First-principles study on the electronic, elastic and thermodynamic properties of three novel germanium nitrides

Yuping Cang; Xiaoling Yao; Dong Chen; Fan Yang; Huiming Yang

doi:10.1088/1674-4926/37/7/072002

Abstract: The ultrasoft pseudo-potential plane wave method combined with the quasi-harmonic approach have been used to study the electronic, elastic and thermodynamic properties of the tetragonal, monoclinic and orthorhombic Ge₃N₄. The negative formation enthalpies, the satisfactory of Born's criteria and the linear variations of elastic constants with pressure indicate that the three polymorphs can retain their stabilities in the pressure range of 0-25 GPa. The three Ge₃N₄ are brittle solids at 0 GPa, while they behave in ductile manners in the pressure range of 5-25 GPa. t- and o-Ge₃N₄ are hard materials but anisotropic. m-Ge₃N₄ has the largest ductility among the three phases. The results reveal that m-Ge₃N₄ belongs to an indirect band gap semiconductor, while t- and o-Ge₃N₄ have direct band gaps. For the thermal properties, several interesting features can be observed above 300 K. o-Ge₃N₄ exhibits the largest heat capacity, while m-Ge₃N₄ shows the highest Debye temperature. The results predicted in this work can provide reference data for future experiments.

Key words: density functional theory, elastic moduli, heat capacity, equations of state

References:

[1]	Boyko T D, Hunt A, Zerr A. Electronic structure of spinel-type nitride compounds Si₃N₄, Ge₃N₄ and Sn₃N₄ with tunable band gaps:application to light emitting diodes[J]. Phys Rev Lett, 2013, 111(9): 097402.
[2]	Lee Y M, Jang S H, Han M. Chemical states and photoluminescence of Si_0.3Ge_0.7 nitride film formed by N₂⁺ gas[J]. Appl Phys Lett, 2011, 99(12): 123103.
[3]	Gao S P, Cai G H, Xu Y. Band structures for Ge₃N₄ polymorphs studied by DFT-LDA and GWA[J]. Comput Mater Sci, 2013, 67: 292.
[4]	Soignard E, McMillan P F. Raman spectroscopy of γ-Si₃N₄ and γ-Ge₃N₄ nitride spinel phases formed at high pressure and high temperature:evidence for defect formation in nitride spinels[J]. Chem Mater, 2004, 16(18): 3533.
[5]	Serghiou G, Miehe G, Tschauner O. Synthesis of a cubic Ge₃N₄ phase at high pressure and temperatures[J]. J Chem Phys, 1999, 111: 4659.
[6]	Machon D, Meersman F, Wilding M C. Pressure-induced amorphization and polyamorphism:inorganic and biochemical systems[J]. Prog Mater Sci, 2014, 61: 216.
[7]	Wang V, He H P, Zhang S L. Influence of Mn concentration on the electronic and magnetic properties of Mn doped β-Ge₃N₄:a first-principles study[J]. J Magn Magn Mater, 2012, 324(19): 2972.
[8]	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.
[9]	Ding Y C, Xiang A P, Zhu X H. First principles study on electronic and optical properties of Al-doped γ-Ge₃N₄[J]. Int J Mod Phys B, 2012, 26(32): 1250200.
[10]	Wang H, Chen Y, Kaneta Y. First-principles study on effective doping to improve the optical properties in spinel nitrides[J]. J Alloys Compd, 2010, 491(1/2): 550.
[11]	He H L, Sekine T, Kobayashi T. Phase transformation of germanium nitride Ge₃N₄ under shock wave compression[J]. J Appl Phys, 2001, 90: 4403.
[12]	Leinenweber K, O'Keeffe M, Somayazulu M. Synthesis and structure refinement of the spinel, γ-Ge₃N₄[J]. Chem Euro J, 1999, 5(10): 3076.
[13]	Wang Z, Zhao Y, Schiferl D. Threshold pressure for disappearance of size-induced effect in spinel-structure Ge₃N₄ nanocrystals[J]. J Phys Chem B, 2003, 107(51): 14151.
[14]	Luo Y S, Cang Y P, Chen D. Determination of the finite-temperature anisotropic elastic and thermal properties of Ge₃N₄:a first-principles study[J]. Comput Condens Matter, 2014, 1(1): 1.
[15]	Cui L, Hu M, Wang Q. Prediction of novel hard phases of Si₃N₄:first-principles calculations[J]. J Solid State Chem, 2015, 228: 20.
[16]	Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects[J]. Phys Rev, 1965, 140(4A): A1133.
[17]	Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple[J]. Phys Rev Lett, 1996, 77(18): 3865.
[18]	Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[J]. Phys Rev B, 1990, 41(11): 7892.
[19]	Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations[J]. Phys Rev B, 1976, 13(12): 5188.
[20]	Shanno D F, Kettler P C. Optimal conditioning of quasi-Newton methods[J]. Math Comput, 1970, 24(111): 657.
[21]	Blanco M A, Francisco E, Luańa V. Isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model[J]. Comput Phys Commun, 2004, 158(1): 57.
[22]	Sahli B, Bouafia H, Abidri B. First-principles prediction of structural, elastic, electronic and thermodynamic properties of the cubic SrUO₃-perovskite[J]. J Alloys Compd, 2015, 635: 163.
[23]	Pugh S F. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals[J]. Philos Mag, 1954, 45(7): 823.
[24]	Zhang J D, Yang K. Theoretical study of the thermodynamics properties of cubic Zr₃N₄ and Hf₃N₄ under high pressures[J]. J Alloys Compd, 2014, 608: 90.
[25]	Chen X Q, Niu H Y, Li D Z. Modeling hardness of polycrystalline materials and bulk metallic glasses[J]. Intermetallics, 2011, 19(9): 1275.
[26]	Milstein F, Zhao J H, Chantasiriwan S. Applicability of Born's stability criterion to face-centered-cubic crystals in [111] loading[J]. Appl Phys Lett, 2005, 87(25): 251919.
[27]	Liu Q J, Ran Z, Liu F S. Phase transitions and mechanical stability of TiO₂ polymorphs under high pressure[J]. J Alloys Compd, 2015, 631: 192.
[28]	Liu Q J, Zhang N C, Sun Y Y. Density-functional theory study of the pressure-induced phase transition in hydronitrogen compound N₄H₄[J]. Phys Lett A, 2014, 378(18/19): 1333.
[29]	Yang J W, Gao T, Guo L Y. Ab initio study of the structural, mechanical, and dynamical properties of the rare-earth dihydrides XH₂ (X=Sc, Y, and La)[J]. Physica B, 2013, 429: 119.
[30]	Molina B, Sansores L E. Electronic structure of Ge₃N₄ possible structures[J]. Int J Quant Chem, 2000, 80(2): 249.
[31]	Yang M, Wang S J, Feng Y P. Electronic structure of germanium nitride considered for gate dielectrics[J]. J Appl Phys, 2007, 102: 013507.

[1]	Boyko T D, Hunt A, Zerr A. Electronic structure of spinel-type nitride compounds Si₃N₄, Ge₃N₄ and Sn₃N₄ with tunable band gaps:application to light emitting diodes[J]. Phys Rev Lett, 2013, 111(9): 097402.
[2]	Lee Y M, Jang S H, Han M. Chemical states and photoluminescence of Si_0.3Ge_0.7 nitride film formed by N₂⁺ gas[J]. Appl Phys Lett, 2011, 99(12): 123103.
[3]	Gao S P, Cai G H, Xu Y. Band structures for Ge₃N₄ polymorphs studied by DFT-LDA and GWA[J]. Comput Mater Sci, 2013, 67: 292.
[4]	Soignard E, McMillan P F. Raman spectroscopy of γ-Si₃N₄ and γ-Ge₃N₄ nitride spinel phases formed at high pressure and high temperature:evidence for defect formation in nitride spinels[J]. Chem Mater, 2004, 16(18): 3533.
[5]	Serghiou G, Miehe G, Tschauner O. Synthesis of a cubic Ge₃N₄ phase at high pressure and temperatures[J]. J Chem Phys, 1999, 111: 4659.
[6]	Machon D, Meersman F, Wilding M C. Pressure-induced amorphization and polyamorphism:inorganic and biochemical systems[J]. Prog Mater Sci, 2014, 61: 216.
[7]	Wang V, He H P, Zhang S L. Influence of Mn concentration on the electronic and magnetic properties of Mn doped β-Ge₃N₄:a first-principles study[J]. J Magn Magn Mater, 2012, 324(19): 2972.
[8]	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.
[9]	Ding Y C, Xiang A P, Zhu X H. First principles study on electronic and optical properties of Al-doped γ-Ge₃N₄[J]. Int J Mod Phys B, 2012, 26(32): 1250200.
[10]	Wang H, Chen Y, Kaneta Y. First-principles study on effective doping to improve the optical properties in spinel nitrides[J]. J Alloys Compd, 2010, 491(1/2): 550.
[11]	He H L, Sekine T, Kobayashi T. Phase transformation of germanium nitride Ge₃N₄ under shock wave compression[J]. J Appl Phys, 2001, 90: 4403.
[12]	Leinenweber K, O'Keeffe M, Somayazulu M. Synthesis and structure refinement of the spinel, γ-Ge₃N₄[J]. Chem Euro J, 1999, 5(10): 3076.
[13]	Wang Z, Zhao Y, Schiferl D. Threshold pressure for disappearance of size-induced effect in spinel-structure Ge₃N₄ nanocrystals[J]. J Phys Chem B, 2003, 107(51): 14151.
[14]	Luo Y S, Cang Y P, Chen D. Determination of the finite-temperature anisotropic elastic and thermal properties of Ge₃N₄:a first-principles study[J]. Comput Condens Matter, 2014, 1(1): 1.
[15]	Cui L, Hu M, Wang Q. Prediction of novel hard phases of Si₃N₄:first-principles calculations[J]. J Solid State Chem, 2015, 228: 20.
[16]	Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects[J]. Phys Rev, 1965, 140(4A): A1133.
[17]	Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple[J]. Phys Rev Lett, 1996, 77(18): 3865.
[18]	Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[J]. Phys Rev B, 1990, 41(11): 7892.
[19]	Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations[J]. Phys Rev B, 1976, 13(12): 5188.
[20]	Shanno D F, Kettler P C. Optimal conditioning of quasi-Newton methods[J]. Math Comput, 1970, 24(111): 657.
[21]	Blanco M A, Francisco E, Luańa V. Isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model[J]. Comput Phys Commun, 2004, 158(1): 57.
[22]	Sahli B, Bouafia H, Abidri B. First-principles prediction of structural, elastic, electronic and thermodynamic properties of the cubic SrUO₃-perovskite[J]. J Alloys Compd, 2015, 635: 163.
[23]	Pugh S F. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals[J]. Philos Mag, 1954, 45(7): 823.
[24]	Zhang J D, Yang K. Theoretical study of the thermodynamics properties of cubic Zr₃N₄ and Hf₃N₄ under high pressures[J]. J Alloys Compd, 2014, 608: 90.
[25]	Chen X Q, Niu H Y, Li D Z. Modeling hardness of polycrystalline materials and bulk metallic glasses[J]. Intermetallics, 2011, 19(9): 1275.
[26]	Milstein F, Zhao J H, Chantasiriwan S. Applicability of Born's stability criterion to face-centered-cubic crystals in [111] loading[J]. Appl Phys Lett, 2005, 87(25): 251919.
[27]	Liu Q J, Ran Z, Liu F S. Phase transitions and mechanical stability of TiO₂ polymorphs under high pressure[J]. J Alloys Compd, 2015, 631: 192.
[28]	Liu Q J, Zhang N C, Sun Y Y. Density-functional theory study of the pressure-induced phase transition in hydronitrogen compound N₄H₄[J]. Phys Lett A, 2014, 378(18/19): 1333.
[29]	Yang J W, Gao T, Guo L Y. Ab initio study of the structural, mechanical, and dynamical properties of the rare-earth dihydrides XH₂ (X=Sc, Y, and La)[J]. Physica B, 2013, 429: 119.
[30]	Molina B, Sansores L E. Electronic structure of Ge₃N₄ possible structures[J]. Int J Quant Chem, 2000, 80(2): 249.
[31]	Yang M, Wang S J, Feng Y P. Electronic structure of germanium nitride considered for gate dielectrics[J]. J Appl Phys, 2007, 102: 013507.

[1]	Dong Chen, Yuping Cang, Yongsong Luo. Electronic structures and phase transition characters of β-, P61-, P62- and δ-Si₃N₄ under extreme conditions: a density functional theory study. J. Semicond., 2015, 36(2): 023003. doi: 10.1088/1674-4926/36/2/023003
[2]	M. Benaida, K. E. Aiadi, S. Mahtout, S. Djaadi, W. Rammal, M. Harb. Growth behavior and electronic properties of Ge_{n + 1} and AsGe_n (n = 1–20) clusters: a DFT study. J. Semicond., 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101
[3]	Ying Yang, Qing Feng, Weihua Wang, Yin Wang. First-principle study on the electronic and optical properties of the anatase TiO₂ (101) surface. J. Semicond., 2013, 34(7): 073004. doi: 10.1088/1674-4926/34/7/073004
[4]	Zhonghua Yang, Guili Liu, Yingdong Qu, Rongde Li. First-principle study on energy gap of CNT superlattice structure. J. Semicond., 2015, 36(10): 102002. doi: 10.1088/1674-4926/36/10/102002
[5]	Yuxiang Qin, Deyan Hua, Xiao Li. First principles study on the surface-and orientation-dependent electronic structure of a WO₃ nanowire. J. Semicond., 2013, 34(6): 062002. doi: 10.1088/1674-4926/34/6/062002
[6]	Dahua Ren, Baoyan Xiang, Cheng Hu, Kai Qian, Xinlu Cheng. The electronic and optical properties of amorphous silica with hydrogen defects by ab initio calculations. J. Semicond., 2018, 39(4): 042002. doi: 10.1088/1674-4926/39/4/042002
[7]	Azeem Nabi, Zarmeena Akhtar, Tahir Iqbal, Atif Ali, Arshad Javid. The electronic and magnetic properties of wurtzite Mn:CdS, Cr:CdS and Mn:Cr:CdS: first principles calculations. J. Semicond., 2017, 38(7): 073001. doi: 10.1088/1674-4926/38/7/073001
[8]	Jinbo Pan, Qimin Yan. Data-driven material discovery for photocatalysis: a short review. J. Semicond., 2018, 39(7): 071001. doi: 10.1088/1674-4926/39/7/071001
[9]	Haitao Li, Jun Qian, Fangfang Han, Tinghui Li. Density functional theory studies of the optical properties of a β-FeSi₂ (100)/Si (001) interface at high pressure. J. Semicond., 2013, 34(7): 072003. doi: 10.1088/1674-4926/34/7/072003
[10]	Song Qinglin, Xia Shanhong, Chen Shaofeng, Zhang Jiangang. Thermal Characteristics of silicon nitride Thin membrane. J. Semicond., 2003, 24(S1): 47.
[11]	Liu Hongxia, Zhang Heming, Song Jiuxu, Zhang Zhiyong. Electronic structures of an (8, 0) boron nitride/carbon nanotube heterojunction. J. Semicond., 2010, 31(1): 013001. doi: 10.1088/1674-4926/31/1/013001
[12]	Jiahong Zhang, Qingquan Liu, Yixian Ge, Fang Gu, Min Li, Xiaoli Mao, Hongxia Cao. Extraction of interface state density and resistivity of suspended p-type silicon nanobridges. J. Semicond., 2013, 34(5): 052002. doi: 10.1088/1674-4926/34/5/052002
[13]	Sun Lin, Yang Wenwei, Xiang Cailan, Yu Zhiping, Tian Lilin. A Broyden Method for Self-Consistent Solution of Schrdinger and Poisson Equations. J. Semicond., 2005, 26(12): 2344.
[14]	Jian Qin, Ruohe Yao. Modeling of current-voltage characteristics for dual-gate amorphous silicon thin-film transistors considering deep Gaussian density-of-state distribution. J. Semicond., 2015, 36(12): 124005. doi: 10.1088/1674-4926/36/12/124005
[15]	Bin Li, Lun Xiong, Chuan Lai, Yumei Tang. Investigation of internally finned LED heat sinks. J. Semicond., 2018, 39(3): 034002. doi: 10.1088/1674-4926/39/3/034002
[16]	Liu Yumin, Yu Zhongyuan, Yang Hongbo, Huang Yongzhen. Influences of Differently Shaped Quantum Dots on Elastic Strain Field Distributions. J. Semicond., 2005, 26(12): 2355.
[17]	Wang Hongyi, Lai Xinquan, Li Yushan. Reducing the Slope Compensation Effect on the Load Capacity of DC-DC Converters. J. Semicond., 2006, 27(8): 1484.
[18]	Wei Yuan, Xinzhou Wu, Weibing Gu, Jian Lin, Zheng Cui. Printed stretchable circuit on soft elastic substrate for wearable application. J. Semicond., 2018, 39(1): 015002. doi: 10.1088/1674-4926/39/1/015002
[19]	Dechun Bao, Lichuan Luo, Zhaohua Zhang, Tianling Ren. A power management circuit with 50% efficiency and large load capacity for triboelectric nanogenerator. J. Semicond., 2017, 38(9): 095001. doi: 10.1088/1674-4926/38/9/095001
[20]	Jianping Yao. Large-capacity and low-loss integrated optical buffer. J. Semicond., 2019, 40(5): 050205. doi: 10.1088/1674-4926/40/5/050205

First-principles study on the electronic, elastic and thermodynamic properties of three novel germanium nitrides

Search

GET CITATION

Share:

Article Metrics

History

Email This Article