1.
Introduction

Gallium oxide (Ga₂O₃) has five poly-types, namely, α, β, γ, δ, and ε. β-Ga₂O₃ is the most stable among them, belonging to the monoclinic crystal system^[1]. The band-gap energy (E_g) of β-Ga₂O₃ is about 4.8 eV as reported, which exceeds a lot of wide band-gap semiconductors such as silicon carbide (SiC) and gallium nitride (GaN)^[2]. Besides, β-Ga₂O₃ can be grown from a melt source, therefore, its growth rate is high^[3]. This means it has a lower production cost than other ultra-wide band-gap semiconductors such as aluminum nitride (AlN) and diamond (C), whose growth rates are relatively low because they can be grown from diluted vapor sources only.



β-Ga₂O₃ single crystals have been prepared by the Bernoulli process, floating zone (FZ) process, Czochralski (Cz) process and edge defined film-fed growth (EFG) method^{[3, 4]}. Compared with other methods, the EFG method reduces the area of the solid-liquid interface, which inhibits the volatilization of Ga₂O₃. In addition, the EFG method can be precisely controlled with a very high growth speed and the separation coefficient is close to 1^[1]. As reported, β-Ga₂O₃ single crystal can be used in UV optical detectors, Schottky barrier diodes, field-effect transistors and substrates for light-emitting diodes (LEDs)^[5–8]. Mostly, the properties of pure β-Ga₂O₃ cannot meet the requirements of the applications mentioned above, especially the electrical properties. Therefore, doping is necessary to obtain the ideal electrical properties such as resistivity, carrier concentration and so on. From the previous studies, it was found that the n-type carrier concentration and the absorption cut-off wavelength of β-Ga₂O₃ single crystals can be changed by using silicon (Si) or tin (Sn) as a dopant^[4]. However, so far the dopant effect on the electrical and optical properties has not been investigated systematically.



In this work, the growth of large scale high quality β-Ga₂O₃ single crystals by the EFG process was reported. The quality of the crystal was evaluated by the High-resolution X-ray diffraction (HRXRD). The surface roughness of the polished sample was measured by an atomic force microscope (AFM). Both the unintentionally doped and Si-doped β-Ga₂O₃ single crystals were characterized by Raman spectra. The electrical properties and optical properties of both the unintentionally doped and Si-doped β-Ga₂O₃ single crystals were investigated systematically.

2.
Experimental methods

β-Ga₂O₃ bulk crystals were grown by the EFG process. 6N-grade Ga₂O₃ powder was used as the raw material. Different content of silicon dioxide (SiO₂) powder was added to the Ga₂O₃powder in order to prepare Si-doped n-type crystals. The powder mixture was placed in an iridium (Ir) crucible with an Ir die in the center. The growth atmosphere was a mixture of 20% argon (Ar) and 80% carbon dioxide (CO₂) with a pressure of 1.5 atm. A radio-frequency (RF) induction coil was used as a heat source. When the temperature reached the melting point of Ga₂O₃, the melt moved to the surface of the Ir die through a slit in the die by the capillary effect. Then the β-Ga₂O₃ seed placed above the crucible was moved to the die to contact with the melt. The process of melting back the seed, which usually lasted for several minutes, is important for reducing dislocation density. The shape of the grown crystal with the EFG method is determined by the shape of the top surface of the die, which in this work is rectangular with dimensions of 4 × 51 mm². The growth direction and principal surface were the [010] direction and (100) plane of the β-Ga₂O₃ single crystal, respectively. The pulling rate was set to be 10 mm/h.



The grown β-Ga₂O₃ bulk crystals were processed to make a 2-inch wafer and four 10 × 10 × 1.5 mm³ samples for measurements. At first, the wafer and samples were made from the β-Ga₂O₃ bulk crystals by wire cutting. Then the wafer and all the samples were ground by diamond slurry and polished by chemically mechanical polishing. The number of samples and the corresponding nominal doping content of SiO₂ power are shown in Table 1.

Number of samples	Doping content of SiO2 power/100 g Ga2O3 power (mg)
Sample 1	0
Sample 2	0.5
Sample 3	4.0
Sample 4	15.0

Table1.
The number of samples and the corresponding doping content of SiO₂ power.



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Number of samples	Doping content of SiO2 power/100 g Ga2O3 power (mg)
Sample 1	0
Sample 2	0.5
Sample 3	4.0
Sample 4	15.0

The surface roughness of the samples was measured by AFM (Dimension Edge, Germany) and the mapping area was 10 × 10 μm². The twin boundaries and crystal quality were investigated using HRXRD (Delta-X, Germany) of the copper K_α1 line (λ = 1.54056 ?). A Ge monochromator was used for high-resolution measurement and the step size was 5 arcsec. Several points on per polished (100)-oriented sample, along and perpendicular to the growing direction were measured to guarantee the accuracy. A Raman spectrometer (LabRam HR800, French) was used to characterize the Raman spectra of the unintentionally doped and Si-doped β-Ga₂O₃ crystals. Transmittance and absorption of the samples from 200 to 2500 nm was studied by an ultraviolet visible near infrared photometer (Carry5000, USA). The Hall measurement system was used to investigate the electrical properties of β-Ga₂O₃ crystals. Ohmic contacts were prepared by evaporation of Ti (50 nm)/Au (200 nm) bilayer, which were located on the four corners of the samples.

3.
Results and discussion

3.1
Appearance of EFG-grown crystals and wafers

The typical dimensions of the EFG-grown β-Ga₂O₃ bulk crystals are 50–60 mm length, 50 mm width and 3–4 mm thickness. The crystals were cut perpendicular to the [010] direction to remove the seed. Fig. 1 shows the appearance of the as-grown unintentionally doped and Si-doped β-Ga₂O₃ single crystals. From the figure, the unintentionally doped β-Ga₂O₃ crystal is colorless. With the Si doping, the color of the crystal changes from colorless to blue. The intensity of such blue color increases with the Si content, which is in accordance with the previous research^[4]. The width and thickness of the crystal depends on the shape of the die top, and the grown length depends on the amount of raw powder put in the crucible. Fig. 2(a) shows the polished Si-doped β-Ga₂O₃ single crystal wafer. The wafer is made from the bulk crystal shown in Fig. 1 with a 2-inch diameter and (100) surface orientation. Fig. 2(a) clearly shows that the grown crystal has no cracks and no twin boundaries. The samples after the cutting and polishing process are shown in Fig. 2(b). The samples are 10 × 10 × 1.5 mm³ with (100) surface orientation.






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Figure1.
(Color online) The appearance of as-grown β-Ga₂O₃ single crystals. Sample 1 represents unintentionally doped β-Ga₂O₃ crystal and Sample 2 to Sample 4 represent Si-doped β-Ga₂O₃ single crystals with an increasing Si content.






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Figure2.
(Color online) (a) β-Ga₂O₃ wafer after polishing. (b) Polished β-Ga₂O₃ crystal samples cut from the bulk crystal.

3.2
Surface roughness

Fig. 3 shows the two-dimension surface morphologies for a 10 × 10 μm² scanned area of all the samples. The surface roughness of Samples 1–4 are 0.203, 0.085, 0.327 and 0.299 nm, respectively. Such low surface roughness indicates that process technology including cutting, grinding and polishing is excellent and it provides a base for the subsequent test eliminating the effect of surface quality.






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Figure3.
(Color online) The two-dimension surface morphologies of all the samples.

3.3
Crystal quality

The crystalline quality was evaluated by HRXRD. The measured data of full width at half maximum (FWMH) ranges from 19.06 to 46.0 arcsec. The FWMH of unintentionally doped β-Ga₂O₃ crystal is as low as 19.06 arcsec and the peak is symmetrical, as shown in Fig. 4. The results indicated a good crystalline quality without twinning and a low defect density, which is better than the quality from CZ grown β-Ga₂O₃^[9].






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Figure4.
Rocking curve of the polished unintentionally doped β-Ga₂O₃ crystal sample.

3.4
Raman spectra

Fig. 5 shows the Raman spectra of Sample 1 and Sample 4. The peaks showed up at 113.2, 145.1, 169.5, 199.6, 319.8, 346.1, 417.5, 475.8, 629.9, 659.9, 767.0 cm^?1 are sharp and narrow, indicating high crystal quality and they match very well to those observed in other references^{[10, 11]}. The Raman peaks can be divided into three parts: libration and translation of the Ga_IO₄ chains, deformation of the Ga_IO₄ and Ga_IIO₆, and stretching and bending of the Ga_IO₄^[12]. The position and shape of peaks detected in Sample 1 and Sample 4 are similar, but the intensity of peaks changes at 346.1, 659.9 and 767.0 cm^?1. The specific reason for the change is still unclear, which needs further research.






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Figure5.
(Color online) Raman spectra of EFG grown unintentionally doped and Si-doped β-Ga₂O₃ crystal.

3.5
Electrical properties

The electrical properties including resistivity, mobility, carrier concentration and conductive type of unintentionally doped β-Ga₂O₃ crystal and Si-doped β-Ga₂O₃ crystal were measured by the Hall measurement system. Table 2 shows the test results of all four samples. Both unintentionally doped β-Ga₂O₃ crystal and Si-doped β-Ga₂O₃ crystal present N-type conductivity, which means the major carrier is electrons. The donor exists whether the crystal is doped or not. For Sample1, nothing is doped intentionally so the carrier mainly depends on oxygen vacancies. Oxygen vacancies are generated in the growth process due to the decomposition of raw Ga₂O₃ at high temperature. Though the EFG process has reduced the area of the solid–liquid interface and the growth atmosphere has been optimized, the decomposition of raw Ga₂O₃ at high temperature cannot be eliminated completely. The carrier concentration of Sample 1 is 5.22 × 10¹⁶ cm^?3 in accordance with the reported concentration of oxygen vacancies^[13]. Si is known to act as a shallow donor in β-Ga₂O₃. With the increase of Si content, the resistivity decreases gradually and the carrier concentration increases accordingly, indicating that the changes in electrical properties of Sample 2, Sample 3 and Sample 4 are actually caused by Si doping. When the doped Si content reaches almost 70 ppm, the carrier concentration reaches up to 6.12 × 10¹⁸ cm^?3. According to the calculation, about 2 ppm Si corresponds to an atomic concentration of 2.5 × 10¹⁷ cm^?3 per unit volume. This means that the percentage of Si atoms which act as donors is higher than 70%. In previous studies, the Si⁴⁺ is assumed to evenly substitute Ga³⁺ in the two cationic sites, Ga₄ and Ga₆ (four- and six-fold coordination, respectively)^[14]. According to EPR, the donors are located in a four-fold symmetric site, and therefore, only half of the Si atoms (Si_Ga4) are potential donors^[14]. However, the results of this work cannot match the previous observation, indicating that Si may be doped in other forms except substitution. Besides, the mobilities of all samples are higher than 90 cm²/(V·s), indicating an excellent crystal quality in accordance with the results of HRXRD.

Sample	Resistivity (Ω·cm)	Mobility (cm2/(V·s))	Carrier concentration (cm?3)	Conductive type
Sample 1	1.10	109	5.22 × 1016	N
Sample 2	0.259	123	2.55 × 1017	N
Sample 3	0.042	96	1.71 × 1018	N
Sample 4	0.013	90	6.12 × 1018	N

Table2.
The Hall test results of EFG grown unintentionally doped and Si-doped β-Ga₂O₃ crystal.



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Sample	Resistivity (Ω·cm)	Mobility (cm2/(V·s))	Carrier concentration (cm?3)	Conductive type
Sample 1	1.10	109	5.22 × 1016	N
Sample 2	0.259	123	2.55 × 1017	N
Sample 3	0.042	96	1.71 × 1018	N
Sample 4	0.013	90	6.12 × 1018	N

3.6
Optical properties

Fig. 6(a) shows the transmittance spectra of as-grown β-Ga₂O₃ crystals obtained with a wide spectrum of free electron concentrations. The transmittance of Sample 1, a nominally unintentionally doped crystal, can be higher than 80% in the ultraviolet-visible region, and there is no obvious decrease even in the infrared region. With the increase of Si doping, the transmittance in the ultraviolet-visible region becomes lower and decreases sharply in the infrared region. Especially for Sample 4, when the wavelength is beyond 1500 nm, the transmittance almost decreases to zero. The decrease of transmittance in the infrared region is due to the absorption of free electron concentrations^[9]. Transmittance spectra at 250 to 400 nm are amplified in the inset of Fig. 6(b). All the curves have a shoulder at 270 to 280 nm corresponding to a specific energy level. The shoulder exists in both unintentionally doped and Si-doped β-Ga₂O₃ crystals so it may be caused by an intrinsic defect rather than a doping element. This phenomenon has been observed in many articles but no final conclusion has been made^[15]. Harwig et al.^[16] proposed the presence of a self-trapped hole (STH) level in β-Ga₂O₃, which is calculated to be about 0.25 eV above the top valence band. The electron is excited to the conduction band, and the hole is transited above the valence band maximum and trapped in a local electric field induced by small displacements of oxygen atoms to form STH^[2], and the transition of the electron causes the absorption at 270 to 280 nm. The present measurements support the above assumption.






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Figure6.
(Color online) Transmittance spectra of EFG grown unintentionally doped and Si-doped β-Ga₂O₃ crystal.




The absorption coefficient α and photon energy can be related by applying the Tauc model, and the Davis and Mott model in the absorbance region: αhν = A (hν – E_g)ⁿ, where A is a constant depending on the transition probability, hν is the photon energy, E_g is the optical band gap and n is equal to 1/2 for a direct gap while 2 for an indirect gap. It is generally thought that β-Ga₂O₃ crystal has a direct band gap^[15]. So the variation of absorption coefficient with photon energy should follow the above relation with n = 1/2. The band gaps of the crystals can be evaluated in the standard manner from a plot of (αhν)² as a function of the energy of the incident radiation and extrapolating the linear part of the curve to intercept the energy axis, as shown in Fig. 6(b). The band gaps of all samples are from 4.65 to 4.75 eV and become a little wider with the increase of Si doping as discovered by Takakura et al.^[17]. This phenomenon called the Burstein-Moss broadening effect may be due to the electrons provided by doped Si atoms occupying a part of energy levels located at the conduction band bottom^[18].

4.
Conclusion

β-Ga₂O₃ single crystals are successfully grown by the EFG method under a mixture atmosphere of 20% argon and 80% carbon dioxide. The FWHM of the rocking curve is only 19.06 arcsec, indicating the high crystalline quality of the EFG grown crystal. The best surface roughness is as low as 0.085 nm, suggesting an excellent process technology including cutting, grinding and polishing. Raman spectra of unintentionally doped and Si-doped β-Ga₂O₃ crystals show no obvious difference, which indicates that a small amount of Si doping has not affected the crystal structure. The carrier density, carrier mobility and electrical resistivity of unintentionally doped β-Ga₂O₃ crystal are measured to be 5.22 × 10¹⁶ cm^?3, 109 cm²/(V·s) and 1.10 Ω·cm, respectively. With the increase of Si content doped into β-Ga₂O₃ crystal, the resistivity decreases gradually and the carrier concentration increases accordingly. The transmittance of unintentionally doped crystal can be higher than 80% in the ultraviolet-visible region and has no obvious decrease even in the infrared region. The band gap of the unintentionally doped β-Ga₂O₃ crystal is about 4.68 eV and the band gaps become a little wider with the increase of Si doping. In conclusion, these data are necessary for future investigation of material and device design.