Conformational Stability of 4H-SiC in Dual Dimensions: From Microscopic Thermodynamics to Macroscopic Mechanical Properties +

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4H-silicon carbide (4H-SiC), as a representative wide-bandgap semiconductor material, exhibits significant potential in power electronics and high-temperature, high-frequency devices. However, the concept of “conformational stability” carries a dual connotation within SiC research and industry. It refers both to the thermodynamic stability of the specific atomic stacking sequence of the 4H polytype relative to other polytypes (e.g., 3C-SiC, 6H-SiC), and to the mechanical stability of the wafer in resisting shape changes such as bowing and warping during actual wafer processing and application.

1. Thermodynamic Conformational Stability of 4H-SiC: Energetic Competition of Atomic Stacking Sequences

The crystal structure of 4H-SiC is formed by the stacking of Si-C bilayers along the [0001] direction following a specific ABCB sequence, which constitutes its so-called “conformation.” Its stability issue first manifests in the energetic competition with other polytypes (e.g., cubic 3C, hexagonal 6H). For a long time, explaining the coexistence of multiple polytypes under similar growth conditions and understanding the mechanism behind the formation of 3C-SiC inclusions in 4H-SiC homoepitaxy have been central challenges for theoretical research.

Density Functional Theory (DFT) calculations are powerful tools for investigating this problem. Systematic studies by Ramakers et al. show that at T=0K, the bulk energy differences between different polytypes are extremely small (on the order of ~1meV/SiC), and the calculation results strongly depend on the computational methodology employed. They compared various DFT codes such as VASP, CP2K, and FHI-aims, along with numerous exchange-correlation functionals like LDA, PBE, PBEsol, and HSE06. The study found that, except for the meta-GGA SCAN functional, most conventional DFT methods predict the 4H and 6H polytypes to be slightly more stable than 3C by approximately 1-5 meV/SiC, while the 2H polytype is the least stable. This is consistent with conclusions from many early ab initio studies, indicating that bulk energies at T=0 K alone cannot explain the experimentally observed ease of 3C-SiC formation at low temperatures and the preference for 4H/6H at high growth temperatures.

Fig. 1 Relaxed energies of 3C, 6H, 4H, and 2H structures as a function of hexagonality for different DFT codes, exchange-correlation functionals, and basis sets

To bridge the gap between theory and experiment, temperature effects must be considered. By calculating the vibrational contribution to the Helmholtz free energy (F_vib (T)= U_vib – TS_vib) using Density Functional Perturbation Theory (DFPT), studies found that as temperature increases, the free energy of hexagonal polytypes (4H, 6H) further decreases relative to 3C. At typical chemical vapor deposition (CVD) epitaxial temperatures (~1800K), vibrational free energy stabilizes 4H (6H) over 3C by about -3.0 (-2.8)meV/SiC. However, even after accounting for this, bulk thermodynamic stability still favors 4H/6H, contradicting the observation of 3C and 3C inclusion formation at lower temperatures.

Studies show that van der Waals (vdW) corrections significantly impact conclusions but must be treated cautiously. While early DFT-D2 corrections drastically altered polytype stability order, strongly stabilizing the 3C phase, more advanced vdW methods (e.g., DFT-D3(BJ), vdW-MBD) cause negligible corrections to stability and more accurately predict lattice constants. Therefore, researchers argue that, aside from the most advanced vdW methods, other vdW corrections might introduce spurious errors when calculating bulk SiC energies.

Beyond bulk and temperature effects, surface energy is considered another key factor determining polytype stability, especially dominating growth kinetics. Research by Mercier and Nishizawa indicated significant differences in the surface energy of Si-terminated (0001) faces. Calculations by Ramakers et al. confirmed that for Si-terminated faces, the 3C surface is the most stable, with an energy lower than hexagonal polytype surfaces, with a maximum difference up to 158meV/dangling bond (for 2H). This difference reduces to 59meV/dangling bond after including spin polarization but remains significantly larger than bulk energy differences. In contrast, the energy differences for C-terminated faces are smaller and follow a different order. Since industrial-standard epitaxial growth is typically performed on Si-terminated off-axis substrates, the more stable 3C surface provides a driving force for 3C-SiC nucleation.

Fig. 2 Surface energy relative to the 3C polytype for Si-terminated and C-terminated surfaces as a function of surface hexagonality

2. Mechanical Conformational Stability of 4H-SiC Wafers: Stress, Defects, and Doping

In practical wafer manufacturing and device processing, “conformational stability” more often refers to the wafer’s ability to resist bow and warp deformation and maintain a planar shape after undergoing processes like slicing, grinding, and thinning. This stability directly affects subsequent lithography, epitaxial growth processes, and the reliability of automated robotic handling.

Yield improvement demands drive the growth of larger-diameter, longer boules via the Physical Vapor Transport (PVT) method, but process modifications can introduce undesired internal stresses. Research by Manning et al. focused on 150 mm n-type 4H-SiC wafers, systematically thinning them until they lost planar conformational stability (i.e., exhibited bow reversal), to evaluate the impact of different growth and heat treatment processes on internal stress levels. They found that by physically modifying the growth chamber and applying specific in-line heat treatments, the average critical thickness for wafer instability could be reduced from 298μm for the control process to 260μm, a 13% reduction. This indicates that the growth chamber modification effectively alleviated the internal stresses leading to conformational instability.

Fig. 3 (a) Trend of critical thickness for wafer instability vs. normalized axial position for test processes A, B, and C with linear fits; (b) Comparison of average critical thickness for processes A and C

Post-thinning instability is analogous to the Twyman effect principle, where wafer curvature changes with decreasing thickness due to unbalanced surface stresses. The root cause can be traced back to internal stress sources within the crystal, primarily including the spatial non-uniform distribution of dislocations and variations in nitrogen doping concentration.

Dislocation distribution is a key factor affecting mechanical stability. Defect mapping analysis of representative wafers revealed that conformational stability closely correlates with dislocation density in the edge region. Wafers from the more stable Process A exhibited lower threading edge dislocation (TED) density in the edge region and a more uniform distribution of basal plane dislocations (BPD). In contrast, wafers from Process B, without heat treatment, showed a high concentration of BPD clustering at the edge. X-ray topography (XRT) scans further confirmed that heat treatment aids in redistributing BPDs, making them more uniform across the wafer and thus reducing local stress concentration. The study concluded that the axial position of the wafer within the crystal boule has a stronger influence on BPD distribution and conformational stability than the heat treatment itself.

Fig. 4 Contour maps of (a) threading edge dislocation (TED), (b) threading screw dislocation (TSD), and (c) basal plane dislocation (BPD) density distribution for representative wafers from processes A, B, and C

Nitrogen doping concentration indirectly affects mechanical stability by influencing the material’s elastic modulus. In another study by Manning et al., after achieving a 40% increase in axial growth rate via PVT process adjustments, some wafers exhibited planar conformational instability. Nanoindentation tests on stable and unstable wafers showed average elastic moduli of 427±6GPa and 439±6GPa, respectively, with the latter being higher and showing greater intra-wafer variation (~15GPa). A correlation exists between elastic modulus and resistivity (inversely related to nitrogen concentration) measured by contactless eddy current methods: regions with typically lower resistivity (higher nitrogen doping) also tend to have lower elastic modulus. However, this relationship is nonlinear, suggesting a complex mechanism by which nitrogen affects stiffness.

Fig. 5 (a) Box plots of elastic modulus measured along the [11-20] diameter for selected stable and unstable wafers; (b), (c) Resistivity distribution maps for the corresponding wafers

Nitrogen doping causes lattice constant contraction, theoretically potentially strengthening bonds, yet a reduced modulus is observed. One possible explanation is that nitrogen incorporation may promote the formation of point defects like carbon vacancies, which are known to significantly reduce the elastic modulus of SiC. Therefore, the growth chamber modification (Process A) might optimize the thermal field, reducing edge TEDs and associated strain, thereby offsetting the potential increase in elastic modulus and stress that could arise from reduced nitrogen concentration (increased resistivity), ultimately improving the wafer’s conformational stability.

In conclusion, the conformational stability of 4H-SiC is a multi-scale issue spanning from the atomic to the macroscopic level. At the atomic scale, the thermodynamic stability of its ABCB stacking sequence stems from subtle bulk energy balances, temperature-driven vibrational entropy contributions, and competition from surface energies at the growth interface. Among these, the lower surface energy of the Si-terminated surface is a key driving force for the heterogeneous nucleation of 3C-SiC on 4H substrates, explaining the origin of 3C inclusion defects in epitaxial layers.

At the macroscopic scale, the mechanical conformational stability of SiC wafers is primarily determined by the internal stress field introduced during growth and processing, which is modulated by the spatial distribution uniformity of dislocations (especially TEDs and BPDs) and nitrogen doping concentration gradients. Uniform dislocation distribution and optimized doping homogeneity help reduce internal stress gradients, thereby enhancing the shape stability of wafers during thinning and usage.

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References:

1. Ramakers, S., Marusczyk, A., Amsler, M., Eckl, T., Mrovec, M., Hammerschmidt, T., & Drautz, R. (2022). Effects of thermal, elastic, and surface properties on the stability of SiC polytypes. Physical Review B, 106(7), 075201.
2. Manning, I., Searson, J., Moeggenborg, K., Gave, M., Chung, G., & Sanchez, E. (2023). Improvement of the Conformational Stability of 150 mm 4H SiC Wafers. Solid State Phenomena, 343, 15-19.
3. Manning, I., Matsuda, Y., Chung, G., Sanchez, E., Dudley, M., Ailihumaer, T., & Raghothamachar, B. (2020, August). Progress in bulk 4H SiC crystal growth for 150 mm wafer production. In Materials Science Forum (Vol. 1004, pp. 37-43). Trans Tech Publications Ltd.