WJCMP  Vol.2 No.3 , August 2012
Ab Initio Calculations for the Effect of Pressure on the Structural Properties of Si Nanoclusters
Abstract: Lattice constant, bulk modulus, Young modulus, valence band width, conduction band width, energy gap, vibrational energy, and plasmon energy have been calculated under compression and tensile stresses in the range (0 ± 10 GPa) for 8, 54, 128 atom clusters of silicon by means of density functional theory method with restricted Hartree-Fock theory within the framework of large unit cell approach. It is found that the results deduced from eight atom cluster are in good agreement with the corresponding experimental values. On the other hand, bulk modulus, young modulus, valence band width, energy gap, and Plasmon energy increase (decrease) under compression (tensile), while volume decreases (increases) with compression (tensile). The vibrational energy has a minimum value at the ground state point. The conduction band width has no systematic behavior with pressure.
Cite this paper: N. Nama, Z. Mijbil, H. Aboud and A. Abdul-Lettif, "Ab Initio Calculations for the Effect of Pressure on the Structural Properties of Si Nanoclusters," World Journal of Condensed Matter Physics, Vol. 2 No. 3, 2012, pp. 133-138. doi: 10.4236/wjcmp.2012.23022.

[1]   M. Gabrysch, “Electronic Properties of Diamond,” Uppsala University, 2008.

[2]   M. Virgilio, G. Pizzi and G. Grosso, “Optical Gain in Short Period Si/Ge Superlattices on [001]-SiGe Substrates,” Journal of Applied Physics, Vol. 110, No. 8, 2011, Article ID: 083105. doi:10.1063/1.3651196

[3]   M. Upadhyay, S. Murugavel, M. Anbarasu and T. R. Ravindran, “Structural Study on Amorphous and Crystalline State of Phase Change Material,” Journal of Applied Physics, Vol. 110, No. 8, 2011, Article ID: 083711. doi:10.1063/1.3653265

[4]   F. Cataldo, “Carbon Allotropy and Carbon Black,” Kautschuk Gummi Kunststoffe, Vol. 54, No. 1-2, 2001, pp. 22-28.

[5]   C. W. Myles, J. Dong and O. F. Sankey, “Structural and Electronic Properties of Tin Clathrate Materials,” Physical Review B, Vol. 64, 2001, Article ID: 165202. doi:10.1103/PhysRevB.64.165202

[6]   M. Gaith and I. Alhayek, “Correlation between Overall Elastic Stiffness, Bulk Modulus and Interatomic Distance in Anisotropic Materials: Semiconductors,” Reviews on Advanced Materials Science, Vol. 21, No. 2, 2009, pp. 183-191.

[7]   R. E. Stallcup II, L. M. Villarreal, S. C. Lim, I. Akwani, A. F. Aviles and J. M. Perez, “Atomic Structure of the Diamond (100) Surface Studied Using Scanning Tunneling Microscopy,” Journal of Vacuum Science and Technology B, Vol. 14, No. 2, 1996, pp. 929-932. doi:10.1116/1.589177

[8]   B. K. Serdega, E. V. Nikitenko and Prikhodenko, “Effect of Surface Condition on Strain in Semiconductor Crystal Sample,” Semiconductor Physics, Quantum Electronics and Optoelectronics, Vol. 4, No. 1, 2001, pp. 9-11.

[9]   J. Pollmann, P. Krüger, M. Rohlfing, M. Sabisch and D. Vogel, “Ab Initio Calculations of Structural and Electronic Properties of Prototype Surfaces of Group IV, III-V and II-VI Semiconductors,” Applied Surface Science, Vol. 104-105, 1996, pp. 1-16. doi:10.1016/S0169-4332(96)00114-6

[10]   A. Otero-de-la-Roza and V. Lua?a, “Topological Characterization of the Electron Density Laplacian in Crystals. The Case of the Group IV Elements,” Journal of Chemical Theory and Computation, Vol. 6, No. 12, 2010, pp. 3761-3979. doi:10.1021/ct100269e

[11]   L. A. Woldering, L. Abelmann and M. C. Elwenspoek, “Predicted Photonic Band Gaps in Diamond-Lattice Crystals Built from Silicon Truncated Tetrahedrons,” Journal of Applied Physics, Vol. 110, No. 4, 2011, Article ID: 043107. doi:10.1063/1.3624604

[12]   Q. Zhou, X. Hu, K. Al-Hemyari, K. McCarthy, L. Domash and J. A. Hudgings, “High Spatial Resolution Characterization of Silicon Solar Cells Using Thermoreflectance Imaging,” Journal of Applied Physics, Vol. 110, No. 5, 2011, Article ID: 053108. doi:10.1063/1.3629979

[13]   J. Kim and D. Ahn, “Effect of Indirect Interband Absorp- tion in Ge/SiGe Quantum Wells,” Journal of Applied Physics, Vol. 110, No. 8, 2011, Article ID: 083119. doi:10.1063/1.3656688

[14]   N. A. Nama, M. A. Abdulsattar and A. M. Abdul-Lettif, “Surface and Core Electronic Structure of Oxidized Sili- con Nanocrystals,” Journal of Nanomaterials, Vol. 2010, 2010, Article ID: 952172. doi:10.1155/2010/952172

[15]   S. M. Sze and K. K. Ng, “Physics of Semiconductor Devices,” 3rd Edition, John Wiley & Sons, New York, 2007.

[16]   S. J. Clark and G. J. Ackland, “Vibrational and Elastic Effects of Point Defects in Silicon,” Physical Review B, Vol. 48, No. 15, 1993, pp. 10899-10908. doi:10.1103/PhysRevB.48.10899

[17]   M. Luppi and S. Ossicini, “Ab initio Study on Oxidized Silicon Clusters and Silicon Nanocrystals Embedded in SiO: Beyond the Quantum Confinement Effect,” Physical Review B, Vol. 71, No. 3, 2005, Article ID: 035340.

[18]   T. Van Buuren, L. N. Dinh, L. L. Chase, W. J. Siekhaus and L. J. Terminello, “Changes in the Electronic Properties of Si Nanocrystals as a Function of Particle Size,” Physical Review Letters, Vol. 80, No. 17, 1998, pp. 3803- 3806. doi:10.1103/PhysRevLett.80.3803

[19]   P. Carrier, “Curvature Effects on Optical Response of Si Nanocrystals in SiO2 Having Interface Silicon Suboxides,” Physical Review B, Vol. 80, No. 7, 2009, Article ID: 075319. doi:10.1103/PhysRevB.80.075319

[20]   M. A. Abdulsattar and K. H. Al-Bayati, “Corrections and Parametrization of Semiempirical Large Unit Cell Me- thod for Covalent Semiconductors,” Physical Review B, Vol. 75, No. 24, 2007, Article ID: 245201. doi:10.1103/PhysRevB.75.245201

[21]   W. Hehre, L. Radom, P. Schileyer and J. Pople, “Ab Initio Molecular Orbital Theory,” Wiley, New York, 1986.

[22]   M. A. Abdulsattar, “Size Effects of Semiempirical Large Unit Cell Method in Comparison with Nanoclusters Properties of Diamond-Structured Covalent Semiconductors,” Physica E, Vol. 41, No. 9, 2009, pp. 1679-1688. doi:10.1016/j.physe.2009.06.003

[23]   A. Harker and F. Larkins, “A Large Unit Cell Semiem- pirical Molecular Orbital Approach to the Properties of Solids. I. General Theory,” Journal of Physics C, Vol. 12, 1979, pp. 2487-2495.

[24]   A. Harker and F. Larkins, “A Large Unit Cell Semiempirical Molecular Orbital Approach to the Properties of Solids. II. Covalent Materials: Diamond and Silicon,” Journal of Physics C, Vol. 12, 1979, pp. 2497-2508.

[25]   R. Evarestov, M. Petrashen and E. Lodovskaya, “The Translational Symmetry in the Molecular Models of Solids,” Physica Status Solidi (b), Vol. 68, No. 1, 1975, pp. 453-461. doi:10.1002/pssb.2220680145

[26]   M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., “Gaus- sian 03,” Revision B.01, Gaussian, Inc., Pittsburgh, 2003.

[27]   I. O. Radi, M. A. Abdulsattar and A. M. Abdul-Lettif, “Semiempirical LUC-INDO Calculations on the Effect of Pressure on the Electronic Structure of Diamond,” Physica Status Solidi (b), Vol. 244, No. 4, 2007, pp. 1304- 1317. doi:10.1002/pssb.200541329

[28]   C. A. Perottoni, A. S. Pereira and J. A. H. da Jornada, “Periodic Hartree-Fock Linear Combination of Crystalline Orbitals Calculation of the Structure, Equation of State and Elastic Properties of Titanium Diboride,” Jour- nal of Physics: Condensed Matter, Vol. 12, No. 32, 2000, pp. 7205-7222. doi:10.1088/0953-8984/12/32/305

[29]   J. Xie, S. P. Chen, J. S. Tse, S. de Gironcoli and S. Baroni, “High-Pressure Thermal Expansion, Bulk Modulus, and Phonon Structure of Diamond,” Physical Review B, Vol. 60, No. 13, 1999, pp. 9444-9449. doi:10.1103/PhysRevB.60.9444

[30]   J. Zheng, C. H. A. Haun, A. T. S. Wee, R. Wang and Y. Zheng, “Ground State Properties of Cubic C-BN Solid Solutions,” Journal of Physics: Condensed Matter, Vol. 11, No. 3, 1999, pp. 927-935. doi:10.1088/0953-8984/11/3/030

[31]   S. Q. Wang and H. Q. Ye, “Plane-Wave Pseudopotential Study on Mechanical and Electronic Properties for IV and III-V Crystalline Phases with Zinc-Blende Structure,” Physical Review B, Vol. 66, 2002, Article ID: 235111. doi:10.1103/PhysRevB.66.235111

[32]   T. Faisst, “Temperature Dependence of the Thermal Ex- pansion Coefficient, Bulk Modulus and Magnetic Grueneisen Constant of Nickel Near the Curie Point,” Journal De Physique, Vol. 49, No. 12, 1988, pp. 65-66. doi:10.1051/jphyscol:1988819

[33]   W. Kim, M. Kim, Y. Chang, J. Shin and J. Bae, “Fatigue Crack Growth Behavior of NR and HNBR Based Vulcanizates with Potential Application to Track Pad for Heavy Weight Vehicles,” Macromolecular Research, Vol. 11, No. 2, 2003, pp. 73-79. doi:10.1007/BF03218333

[34]   Z. Y. Mijbil, H. I. Aboud and A. M. Abdul-Lettif, “Varia- tion of the Structural Properties of IV Element Nano Clusters Due to Tensile Stress,” World Journal of Con- densed Matter Physics, Vol. 2, 2012, pp. 16-23. doi:10.4236/wjcmp.2012.21003

[35]   P. E. Van Camp, V. E.Van Doren and J. T. Devreese, “Ground-State and Electronic Properties of Covalent Solids,” Physical Review, Vol. 38, No. 17, 1988, pp. 12675- 12678. doi:10.1103/PhysRevB.38.12675

[36]   S. Q. Wang and H. Q. Ye, “Plane-Wave Pseudopotential Study on Mechanical and Electronic Properties for IV and III-V Crystalline Phases with Zinc-Blende Structure,” Physical Review B, Vol. 66, 2002, Article ID: 235111. doi:10.1103/PhysRevB.66.235111

[37]   P. K. Lam, M. L. Cohen, and G. Martinez, “Analytic Relation between Bulk Moduli and Lattice Constants,” Phy- sical Review B, Vol. 35, No. 17, 1987, pp. 9190-9194. doi:10.1103/PhysRevB.35.9190

[38]   S. H. Lee, J. H. Kang and M. H. Kang, “Structural Properties of Semiconductors in the Generalized Gradient Ap- proximation,” Journal of the Korean Physical Society, Vol. 31, No. 3, 1997, pp. 811-814.

[39]   M. Welkowsky and R. Braunstein, “Interband Transitions and Exciton Effects in Semiconductors,” Physical Review B, Vol. 5, No. 3, 1972, pp. 497-509. dio:10.1103/PhysRevB.5.497

[40]   C. Kittel, “Introduction to Solid State Physics,” 5th Edi- tion, John Wiley & Sons, New York, 1976.

[41]   A. Mujica, A. Rubio, A. Munoz and R. J. Need, “High Pressure Phaces of Group-IV, III-V, and II-VI Com- pounds,” Reviews of Modern Physics, Vol. 75, 2003, pp. 863-907. doi:10.1103/RevModPhys.75.863

[42]   J. R. Chelikowsky, "High-Pressure Phase Transition in Diamond and Zinc-Blende Semiconductors,” Physical Review B, Vol. 35, No. 3, 1987, pp. 1174-1180. doi:10.1103/PhysRevB.35.1174

[43]   S. Casolo, E. Flage-Larsen, O. M. L?vvik, G. R. Darling and G. F. Tantardini, “Role of the Self-Interaction Error in Studying First Principles Chemisorption on Graphene,” 2010.

[44]   M. Kuisma, J. Ojanen, J. Enkovaara and T. T. Rantala, “Kohn-Sham Potential with Discontinuity for Band Gap Materials,” 2010.

[45]   J. P. Connerade, P. Kengkan, P. A. Lakshmi and R. Se- maoune, “Scaling Laws for Atomic Compressibility,” Journal of Physics B: Atomic and Molecular Optical Physics, Vol. 33, 2000, pp. L847-L854.

[46]   S. M. Sze, “Semiconductor Devices: Physics and Technology,” Dar Al-Hikma, Mosul, 1990.

[47]   J. Z. Jiang, H. Lindelov, L. Gerward, K. St?hl, J. M. Recio, P. Mori-Sanchez, S. Carlson, M. Mezouar, E. Dooryhee, A. Fitch and D. J. Frost, “Compressibility and Thermal Expansion of Cubic Silicon Nitride,’’ Physical Review B, Vol. 65, 2002, Article ID: 161202(R). doi:10.1103/PhysRevB.65.161202

[48]   M. P. D’Evelyn and T. Taniguchi, “Elastic Properties of Translucent Polycrystalline Cubic Boron Nitride as Characterized by the Dynamic Resonance Method,” GE Research & Development Center, General Electric Company, 1998.

[49]   B. T. Wang, P. Zhang, H. L. Shi, B. Sun and W. D. Li, “Mechanical and Chemical Bonding Properties of Ground State BeH2,” The European Physical Journal B, Vol. 74, No. 3, 2010, pp. 303-308. doi:10.1140/epjb/e2010-00081-x

[50]   L. C. M. Miranda and D. ter Haar, “Plasma Effects in Sound Amplification in Piezo-Electric Semiconductors,” Revista Brasileira de Física, Vol. 2, No. 2, 1972, pp. 77- 86.

[51]   J. A. Sanjurjo, E. López-Cruz, P. Vogl and M. Cardona, “Dependence on Volume of the Phonon Frequencies and the IR Effective Charges of Several III-V Semiconduc- tors,” Physical Review B, Vol. 28, No. 8, 1983, pp. 4579-4584. doi:10.1103/PhysRevB.28.4579

[52]   E. Burstein, S. Perkowitz and M. H. Brodsk, “The Dielectric Properties of the Cubic iv-vi Compound Semiconductors,’’ Journal De Physique, Vol. 29, No. 11-12, 1968, pp. 78-83. doi:10.1051/jphyscol:1968411

[53]   K. Parliński, “First-Principles Calculations of Vibrational and Thermodynamical Properties of Solids,” Materials Science-Poland, Vol. 23, No. 2, 2005, pp. 357-363.

[54]   T. Iitaka and T. Ebisuzaki, “First-Principles Calculation of Elastic Properties of Solid Argon at High Pressures,” Riken Review, No. 48, 2001, pp. 12-15.

[55]   J. Xie, S. de Gironcoli, S. Baroni and M. Scheffler, “First-Principles Calculation of the Thermal Properties of Silver,” Physical Review B, Vol. 59, No. 2, 1999, pp. 965-969. doi:10.1103/PhysRevB.59.965

[56]   J. Polit, E. M. Sheregii, J. Cebulski, B. V. Robouch, A. Marcelli, M. Cestelli Guidi, M. Piccinini, A. Kisiel, P. Zajdel, E. Burattini and A. Mycielski, “Phonon and Vi- brational Spectra of Hydrogenated CdTe,” Journal of Ap- plied Physics, Vol. 100, 2006, Article ID: 013521. doi:10.1063/1.2211368

[57]   J. N. Murrel, S. F. A. Kettle and J. M. Tedder, “The Chemical Bond,” 2nd Edition, University of Basrah, Basrah, 1982.