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 mC, where VSi and VC formations are favorable at large mC (corresponding to C-rich) and small mC (Si-rich), respectively. On the other hand, NC formation is more favorable than NSi formation over the entire range of mC 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 J1 (51.70 meV) with J3 (9.92 meV) favoring 3C-stacking is much larger than that of negative J2 (-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 J1 (2.33 meV), J2 (-1.41 meV), and J3 (0.51 meV). This implies that the layer interaction in SiC becomes strong and long-range due to N-doping. Considering coordinate of (|J2|/J1, J3/J1) 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 J1 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 J1 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.