Abstract
We report the results of the systematic investigation into correlations between energetics and hexagonal stacking configurations for carbon, silicon, SiC, BN, AlN, GaN, and InN polytypes with sp3-bonded networks. The atomistic geometry, energetics, and electronic structure for these compounds with up to the periodic stacking length of L = 8 have been carefully calculated based on the density functional theory within the generalized gradient approximation (GGA). Using the Axial Next-Nearest-Neighbor Ising model extracted from the GGA calculations, we have also studied the energetics for more than 6 million kinds of nonequivalent stacking polytypes with up to L = 30, whose configurations have been deduced by the efficient polytype generation algorithm [E. Estevez-Rams and J. Martinez-Mojicar, Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 529 (2008)], and illustrated some trends of structural and energetic properties for these compounds.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig1.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Tab1.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Tab2.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Tab3.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Tab4.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig2.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig3.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig4.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig5.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Tab5.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig6.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig7.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig8.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1557%2Fjmr.2012.206/MediaObjects/43578_2013_28010007_Fig9.jpg)
Similar content being viewed by others
References
E. Estevez-Rams and J. Martinez-Mojicar: The symmetry of HK codes representing close-packed structures and the efficient generation of non-equivalent polytypes of a given length. Acta Crystallogr., Sect. A: Found. Crystallogr. 64, 529 (2008).
N. Bernstein, H.J. Gotsis, D.A. Papaconstantopoulos, and M.J. Mehl: Tight-binding calculations of the band structure and total energies of the various polytypes of silicon carbide. Phys. Rev. B 71, 075203 (2005).
C. Raffy, J. Furthmüller, and F. Bechstedt: Properties of hexagonal polytypes of group-IV elements from first-principles calculations. Phys. Rev. B 66, 075201 (2002).
K. Kobayashi and S. Komatsu: First-principles study of BN, SiC, and AlN polytypes. J. Phys. Soc. Jpn. 77, 084703 (2008).
C.H. Park, B-H. Cheong, K-H. Lee, and K.J. Chang: Structural and electronic properties of cubic, 2H, 4H, and 6H SiC. Phys. Rev. B 49, 4485 (1994).
S. Limpijumnong and W.R.L. Lambrecht: Total energy differences between SiC polytypes revisited, Phys. Rev. B 57, 12017 (1998).
X.Y. Xue, R.Q. Zhang, and X.H. Zhang: Structural and electronic properties of 9R diamond polytype. Solid State Commun. 136, 41 (2005).
P. Käckell, B. Wenzien, and F. Bechstedt: Influence of atomic relaxations on the structural properties of SiC polytypes from ab initio calculations. Phys. Rev. B 50, 17037 (1994).
M.J. Rutter and V. Heine: Energetics of stacking boundaries on the {0001} surfaces of silicon carbide. J. Phys. Condens. Matter 9, 8213 (1997).
N.W. Jepps and T.F. Page: Polytypic transformations in silicon carbide. Prog. Cryst. Growth Charact. Mater. 7, 259 (1983).
H. Jagodzinski: Polytypism in SiC crystals. Acta Crystallogr. 7, 300 (1954).
C-Y. Yeh, Z.W. Lu, S. Froyen, and A. Zunger: Zinc-blende-wurtzite polytypism in semiconductors. Phys. Rev. B 46, 10086 (1992).
A.F. Wright: Basal-plane stacking faults and polymorphism in AlN, GaN, and InN. J. Appl. Phys. 82, 5259 (1997).
M.T. Sebastian and P. Krishna: Random, Non-Random and Periodic Faulting in Crystals (Gordon and Breach, Amsterdam, Netherlands, 1994).
S. Clark, M. Segall, P. Pickard, P. Hasnip, M. Probert, K. Refson, and M. Payne: First principles methods using CASTEP. Z. Kristallogr. 220, 567 (2005). The CASTEP code is available from Accelrys Inc.
D. Vanderbilt: Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892 (1990).
J.P. Perdew, K. Burke, and M. Ernzerhof: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
H.J. Monkhorst and J.D. Pack: Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).
A. Bauer, J. Kräußlich, L. Dressler, P. Kuschnerus, J. Wolf, K. Goetz, and P. Käckell: High-precision determination of atomic positions in crystals: The case of 6H- and 4H-SiC. Phys. Rev. B 57, 2647 (1998).
W.R.L. Lambrecht, S. Limpijumnong, S.N. Rashkeev, and B. Segall: Electronic band structure of SiC polytypes: A discussion of theory and experiment. Phys. Status Solidi B 202, 5 (1997).
C. Cheng, R.J. Needs, and V. Heine: Inter-layer interactions and the origin of SiC polytypes. J. Phys. C: Solid State Phys. 21, 1049 (1988).
C. Cheng, V. Heine, and I.L. Jones: Silicon carbide polytypes are equilibrium structures. J. Phys. Condens. Matter 2, 5097 (1990).
V. Heine, C. Cheng, and R.J. Needs: The preference of silicon carbide for growth in the metastable cubic form. J. Am. Ceram. Soc. 74, 2630 (1991).
A. Zoroddu, F. Bernardini, P. Ruggerone, and V. Fiorentini: First-principles prediction of structure, energetics, formation enthalpy, elastic constants, polarization, and piezoelectric constants of AlN, GaN, and InN: Comparison of local and gradient-corrected density-functional theory. Phys. Rev. B 64, 045208 (2001).
K. Karch and F. Bechstedt: Ab initio lattice dynamics of BN and AlN: Covalent versus ionic forces. Phys. Rev. B 56, 7404 (1997).
Acknowledgments
The authors sincerely thank the Director General of Corporate Research and Development Laboratories, T. Miyake for giving us an opportunity to carry out this research. The authors’ gratitude also goes to M. Igarashi, Y. Ohashi, A. Yauchi, and Y. Sumitomo (Sumitomo Metal Industries, Ltd.) for their encouragement in this work. The authors would like to also thank Prof. K. Suzuki for fruitful discussions on the SiC polytype systems.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Moriguchi, K., Kamei, K., Kusunoki, K. et al. Comparative studies on total energetics of nonequivalent hexagonal polytypes for group IV semiconductors and group III nitrides. Journal of Materials Research 28, 7–16 (2013). https://doi.org/10.1557/jmr.2012.206
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2012.206