High quality and wafer-scale cubic silicon carbide single crystals

Silicon carbide (SiC) is an important semiconductor material for fabricating power electronic devices that exhibit higher switch frequency, lower energy loss and substantial reduction both in size and weight in comparison with its Si-based counterparts1-4. Currently, most devices, such as metal-oxide-semiconductor field effect transistors, which are core devices used in electric vehicles, photovoltaic industry and other applications, are fabricated on a hexagonal polytype 4H-SiC because of its commercial availability5. Cubic silicon carbide (3C-SiC), the only cubic polytype, has a moderate band gap of 2.36 eV at room-temperature, but a superior mobility and thermal conduction than 4H-SiC4,6-11. Moreover, the much lower concentration of interfacial traps between insulating oxide gate and 3C-SiC helps fabricate reliable and long-life devices7-10,12-14. The growth of 3C-SiC crystals, however, has remained a challenge up to now despite of decades-long efforts by researchers because of its easy transformation into other polytypes during growth15-19, limiting the 3C-SiC based devices. Here, we report that 3C-SiC can be made thermodynamically favored from nucleation to growth on a 4H-SiC substrate by top-seeded solution growth technique(TSSG), beyond what's expected by classic nucleation theory. This enables the steady growth of quality and large sized 3C-SiC crystals (2~4-inch in diameter and 4.0~10.0 mm in thickness) sustainable. Our findings broaden the mechanism of hetero-seed crystal growth and provide a feasible route to mass production of 3C-SiC crystals,offering new opportunities to develop power electronic devices potentially with better performances than those based on 4H-SiC.

SiC as a higher Si/C ratio in gas species is required.A modified method, close-space PVT, by which a high enough Si/C ratio can be created by separation of raw SiC powder and seed 1~2 mm, allows to grow 3C-SiC 22,23 .This is not a practical pathway to mass production considering the very limited thickness.In addition, early attempts to grow 3C-SiC from high temperature melts are not successful either on 6H-or 4H-SiC seeds because these two polytype inclusions always coexist along the grown 3C-SiC 18 .Alternatively, 3C-SiC films are directly deposited on Si substrate then further process into devices on it.But the large lattice mismatch (~19%) and thermal expansion mismatch (~8%) result in too high density of defects, significantly deteriorating the performances of devices 7 .Recently, a reduction in defects for 3C-crystals can be achieved by further PVT on a free-standing single crystal first prepared by chemical vapor deposition on Si substrates 24 .But the grown boules' thickness and the efficiency are still problematic towards mass production of wafers although in-situ switch between the two involved growth methods is feasible 25 .
Structurally, 3C-SiC differs from 4H-SiC in the stacking of identical Si-C bilayers 26 .In 3C-SiC, the bilayers are stacked as a crystallographic plane (111) in the sequence ABC 26 .In contrast, in 4H-SiC, the bilayers are stacked as a (0001) plane in the sequence ABCB 26 .The two stacking ways do not cause a significant difference in formation energy, typically a few meV per formula higher for 3C-SiC than for 4H-SiC at zero Kelvin 26 .At temperatures around 1727 ℃, the energy difference between 3C-SiC and 4H-SiC widens to about 5~10 meV per formula, enhancing the stability of 4H-SiC further.However, it is not clear why 3C-SiC is often found as inclusions in 4H-SiC films deposited at around 1650 ℃.Ramakers et al. 27 proposed that surface tension plays a crucial role in stabilizing 3C-SiC over 4H-SiC and 6H-SiC, as the former has surface tension that is 20~150 meV per SiC lower than the latter two.This also means that the 3C polytype may be energetically favored over a certain temperature range if surface tension contributes significantly to the change in the overall formation energy, which depends on different surface reconstruction configurations.

Considerations on stabilizing 3C-SiC over 4H-SiC and crystal growth
We start off our exploration of growing 3C-SiC single crystals by employing the TSSG.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 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.It is possible to achieve a lower enough interfacial energy for 3C polytype than for 4H, which will prioritize the nucleation and subsequent growth for former, and suppress that for the latter.Second, 4H-SiC crystals larger than 4-inch can be successfully obtained by TSSG at 1700~1800 ℃ 28 .In this work, 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.Fig. 1a shows the schematic setup for growing 3C-SiC by TSSG.Crucibles made from high purity graphite serve as container and carbon source.Inside the crucible, a temperature gradient is set as 5~15 ℃/cm with a temperature of top melt at about 1850 ℃ by induction heating.The melt is usually composed of Cr, Ce and Si, which become a liquid above 1680 ℃ (Supplementary Fig. 1) and act 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 into the melt 28 .2) thermal conventions convey these C atoms from the bottom to top and 3) the C and Si atoms will combine and crystallize onto the seed as SiC crystal where the temperature is several to a dozen of degrees lower, see Fig. 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 and the growth is performed under a mixed Ar/N2 gas.
For a typical vicinal (0001) surface, the Gibbs free energy change  ℎ = π 2 ℎ •  + 2πℎ •  4 , if a two-dimensional 4H-SiC nucleus with a radius of  forms on a 4H-SiC step terrace.In comparison, the change  ℎ = π 2 terrace, where  is the Gibbs free energy change from liquid to solid per volume,  4 ,  3 ,  4/ ,  3/ the interfacial energies between lateral surfaces, (0001), (111) facets to melts for 4H-and 3C-SiC, respectively;  3/4 the interfacial energy for (0001) and (111) crystallographic planes between the two polytypes, ℎ the height of the island.It is reasonable to assume that  4 ≈  3 because these lateral surfaces form from stacking Si-C bilayers in a similar spacing but in a different sequence, their interfacial energies will approach equal if averaging the fluctuations of interactions at a macro-scale. 3/4 ≈ 0 is a reasonable assumption because of the negligible lattice mismatch between 4H-(0001) and 3C-(111).Therefore, the  ℎ is always smaller than the  ℎ if the  3/ −  4H/ < 0. This means that nucleation and crystal growth are favored for 3C than for 4H if the difference between  ℎ −  ℎ is large enough.It is expected that nucleation easily occurs on 4H substrate and its step flow is faster than that for 4H, leading to the total coverage of 3C-SiC on 4H-SiC substrate.Then the growth of 3C will proceed steadily.Fig. 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  3/ −  4H/ is negative enough when N2 partial pressures (  2 ) above the melts is in the range of 15~20 kPa, justifying the above arguments and expectations.Fig. 1d-f and Supplementary Fig. 2 a, b show the photographs for 2~4-inch 3C-SiC crystal boules grown under   2 of 20 kPa, respectively.The thickness varies between 4.0~10.0mm in an 84 h-long growth duration (Table 1).The growth rate is about 50~113 μm/h, a little bit lower than 150 μm/h for the PVT method 20 .The 1 mm thick wafers are black in color (Supplementary Fig. 2c) because of high carrier density introduced by N-doping.It is green color under strong light (Fig. 1g) 29 .

Structural, defective and property characterizations
Raman scattering measurement are performed on total 20 sites across the entire wafer surface.
All spectra are nearly same, only the peaks at 796 cm -1 are present (Fig. 2a, b).The peak is assigned to be the 3C-SiC's transversal optical mode (TO) [30][31][32] .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 32,33 .A small peak (marked by an arrow) at 741 cm -1 are probably due to the stacking faults or stress 30,31 .To obtain the information on the evolution of the transition from 4H to 3C, we did the Raman scattering on a cross section of the grown boule and the results are shown in Fig. 2b and Supplementary Fig. 3.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.Then the single phase of 3C is maintained throughout the boule.The observation of photoluminescence (PL) at 523 nm (Fig. 2c) corresponds well to the bandgap of 2.36 eV, confirming the 3C polytype.
The boule surface is quite flat, but growth steps from 9~22 nm are clearly seen (Supplementary Fig. 4).Single crystal and powder X-ray diffraction on small grains cracked from the boule confirms the polytype is 3C with refined lattice parameter a = 4.3563(4) Å (Supplementary Fig. 5, Supplementary Tables 1 and 2), similar to the previously reported results 7 .Plan-view highangle annular dark field scanning transmission electron microscopy (HAADF-STEM) taken on a spherical aberration TEM (Fig. 2d) clearly identify Si and C atoms arrayed in a manner of ABC sequence and the selected area diffraction pattern in inset of Fig. 2d along [11 ̅ 0] zone axis (Z.A.) can be indexed based on a space group of F-43m.Electron energy loss spectrum (EELS) mapping results (Supplementary Fig. 6) 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 (Supplementary Fig. 7).
The crystal grows by stacking of (111) crystallographic planes as only the diffraction peaks (111) and ( 222) are present in the θ-2θ scan on the surface of the grown boule, see Fig. 3a.To assess the crystallinity of the wafer, we perform the X-ray rocking curve (XRC) measurement.
The full width at half maximum (FWHM) for as-grown (111) surface (Fig. 3b) ranges from 28.8 to 32.4 arcsec with an average of 30.0 arcsec (Table 1).The FWHM is very homogeneous across the whole wafer, indicating the high uniformity.To our best knowledge, this value stands for the best results on wafers larger than 2-inch obtained so far (Supplementary Table 3).Defects are characterized on the wafer after being etched at 500 ℃ for 10 min in KOH melt.
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 (Supplementary Fig. 11).Supplementary Fig. 12a shows the variations of electrical resistivity with temperature from 5 to 300 K. We can see that the samples grown under   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 0.58 mΩ•cm (Table 1, Supplementary Table 5 and 6), more than one-order lower than the 4H-SiC's (15~28 mΩ•cm) (Supplementary Table 8) 44 .We note that the crystal grown with   2 of 10 kPa behaves like a semiconductor below about 100 K (Supplementary Fig. 12a).The carrier density for the 20 kPa sample is calculated to be 1.89×10 20 /cm 3 (Supplementary Fig. 12b and Supplementary Table 5), in good agreement with the measured N concentration 1.99×10 20 /cm 3 by SIMS (Supplementary Fig. 13).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 cm 2 /V• s (Supplementary Table 5).The mobility can be enhanced to be 66.24 cm 2 /V• s when the carrier density is lowered (Supplementary Fig. 12c, Supplementary Tables 5 to 7), meanwhile the resistivity mounts up to 5.77 mΩ•cm, about one fourth of 4H-SiC's (15~28 mΩ•cm) at room temperature 44 , which is much lower than the reported results (Supplementary Table 8).In this case, the PL at about 523 nm due to the band-edges transition is observed, as state above, see Fig. 2c.

Measurements of surface tension and contact angles of melts to substrates
To justify our arguments that the interfacial energy plays an important role in growing 3C-SiC crystal, we measured the surface tension of melts and their contact angles with 3C-and 4H-SiC crystals at high temperatures and different   2 .Fig. 4a, b are the photographs of the liquid drop at 1850 ℃ under   2 of 20 kPa (Melt 4) on 3C-(111) and semi-insulating 4H-SiC (0001) crystals, respectively, indicating the contact angles are 40.38°± 0.64° and 45.55° ± 0.07°.The measured surface tension is   4 = 761.24± 27.83 mN/m at the same temperature (Fig. 4c and Supplementary Figs. 14 and 15).According to Young's equation  / 4 =   −   4 cos , it is easily obtained that the interfacial energies for 3C and 4H are  3/ 4 = 2151.11± 21.90 mN/m and  4/ 4 = 2390.89± 19.50 mN/m (Supplementary Table 9), where σ SiC is estimated from the results in Ref. 27. Fig. 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) of single crystals based on Young's equation with   2 measured for many times (Supplementary Figs. 14 and 15).The melt's surface tension decreases as increasing   2 , which can be attributed to the dissolved N in the melt (Supplementary Fig. 16).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   2 .Our results indicate that other polytype inclusions are present when the   2 is below 10 kPa.Optimal pressures of   2 ranging from 15 to 20 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 (Supplementary Fig. 17).
The results presented here demonstrate that bulk 3C-SiC crystals can be grown through changing the interfacial energy of melt.More importantly, this TSSG route provides a reliable method to grow high-quality wafer-scale 3C-SiC, exhibiting the potential for further mass production.Thus-grown crystals are very suitable used as substrates for homogeneous epitaxy and device fabrication in terms of high-crystallinity, high conductivity and availability.Better homoepitaxy 3C films and the power devices are expected to be fabricated, and thus boost the SiC industry further.Alteration of interfacial energy reported here could be applied to other layered materials to obtain the single crystals that otherwise are difficulty to grow.

Fig. 1 |
Fig. 1 | TSSG growth of 3C-SiC single crystals.a, Schematic of the setup for growing 3C-SiC by TSSG.b, Schematic of three basic growth processes for TSSG: 1. Dissolving C from the graphite crucible at high temperature region, 2. Transportation of C from the high temperature region to the low temperature driven by the convection, 3. Crystallization of SiC on the low temperature seed crystal.c, Proposed growth model of 3C-SiC on a 4H-SiC seed via TSSG.d-f, Photographs of 2-, 3-inch 3C-SiC boule after rounded cutting process and asgrown 4-inch 3C-SiC boule.The thickness of the 2~4-inch 3C-SiC boule is above 4.0 mm.g, Photograph of 3C-SiC single crystal wafer.

Fig. 2 |
Fig. 2 | Identification and confirmation of 3C-SiC polytype for as-grown crystals.a, Raman spectra of 3C-SiC measured on 20 points on the 2-inch crystal.The inset shows the distribution of all measured points.b, Raman spectra of seed 4H-SiC, TZ (transition zone) and grown 3C-SiC.c, PL spectrum of 3C-SiC measured at 300 K. d, Plan-view high-angle annular dark field scanning TEM (HAADF-STEM) image of 3C-SiC.Si and C atoms are superimposed.Inset is SAED measured along [11 ̅ 0] Z.A. (zone axis).

Fig. 3 |
Fig. 3 | Characterizing the crystallinity and defects of 3C-SiC wafer.a, X-ray diffraction (XRD) spectrum for 3C-SiC wafer, showing the growing surface is (111) plane.b, X-ray rocking curve (XRC) of (111) plane, and the FWHM ranges from 28.8 to 32.4 arcsec.The inset shows the distribution of 9 measured points.c-f, OM (Optical microscope) images for 3C-SiC wafer after etch at 500 ℃ for 10 min in KOH melt, revealing the existence of SF (stacking fault), TSDs (threading screw dislocations), and TEDs (threading edge dislocations) defects in the 3C-SiC wafers.g, h HAADF-STEM images of a SF composed of three layers of SiC.