High-Quality and Wafer-Scale Cubic Silicon Carbide Single Crystals

2.1 Considerations on Stabilizing and Growth of 3C- over 4H-SiC

We start off our exploration of growing 3C-SiC single crystals by employing the TSSG technique. Our strategy is based on two primary considerations. First, the interfacial energy between SiC and melts can be more easily adjusted through altering their chemical compositions in TSSG in comparison to PVT, in which only the interface between SiC and gaseous phase exists. Liquid phases are generally thought to be has a more significant effect in changing the interfacial energy than gaseous phases do.^[29] It is possible to achieve a lower enough interfacial energy for 3C- over 4H-SiC, which will prioritize the nucleation and subsequent growth for former, and suppress that for the latter. Second, 4H-SiC crystals larger than 4-inch have been successfully obtained by TSSG at 1700–1800 °C.^[30] In this study, we demonstrate that our strategy works well and bulky 3C-SiC crystals up to 4-inch in diameter and more than 4.0 mm in thickness are successfully grown.

Figure 1a shows the schematic setup for growing 3C-SiC by TSSG. Crucibles made from high-purity graphite serve as both container and carbon source. Inside the crucible, a melt temperature gradient is set as 5–15 °C cm⁻¹ with a temperature of top melt at about 1850 °C by induction heating. The melt is usually composed of Cr, Ce, and Si, which become a liquid above 1680 °C (Figure S1, Supporting Information) and act as a flux having a solubility of C depending on temperature and composition. Three basic steps are involved in the growth process: 1) the flux dissolves the crucible bottom and 10–15 at. % C enter the flux;^[30] 2) thermal conventions convey these C atoms from the bottom to top; and 3) the C and Si atoms combine and crystallize onto the seed as SiC crystal where the temperature is several to a dozen of degrees lower, see Figure 1b. The stable growth of SiC crystal requires the C flow is at equilibrium among these three steps. In a typical run, we use commercial semi-insulating 4H-SiC (0001) wafers as seed crystals, and the growth is performed under a mixed Ar/N₂ gas.

It is reasonable to assume that σ_4Hside ≈ σ_3Cside because these lateral surfaces form from stacking Si-C bilayers in a similar spacing but in a different sequence, their surface energies will approach equal if averaging the fluctuations of interactions at a macro-scale. σ_3C/4H ≈ 0 is a reasonable assumption because of the negligible lattice mismatch between 4H-(0001) and 3C-(111). Therefore, the ΔG_hetero is always smaller than the ΔG_homo if the σ_3C/Melt − σ_4H/Melt < 0. This means that nucleation and crystal growth are favored for 3C- than for 4H- if the difference between ΔG_homo − ΔG_hetero is large enough. It is expected that 3C- nucleation easily occurs on 4H- substrate and its step flow is faster than that for 4H-, leading to the total coverage of 3C- on 4H- substrate. Then, the growth of 3C- will proceed steadily. Figure 1c schematically describes the possible route for the phase transition starting from preferential hetero-nucleation to subsequent growth for 3C-SiC single crystal on the condition that it has a lower enough interfacial energy with melts. In this study, it is found that the σ_3C/Melt − σ_4H/Melt is negative enough when N₂ partial pressures ($p_{{\mathrm{N}}_2}$) above the melt is over 15 kPa, justifying the above arguments and expectations. Figure 1d–f and Figure S2a,b, Supporting Information show the photographs for 2–4-inch 3C-SiC crystal boules grown under $p_{{\mathrm{N}}_2}$ of 20 kPa, respectively. The thickness varies between 4.0 and 10.0 mm in an 84 h-long growth duration (Table 1). The growth rate is about 50–113 μm h⁻¹, a little bit lower than 150 μm h⁻¹ for the PVT method.^[21] The 1 mm thick wafers are black in color (Figure S2, Supporting Information) because of high carrier density introduced by N-doping. It is green color under strong light (Figure 1g).^[31]

2.2 Properties and Defect Study of 3C-SiC

Raman scattering measurements are performed on a total of 20 sites across the entire wafer surface. All spectra are nearly the same, only the peak at 796 cm⁻¹ is present (Figure 2a,b). The peak is assigned to be the 3C-SiC's transversal optical mode (TO).^[32-34] Another characteristic mode, the longitudinal optical one (located at 975 cm⁻¹), which is dependent on the carrier density, does not appear. No folded transverse optical modes at 776 and 707 cm⁻¹ for 4H- and 6H-SiC are observed.^{[34, 35]} A small peak (marked by an arrow) at 741 cm⁻¹ are probably due to the stacking faults or stress.^{[32, 33]} To obtain the information on the evolution of the transition from 4H to 3C, we conduct the Raman scattering measurements on a cross section of the grown boule and the results are shown in Figure 2b and Figure S3, Supporting Information. It is clearly seen that the 3C occurs immediately at the upper surface of the seed, following a transition zone (TZ) about 20 μm consisting of both 3C and 4H. The single phase of 3C is maintained throughout the boule. The observation of photoluminescence (PL) at 523 nm (Figure 2c) corresponds well to the bandgap of 2.36 eV, further confirming the 3C polytype.

The boule surface is quite flat, but growth steps of 9–22 nm are clearly seen (Figure S4, Supporting Information). Single crystal and powder X-ray diffraction results on small grains cracked from the boule confirm the polytype is 3C with refined lattice parameter a = 4.3563(4) Å (Figure S5, Tables S1 and S2, Supporting Information), similar to the previously reported results.^[8] Plan-view high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) taken on a spherical aberration TEM (Figure 2d) clearly identifies Si and C atoms arrayed in a manner of ABC sequence. The selected area diffraction pattern shown in inset of Figure 2d along $\left[1\overline{1}0\right]$ zone axis (Z.A.) is well indexed based on a space group of F-43m. Electron energy loss spectrum (EELS) mapping results (Figure S6, Supporting Information) indicate the homogeneous distribution of C and Si at a nanoscale level. Energy dispersive spectroscopy (EDS) mapping results also indicate the homogeneous distribution of Si, C, and N (Figure S7, Supporting Information).

The crystal grows by stacking of (111) crystallographic planes as only diffraction peaks (111) and (222) are present in the θ-2θ scan on the surface of the grown boule, see Figure 3a. To assess the crystallinity of the wafer, we perform the X-ray rocking curve (XRC) measurements. The full width at half maximum (FWHM) for as-grown (111) surface (Figure 3b) ranges from 28.8 to 32.4 arcsec with an average value of 30.0 arcsec (Table 1). The FWHM is very homogeneous across the whole wafer, indicating the high uniformity of 3C-SiC. To our best knowledge, the values stand for the best results on wafers larger than 2-inch obtained so far (Table S3, Supporting Information). Defects are characterized on the wafer after being etched at 500 °C for 10 min in KOH melt. Linear ridges, triangle pits, and rounded-triangle pits are clearly seen on Si-terminated surface under an optical microscope (OM) and a scanning electron microscope (SEM) (Figure 3c–f). The ridges from dozens to more than 100 μm in length are due to the stacking fault (SF) (Figure 3c,f, Figure S8, Supporting Information), a common defect in 3C-SiC.^{[9, 24, 36, 37]} The thickness of typical SFs revealed by the bright-field and dark-field TEM images (Figure 3g,h) is three layers of (111) planes. Its density, defined by the total length of all SFs divided by the observed area, is averaged to be 92.2 cm⁻¹ (Table 1, Figure S9, Supporting Information), much less than what is previously reported (Table S4, Supporting Information). Our results are in good agreement with the reported results that N-doping can substantially increase the SFs length.^[38] In addition, the SFs, seen from a slice of 3C-SiC, are delimited by two triangle pits or two rounded-triangle pits (Figure S10, Supporting Information). The typical triangle pits are ~5 μm in size, probably originating from thread screw dislocations (TSDs) (Figure 3c,d). The rounded-triangle pits, a little bit smaller in size, are from thread edge dislocations (TEDs) (Figure 3c,e, Figure S9, Supporting Information).^{[36, 37, 39-41]} They are about 4.3 × 10⁴ cm⁻² and 13.9 × 10⁴ cm⁻² in density, respectively (Figure S9, Supporting Information). No double-positioning boundaries (DPBs), which are quite common in 3C-SiC,^{[23, 26, 42-44]} are observed in our 3C-SiC wafers.

The electrical characterizations are conducted on a slab crystal cut from the grown boules. Electrical resistivity, carrier density, and mobility are measured by the standard six-wire method (Figure S11, Supporting Information). Figure S12a, Supporting Information shows the variations of electrical resistivity with temperature from 5 to 300 K. We can see that the samples grown under $p_{{\mathrm{N}}_2}$ of 15 and 20 kPa exhibit a metallic character. The resistivity decreases with lowering temperature, suggesting the 3C-SiC should become a semi-metal with a room-temperature resistivity of 0.58 mΩ·cm (Table 1, Tables S5 and S6, Supporting Information), much lower than 4H-SiC's (15–28 mΩ·cm) (Table S8, Supporting Information).^[45] We note that the crystal grown with $p_{{\mathrm{N}}_2}$ of 10 kPa behaves like a semiconductor below about 100 K (Figure S12a, Supporting Information). The carrier density for the 20 kPa sample is calculated to be 1.89 × 10²⁰ cm⁻³ (Figure S12b, Table S5, Supporting Information), in good agreement with the doping concentration of N (1.99 × 10²⁰ cm⁻³) measured by secondary ion mass spectroscopy (SIMS) (Figure S13, Supporting Information). It demonstrates that almost all of the doped electrons are activated to the conduction band at room temperature. The calculated mobility ranges from 56.95 to 62.66 cm² (V·s)⁻¹ (Table S5, Supporting Information). The mobility is enhanced to be 66.24 cm² (V·s)⁻¹ when the carrier density is lowered (Figure S12c, Tables S5–S7, Supporting Information), meanwhile the resistivity mounts up to 5.77 mΩ·cm, about one fourth of 4H-SiC's (15–28 mΩ·cm) at room temperature,^[45] which is much lower than the reported results (Table S8, Supporting Information). In this case, the PL at about 523 nm due to the band-edges transition is observed, as stated above, see Figure 2c.

2.3 Growth Mechanism for 3C-SiC

It is easily obtained that the interfacial energies for 3C and 4H are σ_3C/Melt 4 = 2151.11 ± 21.90 mN m⁻¹ and σ_4H/Melt 4 = 2390.89 ± 19.50 mN m⁻¹ (Table S9, Supporting Information), where σ_SiC is estimated from the results by Ramakers et al.^[28] Figure 4d shows the variations of melt surface tension, the contact angles of melt on substrates and the calculated interfacial energy between the melt and 3C-(111) and 4H-(0001) single crystals based on Young's equation with $p_{{\mathrm{N}}_2}$ measured for many times (Figures S14 and S15, Supporting Information). The melt's surface tension decreases as increasing $p_{{\mathrm{N}}_2}$, which can be attributed to the dissolved N in the melt (Figure S16, Supporting Information). We can see that interfacial energy between the melt and 3C-(111) is lower than that for 4H-(0001), and their difference widens with the increasing $p_{{\mathrm{N}}_2}$. Our results indicate that other polytype inclusions are present when the $p_{{\mathrm{N}}_2}$ is below 15 kPa. Optimal pressures of $p_{{\mathrm{N}}_2}$ above 15 kPa are required to stabilize the 3C polytype during the growth. We then regrow the crystal on a 3C-SiC seed using the same compositions of flux under 20 kPa N₂ again. Raman scattering measurements confirm the 3C polytype (Figure S17, Supporting Information).