D Chen, Y P Cang, Y S Luo. Electronic structures and phase transition characters of β-, P61-, P62- and δ-Si3N4 under extreme conditions: a density functional theory study[J]. J. Semicond., 2015, 36(2): 023003. doi: 10.1088/1674-4926/36/2/023003.
Abstract: This paper describes the results of structural, electronic and elastic properties of silicon nitride (in its high-pressure P61 and P62 phases) through the first-principles calculation combined with an ultra-soft pseudo-potential. The computed equilibrium lattice constants agree well with the experimental data and the theoretical results. The strongest chemical bond (N--Si bond) shows a covalent nature with a little weaker ionic character. P61-Si3N4 is more stable than P62-Si3N4 due mainly to the fact that the shorter N--Si bond in the P61 phase allows stronger electron hybridizations. We have also predicted the phase stability of Si3N4 using the quasi-harmonic approximation, in which the lattice vibration and phonon effect are both considered. The results show that the β → P61 phase transition is very likely to occur at 42.9 GPa and 300 K. The reason why the β → P61 → δ phase transitions had never been observed is also discussed.
Key words: phase transition, bond lengths, elastic constants, density functional theory
Abstract: This paper describes the results of structural, electronic and elastic properties of silicon nitride (in its high-pressure P61 and P62 phases) through the first-principles calculation combined with an ultra-soft pseudo-potential. The computed equilibrium lattice constants agree well with the experimental data and the theoretical results. The strongest chemical bond (N--Si bond) shows a covalent nature with a little weaker ionic character. P61-Si3N4 is more stable than P62-Si3N4 due mainly to the fact that the shorter N--Si bond in the P61 phase allows stronger electron hybridizations. We have also predicted the phase stability of Si3N4 using the quasi-harmonic approximation, in which the lattice vibration and phonon effect are both considered. The results show that the β → P61 phase transition is very likely to occur at 42.9 GPa and 300 K. The reason why the β → P61 → δ phase transitions had never been observed is also discussed.
Key words:
phase transition, bond lengths, elastic constants, density functional theory
References:
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Swift G A, Üstündag E, Clausen B. High-temperature elastic properties of in situ-reinforced Si3N4[J]. Appl Phys Lett, 2003, 82(7): 1039. |
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Kroll P. Pathways to metastable nitride structures[J]. J Solid State Chem, 2003, 176(2): 530. |
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Ching W Y, Mo S D, Ouyang L Z. Theoretical prediction of the structure and properties of cubic spinel nitrides[J]. J Am Ceram Soc, 2002, 85(1): 75. |
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Jiang J Z, Kragh F, Frost D J. Hardness and thermal stability of cubic silicon nitride[J]. J Phys: Condens Matter, 2001, 13(22). |
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Kuwabara A, Matsunaga K, Tanaka I. Lattice dynamics and thermodynamical properties of silicon nitride polymorphs[J]. Phys Rev B, 2008, 78(6): 064104. |
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Xu B, Dong J J, McMillan P F. Equilibrium and metastable phase transitions in silicon nitride at high pressure: a firstprinciples and experimental study[J]. Phys Rev B, 2011, 84(1): 014113. |
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Togo A, Kroll P. First-principles lattice dynamics calculations of the phase boundary between β-Si3N4 and c-Si3N4 at elevated temperatures and pressure[J]. J Comput Chem, 2008, 29(13): 2255. |
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He H L, Sekine T, Kobayashi T. Shock-induced phase transition of β-Si3N4 to c-Si3N4[J]. Phys Rev B, 2000, 62(17): 11412. |
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Tatsumi K, Tanaka I, Adachi H. Theoretical prediction of postspinel phases of silicon nitride[J]. J Am Ceram Soc, 2002, 85(1): 7. |
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Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple[J]. Phys Rev Lett, 1996, 77(18): 3865. |
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Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations[J]. Phys Rev B, 1976, 13(12): 5188. |
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Pfrommer B G, Côté M, Louie S G. Relaxation of crystals with the quasi-Newton method[J]. J Comput Phys, 1997, 131(1): 233. |
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Yu B H, Chen D. Phase transition character and thermodynamic modeling of the P6 and P6' hexagonal Si–N system supplemented by first-principles calculations[J]. J Alloys Compd, 2013, 581: 747. |
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Ching W Y, Ouyang L Z, Gale J D. Full ab initio geometry optimization of all known crystalline phases of Si3N4[J]. Phys Rev B, 2000, 61(13): 8696. |
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Yashima M, Ando Y, Tabira Y. Crystal structure and electron density of β-silicon nitride: experimental and theoretical evidence for the covalent bonding and charge transfer[J]. Organ Chem, 2007, 38(28): 28003. |
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Priest H P, Burns F C, Priest G L. Oxygen content of alpha silicon nitride[J]. J Am Ceram Soc, 1973, 56(7): 395. |
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Hirosaki N, Ogata S, Kocer C. Molecular dynamics calculation of the ideal thermal conductivity of single-crystal β- and α-Si3N4[J]. Phys Rev B, 2002, 65(13): 134110. |
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Ching W Y, Xu Y N, Gale J D. Ab initio total energy calculation of β- and α-silicon nitride and the derivation of effective pair potentials with application to lattice dynamics[J]. J Am Ceram Soc, 1998, 81(12): 3189. |
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Born M, Huang K. Dynamical theory of crystal lattices[J]. Oxford: Clarendon, 1956. |
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Ventelon L, Willaime F, Clouet E. Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W[J]. Acta Mater, 2013, 61(11): 3973. |
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Mulliken R S. Electronic population analysis on LCAO-MO molecular wave functions[J]. J Chem Phys, 1955, 23(10): 1833. |
| [34] |
Ren S Y, Ching W Y. Electronic structures of α- and β-silicon nitride[J]. Phys Rev B, 1981, 23(10): 5454. |
| [35] |
Oh J W, Kim C Y, Nahm K S. The hydriding kinetics of LaNi4.5AL0.5 with hydrogen[J]. J Alloys Compd, 1998, 278(1/2): 270. |
| [36] |
He J L, Wu E D, Wang H T. Ionicties of boron–boron bonds in B12 icosahedra[J]. Phys Rev Lett, 2005, 94(1): 015504. |
| [37] |
Ching W Y, Mo S D, Ouyang L Z. Electronic and optical properties of the cubic spinel phase of c-Si3N4, c-Ge3N4, c-SiGe2N4, and c-GeSi2N4[J]. Phys Rev B, 2001, 62(24): 245110. |
| [1] |
Chen J Y, Guo Y L, Wen Y G. Graphene: two stage metal catalyst free growth of high quality polycrystalline graphene films on silicon nitride substrates[J]. Adv Mater, 2013, 25(7): 938. |
| [2] |
Boyko T D, Hunt A, Zerr A. Electronic structure of spineltype nitride compounds Si3N4, Ge3N4, and Sn3N4 with tunable band gaps: application to light emitting diodes[J]. Phys Rev Lett, 2013, 111(9): 097402. |
| [3] |
Liu Y X, Davanco M, Aksyuk V. Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators[J]. Phys Rev Lett, 2013, 110(22): 223603. |
| [4] |
Swift G A, Üstündag E, Clausen B. High-temperature elastic properties of in situ-reinforced Si3N4[J]. Appl Phys Lett, 2003, 82(7): 1039. |
| [5] |
Kocer C, Hirosaki N, Ogata S. Ab initio calculation of the ideal tensile and shear strength of cubic silicon nitride[J]. Phys Rev B, 2003, 67(3): 035210. |
| [6] |
Zerr A, Miehe G, Serghiou G. Synthesis of cubic silicon nitride[J]. Nature (London), 1999, 400(7): 340. |
| [7] |
Kroll P, von Appen J. Post-spinel phases of silicon nitride[J]. Phys Status Solidi B, 2001, 226(1). |
| [8] |
Kroll P. Pathways to metastable nitride structures[J]. J Solid State Chem, 2003, 176(2): 530. |
| [9] |
Ching W Y, Mo S D, Ouyang L Z. Theoretical prediction of the structure and properties of cubic spinel nitrides[J]. J Am Ceram Soc, 2002, 85(1): 75. |
| [10] |
Danilenko N V, Oleinik G S, Dobrovol’skii V D. Microstructural features of the α→β transformation in silicon nitride at high pressures and temperatures[J]. Sov Powder Metal Met Ceram, 1992, 31(12): 1035. |
| [11] |
Lee D D, Kang S J L, Petzow G. Effect of α to β (β’) phase transition on the sintering of silicon nitride ceramics[J]. J Am Ceram Soc, 1990, 73(3): 767. |
| [12] |
Jiang J Z, Kragh F, Frost D J. Hardness and thermal stability of cubic silicon nitride[J]. J Phys: Condens Matter, 2001, 13(22). |
| [13] |
Kuwabara A, Matsunaga K, Tanaka I. Lattice dynamics and thermodynamical properties of silicon nitride polymorphs[J]. Phys Rev B, 2008, 78(6): 064104. |
| [14] |
Xu B, Dong J J, McMillan P F. Equilibrium and metastable phase transitions in silicon nitride at high pressure: a firstprinciples and experimental study[J]. Phys Rev B, 2011, 84(1): 014113. |
| [15] |
Togo A, Kroll P. First-principles lattice dynamics calculations of the phase boundary between β-Si3N4 and c-Si3N4 at elevated temperatures and pressure[J]. J Comput Chem, 2008, 29(13): 2255. |
| [16] |
He H L, Sekine T, Kobayashi T. Shock-induced phase transition of β-Si3N4 to c-Si3N4[J]. Phys Rev B, 2000, 62(17): 11412. |
| [17] |
Tatsumi K, Tanaka I, Adachi H. Theoretical prediction of postspinel phases of silicon nitride[J]. J Am Ceram Soc, 2002, 85(1): 7. |
| [18] |
Anatole von Lilienfeld O, Tavernelli I, Rothlisberger U. Optimization of effective atom centered potentials for London dispersion forces in density functional theory[J]. Phys Rev Lett, 2004, 93(15): 153004. |
| [19] |
Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects[J]. Phys Rev, 1965, 140(4A). |
| [20] |
Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple[J]. Phys Rev Lett, 1996, 77(18): 3865. |
| [21] |
Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations[J]. Phys Rev B, 1976, 13(12): 5188. |
| [22] |
Pfrommer B G, Côté M, Louie S G. Relaxation of crystals with the quasi-Newton method[J]. J Comput Phys, 1997, 131(1): 233. |
| [23] |
Blanco M A, Francisco E, Luaña V. Gibbs: isothermal-isobaric thermodynamics of solids from energy curves using a quasiharmonic Debye model[J]. Comput Phys Commun, 2004, 158(1): 57. |
| [24] |
Otero-de-la-Roza A, Abbasi-Pérez D, Lua~na V. Lua~na V. Gibbs2: a new version of the quasi-harmonic model code. II. models for solidstate thermodynamics, features and implementation[J]. Comput Phys Commun, 2011, 182: 10-2232. |
| [25] |
Yu B H, Chen D. Phase transition character and thermodynamic modeling of the P6 and P6' hexagonal Si–N system supplemented by first-principles calculations[J]. J Alloys Compd, 2013, 581: 747. |
| [26] |
Ching W Y, Ouyang L Z, Gale J D. Full ab initio geometry optimization of all known crystalline phases of Si3N4[J]. Phys Rev B, 2000, 61(13): 8696. |
| [27] |
Yashima M, Ando Y, Tabira Y. Crystal structure and electron density of β-silicon nitride: experimental and theoretical evidence for the covalent bonding and charge transfer[J]. Organ Chem, 2007, 38(28): 28003. |
| [28] |
Priest H P, Burns F C, Priest G L. Oxygen content of alpha silicon nitride[J]. J Am Ceram Soc, 1973, 56(7): 395. |
| [29] |
Hirosaki N, Ogata S, Kocer C. Molecular dynamics calculation of the ideal thermal conductivity of single-crystal β- and α-Si3N4[J]. Phys Rev B, 2002, 65(13): 134110. |
| [30] |
Ching W Y, Xu Y N, Gale J D. Ab initio total energy calculation of β- and α-silicon nitride and the derivation of effective pair potentials with application to lattice dynamics[J]. J Am Ceram Soc, 1998, 81(12): 3189. |
| [31] |
Born M, Huang K. Dynamical theory of crystal lattices[J]. Oxford: Clarendon, 1956. |
| [32] |
Ventelon L, Willaime F, Clouet E. Ab initio investigation of the Peierls potential of screw dislocations in bcc Fe and W[J]. Acta Mater, 2013, 61(11): 3973. |
| [33] |
Mulliken R S. Electronic population analysis on LCAO-MO molecular wave functions[J]. J Chem Phys, 1955, 23(10): 1833. |
| [34] |
Ren S Y, Ching W Y. Electronic structures of α- and β-silicon nitride[J]. Phys Rev B, 1981, 23(10): 5454. |
| [35] |
Oh J W, Kim C Y, Nahm K S. The hydriding kinetics of LaNi4.5AL0.5 with hydrogen[J]. J Alloys Compd, 1998, 278(1/2): 270. |
| [36] |
He J L, Wu E D, Wang H T. Ionicties of boron–boron bonds in B12 icosahedra[J]. Phys Rev Lett, 2005, 94(1): 015504. |
| [37] |
Ching W Y, Mo S D, Ouyang L Z. Electronic and optical properties of the cubic spinel phase of c-Si3N4, c-Ge3N4, c-SiGe2N4, and c-GeSi2N4[J]. Phys Rev B, 2001, 62(24): 245110. |
D Chen, Y P Cang, Y S Luo. Electronic structures and phase transition characters of β-, P61-, P62- and δ-Si3N4 under extreme conditions: a density functional theory study[J]. J. Semicond., 2015, 36(2): 023003. doi: 10.1088/1674-4926/36/2/023003.
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Manuscript received: 05 July 2014 Manuscript revised: Online: Published: 01 February 2015
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