High-pressure Effect of Elastic and Mechanical Properties of Hexagonal Gallium Nitride
Main Article Content
Abstract
This study examines an effect of pressure up to 50 GPa on the elastic and mechanical properties of wurtzite gallium nitride (w-GaN) by using classical potential within the Atomistic Tool Kit (ATK)-force field. The obtained results show that the elastic constants and other related parameters, such as Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropy factor and Kleinman parameter increase monotonically with increase of pressure up to 32 GPa. Beyond this pressure, we observed a non-linear behavior with increase in pressure. This might be attributed to the phase transition in GaN in the pressure range of 33.4 - 44.6 GPa. The results obtained for zero pressure are consistent with both experimental data and the theoretical data shown in references.
Keywords:
Elastic constants, mechanical properties, wurtzite gallium nitride, high-pressure
References
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[26] S. Wang, J.-X. Li, Y.-L Du, C. Cui, First-Principles Study on Structural, Electronic and Elastic Properties of Graphene-like Hexagonal Ti2C Monolayer, Comp. Mat. Sc, Vol. 83, 2014, pp. 290–293, https://doi.org/10.1016/j.commatsci.2013.11.025.
[27] L. Feng, N. Li, M. Yang, Z. Liu, Effect of Pressure on Elastic, Mechanical and Electronic Properties of WSe2: A FIrst-Principles Study, Mat. Res. Bull, Vol. 50, 2014, pp. 503–508, https://doi.org/10.1016/j.materresbull.2013.11.016.
[28] L. Bing, L. Rong-Feng, Y. Yong, Y. Xiang-Dong, Characterisation of The High-Pressure Structural Transition and Elastic Properties in Boron Arsenic, Chin. Phys. B, Vol. 19, 2010, pp. 076201, https://doi.org/10.1088/1674-1056/19/7/076201.
[29] S. Bensalem, M. Chegaar, D. Maouche, A. Bouhemadou, Theoretical Study of Structural, Elastic and Thermodynamic Properties of CZTX (X=S and Se) Alloys, J. Alloys and Compounds, Vol. 589, 2014, pp. 137-142, https://doi.org/10.1016/j.jallcom.2013.11.113.
[30] M. Guemou, A. Abdiche, R. Riane, R. Khenata, Ab Initio Study of the Structural, Electronic and Optical Properties of Bas and BN Compounds and BNxAs1−x alloys, Phys. B: Condens. Matter, Vol. 436, 2014, pp. 33–40, https://doi.org/10.1016/j.physb.2013.11.030.
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[34] X.-Q. Chen, H. Niu, D. Li, Y. Li, Modeling Hardness of Polycrystalline Materials and Bulk Metallic Glasses, Intermetallics, Vol. 19, 2011, pp. 1275–1281, https://doi.org/10.1016/j.intermet.2011.03.026.
[35] S.F. Pugh, Relation between the Elastic Moduli and the Plastic Properties of Polycrystalline Pure Metals, Phil. Mag. J. Sc, Vol. 45, 1954, pp. 823–843, https://doi.org/10.1080/14786440808520496.
[36] G.N. Greaves, A.L. Greer, R.S. Lakes, T. Rouxel, Poisson’s Ratio and Modern Materials, Nature Materials, Vol. 10, 2011, pp. 823–837, https://doi.org/10.1038/nmat3134.
[37] Y. Cao, J. Zhu, Y. Liu, Z. Nong, Z. Lai, First-Principles Studies of the Structural, Elastic, Electronic and Thermal properties of Ni3Si, Comp. Mat. Sc, Vol. 69, 2013, pp. 40-45, https://doi.org/10.1016/j.commatsci.2012.11.037.
[38] C. Zener, Theory of Strain Interaction of Solute Atoms, Phys. Rev, Vol. 74, 1948, pp. 639–647, https://doi.org/10.1103/physrev.74.639.
[39] A.W. Harrison, Electronic Structure and Properties of Solids, New York: Dover, 1989.
[2] A. Sadao, Properties of Group-IV, III-V and II-VI Semiconductors, Hoboken (USA) Wiley&Sons, 2005.
[3] S. Nakamura, In Proceedings of International Symposium, Blue Laser and Light Emitting Diodes, 1996.
[4] F.S. Saoud, J.C. Plenet, L. Louail, D. Maouche, Mechanism of the Phase Transition in GaN Under Pressure up to 100 GPa, Comp. Theo. Chem, Vol. 964, 2011, pp. 65-71, https://doi.org/10.1016/j.comptc.2010.11.037.
[5] M. Yamaguchi, T. Yagi, T. Azuhata, T. Sota, K. Suzuki, S. Chichibu, S. Nakamura, Brillouin Scattering Study of Gallium Nitride: Elastic Stiffness Constants, J. Phys.: Condens. Matter, Vol. 9, 1997, pp. 241, https://doi.org/10.1088/0953-8984/9/1/025.
[6] S. Nakamura, T. Mukai, M. Senoh, Candela‐class High‐brightness InGaN/AlGaN Double‐heterostructure Blue‐Light‐Emitting Diodes, Appl. Phys. Lett, Vol. 64, 1994, pp. 1687-1689, https://doi.org/10.1063/1.111832.
[7] S.Y. Davydov, Evaluation of Physical Parameters for the Group III Nitrates: BN, AlN, GaN, and InN, Semiconductors, Vol. 36, 2002, pp. 41–44, https://doi.org/10.1134/1.1434511.
[8] A.F. Wright, Elastic Properties of Zinc-blende and Wurtzite AlN, GaN, and InN, J. Appl. Phys, Vol. 82, 1997, pp. 2833–2839, https://doi.org/10.1063/1.366114.
[9] N. Lebga, S. Daoud, X.-W. Sun, N. Bioud, A. Latreche, Mechanical and Thermophysical Properties of Cubic Rock-Salt AlN Under High Pressure, J. Electronic Mat, Vol. 47, 2018, pp. 3430–3439, https://doi.org/10.1007/s11664-018-6169-x.
[10] A. Polian, M. Grimsditch, I. Grzegory, Elastic Constants of Gallium Nitride, J. Appl. Phys, Vol. 79, 1996, pp. 3343-3344, https://doi.org/10.1063/1.361236.
[11] T. Li-Na, H. Cui-E, Y. Bai-Ru, C. Xiang-Rong, First-principles Calculations of Structure and High Pressure Phase Transition in Gallium Nitride, Chin. Phys, Vol. 16, 2007, pp. 3772–3776, https://doi.org/10.1088/1009-1963/16/12/036.
[12] M.E. Sherwin, T.J. Drummond, Predicted Elastic Constants and Critical Layer Thicknesses for Cubic Phase AlN, GaN, and InN on β‐SiC, J. Appl. Phys, Vol. 69, 1991, pp. 8423-8425, https://doi.org/10.1063/1.347412.
[13] J. Nord, K. Albe, P. Erhart, K. Nordlund, Modelling of Compound Semiconductors: Analytical Bond-order Potential for Gallium, Nitrogen, Gallium Nitride, J. Phys.: Condens. Matter, Vol. 15, 2003, pp. 5649, https://doi.org/10.1088/0953-8984/15/32/324.
[14] Atomistix ToolKit 2017.2. Quantumwise A/S, www.quantumwise.com.
[15] V.A. Savastenko, A.U. Sheleg, Study of the Elastic Properties of Gallium Nitride, Physica Status Solidi (a), Vol. 48, 1978, pp. K135–K139, https://doi.org/10.1002/pssa.2210480253.
[16] M. Born, On the Stability of Crystal Lattices, Math. Proceedings of the Cambridge Philosophical Society, Vol. 36, 1940, pp. 160-172, https://doi.org/10.1017/S0305004100017138.
[17] F. Mouhat, F.-X. Coudert, Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems, Phys. Rev. B, Vol. 90, 2014, pp.22410, https://doi.org/10.1103/physrevb.90.224104.
[18] M.-M. Soumelidou, I. Belabbas, J. Kioseoglou, P. Komninou, J. Chen, T. Karakostas, Strain and Elastic Constants of GaN and InN, Comp. Condens. Matter, Vol. 10, 2017, pp. 25–30, https://doi.org/10.1016/j.cocom.2017.02.001.
[19] K. Kim, W.R.L. Lambrecht, B. Segall, Elastic Constants and Related Properties of Tetrahedrally Bonded BN, AlN, GaN, and InN, Phys. Rev. B, Vol. 53, 1996, pp. 16310–16326, https://doi.org/10.1103/physrevb.53.16310.
[20] M. Ueno, M. Yoshida, A. Onodera, O. Shimomura, K. Takemura, Stability of the Wurtzite-type Structure Under High Pressure: GaN and InN, Phys. Rev. B, Vol. 49, 1994, pp. 14–21, https://doi.org/10.1103/physrevb.49.14.
[21] T. Tsuchiya, K. Kawamura, O. Ohtaka, H. Fukui, T. Kikegawa, Precise Measurement of Equation-of-State and Elastic Properties for GaN up to 16 GPa, Solid State Comm, Vol. 121, 2002, pp. 555-559, https://doi.org/10.1016/S0038-1098(01)00492-6.
[22] P. Perlin, C. Jauberthie-Carillon, J.P. Itie, A. San Miguel, I. Grzegory, A. Polian, Raman Scattering and X-ray-Absorption Spectroscopy in Gallium Nitride Under High Pressure, Phys. Rev. B, Vol. 45, 1992, pp. 83–89, https://doi.org/10.1103/physrevb.45.83.
[23] P. Perlin, C. Jauberthie-Carilln, J.P. Itie, A. San Higuel, I. Grzecory, A. Wlian, High Pressure Phase Transition in Gallium Nitride, High Press. Res, Vol. 7, 1991, pp. 96–98. https://doi.org/10.1080/08957959108245516.
[24] M. Leszczynski, T. Suski, P. Perlin, H. Teisseyre, I. Grzegory, M. Bockowski, J. Major, Lattice Constants, Thermal Expansion and Compressibility of Gallium Nitride, J. Phys. D: Appl. Phys, Vol. 28, No. 4A, 1995, pp. A149–A153, https://doi.org/10.1088/0022-3727/28/4a/029.
[25] J. Serrano, A. Rubio, E. Hernández, A. Muñoz, A. Mujica, Theoretical Study of the Relative Stability of Structural Phases in Group-III Nitrides at High Pressures, Phys. Rev. B, Vol. 62, 2000, pp. 16612–16623, https://doi.org/10.1103/physrevb.62.16612.
[26] S. Wang, J.-X. Li, Y.-L Du, C. Cui, First-Principles Study on Structural, Electronic and Elastic Properties of Graphene-like Hexagonal Ti2C Monolayer, Comp. Mat. Sc, Vol. 83, 2014, pp. 290–293, https://doi.org/10.1016/j.commatsci.2013.11.025.
[27] L. Feng, N. Li, M. Yang, Z. Liu, Effect of Pressure on Elastic, Mechanical and Electronic Properties of WSe2: A FIrst-Principles Study, Mat. Res. Bull, Vol. 50, 2014, pp. 503–508, https://doi.org/10.1016/j.materresbull.2013.11.016.
[28] L. Bing, L. Rong-Feng, Y. Yong, Y. Xiang-Dong, Characterisation of The High-Pressure Structural Transition and Elastic Properties in Boron Arsenic, Chin. Phys. B, Vol. 19, 2010, pp. 076201, https://doi.org/10.1088/1674-1056/19/7/076201.
[29] S. Bensalem, M. Chegaar, D. Maouche, A. Bouhemadou, Theoretical Study of Structural, Elastic and Thermodynamic Properties of CZTX (X=S and Se) Alloys, J. Alloys and Compounds, Vol. 589, 2014, pp. 137-142, https://doi.org/10.1016/j.jallcom.2013.11.113.
[30] M. Guemou, A. Abdiche, R. Riane, R. Khenata, Ab Initio Study of the Structural, Electronic and Optical Properties of Bas and BN Compounds and BNxAs1−x alloys, Phys. B: Condens. Matter, Vol. 436, 2014, pp. 33–40, https://doi.org/10.1016/j.physb.2013.11.030.
[31] W. Voigt, Textbook of crystal physics, 962, Leipzig: Teubner, 1928.
[32] A. Reuss, Calculation of the Yield Point of Mixed Crystals Based on the Plasticity Condition for Single Crystals, ZAMM-J. Appl. Math. Mech, Vol. 9, 1992, pp. 49-58.
[33] E. Schreiber, O.L. Anderson, N. Soga, Elastic Constants and their Measurement, New York: McGraw-Hill, 1973, pp. 1-79.
[34] X.-Q. Chen, H. Niu, D. Li, Y. Li, Modeling Hardness of Polycrystalline Materials and Bulk Metallic Glasses, Intermetallics, Vol. 19, 2011, pp. 1275–1281, https://doi.org/10.1016/j.intermet.2011.03.026.
[35] S.F. Pugh, Relation between the Elastic Moduli and the Plastic Properties of Polycrystalline Pure Metals, Phil. Mag. J. Sc, Vol. 45, 1954, pp. 823–843, https://doi.org/10.1080/14786440808520496.
[36] G.N. Greaves, A.L. Greer, R.S. Lakes, T. Rouxel, Poisson’s Ratio and Modern Materials, Nature Materials, Vol. 10, 2011, pp. 823–837, https://doi.org/10.1038/nmat3134.
[37] Y. Cao, J. Zhu, Y. Liu, Z. Nong, Z. Lai, First-Principles Studies of the Structural, Elastic, Electronic and Thermal properties of Ni3Si, Comp. Mat. Sc, Vol. 69, 2013, pp. 40-45, https://doi.org/10.1016/j.commatsci.2012.11.037.
[38] C. Zener, Theory of Strain Interaction of Solute Atoms, Phys. Rev, Vol. 74, 1948, pp. 639–647, https://doi.org/10.1103/physrev.74.639.
[39] A.W. Harrison, Electronic Structure and Properties of Solids, New York: Dover, 1989.