[Information on BN (Boron Nitride) compounds][BN][SiC][AlN][Top][Japanese(Available)]
(Start, 1/28, 2009)(Update, 3/14, 2019)
BN: Boron nitride as one of III-V compounds (for example, AlN, GaN, GaAs, InN, InSb, etc.)
sp2: h-BN(hexagonal BN), r-BN(rhombohedral BN)
sp3: c-BN(cubic BN), w-BN(wurtzite BN), nH-BN (n = 2, 3, 4, 5, 6,...)
Polytypism: 1D polymorphism (see related references[A. R. Verma and P. Krishna])
2H-BN (w-BN, P63mc)
3C-BN (c-BN, F43m) (zinc-blende structure) = 3H-BN (P3m1)
Possible symmetries of nH polytype ("H": Hexagonal, Binary compound): P63mc, P3m1 (see Ref. [ITC])
Symmetry of Stacked Closest-packed Layers (Table 7.1.5B in Ref. [A. L. Patterson and J. S. Kasper])
[r-BN - c-BN, h-BN - w-BN]
r-BN <-- Pressure, etc. --> c-BN (= 3H-BN)
h-BN <-- Pressure, etc. --> w-BN (= 2H-BN)
[Examples of electronic band structures of BN and related compounds]
[Examples of polytype structures]
SiC(siricon-carbide) has various polytypes. SiC is a IV-IV compound. Although it is possible to consider a pH-BN polytype (p > 3), there are a few works of BN polytypes with the exception of 2H-BN and 3C-BN. 5H-BN was synthesized by Komatsu et al. as a new material. We have investigated 5H-BN using the first-principles molecular dymamics (FPMD) method and obtained its electronic and lattice properties. Moreover, we have investigated 2H-, 3C-(= 3H-), 4H-, 5H-, and 6H-BN(AlN, SiC). AlN is aluminum nitride.
Total energies of BN and AlN polytypes have relation with hexagonality (H [%], mentioned below). The total energy of the BN polytype increases with increasing hexagonality and those of the AlN polytype decreases with increasing hexagonality. This feature is described by the number of the shortest third-neighbor cation-anion pairs in the unit cell.
We have investigated sp2-bonded BN compounds as h-BN and related composite structures. h-BN is a graphite-like hexagonal layered compounds and it has quite flat bands at the top of valence bands and bottom of conduction bands. The electronic band structures of h-BN and related hexagonal layered BN phases in detail have been investigated in ref. . A direct band gap in h-BN has been observed in experiment. In contrast, the band gap of h-BN is direct in the DFT calculations. We have discussed the disagreement between theoretical and experimetal band gap results of h-BN in ref. .
10H-BN and 10H-AlN have been investigated in order to compare them with the previous results. The 10H polytype has 18 structures. All possible symmetries and stacking sequences of the 10H polytype are tabulated in Table I of ref. . We choose four structures as ABCABCBACB(P63mc, H = 20%), ABCABCABAB(P3m1, H = 20%), ABCBCACBCB(P63mc, H = 60%) and ABCBCBCBCB(P3m1, H = 80%). As a result, the total energy of the BN (AlN) polytype increases (decreases) with increasing hexagonality in calculated 2H - 6H and 10H polytypes. 3C-BN (= 3H-BN, c-BN, H = 0%) is most stable and 2H-BN (w-BN, H = 100%) is most unstable in calculated BN polytypes. In contrast, 2H-AlN (w-AlN, H = 100%) is most stable and 3C-AlN (= 3H-AlN, c-AlN, H = 0%) is most unstable in calculated AlN polytypes.
As for the electronic band structures of 2H - 6H and 10H-BN(AlN) polytypes, most band gaps of them are indirect with the exception of 2H-AlN. The difference of delta_1 and delta_2 for 10H-AlN(ABCBCACBCB, H = 60%) is smallest with 0.15 eV in the calculated polytypes without 2H-AlN.
Electronic and structural properties of 6H-AlN(ABCBCB) under various pressure conditions were calculated in order to realize the direct band gap. The indirect band gap of 6H-AlN(ABCBCB) transforms to direct under expansion. The indirect band gap is enhanced under compression. This was presented in the international conference of "Joint AIRAPT-22 & HPCJ-50" (7/26 - 7/31, 2009, Odaiba, Tokyo).
Electronic and lattice properties of 2H - 12H-SiC by LDA[BH] and GGA[PBE] were calculated. We have found that 10H-SiC(ABCACBCACB, H = 40 %, Zhdanov notation: 3322) is most stable in the SiC polytypes calculated by LDA and GGA.
Crystal structures of 2H - 6H, 10H and 12H polytypes are as follows.
As for details of BN, please see the reference [R1]. 5H-BN and related materials have been synthesized by plasma-assisted laser chemical vapor deposition (PAL-CVD)[R2].
- 2H and 3H potytypes(png, 30kb)
- 4H and 5H potytypes(png, 130kb)
- 6H potytypes(png, 138kb)
- 10H potytypes(png, 182kb, see ref. )
- 12H potytype(ABCABCACBACB, H = 17 %, png, 171kb) and its electronic band structure(Indirect band gap: Gamma - M)
- 2H - 12H polytypes(png, 48kb)[medium](png, 88kb)[small](png, 45kb)
- [Total energies of BN,SiC,AlN - Hexiagonality](png, 43.1 kb)
- [Total energies of SiC - Hexagonality](png, 28.1 kb)
- [Band gaps of SiC - Hexagonality](png[color], 33.4 kb)
It is possible to transform from one notation to the other notations with the exception of Ramsdell notation.
- Ramsdell notation: 2H, 3C, 4H, 5H, 6H,..... (H: Hexagonal), 3C (C: Cubic), 9R, 15R,..... (R: Rhombohedral)
- ABC notation: ABC (3C [3H]), ABCACB (6H), ABCBCB (6H), ABCABCBCBC (10H),.....
- Zhdanov notation: 33 (6H, ABCACB), 2112 (6H, ABCBCB), 41 (5H, ABCBC),.....
- Jagodzinski notation (h-c notation): hcchcc (6H, ABCACB), hhhchc (6H, ABCBCB), hhccc (5H, ABCBC),.....
- Hägg notation: +++--- (6H, ABCACB), ++-+-- (6H, ABCBCB), ++++- (5H, ABCBC),.....
- A -> B -> C -> A : Cyclic -> Hägg notation "+"
- A -> C -> B -> A : Anticyclic -> Hägg notation "-"
"++" -> c, ABC(=BCA, CAB)
"--" -> c, ACB(=BAC, CBA)
"+-" -> h, ABA(=BCB, CAC)
"-+" -> h, ACA(=BAB, CBC)
Hexagonality (H [%]): H = (Number of hexagonal cation-anion [BN] bilayers)/(Number of cation-anion [BN] bilayers)
The BN polytype consists of cubic and hexagonal BN bilayers. This is the same for other sp3 bonded polytype as AlN, SiC, etc. In detail, please see Ref. .
For example: 2H (H = 100 %), 3H (H = 0 %), 4H (H = 50 %), 5H (H = 40 %), 6H (H = 33, 67 %), 10H (H = 20, 40, 60, 80 %),....
Zhdanov notation (2H - 9H)
2H : 11
3H(=3C) : Infinite
4H : 22
5H : 41
6H : 33
6H : 2211
7H : 52
7H : 4111
7H : 3121
8H : 71
8H : 44
8H : 3212
8H : 3311
8H : 221111
8H : 211211
9H : 63
9H : 5211
9H : 5112
9H : 4221
9H : 4122
9H : 3231
9H : 312111
9H : 311121
9H : 411111
Stacking sequences of 5H and 6H polytypes
Table of possible stacking sequences for [5H polytype](png, 9kb)
It is possible to consider 30 stacking sequences in the 5H polytype.
All of them are the same structure.
Table of possible stacking sequences for [6H polytype](png, 9kb)
It is possible to consider 54 stacking sequences in the 6H polytype. They are classified into three groups as ABCACB(P63mc, H = 33 %), ABCBCB and ABCBAB. ABCBCB is equal to ABCBAB(P3m1, H = 67 %). Consequently, the 6H polytype has two different structures as ABCACB and ABCBCB.
In detail, please see references .
Related link, references, etc. [Head]
-  S. Komatsu, K. Okada, Y. Shimizu, and Y. Moriyoshi: J. Phys. Chem. B103 (1999) 3289 [5H-BN].
-  K. Kobayashi and S. Komatsu: J. Phys. Soc. Jpn. 76 (2007) 113707 [5H-BN].
-  K. Kobayashi and S. Komatsu: J. Phys. Soc. Jpn. 77 (2008) 084703 [2H - 6H-BN(AlN, SiC)][6H-AlN][6H-SiC]), and related references therein.
-  K. Kobayashi, K. Watanabe, and T. Taniguchi: J. Phys. Soc. Jpn. 76 (2007) 104707 [h-BN].
-  K. Watanabe, T. Taniguchi, and H. Kanda: Nat. Mater. 3 (2004) 404 [Experiment for h-BN].
-  K. Kobayashi and S. Komatsu: J Phys. Soc. Jpn. 78 (2009) 044706 [10H-BN, 10H-AlN].
-  K. Kobayashi and S. Komatsu, "First-Principles Study of 6H-AlN under various pressure conditions", J. Phys.: Conf. Ser. 215, 012111(2010)[AIRAPT22].
-  S. Komatsu, K. Kobayashi, Y. Sato, D. Hirano, T. Nakamura, T. Nagata, T. Chikyo, T. Watanabe, T. Takizawa, K. Nakamura, and T. Hashimoto: Journal of Physical Chemistry C 114, 13176 - 13186(2010).
-  K. Kobayashi and S. Komatsu: "First-Principles Study of 30H-BN polytypes", Materials Transactions, Vol. 51, No. 9 (2010) 1497[6H-BN, 30H-BN].
-  K. Kobayashi and S. Komatsu: "First-Principles Study of 8H-, 10H-, 12H-, and 18H-SiC Polytypes", Journal of the Physical Society of Japan, Vol. 81, No. 2 (2012) 024714[8H-SiC, 10H-SiC, 12H-SiC, 18H-SiC][BH][PBE].
-  K. Kobayashi and S. Komatsu, "First-Principles Study of Various BN, SiC, and AlN polytypes", Trans. MRS-J, Vol. 37, 583-588 (2012)[https page, go to JST][IUMRS-ICEM2012][48H-BN][20H-SiC][30H-AlN].
-  K. Kobayashi and S. Komatsu, "First-Principles Study of AlBN and Related Polytypes", Trans. MRS-J, Vol. 38, 485-492 (2013)[4H-AlBN][4H-AlAsN][4H-AlPN][2H-, 3H-, 5H-, 6H-, and 12H-AlBN][3x2H-AlBN].
-  No data.
- (Other related papers)
- [Z] K. Kobayashi: Materials Transactions, Vol. 46, No. 6 (2005) 1094 [Anisotropic compression].
- [Electronic band structures of BN compounds]
- [10H-BN](ABCABCBACB [H = 20%], P63mc, png[46 kb])
- [5H-BN](P3m1, png[40 kb])
- [4H-BN](P63mc, wide, png[63.5 kb])
- [c-BN](3C-BN, png[7 kb])
- [3H-BN](= 3C-BN, P3m1, png[33.3 kb])
- [w-BN](2H-BN, png[7.6 kb])
- [2H-BN](w-BN, P63mc, wide, png[27.8 kb])
- [h-BN](A-B stacking, P63/mmc, png[26 kb])
- [h-BN](A-A stacking, P6_m2, png[23.4 kb])
- [h-BN](type B, P63/mmc, png[26 kb])
- [r-BN](rhombohedral BN, ABC stacking, png[28 kb])
- [Elctronic band structures of AlN polytypes]
- [10H-AlN](ABCBCBCBCB [H = 80%], P3m1, png[43.7 kb])
- [6H-AlN] as ABCACB [P63mc] and ABCBCB [P3m1] (png[173 kb])
- [3H-AlN](= 3C-AlN, P3m1, png[27 kb])
- [2H-AlN](P63mc, png[24.3 kb])
- [Elctronic band structures of SiC polytypes]
- [4H-SiC](P63mc, wide, png[36 kb])
- [10H-SiC](ABCACBCACB [H = 40%], P3m1, png[56 kb])
- [Related web pages]
- [BN compounds]
- Close-packed structures by P. Krishna and D. Pandey: International Union of CRYSTALLOGRAPHY(IUCr)[Useful]
- POLYTYPISM IN SILICON CARBIDE by Dr. J. F. Kelly(Industrial Materials Group of Birkbeck College, University of London)
- [Related references for BN]
- [R1] O. Mishima and K. Era: in Electric Refractory Materials, ed. Y. Kumashiro (Marcel Dekker, New York, 2000) pp. 495-556, and references therein.
- [R2] S. Komatsu: J. Phys. D: Appl. Phys. 40 (2007) 2320 [Review].
- [R3] S. Komatsu, Y. Sato, D. Hirano, T. Nakamura, K. Koga, A. Yamamoto, T. Nagata, T. Chikyo, T. Watanabe, and T. Takizawa: Journal of Physics D: Applied Physics 42 (2009) 225107[P-type sp3-bonded BN/n-type Si][Heterodiode][Solar cell][Laser-plasma synchronous CVD method].
- [Ra] F. Oba, A. Togo, I. Tanaka, K. Watanabe, and T. Taniguchi, Phys. Rev. B81, 075125(2010)[VASP-PAW][Doping of h-BN][Intercalation][Prediction].
- [h-BN] L. Liu, Y. P. Feng, and Z. X. Shen: Phys. Rev. B68 (2003) 104102.
- [ADDF]H. Tokoyama, H. Yamakado and K. Ohno, Chemistry Letters (doi:10.1246/cl.151114)(2015)[Automated exploration][ADDF][GRRM]
- [Recent papers for h-BN]
- [h-BN][Layered BN] B. Huang, X. K. Cao, H. X. Jiang, J. Y. Lin and S.-H. Wei, Phys. Rev. B86, 155202(2012)[Significantly enhanced optical transition].
- [h-BN] S.-P. Gao, Solid State Communications 152 (2012) 1817[Band gap characters][Dispersion corrected][GW].
- [h-BN] G. Cassabois, P. Valvin, B. Gil, "Hexagonal boron nitride is an indirect bandgap semiconductor", arXiv:1512.02962.
- [h-BN] S. M. Gilbert, T. Pham, M. Dogan, S. Oh, B. Shevitski, G. Schumm, S. Liu, P. Ercius, S. Aloni, M. L. Cohen, A. Zettl, "Alternative Stacking Sequences in Hexagonal Boron Nitride", arXiv:1810.04814.
- [Related references for Polytype (Polytypism)]
- International Table for Crystallography, ed. A. J. C. Wilson and E. Prince (Kluwer, Dordrecht, 2004) Vol. C, Chap. 9.2 by S. Durovic, P. Krishna ans D. Pandey, pp. 744 - 765.
- A. R. Verma and P. Krishna: Polymorphism and Polytypism in Crystals (Wiley, New York, 1966).
- J. E. Iglesias: Acta. Cryst. A62(2006) 178.
- A. L. Patterson and J. S. Kasper: ``International Tables for X-ray Crystallography'', ed. J. S. Kasper and K. Lonsdale (The Kynoch Press, Birmingham, 1967) Vol. 2, pp. 342 - 354.
- T. J. McLarnan: Z. Kristallogr. 155 (1981) 269.
- Z. Inoue: J. Mater. Sci. 17 (1982) 3189.
- A. L. Ortiz, F. Sanchez-Bajo, F. L. Cumbrera and F. Guiberteau, J. Appl. Cryst. 46 (2013) 242 -247[Prolific polytypism][SiC].
- [Related papers for BN, SiC, AlN and related materials]
- Z. Pan, H. Sun, Yi Zhang and C. Chen: Phys. Rev. Lett., Vol. 102, No. 5, 055503(2009)[Harder than diamond][Hexagonal diamond, w-BN][PARATEC].
- L. Zhou, X. Ni, Ü. Özgür, H. Morkoç, R. P. Devaty, W. J. Choyke and D. J. Smith: Journal of Crystal Growth, Vol. 311, Issue 6 (2009) 1456-1459 [6H-AlN, m-plane AlN/SiC interface, Experiment]. <-- Consistent with our resutls for 6H-AlN polytypes .
- [C][Si][SiC][BN][AlN][GaN][InN]K. Moriguchi, K. Kamei, K. Kusunoki, N. Yashiro and N. Okada, J. Mater. Res., Vol. 28 (2013) 7-16[Comparative studies][Nonequivalent hexagonal polytypes].
- [Related paper](IUCr)
- [Code by author of above related paper](text format, IUCr electronic archives[Reference: ZM5042])
- [Floating Electron States]Y. Matsushita, S. Furuya and A. Oshiyama, Phys. Rev. Lett., Vol. 108, No. 24, 246404(2012)[Covalent semiconductor][SiC][GaN][AlN][BN][Si][C].
- [Interstitial Channels]Y. Matsushita and A. Oshiyama, Phys. Rev. Lett., Vol. 112, No. 13, 136403(2014)[Control band gaps][Effective mass][Tetrahedrally bonded][SiC].
- [Electron Confinement Due to Stacking Control of Atomic Layers]Y. Matsushita, S. Furuya and A. Oshiyama, J. Phys. Soc. Jpn. 83 (2014) 094713[RSDFT][SiC][Roles of floating states][Spontaneous polarization].
- [Electronic states floating]Y. Matsushita A. Oshiyama, J. Phys. Soc. Jpn. 86 (2017) 054702[Comprehensive study][Band-gap variation][sp3-bonded semiconductor][Electronic states floating][Internal space].
- [Electron and Hole Confinement in Hetero-Crystalline SiC Superlattice]Y. Sugihara, K. Uchida and A. Oshiyama, J. Phys. Soc. Jpn. 84 (2015) 084709.
- [SiC][A simple approach to the polytypism in SiC]T. Ito, T. Akiyama and K. Nakamura, Journal of Crystal Growth 362, 207-210(2013).
- [SiC][Systematic theoretical investigations][Vacancy][N substitution]T. Ito, T. Akiyama and K. Nakamura, Phys. Status Solidi C (2013) in press.
- [10H-SiC]S. Nakashima, T. Tomita, N. Kuwahara, T. Mitani, M. Tomobe, S. Nishizawa and H. Okumura, J. Appl. Phys. 114, 193510(2013)[Raman intensity profiles][Zone-folded modes]
- [SiC]S. Kawanishi, T. Mizoguchi, arXiv:1512.04626[Effect of van der Waals interactions][Stability]
- [STAM][Superconductor][SiC]Science and Technology of Advanced Materials(STAM)[Focus on Superconductivity in Semiconductors], Vol.9, Issue 4(2008).
- [AlN]Y. C. Cheng, H. T. Chen, X. X. Li, X. L. Wu, J. Zhu, S. H. Li, and Paul K. Chu: Journal of Applied Physics 105 (2009) 083511[CASTEP][PWSCF][2H-,4H- and 6H-AlN][Optical and vibrational properties].
- [AlN]Y. C. Cheng, X. L. Wu, S. H. Li, and Paul K. Chu: Applied Physics Letters 95 (2009) 121902[QUANTUM-ESPRESSO][4H-AlN][Stress influence][Band-edge luminescence].
- [BH] U. von Barth and L. Hedin, J. Phys. C5, 1629(1972).
- [PBE] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865(1996).
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