Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress

Journal of the Mechanics and Physics of Solids

Volumn 56, Issue 11, 2008, Pages 3144-3166

  Park, Harold S ^a   Klein, Patrick A ^b  

^a UCB 450   (United States)

^b Franklin Templeton Investments   (United States)

Author keywords

Finite elements; Nanowires; Resonant frequency; Surface Cauchy Born; Surface stress

Indexed keywords

ASPECT RATIO; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DEFORMATION; ELECTRIC WIRE; KINEMATICS; MATERIALS HANDLING EQUIPMENT; MECHANICS; NANOSTRUCTURED MATERIALS; NANOSTRUCTURES; NANOWIRES; NATURAL FREQUENCIES; STRAIN MEASUREMENT; SURFACES; THEOREM PROVING;

FINITE ELEMENTS; RESONANT FREQUENCY; SURFACE CAUCHY-BORN; SURFACE STRESS;

SURFACE PROPERTIES;

EID: 53249121012     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.08.003     Document Type: Article

References (83)

1. Balamane H., Halicioglu T., and Tiller W.A. Comparative study of silicon empirical interatomic potentials. Phys. Rev. B 46 4 (1992) 2250-2279
2. Barnes W.L., Dereux A., and Ebbeson T.W. Surface plasmon subwavelength optics. Nature 424 (2003) 824-830
3. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2002), Wiley, New York
4. Cammarata R.C. Surface and interface stress effects in thin films. Progr. Surf. Sci. 46 1 (1994) 1-38
5. Canham L.T. Silicon quantum wire array fabricated by electrochemical and chemical dissolution of wafers. Appl. Phys. Lett. 57 10 (1990) 1046-1048
6. Carr D.W., Evoy S., Sekaric L., Craighead H.G., and Parpia J.M. Measurement of mechanical resonance and losses in nanometer scale silicon wires. Appl. Phys. Lett. 75 7 (1999) 920-922
7. Chen Y., Dorgan B.L., McIlroy D.N., and Aston D.E. On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires. J. Appl. Phys. 100 (2006) 104301
8. Cleland A.N., and Roukes M.L. Fabrication of high frequency nanometer scale mechanical resonators from bulk Si crystals. Appl. Phys. Lett. 69 18 (1996) 2653-2655
9. Cleland A.N., and Roukes M.L. Noise processes in nanomechanical resonators. J. Appl. Phys. 92 5 (2002) 2758-2769
10. Craighead H.G. Nanoelectromechanical systems. Science 290 (2000) 1532-1535
11. Cuenot S., Frétigny C., Demoustier-Champagne S., and Nysten B. Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys. Rev. B 69 (2004) 165410
12. Davis Z.J., and Boisen A. Aluminum nanocantilevers for high sensitivity mass sensors. Appl. Phys. Lett. 87 (2005) 013102
13. Daw M.S., and Baskes M.I. Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29 12 (1984) 6443-6453
14. Diao J., Gall K., and Dunn M.L. Surface-stress-induced phase transformation in metal nanowires. Nat. Mater. 2 10 (2003) 656-660
15. Diao J., Gall K., Dunn M.L., and Zimmerman J.A. Atomistic simulations of the yielding of gold nanowires. Acta Mater. 54 (2006) 643-653
16. 2 nanowires driven by mechanical or electrical field excitation. J. Appl. Phys. 93 1 (2003) 226-230
17. Dingreville R., Qu J., and Cherkaoui M. Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J. Mech. Phys. Solids 53 (2005) 1827-1854
18. Ekinci K.L. Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS). Small 1 8-9 (2005) 786-797
19. Ekinci K.L., and Roukes M.L. Nanoelectromechanical systems. Rev. Sci. Instrum. 76 (2005) 061101
20. Ekinci K.L., Yang Y.T., and Roukes M.L. Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95 5 (2004) 2682-2689
21. Evoy S., Carr D.W., Sekaric L., Olkhovets A., Parpia J.M., and Craighead H.G. Nanofabrication and electrostatic operation of single-crystal silicon paddle oscillators. J. Appl. Phys. 86 11 (1999) 6072-6077
22. Evoy S., Olkhovets A., Sekaric L., Parpia J.M., Craighead H.G., and Carr D.W. Temperature-dependent internal friction in silicon nanoelectromechanical systems. Appl. Phys. Lett. 77 15 (2000) 2397-2399
23. Foiles S.M., Baskes M.I., and Daw M.S. Embedded-atom-method functions for the FCC metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33 12 (1986) 7893-7991
24. Gurtin M.E., and Murdoch A. A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57 (1975) 291-323
25. Gurtin M.E., Markenscoff X., and Thurston R.N. Effects of surface stress on the natural frequency of thin crystals. Appl. Phys. Lett. 29 9 (1976) 529-530
26. Haiss W. Surface stress of clean and adsorbate-covered solids. Rep. Progr. Phys. 64 (2001) 591-648
27. Hasmy A., and Medina E. Thickness induced structural transition in suspended FCC metal nanofilms. Phys. Rev. Lett. 88 9 (2002) 096103
28. Heidelberg A., Ngo L.T., Wu B., Phillips M.A., Sharma S., Kamins T.I., Sader J.E., and Boland J.J. A generalized description of the elastic properties of nanowires. Nano Lett. 6 6 (2006) 1101-1106
29. Hoffmann S., Utke I., Moser B., Michler J., Christiansen S.H., Schmidt V., Senz S., Werner P., Gosele U., and Ballif C. Measurement of the bending strength of vapor-liquid-solid grown silicon nanowires. Nano Lett. 6 4 (2006) 622-625
30. Houston B.H., Photiadis D.M., Marcus M.H., Bucaro J.A., Liu X., and Vignola J.F. Thermoelastic loss in microscale oscillators. Appl. Phys. Lett. 80 7 (1976) 1300-1302
31. Huang Z.P., and Sun L. Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis. Acta Mech. 190 (2007) 151-163
32. Huang Z.P., and Wang J. A theory of hyperelasticity of multi-phase media with surface/interface energy effect. Acta Mech. 182 (2006) 195-210
33. Huang G.Y., Gao W., and Yu S.W. Model for the adsorption-induced change in resonance frequency of a cantilever. Appl. Phys. Lett. 89 (2006) 043506
34. Huang X.M.H., Zorman C.A., Mehregany M., and Roukes M.L. Nanodevice motion at microwave frequencies. Nature 42 (2003) 496
35. Husain A., Hone J., Postma H.W.C., Huang X.M.H., Drake T., Barbic M., Scherer A., and Roukes M.L. Nanowire-based very-high-frequency electromechanical oscillator. Appl. Phys. Lett. 83 6 (2003) 1240-1242
36. Ilic B., Craighead H.G., Krylov S., Senaratne W., Ober C., and Neuzil P. Attogram detection using nanoelectromechanical oscillators. J. Appl. Phys. 95 7 (2004) 3694-3703
37. Jing G.Y., Duan H.L., Sun X.M., Zhang Z.S., Xu J., Li Y.D., Wang J.X., and Yu D.P. Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Phys. Rev. B 73 (2006) 235409
38. Kondo Y., Ru Q., and Takayanagi K. Thickness induced structural phase transition of gold nanofilm. Phys. Rev. Lett. 82 4 (1999) 751-754
39. Lachut M.J., and Sader J.E. Effect of surface stress on the stiffness of cantilever plates. Phys. Rev. Lett. 99 (2007) 206102
40. Lavrik N.V., Sepaniak M.J., and Datskos P.G. Cantilever transducers as a platform for chemical and biological sensors. Rev. Sci. Instrum. 75 7 (2004) 2229-2253
41. Li D., Wu Y., Kim P., Shi L., Yang P., and Majumdar A. Thermal conductivity of individual silicon nanowires. Appl. Phys. Lett. 83 14 (2003) 2934-2936
42. Li M., Mayer T.S., Sioss J.A., Keating C.D., and Bhiladvala R.B. Template-grown metal nanowires as resonators: performance and characterization of dissipative and elastic properties. Nano Lett. 7 11 (2007) 3281-3284
43. Li X., Ono T., Wang Y., and Esashi M. Ultrathin single-crystalline-silicon cantilever resonators: fabrication technology and significant specimen size effect on Young's modulus. Appl. Phys. Lett. 83 15 (2003) 3081-3083
44. Liang H., Upmanyu M., and Huang H. Size-dependent elasticity of nanowires: nonlinear effects. Phys. Rev. B 71 (2005) 241403R
45. Liang W., Zhou M., and Ke F. Shape memory effect in Cu nanowires. Nano Lett. 5 10 (2005) 2039-2043
46. Lieber C.M. Nanoscale science and technology: building a big future from small things. MRS Bull. 28 7 (2003) 486-491
47. Lu P., Lee H.P., Lu C., and O'Shea S.J. Surface stress effects on the resonance properties of cantilever sensors. Phys. Rev. B 72 (2005) 085405
48. McFarland A.W., Poggi M.A., Doyle M.J., Bottomley L.A., and Colton J.S. Influence of surface stress on the resonance behavior of microcantilevers. Appl. Phys. Lett. 87 (2005) 053505
49. Miller R.E., and Shenoy V.B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11 (2000) 139-147
50. Nam C.Y., Jaroenapibal P., Tham D., Luzzi D.E., Evoy S., and Fischer J.E. Diameter-dependent electromechanical properties of GaN nanowires. Nano Lett. 6 2 (2006) 153-158
51. Namazu T., Isono Y., and Tanaka T. Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM. J. Microelectromechanical Syst. 9 4 (2000) 450-459
52. Ohnishi H., Kondo Y., and Takayanagi K. Quantized conductance through individual rows of suspended gold atoms. Nature 395 (1998) 780-783
53. Park H.S. Strain sensing through the resonant properties of deformed metal nanowires. J. Appl. Phys. 104 (2008) 013516
54. Park H.S. Surface stress effects on the resonant properties of silicon nanowires. J. Appl. Phys. 103 (2008) 123504
55. Park H.S., and Klein P.A. Surface Cauchy-Born analysis of surface stress effects on metallic nanowires. Phys. Rev. B 75 (2007) 085408
56. Park H.S., and Klein P.A. A surface Cauchy-Born model for silicon nanostructures. Comput. Methods Appl. Mech. Eng. 197 (2008) 3249-3260
57. Park H.S., Gall K., and Zimmerman J.A. Shape memory and pseudoelasticity in metal nanowires. Phys. Rev. Lett. 95 (2005) 255504
58. Park H.S., Klein P.A., and Wagner G.J. A surface Cauchy-Born model for nanoscale materials. Int. J. Numer. Methods Eng. 68 (2006) 1072-1095
59. Petrova H., Perez-Juste J., Zhang Z.Y., Zhang J., Kosel T., and Hartland G.V. Crystal structure dependence of the elastic constants of gold nanorods. J. Mater. Chem. 16 40 (2006) 3957-3963
60. Rubio G., Agrait N., and Vieira S. Atomic-sized metallic contacts: mechanical properties and electronic transport. Phys. Rev. Lett. 76 13 (1996) 2302-2305
61. Sader J.E. Surface stress induced deflections of cantilever plates with applications to the atomic force microscope: rectangular plates. J. Appl. Phys. 89 5 (2001) 2911-2921
62. Sharma P., Ganti S., and Bhate N. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82 4 (2003) 535-537
63. Shenoy V.B. Atomistic calculations of elastic properties of metallic FCC crystal surfaces. Phys. Rev. B 71 (2005) 094104
64. Sun C.T., and Zhang H. Size-dependent elastic moduli of platelike nanomaterials. J. Appl. Phys. 92 2 (2003) 1212-1218
65. Sundararajan S., Bhushan B., Namazu T., and Isono Y. Mechanical property measurements of nanoscale structures using an atomic force microscope. Ultramicroscopy 91 (2002) 111-118
66. Tadmor E., Ortiz M., and Phillips R. Quasicontinuum analysis of defects in solids. Philos. Mag. A 73 (1996) 1529-1563
67. Tahoe, 〈http://tahoe.ca.sandia.gov〉.
68. Tang Z., Zhao H., Li G., and Aluru N.R. Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures. Phys. Rev. B 74 (2006) 064110
69. Trilinos, 〈http://software.sandia.gov/trilinos/index.html〉.
70. Verbridge S.S., Parpia J.M., Reichenbach R.B., Bellan L.M., and Craighead H.G. High quality factor resonance at room temperature with nanostrings under high tensile stress. J. Appl. Phys. 99 (2006) 124304
71. Verbridge S.S., Shapiro D.F., Craighead H.G., and Parpia J.M. Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators. Nano Lett. 7 6 (2007) 1728-1735
72. Wan J., Fan Y.L., Gong D.W., Shen S.G., and Fan X.Q. Surface relaxation and stress of FCC metals: Cu, Ag, Au, Ni, Pd, Pt, Al and Pb. Modelling Simulation Mater. Sci. Eng. 7 (1999) 189-206
73. Wang J., Duan H.L., Huang Z.P., and Karihaloo B.L. A scaling law for properties of nano-structured materials. Proc. R. Soc. A 462 (2006) 1355-1363
74. Weaver W., Timoshenko S.P., and Young D.H. Vibration Problems in Engineering (1990), Wiley, New York
75. Wei G., Shouwen Y., and Ganyun H. Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17 (2006) 1118-1122
76. Wiley B.J., Wang Z., Wei J., Yin Y., Cobden D.H., and Xia Y. Synthesis and electrical characterization of silver nanobeams. Nano Lett. 6 10 (2006) 2273-2278
77. Wong E.W., Sheehan P.E., and Lieber C.M. Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277 (1997) 1971-1975
78. Wu B., Heidelberg A., and Boland J.J. Mechanical properties of ultrahigh-strength gold nanowires. Nat. Mater. 4 (2005) 525-529
79. Xia Y., Yang P., Sun Y., Wu Y., Mayers B., Gates B., Yin Y., Kim F., and Yan H. One-dimensional nanostructures: synthesis, characterization, and applications. Adv. Mater. 15 5 (2003) 353-389
80. Yang J., Ono T., and Esashi M. Surface effects and high quality factors in ultrathin single-crystal silicon cantilevers. Appl. Phys. Lett. 77 23 (2000) 3860-3862
81. Yang J., Ono T., and Esashi M. Investigating surface stress: surface loss in ultrathin single-crystal silicon cantilevers. J. Vac. Sci. Technol. B 19 2 (2001) 551-556
82. Yasumura K.Y., Stowe T.D., Chow E.M., Pfafman T., Kenny T.W., Stipe B.C., and Rugar D. Quality factors in micron- and submicron-thick cantilevers. J. Microelectromechanical Syst. 9 1 (2000) 117-125
83. Zhou L.G., and Huang H. Are surfaces elastically softer or stiffer?. Appl. Phys. Lett. 84 11 (2004) 1940-1942