An Interpretation for Defect-Induced Structural Transformation in SiC
Authors: Ito Tomonori , Akiyama Toru , Nakamura Kohji , Pradipto Abdul-Muizz 
Published: February 2020

Silicon carbide (SiC) has been considered as one of the alternative power semiconductor materials due to its excellent properties such as wide band gap, high break down field, and high thermal conductivity. Although SiC with 3C (zinc blende) is suitable for high-frequency power devices from its high electron mobility and high electron-saturation-velocity, SiC is well known as having dozens of polytypes including 4H and 6H in addition to 2H (wurtzite) and 3C that consist of different ordered stacking sequences of SiC atomic double layers. The 3C-SiC is believed to be more stable than the hexagonal structure at low temperatures. In contrast, 2H-SiC, which has the simplest stacking sequence, is rarely observed at high temperatures. Moreover, point defects also affect the stable polytype in SiC. Heavily Nitrogen (N)-doped single crystals of 6H-SiC were completely transformed into 3C-SiC by annealing in vacuum at presence of Si vapor at 2080 K and 2180 K (hereafter Case I). The 3C-SiC-like bands was also observed in 4H-SiC epilayers with heavily N-doping after thermal annealing (hereafter Case II). Presuming that vacancy formation is related to temperature, point defects such as vacancy and N in SiC are crucial factor for the structural transformation between hexagonal and cubic structures. In this study, the structural transformation in SiC is simply interpreted by considering point defect formation with the aid of ab initio calculations.
Ab initio total energy calculations in a √3×√3×12 unit cell imply that stable stacking for SiC is 6H with Si-vacancy (VSi), 4H with C-vacancy (VC) and N substituting for Si (NSi), and 3C with N substituting for C (NC), whereas 2H-stacking does not appear as a stable stacking in these systems. Furthermore, the formation energy calculations reveal that vacancy formation depends on C chemical potential m
C, where VSi and VC formations are favorable at large m
C (corresponding to C-rich) and small m
C (Si-rich), respectively. On the other hand, NC formation is more favorable than NSi formation over the entire range of m
C and independent of conditions because of very small difference in covalent radius between N and C. Comparing these calculated results with the experimental finding in the Case I for transformation from 6H to 3C, thermal treatment with presence of Si vapor at high temperatures suppresses VSi formation favoring 6H-stacking while it enhances VC formation to be occupied by N (NC) in addition to N substitution for C (NC) that transform 6H to 3C. The Case II can be also interpreted by considering NC. Thermal annealing for N-doped 4H-SiC favored by VC easily produces NC with N occupying VC and substituting for C to realize 3C-SiC bands at high N-doped region in 4H-SiC epilayers. These results suggest that NC is crucial for the transformation from hexagonal stacking such as 6H and 4H to cubic stacking 3C.
In order to give physical interpretation for the transformation to 3C-SiC with NC, the interaction energies Jn
between nth neighbor SiC double layers are estimated in the range of n ≤ 3 using the axial next nearest neighbor Ising (ANNNI) model and calculated total energies for SiC polytypes obtained in this study. The calculated results elucidate that the absolute value of positive J
1 (51.70 meV) with J
3 (9.92 meV) favoring 3C-stacking is much larger than that of negative J
2 (-16.66 meV) inducing hexagonal stacking. It should be noted that the Jn
values are one order of magnitude greater than those of perfect SiC such as J
1 (2.33 meV), J
2 (-1.41 meV), and J
3 (0.51 meV). This implies that the layer interaction in SiC becomes strong and long-range due to N-doping. Considering coordinate of (|J
2|/J
1, J
3/J
1) in the ANNNI phase diagram, it is also found that (0.31, 0.19) for SiC with NC is located in the stable region of 3C and is more distant from the multi-phase degeneracy point (0.5, 0) inducing polytype and phase boundary between 3C and 4H than (0.61, 0.21) for perfect SiC. This clarifies that the large J
1 in SiC with NC stabilizes 3C-stacking to dominate the structural transformation to 3C due to N-doping. Furthermore, atomistic interaction between the nearest neighbor layers corresponding to J
1 is also qualitatively discussed in terms of electrostatic interaction between bond charges located at the center of interatomic bonds and that between ionic charges located at the lattice sites on the basis of a simple energy description and charge distribution obtained by ab initio calculations.