Local bond average for the size and temperature dependence of elastic and vibronic properties of nanostructures

International Journal of Nanotechnology

Volumn 6, Issue 7-8, 2009, Pages 640-652

  Gu, Mingxia ^a   Sun, Chang Q ^b   Tan, Cher Ming ^b   Wang, Shanzhong ^c  

^a INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c STMICROELECTRONICS   (Singapore)

Author keywords

Elastic properties; Local bond average; Nanostructures; Vibronic properties

Indexed keywords

BOND LENGTH; NANOSTRUCTURED MATERIALS; NANOSTRUCTURES; OPTICAL CORRELATION; TEMPERATURE DISTRIBUTION;

ELASTIC PROPERTIES; LOCAL BOND AVERAGE; OPTICAL PHONON FREQUENCIES; TEMPERATURE AND PRESSURES; TEMPERATURE DEPENDENCE; TEMPERATURE-DEPENDENT CHANGES; TEMPERATURE-INDUCED; VIBRONIC PROPERTIES;

OPTICAL PROPERTIES;

EID: 66749180492     PISSN: 14757435     EISSN: None     Source Type: Journal    
DOI: 10.1504/IJNT.2009.025302     Document Type: Article

References (58)

1. Delph, T.J. (2005) 'Local stresses and elastic constants at the atomic scale', Proc. R. Soc A., Vol. 461, pp.1869-1888. (Pubitemid 40991905)
2. Cormier, J., Rickman, J.M. and Delph, T.J. (2001) 'Stress calculation in atomistic simulations of perfect and imperfect solids', J. Appl. Phys., Vol. 89, pp.99-104. (Pubitemid 33703762)
3. Sun, C.Q., Pan, L.K., Li, C.M. and Li, S. (2005) 'Size-induced acoustic hardening and optic softening of phonons in CdS, InP, CeO2, SnO2, and Si nanostructures', Phys. Rev. B, Vol. 72, pp.134301. (Pubitemid 43028850)
4. Sun, C.Q., Li, S. and Li, C.M. (2005) 'Impact of bond-order loss on surface and nanosolid mechanics', J. Phys. Chem. B, Vol. 109, pp.415-423. (Pubitemid 40120989)
5. Au Yeung, T.C., Sun, C.Q., Chiam, T.C., Ramanathan, R., Shangguan, W.Z. and Kam, C.H. (2005) 'Effect of surface bond-oder loss on the dc conductance of a metallic nanosolid', J. Appl. Phys., Vol. 98, pp.104308.
6. Sun, C.Q., Li, C.M., Bai, H.L. and Jiang, E.Y. (2005) 'Melting point oscillation of a solid over the whole range of sizes', Nanotechnology, Vol. 16, pp.1290-1293. (Pubitemid 40878638)
7. Gysin, U., Rast, S., Ruff, P., Meyer, E., Lee, D.W., Vettiger, P. and Gerber, C. (2004) 'Temperature dependence of the force sensitivity of silicon cantilevers', Phys. Rev. B, Vol. 69, pp.045403.
8. Wachtman, J.B., Tefft Jr., W.E., Lam Jr., D.G. and Apstein, C.S. (1961) 'Exponential temperature dependence of Young's modulus for several oxides', Phys. Rev., Vol. 122, pp.1754.
9. Bruls, R.J., Hintzen, H.T., With de, G. and Metselaar, R. (2001) 'The temperature dependence of the Young's modulus of MgSiN2, AlN, and Si3N4', J. Eur. Ceram. Soc., Vol. 21, pp.263.
10. Nandanpawar, M.L. and Rajagopalan, S. (1978) 'Wachtman's equation and temperature dependence of bulk moduli in solids', J. Appl. Phys., Vol. 49, pp.3976. (Pubitemid 8635293)
11. Anderson, O.L. (1966) 'Derivation of Wachtman's equation for the temperature dependence of elastic moduli of oxide compounds', Phys. Rev., Vol. 144, pp.553.
12. Gu, M.X., Zhou, Y.C., Pan, L.K., Sun, Z., Wang, S.Z. and Sun, C.Q. (2007) 'Temperature dependence of the elastic and vibronic behavior of Si, Ge and diamond crystals', J. Appl. Phys., Vol. 102, pp.083524. (Pubitemid 350025638)
13. Fine, M.E. (1953) 'Elasticity and thermal expansion of germanium between -195 and 275', J. Appl. Phys., Vol. 24, pp.338.
14. Dingreville, R., Qu, J.M. and Cherkaoui, M. (2005) 'Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films', J. Mech. Phys. Solids, Vol. 53, pp.1827. (Pubitemid 40822338)
15. Jing, G.Y., Duan, H.L., Sun, X.M., Zhang, Z.S., Xu, J., Li, Y.D., Wang, J.X. and Yu, D.P. (2006) 'Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy', Phys. Rev. B, Vol. 73, pp.235409.
16. Miller, R.E. and Shenoy, V.B. (2000) 'Size-dependent elastic properties of nanosized structural elements', Nanotechnology, Vol. 11, pp.139.
17. Chen, C.Q., Shi, Y., Zhang, Y.S., Zhu, J. and Yan, Y.J. (2006) 'Size dependence of Young's modulus in ZnO nanowires', Phys. Rev. Lett., Vol. 96, pp.075505. (Pubitemid 43291095)
18. Song, J., Wang, X., Riedo, E. and Wang, Z.L. (2005) 'Elastic property of vertically aligned nanowires', Nano Lett., Vol. 5, pp.1954. (Pubitemid 41546320)
19. Bai, X.D., Gao, P.X., Wang, Z.L. and Wang, E.G. (2003) 'Dual-mode mechanical resonance of individual ZnO nanobelts', Appl. Phys. Lett., Vol. 82, pp.4806.
20. Nilsson, S.G., Borrise, X. and Montelius, L. (2004) 'Size effect on Young's modulus of thin chromium cantilevers', Appl. Phys. Lett., Vol. 85, pp.3555.
21. Li, X., Ono, T., Wang, Y. and Esashi, M. (2003) 'Ultrathin single-crystalline-silicon cantilever resonators: fabrication technology and significant specimen size effect on Young's modulus', Appl. Phys. Lett., Vol. 83, pp.3081.
22. Li, X., Wang, X., Xiong, Q. and Eklund, P.C. (2005) 'Mechanical properties of ZnS nanobelts', Nano Lett., Vol. 5, pp.1982-1986. (Pubitemid 41548442)
23. Gaire, C., Ye, D.X., Tang, F., Picu, R.C., Wang, G.C. and Lu, T.M. (2005) 'Mechanical testing of isolated amorphous silicon slanted nanorods', J. Nanosci. Nanotechnol., Vol. 5, pp.1893. (Pubitemid 44701357)
24. Wu, B., Heidelberg, A. and Boland, J.J. (2005) 'Mechanical properties of ultrahigh-strength gold nanowires', Nat. Mater., Vol. 4, pp.525. (Pubitemid 40952746)
25. Wu, B., Heidelberg, A., Boland, J.J., Sader, J.E., Sun, X. and Li, Y. (2006) 'Microstructure-hardened silver nanowires', Nano Lett., Vol. 6, pp.468.
26. Sun, C.Q., Shi, Y., Li, C.M., Li, S. and Au Yeung, T.C. (2006) 'Size-induced under cooling and overheating in phase transition in bare and embedded clusters', Phys. Rev. B, Vol. 73, pp.075408. (Pubitemid 43270759)
27. Sun, C.Q. (2007) 'Size dependence of nanostructures: impact of bond order deficiency', Prog. Solid State Chem., Vol. 35, pp.1-159. (Pubitemid 44781442)
28. Piprek, J. and Nakamura, S. (2001) 'Physics of high-power InGaN/GaN lasers', IEE Proceedings-Optoelectronics, Vol. 149, pp.145.
29. Jain, S.C., Willander, M., Narayan, J. and van Overstraeten, R. (2000) 'III-nitrides: growth, characterization, and properties', J. Appl. Phys., Vol. 87, pp.965.
30. Link, A., Bitzer, K., Limmer, W., Sauer, R., Kirchner, C., Schwegler, V., Kamp, M., Ebling, D.G. and Benz, K.W. (1999) 'Temperature dependence of E2 and A1(LO) phonons in GaN and AlN', J. Appl. Phys., Vol. 86, pp.6256.
31. Li, W.S., Shen, Z.X., Feng, Z.C. and Chua, S.J. (2000) 'Temperature dependence of Raman scattering in hexagonal gallium nitride films', J. Appl. Phys., Vol. 87, pp.3332.
32. Kuball, M., Hayes, J.M., Shi, Y., Edgar, J.H., Prins, A.D., van Uden, N.W.A. and Dunstan, D.J. (2001) 'Raman scattering studies on single-crystalline bulk AlN: temperature and pressure dependence of the AlN phonon modes', J. Cryst. Growth, Vol. 231, pp.391.
33. Pu, X.D., Chen, J., Shen, W.Z., Ogawa, H. and Guo, Q.X. (2005) 'Temperature dependence of Raman scattering in hexagonal indium nitride films', J. Appl. Phys., Vol. 98, pp.033527. (Pubitemid 41204768)
34. Tanaka, A., Onari, S. and Arai, T. (1992) 'Raman-Scattering from Cdse microcrystals embedded in a germanate glass matrix', Phys. Rev. B, Vol. 45, pp.6587.
35. Ursaki, V.V., Tiginyanu, I.M., Zalamai, V.V., Rusu, E.V., Emelchenko, G.A., Masalov, V.M. and Samarov, E.N. (2004) 'Multiphonon resonant Raman scattering in ZnO crystals and nanostructured layers', Phys. Rev. B, Vol. 70, pp.155204. (Pubitemid 40044809)
36. Tang, H. and Herman, I.P. (1991) 'Microprobe scattering of solid silicon and germanium at the melting temperature', Phys. Rev. B, Vol. 43, pp.2299.
37. Su, Z., Sha, J., Pan, G., Liu, J., Yang, D., Dickinson, C. and Zhou, W. (2006) 'Temperature-dependent Raman scattering of silicon nanowires', J. Phys. Chem. B, Vol. 110, pp.1229. (Pubitemid 43301122)
38. Liu, M.S., Bursill, L.A. and Prawer, S. (2000) 'Temperature dependence of the first-order Raman phonon lime of diamond', Phys. Rev. B, Vol. 61, pp.3391.
39. Cui, J.B., Amtmann, K., Ristein, J. and Ley, L. (1998) 'Noncontact temperature measurements of diamond by Raman scattering spectroscopy', J. Appl. Phys., Vol. 83, pp.7929. (Pubitemid 128588728)
40. Darakchieva, V., Paskov, P.P., Valcheva, E., Paskova, T., Monemar, B., Schubert, M., Lu, H. and Schaff, W.J. (2004) 'Deformation potentials of the E1(TO) and E2 modes of InN', Appl. Phys. Lett., Vol. 84, pp.3636.
41. Klemens, P.G. (1966) 'Anharmonic decay of optical phonons', Phys. Rev., Vol. 148, pp.845-848.
42. Balkanski, M., Wallis, R.F. and Haro, E. (1983) 'Anharmonic effects in light-scattering due to optical phonons in silicon', Phys. Rev. B, Vol. 28, pp.1928.
43. Menéndez, J. and Cardona, M. (1984) 'Temperature-dependence of the 1st-order Raman-scattering by phonons in Si, Ge, and a-Sn - anharmonic effects', Phys. Rev. B, Vol. 29, pp.2051.
44. Viera, G., Huet, S. and Boufendi, L. (2001) 'Crystal size and temperature measurements in nanostructured silicon using Raman spectroscopy', J. Appl. Phys., Vol. 90, pp.4175. (Pubitemid 33025206)
45. Jiménez, J., Martín, E., Torres, A. and Landesman, J.P. (1998) 'Temperature dependence of the Raman spectrum of AlxGa1-xAs ternary alloys', Phys. Rev. B, Vol. 58, pp.10463.
46. Debernardi, A. and Cardona, M. (1999) 'First principles calculation of the real part of phonon self energy in compound semiconductors', Physica B, Vols. 263-264, pp.687.
47. Lang, G., Karch, K., Schmitt, M., Pavone, P., Mayer, A.P., Wehner, R.K. and Strauch, D. (1999) 'Anharmonic line shift and linewidth of the Raman mode in covalent semiconductors', Phys. Rev. B, Vol. 59, pp.6182.
48. Diéguez, A., Romano-Rodrýguez, A., Vilà, A. and Morante, J.R. (2001) 'The complete Raman spectrum of nanometric SnO2 particles', J. Appl. Phys., Vol. 90, pp.1550. (Pubitemid 33664589)
49. Anastassakis, E. and Liarokapis, E. (1987) 'Polycrystalline Si under strain: elastic and lattice-dynamical considerations', J. Appl. Phys., Vol. 62, pp.3346.
50. Korotcov, A.V., Huang, Y.S., Tsai, D.S. and Tiong, K.K. (2006) 'Raman scattering characterization of vertical aligned 1D IrO2 nanocrystals grown on single crystal oxide substrates', Solid State Commun., Vol. 137, pp.310-314. (Pubitemid 43145887)
51. Campbell, I.H. and Fauchet, P.M. (1986) 'The effects of microcrystal size and shape on the one phonon Raman spectra of crystalline semiconductors', Solid State Commun., Vol. 58, pp.739. (Pubitemid 16591424)
52. Wang, R.P., Zhou, G.W., Liu, Y.L., Pan, S.H., Zhang, H.Z., Yu, D.P. and Zhang, Z. (2000) 'Raman spectral study of silicon nanowires: high-order scattering and phonon confinement effects', Phys. Rev. B, Vol. 61, pp.16827.
53. Piscanec, S., Cantoro, M., Ferrari, A.C., Zapien, J.A., Lifshitz, Y., Lee, S.T., Hofmann, S. and Robertson, J. (2003) 'Raman spectroscopy of silicon nanowires', Phys. Rev. B, Vol. 68, pp.241312.
54. Alim, K.A., Fonoberov, V.A. and Balandin, A.A. (2005) 'Origin of the optical phonon frequency shifts in ZnO quantum dots', Appl. Phys. Lett., Vol. 86, pp.053103. (Pubitemid 40870889)
55. Alim, K.A., Fonoberov, V.A., Shamsa, M. and Balandina, A.A. (2005) 'Micro-Raman investigation of optical phonons in ZnO nanocrystals', J. Appl. Phys., Vol. 97, pp.124313. (Pubitemid 40925359)
56. Hwang, Y.N., Shin, S., Park, H.L., Park, S.H., Kim, U., Jeong, H.S., Shin, E.J. and Kim, D. (1996) 'Effect of lattice contraction on the Raman shifts of CdSe quantum dots in glass matrices', Phys. Rev. B, Vol. 54, pp.15120. (Pubitemid 126836802)
57. Kim, Y.K. and Jang, H.M. (2001) 'Lattice contraction and cation ordering of ZrTiO4 in the normal-to-incommensurate phase transition', J. Appl. Phys., Vol. 89, pp.6349. (Pubitemid 33599378)
58. Mishra, P. and Jain, K.P. (2000) 'Temperature-dependent Raman scattering studies in nanocrystalline silicon and finite-size effects', Phys. Rev. B, Vol. 62, pp.14790. (Pubitemid 32323695)