low-angle grains or twin boundaries. FWHM values of the epi-ready (100) 4° off oriented wafers were between 25 and 35 arc sec.⁵⁵ Co-doping 2 in. diameter crystals with Al (5 mol. %) resulted in a bit broader rocking curve of FWHM = 33 arc sec [Fig. 4(b)]. An Al incorporation into the β-Ga₂O₃ crystals lattice causes easier formation of oxygen-related point defects (lower formation energy) and larger lattice distortion.⁷⁰ Si-doped, 2 cm diameter β-Ga₂O₃ crystal revealed yet broader rocking curve of FWHM = 46 arc sec [Fig. 4(b)]. Simply, Si-doped crystals of small diameter (2 cm) were grown at much lower oxygen concentration (1–4 vol. %) in the growth atmosphere as compared with large diameter crystals (2 in.) shown in Fig. 1. This may lead to a higher density of point defects (especially oxygen vacancies) as the result of the thermal decomposition of the melt and larger density of structural defects, like dislocations (for thermodynamics of Ga₂O₃ and impact of oxygen concentration in the growth atmosphere on the crystal growth stability, see e.g., Ref. 55).

A relation between free electron (measured by Hall effect, system HMS 7504 Lake Shore, see details e.g., in Ref. 71) and Si (measured by Inductively Coupled Plasma Optical Emission Spectroscopy, ICP-OES, system Thermo Fisher Scientific, iCap7400) concentrations of Si-doped β-Ga₂O₃ crystals is shown in Fig. 5. An approximately 1:1 relation indicates almost full activation of Si in the crystals, similar to smaller diameter crystals.⁷ Occasional deviation from this relation arises from a nonuniform radial and axial Si distribution due to segregation phenomenon (low segregation coefficient ≈0.1). Because the crystallization ratio is rather small (about 15%), the axial Si segregation supposed to be small; however, it might be larger at regions of large changes in the interface shape, in particular, in the region of the interface inversion. On the other hand, changes in the interface shape will induce some radial Si segregation, which may differ between crystals. Here, in highly conducting crystals, a possible contribution of hydrogen in the free electron concentration, which is visible at smaller n_e values (<10¹⁸ cm⁻³),⁷ does not play a significant role, as it is governed by the Si concentration. The same relates to trace impurities, such as Ir, Fe, Al, Ca, Mg, and Zr (determined by ICP-OES), which are always found in bulk β-Ga₂O₃ crystals grown by the Czochralski method with a typical concentration of around or below 10¹⁷ cm⁻³ each.^55,72

2 in. diameter, Si-doped β-Ga₂O₃ single crystals revealed free electron concentration (n_e), electron mobility, and resistivity from Hall effect measurements at room temperature (RT) in the ranges of 1.6–9 × 10¹⁸ cm⁻³, 118 – 52 cm² V⁻¹ s⁻¹, and 4 – 1 × 10⁻² Ω cm, respectively. We noticed, however, that n_e values may differ within an as-grown crystal by factor of 2–3, which might be correlated with changes in the interface shape and associated differences in Si incorporation. Annealing at elevated temperatures (<1000 °C) made the ne values and resistivity more uniform (see Fig. 3). Figure 6 shows a relation between Hall electron mobility and free electron concentration for 2 in. diameter Si- and Si+Al-doped β-Ga₂O₃ single crystals, in comparison with 2 cm diameter ones. At n_e > 10¹⁸ cm⁻³, all the crystals show a dominant electron scattering at ionized impurities.⁷³ Comparing both diameter crystals, it is clear that an average Hall electron mobility is higher for 2 in. diameter crystals at similar n_e values, which is likely due to a better structural quality of the samples from larger crystals (for comparison see rocking curves in Fig. 4). The Hall electron mobility for Al co-doped 2 in. diameter crystals is in average lower than in those doped with Si only, which was already observed for 2 cm diameter crystals.⁵⁷ This is likely due to above-mentioned lattice distortion, which leads to a larger scattering of free electrons and, thus, electron mobility reduction.

Figure 7 shows the temperature-dependent (22–300 K) resistivity and free electron concentration of Si-doped β-Ga₂O₃ single crystals having different n_e values at RT (measured by Hall effect with the use of a closed-cycle refrigerator cryostat). For very low Si doping level, resulting in n_e = 5 × 10¹⁷ cm⁻³ at RT, the relation is typical for normal semiconductors. For higher Si doping level and n_e = 5 × 10¹⁸ cm⁻³ at RT, the behavior is typical for degenerate semiconductors, as both the resistivity and n_e are basically temperature independent (metallic-like conductivity). Between these n_e values, i.e., for n_e = 2.2 and 3.5  × 10¹⁸ cm⁻³ at RT (Fig. 7), we can observe a very weak dependence indicating a semiconductor–metal transition region (Mott transition), which match previously reported values (n_e = 3–5 × 10¹⁸ cm⁻³) for β-Ga₂O_3.^74,75

Similar relations, but for a temperature range of 300–600 K, are shown in Fig. 8 (measured by Hall effect with the use of an oven module). In each case, the resistivity (ρ) increases by a factor of about 2 at 600 K [Fig. 8(a)]. As can be seen in Fig. 8(b), there is only a minor increase in the free electron concentration (n_e) as basically all shallow donors had been ionized at around RT. At higher temperatures, deeper electron traps are being depopulated and release electrons that contribute to the electrical conductivity. The factor that increases the resistivity above RT is a decrease in the Hall electron mobility (μ_e), also by a factor of about 2 $(ρ∼1neμe)$⁠. This is due to a higher amplitude of lattice vibrations, which enhance scattering of the free electrons at phonons. The scattering is higher at higher free electron concentration, which is well visible in Fig. 8(b) for two samples with the highest n_e values (3.5 and 5 × 10¹⁸ cm⁻³). Such factor of resistivity increase in β-Ga₂O₃ is typical for metals in the same temperature range.

Two inch diameter bulk β-Ga₂O₃ single crystals of high electrical conductivity, achieved by Si-doping, were grown by the Czochralski method. Crystal samples showed high structural quality (FWHM of the rocking curve ≤ 25 arc sec) and good surface smoothness (RMS < 200 pm) after polishing and surface treatment. The free electron concentration, Hall mobility, and resistivity at RT were in the range of 1.6–9 × 10¹⁸ cm⁻³, 118 – 52 cm² V⁻¹ s⁻¹, and 4 – 1 × 10⁻² Ω cm, respectively. The electrical properties are not affected by a heat treatment in the presence of oxygen at temperatures up to 1000 °C. Highly conducting crystals revealed a degenerated semiconducting state, as concluded from temperature-dependent electrical properties. High temperature electrical properties revealed an increase in the resistivity by a factor of two at 600 K. Both the structural quality and electrical properties make the crystals well suited as substrates for homoepitaxy and electronic device fabrication in the vertical configuration.

This work was funded by the Bundesministerium für Bildung und Forschung (BMBF) project under Grant No. 16ES1084K. It was partly performed in the framework of GraFOx, a Leibniz-Science Campus partially funded by the Leibniz Association—Germany. The authors express their gratitude to Dr. Frank M. Kießling from the Leibniz-Institut für Kristallzüchtung (IKZ) for critical reading of the manuscript. Thomas Wurche, Dr. Uta Juda, and Manuela Imming-Friedland (IKZ) are acknowledged for preparation of some of the crystal samples used in this study.