Surface Morphology of 6-Inch SiC Single Crystals in Solution Growth on Si-Face, C-Face and ($10\overline{1}\overline{2}$) Plane

Abstract

For solution growth of 6-inch 4H-SiC bulk crystals, the surface step morphology of the crystals grown on Si-face, C-face and ($10\overline{1}\overline{2}$) plane was systematically characterized by laser confocal microscopy. The 2D-nucleation and step-bunching were likely to occur during the 30 h growth on Si-face, leading to a rough surface with a macro-step height over 60 μm. By contrast, the step heights were maintained at 0.1–1 μm during 60 h growth on C-face, exhibiting good morphological stability for long-term growth. Moreover, the SiC crystal grown on the ($10\overline{1}\overline{2}$) plane illustrated its excellence in producing fine steps, which is attributed to the smaller interfacial energy between the solution and ($10\overline{1}\overline{2}$) substrates, suggesting that it offers a better approach to growing SiC single bulk crystals.

1. Introduction

Silicon carbide (SiC) is promising for producing power devices due to its advantageous properties such as its wide band gap and high breakdown voltage. To elicit the intrinsic capabilities of SiC power devices, as well as to produce them at low cost for a wide range of uses for industries, high-quality SiC single crystals with a large diameter are required [1]. Common polytypes of SiC include 3C, 4H, 6H, and 15R, where C denotes the cubic crystal system, H the hexagonal crystal system, and R the rhombohedral crystal system. For 4H-SiC, the stacking sequence of the diatomic carbon-silicon layers can be described as ABCB or ABAC. Commercial production of 4H-SiC bulk crystals has been widely carried out utilizing the sublimation method (PVT, physical vapor transport). However, P-type SiC wafers have not yet widely achieved the adoption of SiC-IGBT (Insulated Gate Bipolar Transistor) power devices, due to the high costs compared to Si-IGBT devices. Additionally, high density of defects (in the order of 10³/cm²) such as threading screw dislocations (TSDs), threading edge dislocations (TEDs) and basal plane dislocations (BPDs) are frequently found via high-temperature sublimation (2200–2400 °C). Also, it is challengeable for PVT to produce P-type SiC crystals, since Al is prone to sublimate at the early stage of the growth. To overcome these drawbacks, top-seeded solution growth (TSSG) has attracted significant attention as a candidate for producing high-quality, low-cost SiC bulk crystals. Solution growth allows SiC crystals to grow at lower temperatures (1600–1900 °C) and under conditions close to the thermal equilibrium state. Al is melted homogenously in the solution, which is conducive to high Al concentration and low resistivity of P-type SiC crystals. In addition, the TSDs are frequently converted to BPDs at the initial stage in solution growth, so the TSD density remarkably decreased as the growth progressed, achieving crystals with ultra-low dislocation density [2]. In addition, like the RAF method [3], threading dislocations can also be drastically decreased by the solution growth on ($1\overline{1}00$) (m-face), since the threading dislocation line and growth direction are mutually orthogonal [4].

Compared to linear defects, body defects like solvent inclusions represent serious deterioration to the crystal quality, which typically links to kinetic step bunching during epitaxial growth of semiconductor thin films because of asymmetric diffusion of adatoms across a step, forming a hill-and-valley surface morphology [5]. Severe step bunching during crystal growth typically results in macro-steps with a height of several hundred nanometers, which often evolve into bunched steps with heights ranging from several to tens of micrometers. These macro-steps change into trench-like defects, leading to surface roughening and causing solvent inclusion or the generation of parasitic polytypes. Therefore, to obtain high-quality SiC single crystals, it is necessary to maintain a smooth and stable growth interface during the growth process to achieve a lower growth step height. Hence, it is realized that the crystal quality can be judged by surface morphology of SiC crystals grown by solution methods, and smooth growth interface is the prerequisite for stable solution growth.

Doping aluminum into the solution has proven to be effective for reducing the step stiffness and slope of the steps [6], resulting in a smooth surface morphology, since the addition of aluminum can reduce the viscosity of the melt and decrease the solid–liquid interfacial energy between the solution and the SiC [7]. Besides elemental doping, step-height reduction can be realized by convection control [8]. It is pointed out that the smooth surface can be achieved when solution flow is anti-parallel to step-flow direction. However, it is difficult to apply the unidirectional flow in an axisymmetric TSSG set-up. Umezaki et al. [9] shifted the rotational axis away from the center of the seed crystal, expanding the smooth area where the solution flow direction was opposite to the step-flow direction. Daikoku et al. [10] developed solution growth on concave surfaces (SGCS) under conditions in which the solution flow is directed from the center to the periphery, obtaining 43.2 mm-diameter wafers without solvent inclusions. Zhu et al. [11] deviated the seeds by 30 mm from the center of the crucible and kept the graphite rod fixed and only rotating around the crucible, forming a unidirectional flow. Nakanishi et al. [12] explained the micro mechanism of macro-steps interaction. The computational fluid dynamics (CFD) results showed that instability occurs in the no solution flow and parallel solution flow cases, while stabilization occurs in the anti-parallel solution flow case.

To determine the probability of 4H-SiC replication, Daikoku et al. [13] compared the surface roughness differences between 50 mm-diameter SiC crystals grown on the C-face and {$1\overline{1}0\mathrm{m}$} planes (m = 0 to −4). The results indicated that the roughness of the {$1\overline{1}0\mathrm{m}$} planes was consistently higher than that of the C-face after long-term growth. However, the experimental results obtained by Mitani et al. [14] showed that {$1\overline{1}0\mathrm{m}$} (m = 1 and 2) planes provided smaller step height compared to C-face plane in relatively short growth period. In our unreported work, we observed that even when C-face-grown crystals contain many trench defects and solvent inclusions, the {$1\overline{1}02$} plane remains smooth. Therefore, further studies are important to clarify the distinct surface morphologies of various growth planes.

Moreover, the cost of SiC wafers can be remarkably reduced by enlarging the diameter of wafers. Daikoku et al. [15] enlarged a SiC crystal from a diameter of 12 mm to 27 mm. Danno et al. [16] expanded grown crystal diameters to approximately 15 mm from 4.5 mm seed crystal since the meniscus height was kept low during growth. However, the investigations were rarely reported on the field of 6-inch (150 mm-diameter) SiC bulk solution growth.

In this study, we systematically discussed the surface morphologies of 6-inch SiC crystals grown on Si-face, C-face and ($10\overline{1}\overline{2}$) planes. We found that ($10\overline{1}\overline{2}$) facet growth was more effective to keep step height and width low, maintaining a smooth surface morphology during solution growth.

2. Numerical and Experimental Methods

As shown in Figure 1, solution growth of SiC was performed in a top-seeded solution growth (TSSG) apparatus in argon atmosphere. The 6-inch (150 mm-diameter) substrates of on-axis (semi-insulating) and ($10\overline{1}\overline{2}$)-faceted 4H-SiC were employed as the seed crystals in this work. For investigating the influence of different growth planes on surface morphologies, we grew ($10\overline{1}\overline{2}$) and the on-axis seed with the same process parameters, except for the growth period. The rotation rates of the seed and crucible were controlled at 150 (clockwise) and −20 rpm (counterclockwise), respectively. Si-Cr-Al mixture was melted in the graphite crucible at 50 kPa. The temperature at seed crystals was kept at 1820 °C during growth, which was measured by a FLUKE infrared thermometer. The height of the solution is 25 mm, since short melt heights are conducive to eliminate interfacial instability [17]. For the ($10\overline{1}\overline{2}$) facet growth, the growth period was 30 h, while for the on-axis growth, the growth periods were 30 and 60 h, respectively.

After obtaining the SiC grown crystals, the surface morphologies were investigated using laser confocal microscopy (LSM 900, Carl Zeiss AG, Oberkochen, Germany). The Bragg angle and rocking curve measurement of grown crystal were analyzed by X-ray diffraction (D8 Discover, Bruker, Germany). SiC polytypes were confirmed by a confocal Raman and harmonic imaging system (alpha 300R, WITec Wissenschaftliche Instrumente und Technologie GmbH, Ulm, Germany). The carrier mobility and resistivity were obtained by the Hall test (8404, Lake shore Cryotronice, Westerville, OH, USA). The contact angles between highly pure melt droplet and on-axis and ($10\overline{1}\overline{2}$) substrate were measured by a high-temperature contact angle meter (OCA25-HTV1800, Dataphysics Imaging GmbH, Stuttgart, Germany).

3. Results and Discussion

3.1. Influence of Si-Face and C-Face on Surface Morphology of On-Axis Grown SiC

The crystal quality can be judged by surface morphology of SiC crystals grown by solution methods. The trench-like defects or giant steps on the surface directly leads to macro-inclusions, which are fatal for the electrical conductivity of SiC compared to any other defects (micro-pipes, dislocations, or stacking faults). Such a phenomenon is common in large-size SiC ingot grown by the solution method, and it is still challenging to thoroughly eliminate. Therefore, a smooth growth interface is the prerequisite for stable solution growth. To further reduce the step height and width, we used on-axis substrates as seed crystals. Figure 2 illustrates the surface morphologies of on-axis crystals grown on the Si-face and C-face. Growth on the C-face tends to induce spontaneous nucleation (Figure 2a), resulting in the formation of hillock-like structures on the crystal surface. In contrast, crystals grown on the Si-face produce a smoother surface (Figure 2b–d).

Figure 3a shows the formation of two-dimensional nucleation steps during growth on the Si-face. Atoms must overcome free energy barriers to achieve layer-by-layer growth on the large surface, forming circular or hexagonal hillocks. The polytype transition frequently occurred when hillock grew adjacent to other hillocks [18]. The polytype transition Raman spectroscopy measurements indicated that the polytype of the hillocks was 6H-SiC. The hillocks were the origins of trench defects [19]. As shown in Figure 3b,h, during on-axis growth, the spiral center supplied fine steps continuously. As growth proceeded, the step density at the growth interface gradually decreased with increasing step height (Figure 3c,i). As shown in Figure 3d–f,j–l, the steps grown on the C-face are very fine, since the Si-face has a larger Ehrlich Schwoebel energy barrier compared to the C-face [20]. In addition, the contact angles between pure Si melt and the Si-face or C-face of a 4H-SiC at different temperature were measured by Syvajarvi et al. [21]. The results showed that the wetting angles on the C-face were higher compared to those on the Si-face, which related to a lower surface energy on the C-face. The surface energies of Si-face and C-face are 1800 and 750 erg/cm², respectively. The lower interfacial energy on the C face indicates that it is energetically more favorable to grow on the C face than on the Si face, provided growth proceeds via two-dimensional nucleation.

As shown in Figure 4, two-dimensional nucleation frequently occurs on the Si-face, and the step height and width are very small (H < 0.5 μm, W < 40 μm). For on-axis Si-face growth, the average height and width of steps are H ~3 μm and W ~40 μm, respectively. The step height decreases as the steps approach the spiral center. The macro-step height reaches 63 μm. By growing on the C-face, the step height and width are greatly reduced to 0.1–1 μm and 5–50 μm, respectively, demonstrating that on-axis SiC crystal growth on the C-face effectively improves the roughness of the growth interface.

3.2. 6-Inch SiC Single Crystals Grown on ($10\overline{1}\overline{2}$) Face

As shown in Figure 5, when growing a 4H-SiC bulk crystal on C-face direction, crystals are likely to exhibit hexagonal shapes, with the formation of ($\overline{1}10\overline{2}$), ($01\overline{1}\overline{2}$), ($10\overline{1}\overline{2}$), ($1\overline{1}0\overline{2}$), ($0\overline{1}1\overline{2}$), and ($\overline{1}01\overline{2}$) planes. This is because, by adding Al in the solution, the anisotropic solution-SiC interfacial energy on the growth face and side face leads to a hexagonal shape. Additionally, in our experimental works, we found that {$1\overline{1}02$} planes are much smoother than C-face, even when the crystals grown on the C-face contained many trench defects and solvent inclusions. Thus, we attempted to grow SiC crystals on {$1\overline{1}02$} planes.

We used several pieces of rectangular ($10\overline{1}\overline{2}$) seed crystals to splice them together, then grind them into 6-inch circular ($10\overline{1}\overline{2}$) seed crystals. Hereafter, 4H-SiC was grown at 1820 °C using the TSSG method, as shown in Figure 6a. The white spherical material is the droplets remaining after the solution is separated from the crystal, with solvent vapor volatilization attached to the surface due to the long-term annealing. In addition, the white substance on the six corners of the crystal is the solution left on the surface of the crystal. Because the seed crystal was directly bonded to a SiC ingot with a thickness of 5 mm, this ingot was then bonded to a graphite holder. So, during the growth process, this SiC ingot made contact with the solution and started to grow, forming a different plane to the ($10\overline{1}\overline{2}$) crystal, with some solution left at the junction of the two. According to laser confocal microscopy results, the ($10\overline{1}\overline{2}$) grown crystals present smooth macroscopic surfaces (Figure 6b,c) with fine steps (only a few tens of nanometers, see Figure 6d). The stable growth on the ($10\overline{1}\overline{2}$) surface is attributed to the fact that the growth mode on this surface is adhesive growth, instead of the step-flow growth on the C surface. In addition, the solid–liquid interfacial energy for growth on the ($10\overline{1}\overline{2}$) face is also a factor that affects the step-stable growth, as will be mentioned later.

The XRD patterns shown in Figure 7a,d indicate that the crystal structure of the layer grown corresponded to C-face and ($10\overline{1}\overline{2}$) grown crystals. The two main peaks of 4H-SiC were observed at the (0004) plane (2θ = 35.7°) and (0008) plane (2θ = 75.4°), while 2θ of the ($10\overline{1}\overline{2}$) grown crystal features at 38.2°. The rocking curves of the grown crystals by C-face and ($10\overline{1}\overline{2}$) were collectively shown in Figure 7e. The full-width half maximum (FWHM) value of the grown crystal on ($10\overline{1}\overline{2}$) plane (71 arcsec) was half of that on C-face (144 arcsec), and this suggested that the crystal grown on the ($10\overline{1}\overline{2}$) plane was better than the crystal grown on the C-face from the crystallinity viewpoint. As seen in Figure 7c,f, the Raman spectra obtained from the grown crystal by LI exhibited transverse optical (TO) peaks at 776 cm⁻¹ and longitudinal optical (LO) peaks at approximately 964 cm⁻¹, suggesting that high 4H-polytype stability of C-face and ($10\overline{1}\overline{2}$) grown crystals.

First principles computations, such as those based on density functional theory (DFT) methods, are important complementary tools to experimental techniques in characterizing surface properties of a material [22]. To confirm the surface energy of SiC C-face and ($10\overline{1}\overline{2}$) plane, the minimal geometric repeat unit of the α-SiC unit cell was geometrically optimized using the CASTEP code [23]. As displayed in Figure 8, the C-face and ($10\overline{1}\overline{2}$) surfaces were cleaved, and supercells were constructed to simulate a larger system consisting of multiple atoms, which is close to the actual material structure, thus overcoming the limitations of a single unit cell. In addition, cleaving the C-face and ($10\overline{1}\overline{2}$) crystal planes and constructing a larger supercell around them can prevent interactions between adjacent surfaces. A vacuum layer of 15 Å was introduced to eliminate interference from periodic boundary conditions (PBC), followed by a subsequent CASTEP geometry optimization. After the geometry optimization, CASTEP energy calculations were performed on the α-SiC unit cell (E_bulk), as well as the C-face and ($10\overline{1}\overline{2}$) surfaces (E_slab), to obtain the final free energy. The surface energies of the C-face and ($10\overline{1}\overline{2}$) surfaces were then calculated using the following equation:

$${\mathrm{E}}_{surf}={\displaystyle \frac{{\mathrm{E}}_{slab}-\mathrm{n}{\mathrm{E}}_{bulk}}{2\mathrm{A}}}$$

(1)

where E_slab and E_bulk represent the total energy of the constructed slab model and the SiC bulk crystal, respectively, and A is the area of the slab model. The final calculated results are concluded in

Table 1. DFT calculation results of C-face and ($10\overline{1}\overline{2}$) plane.

	Eslab [eV]	Ebulk [eV]	n	$\mathbf{A}[{\mathbf{Å}}^2$]	${\mathbf{E}}_{\mathit{surf}}[\mathbf{eV}/{\mathbf{Å}}^2$]	Esurf [J/m2]
C-face	−5241.82	−1314.27	4	33	0.2313	3.7
($10\overline{1}\overline{2}$)	−5235.36	−1314.27	4	71	0.1539	2.5

.

The calculated surface energy of ($10\overline{1}\overline{2}$) surface is 2.5 J/m², which is smaller than that of the C-face (3.7 J/m²). This is because, on polar surfaces, the surface atoms expose more unsaturated bonds, which typically have higher energy. These surface atoms tend to form stronger chemical bonds or more stable structures, leading to higher surface energies for polar surfaces. In contrast, on non-polar surfaces, the atomic arrangement is more uniform, resulting in relatively lower surface energies.

The in situ observations for contact angles of pure Al and Si droplets on the 4H-SiC C-face and ($10\overline{1}\overline{2}$) seeds have been carried out to obtain the interfacial energy. As shown in Figure 9, pure Al and Si bulk were placed on the C-face and ($10\overline{1}\overline{2}$) substrates and melted to 1473 K and 1923 K in a single heating program. The wetting angle can be described as

$$\cos \mathsf{\theta }={\displaystyle \frac{{\sigma }_{SiC}-{\sigma }_{int}}{{\sigma }_{melt}}}$$

(2)

where ${\sigma }_{SiC}$ denotes surface energy of SiC seed, ${\sigma }_{melt}$ is the surface tension of the melt, and ${\sigma }_{int}$ is the interfacial energy between liquid droplet and SiC seed.

The surface tension of liquid pure Al and Si yields the following relationship [24,25]:

$${\sigma }_{\mathrm{pure}\mathrm{Al}}\left(\mathrm{T}\right)=\left\{916.30-\left(0.105\pm 0.015\right)\left(\mathrm{T}-933\right)\right\}\times {10}^{-3} ~\mathrm{N}/\mathrm{m}$$

(3)

$${\sigma }_{\mathrm{pure}\mathrm{Si}}\left(\mathrm{T}\right)=\left\{777-0.243\times \left(T-1687\right)\right\}\times {10}^{-3}~\mathrm{N}/\mathrm{m}$$

(4)

The surface tension of liquid pure Al at 1473 K and Si at 1923 K were estimated to be 0.8515 and 0.7113 N/m, respectively. In Figure 9a,b, the averaged contact angle between Al and C-face at 1073 K is 136.95°. With the increase of temperature, the averaged contact angle decreases to 63.65° at 1473 K. From Figure 9d,e, the averaged contact angles between pure Al droplet and ($10\overline{1}\overline{2}$) plane at 1073 K and 1473 K are 140.45° and 87.1°, respectively. As shown in Figure 9f, the averaged contact angles between pure Si droplet and C-face and ($10\overline{1}\overline{2}$) plane at 1923 K are 48.5° and 38°, respectively. Subsequently, the solid–liquid interfacial energy can be calculated in Equation (2) by referring to the DFT results in Table 1. The interfacial energy of pure Si on the C-face and ($10\overline{1}\overline{2}$) plane are 3.56 J/m² and 1.94 J/m² at 1923 K, indicating that it is more energetically favorable to grow on the ($10\overline{1}\overline{2}$) plane than on the C-face. Similarly, the interfacial energy of pure Al on the ($10\overline{1}\overline{2}$) surface is 2.46 J/m² at 1473 K, which is smaller than that on the C-face surface (3.32 J/m²). This interfacial energy anisotropy explains why Al addition produces a larger reduction in the surface roughness of the ($10\overline{1}\overline{2}$) than that of C-face [13], thus benefitting inclusion-free SiC crystals.

4. Conclusions

This work discusses the effects of Si-face, C-face, and ($10\overline{1}\overline{2}$) plane on step morphology of 6-inch SiC bulk crystals via solution growth. To further reduce step height, a comparison was made between the surface morphologies of on-axis SiC crystals grown on the Si-face and C-face. Finally, the use of the ($10\overline{1}\overline{2}$) facet for growing P-type SiC crystals is proposed.

Step advancement during on-axis growth is free of unidirectional step flow. Smooth surface was obtained on C-face. Hillocks induced by spontaneous nucleation Si-face may lead to polytypes and macro-steps, while the growth on C-face stabilizes homoepitaxy for 4H-SiC.

A 6-inch P-type SiC single crystal was grown using the ($10\overline{1}\overline{2}$) seed crystal, and the crystal surface exhibited nanoscale steps. Compared to crystals grown on the on-axis C-face, the crystals grown on the ($10\overline{1}\overline{2}$) plane exhibited lower FWHM values. Also, Al addition to the solvent contributed to stabilizing ($10\overline{1}\overline{2}$) facet formation since ($10\overline{1}\overline{2}$) seeds exhibit smaller interfacial energy with the pure Al melt compared to C-face seeds. The growth on the ($10\overline{1}\overline{2}$) plane facilitates the achievement of morphological stabilization, while also helping to reduce crystal defects and improve crystal quality.