First-principles study of BN, SiC, and AlN polytypes

We calculated the electronic and lattice properties of BN, SiC and AlN polytypes. The calculated polytypes, are 2H, 3C (= 3H), 4H, 5H, and 6H. These polytypes are sp(3)-bonded compounds. The 6H polytype has two crystal structures as ABCACB and ABCBCB stacking sequences. The lattice properties were optimized automatically by the first-principles molecular dynamics (FPMD) method. Most calculated electronic band structures of these polytypes are non-metallic and their band gaps are indirect. The most stable BN, SiC and AlN polytypes are 3C-BN, 4H-SiC, and 2H-AlN. respectively. The Calculated total energies of BN polytypes are in the order of 3C < 6H(ABCACB) < 5H < 4H < 6H(ABCBCB) < 2H. The Calculated total energies of SiC polytypes are in the order of 4H < 6H(ABCACB) < 3C < 5H < 6H(ABCBCB) < 2H. The calculated total energies of AlN polytypes are in the order of 2H < 6H(ABCBCB) < 4H < 5H < 6H(ABCACB) < 3C. The total energies and energetical stabilities of the BN and AlN polytypes are related to hexagonality which corresponds to the ratio of the number of third-neighbor cation-anion pairs and the number of cation-anion bilayers in the unit cell. 6H-BN(ABCACB) and 6H-SiC(ABCACB) tire energetically more favorable than 6H-BN(ABCBCB) and 6H-SiC(ABCBCB), respectively. If) contrast, 6H-AlN(ABCBCB) is more favorable than 6H-AlN(ABCACB).