Research Papers

In Situ Deformation of Silicon Cantilever Under Constant Stress as a Function of Temperature

[+] Author and Article Information
Ming Gan

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907
e-mail: ganm@purdue.edu

Yang Zhang

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907
e-mail: zhan1076@purdue.edu

Vikas Tomar

Associate Professor
School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907
e-mail: tomar@purdue.edu

1Corresponding author.

Manuscript received April 13, 2014; final manuscript received June 15, 2014; published online July 8, 2014. Assoc. Editor: Hsiao-Ying Shadow Huang.

J. Nanotechnol. Eng. Med 5(2), 021004 (Aug 19, 2014) (9 pages) Paper No: NANO-14-1035; doi: 10.1115/1.4027877 History: Received April 13, 2014; Revised June 15, 2014

This research reports in situ creep properties of silicon microcantilevers at temperatures ranging from 25 °C to 100 °C under uniaxial compressive stress. Results reveal that in the stress range of 50–150 MPa, the strain rate of the silicon cantilever increases linearly as a function of applied stress. The strain rate (0.2–2.5 ×10-6s-1) was comparable to literature values for bulk silicon reported in the temperature range of 1100–1300 °C at one tenth of the reported stress level. The experiments quantify the extent of the effect of surface stress on uniaxial creep strain rate by measuring surface stress values during uniaxial temperature dependent creep.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Tang, C. Y., Zhang, L. C., and Mylvaganam, K., 2012, “Rate Dependent Deformation of a Silicon Nanowire Under Uniaxial Compression: Yielding, Buckling, and Constitutive Description,” Comput. Mater. Sci., 51(1), pp. 117–121. [CrossRef]
Herring, C., 1950, “Diffusional Viscosity of a Polycrystalline Solid,” J. Appl. Phys., 21(5), pp. 437–445. [CrossRef]
Coble, R. L., 1963, “A Model for Boundary Diffusion Controlled Creep in Polycrystalline Materials,” J. Appl. Phys., 34(6), pp. 1679–1682. [CrossRef]
Mukherjee, A. K., Bird, J. E., and Dorn, J. E., 1969, “Experimental Correlations for High-Temperature Creep,” Trans. Am. Soc. Metals, 62, pp. 155–179.
Li, W. B., Henshall, J. L., Hooper, R. M., and Easterling, K. E., 1991, “The Mechanisms of Indentation Creep,” Acta Metall. Mater., 39(12), pp. 3099–3110. [CrossRef]
Lifshitz, I. M., 1963, “On the Theory of Diffusion-Viscous Flow of Polycrystalline Bodies,” Sov. Phys. JETP-USSR, 17(4), pp. 909–920.
Weertman, J., 1968, “Dislocation Climb Theory of Steady-State Creep,” ASM Trans. Q., 61(4), pp. 681–694.
Nix, W. D., and Ilschner, B., 1980, “Mechanisms Controlling Creep of Single Phase Metals & Alloys,” 5th International Conference on the Strength of Metals and Alloys (ICSMA 5), Aachen, Federal Republic of Germany, August 27–31, Pergamon Press, Oxford, UK.
Sherby, O. D., and Burke, P. M., 1968, “Mechanical Behavior of Crystalline Solids at Elevated Temperature,” Prog. Mater. Sci., 13, pp. 323–390. [CrossRef]
Li, H., and Ngan, A. H. W., 2004, “Size Effects of Nanoindentation Creep,” J. Mater. Res., 19(2), pp. 513–522. [CrossRef]
Gan, M., and Tomar, V., 2010, “Role of Length Scale and Temperature in Indentation Induced Creep Behavior of Polymer Derived Si-C-O Ceramics,” Mater. Sci. Eng., A, 527(29–30), pp. 7615–7623. [CrossRef]
Feng, G., and Ngan, A. H. W., 2001, “Creep and Strain Burst in Indium and Aluminium During Nanoindentation,” Scr. Mater., 45(8), pp. 971–976. [CrossRef]
Cao, Z. H., Li, P. Y., Lu, H. M., Huang, Y. L., Zhou, Y. C., and Meng, X. K., 2009, “Indentation Size Effects on the Creep Behavior of Nanocrystalline Tetragonal Ta Films,” Scr. Mater., 60(6), pp. 415–418. [CrossRef]
Mayo, M. J., and Nix, W. D., 1988, “A Micro-Indentation Study of Superplasticity in Pb, Sn, and Sn-38 wt. % Pb,” Acta Metall., 36(8), pp. 2183–2192. [CrossRef]
Lucas, B., and Oliver, W., 1999, “Indentation Power-Law Creep of High-Purity Indium,” Metall. Mater. Trans. A, 30(3), pp. 601–610. [CrossRef]
Asif, S. A. S., and Pethica, J. B., 1997, “Nanoindentation Creep of Single-Crystal Tungsten and Gallium Arsenide,” Philos. Mag. A, 76(6), pp. 1105–1118. [CrossRef]
Alexander, H., and Haasen, P., 1986, “Dislocations in the Diamond Structure,” Solid State Physics: Advances in Research and Applications, F.Seitz, D.Turnbull, and H.Ehrenreich, eds., Academic Press, New York.
Myshlyaev, M. M., Nikitenko, V. I., and Nesterenko, V. I., 1969, “Dislocation Structure and Macroscopic Characteristics of Plastic Deformation at Creep of Silicon Crystals,” Phys. Status Solidi C, 36(1), pp. 89–96. [CrossRef]
Taylor, T. A., and Barrett, C. R., 1972, “Creep and Recovery of Silicon Single Crystals,” Mater. Sci. Eng., 10, pp. 93–102. [CrossRef]
Walters, D. S., and Spearing, S. M., 2000, “On the Flexural Creep of Single-Crystal Silicon,” Scr. Mater., 42(8), pp. 769–774. [CrossRef]
Yao, S. K., Xu, D. H., Xiong, B., and Wang, Y. L., 2013, “The Plastic and Creep Behavior of Silicon Microstructure at High Temperature,” The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), Transducers & Eurosensors XXVII, Barcelona, Spain, pp. 159–162. [CrossRef]
Huff, M. A., Nikolich, A. D., and Schmidt, M. A., 1993, “Design of Sealed Cavity Microstructures Formed by Silicon Wafer Bonding,” J. Microelectromech. Syst., 2(2), pp. 74–81. [CrossRef]
Yasutake, K., Murakami, J., Umeno, M., and Kawabe, H., 1982, “Mechanical Properties of Heat-Treated CZ-Si Wafers From Brittle to Ductile Temperature Range,” Jpn. J. Appl. Phys., Part 1, 21(5), pp. 288–290. [CrossRef]
Li, H., and Ngan, A. H. W., 2005, “Indentation Size Effects on the Strain Rate Sensitivity of Nanocrystalline Ni-25 at. %Al Thin Films,” Scr. Mater., 52(9), pp. 827–831. [CrossRef]
Ma, Z. S., Long, S. G., Zhou, Y. C., and Pan, Y., 2008, “Indentation Scale Dependence of Tip-in Creep Behavior in Ni Thin Films,” Scr. Mater., 59(2), pp. 195–198. [CrossRef]
Gan, M., and Tomar, V., 2011, “Scale and Temperature Dependent Creep Modeling and Experiments in Materials,” JOM, 63(9), pp. 27–34. [CrossRef]
Wolf, I. D., 1996, “Micro-Raman Spectroscopy to Study Local Mechanical Stress in Silicon Integrated Circuits,” Semicond. Sci. Technol., 11(2), pp. 139–154. [CrossRef]
Anastassakis, E., Pinczuk, A., Burstein, E., Pollak, F. H., and Cardona, M., 1970, “Effect of Static Uniaxial Stress on the Raman Spectrum of Silicon,” Solid State Commun., 8(2), pp. 133–138. [CrossRef]
Ganesan, S., Maradudin, A. A., and Oitmaa, J., 1970, “A Lattice Theory of Morphic Effects in Crystals of the Diamond Structure,” Ann. Phys., 56(2), pp. 556–594. [CrossRef]
Animoto, S. T., Chang, D. J., and Birkitt, A. D., 1998, “Stress Measurement in MEMS Using Raman Spectroscopy,” Proc. SPIE, 3512, pp. 123–129. [CrossRef]
Nye, J. F., 1985, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford University, Clarendon Press, Oxford, UK.
Wortman, J. J., and Evans, R. A., 1965, “Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium,” J. Appl. Phys., 36(1), pp. 153–156. [CrossRef]
Frost, H. J., and Ashby, M. F., 1982, Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics, Pergamon, Oxford, UK.
Gan, M., and Tomar, V., 2014, “An in Situ Platform for the Investigation of Raman Shift in Micro-Scale Silicon Structures as a Function of Mechanical Stress and Temperature Increase,” Rev. Sci. Instrum., 85(1), p. 013902. [CrossRef] [PubMed]
Kang, Y., Qiu, Y., Lei, Z., and Hu, M., 2005, “An Application of Raman Spectroscopy on the Measurement of Residual Stress in Porous Silicon,” Opt. Lasers Eng., 43(8), pp. 847–855. [CrossRef]
Nolan, M., Perova, T., Moore, R. A., Moore, C. J., Berwick, K., and Gamble, H. S., 2000, “Micro-Raman Study of Stress Distribution Generated in Silicon During Proximity Rapid Thermal Diffusion,” Mater. Sci. Eng., B, 73(1–3), pp. 168–172. [CrossRef]
Papadimitriou, D., Bitsakis, J., Lopez-Villegas, J. M., Samitier, J., and Morante, J. R., 1999, “Depth Dependence of Stress and Porosity in Porous Silicon: A Micro-Raman Study,” Thin Solid Films, 349(1–2), pp. 293–297. [CrossRef]
Schmidt, U., Ibach, W., Muller, J., Weishaupt, K., and Hollricher, O., 2006, “Raman Spectral Imaging—A Nondestructive, High Resolution Analysis Technique for Local Stress Measurements in Silicon,” Vib. Spectrosc., 42(1), pp. 93–97. [CrossRef]
Li, Q., Qiu, W., Tan, H., Guo, J., and Kang, Y., 2010, “Micro-Raman spectroscopy Stress Measurement Method for Porous Silicon Film,” Opt. Lasers Eng., 48(11), pp. 1119–1125. [CrossRef]
Vetushka, A., Ledinský, M., Stuchlík, J., Mates, T., Fejfar, A., and Kočka, J., 2008, “Mapping of Mechanical Stress in Silicon Thin Films on Silicon Cantilevers by Raman Microspectroscopy,” J. Non-Cryst. Solids, 354(19–25), pp. 2235–2237. [CrossRef]
Naumenko, D., Snitka, V., Duch, M., Torras, N., and Esteve, J., 2012, “Stress Mapping on the Porous Silicon Microcapsules by Raman Microscopy,” Microelectron. Eng., 98, pp. 488–491. [CrossRef]
Amer, M. S., Durgam, L., and El-Ashry, M. M., 2006, “Raman Mapping of Local Phases and Local Stress Fields in Silicon-Silicon Carbide Composites,” Mater. Chem. Phys., 98(2–3), pp. 410–414. [CrossRef]
Bauer, M., Gigler, A. M., Richter, C., and Stark, R. W., 2008, “Visualizing Stress in Silicon Micro Cantilevers Using Scanning Confocal Raman Spectroscopy,” Microelectron. Eng., 85(5–6), pp. 1443–1446. [CrossRef]
Kouteva-Arguirova, S., Seifert, W., Kittler, M., and Reif, J., 2003, “Raman Measurement of Stress Distribution in Multicrystalline Silicon Materials,” Mater. Sci. Eng. B-Solid State Mater. Adv. Technol., 102(1–3), pp. 37–42. [CrossRef]
Goodman, G. G., Pajcini, V., Smith, S. P., and Merrill, P. B., 2005, “Characterization of Strained Si Structures Using SIMS and Visible Raman,” Mater. Sci. Semicond. Process., 8(1–3), pp. 255–260. [CrossRef]
Langdo, T. A., Currie, M. T., Lochtefeld, A., Hammond, R., Carlin, J. A., Erdtmann, M., Braithwaite, G., Yang, V. K., Vineis, C. J., Badawi, H., and Bulsara, M. T., 2003, “SiGe-Free Strained Si on Insulator by Wafer Bonding and Layer Transfer,” Appl. Phys. Lett., 82(24), pp. 4256–4258. [CrossRef]
Urena, F., Olsen, S. H., Siller, L., Bhaskar, U., Pardoen, T., and Raskin, J.-P., 2012, “Strain in Silicon Nanowire Beams,” J. Appl. Phys., 112(11), p. 114506. [CrossRef]


Grahic Jump Location
Fig. 1

(a) A diagram of the experimental setup and (b) a detailed diagram of the mechanical loading and heating to the cantilever

Grahic Jump Location
Fig. 2

The mechanical loading process, combined with deformation measurement and thermal drift evaluation. (a) The overall load–unload curve; (b) the deformation as a function of time during steady state; (c) the thermal drift evaluation; and (d) the mechanical loading curve before and after correction of thermal drift

Grahic Jump Location
Fig. 3

Representative creep curves at (a) 25 °C; (b) 50 °C; and (c) 100 °C

Grahic Jump Location
Fig. 4

(a) Thermal drift as a function of applied load at different temperature and (b) thermal drift as a function of temperature under different loads

Grahic Jump Location
Fig. 5

(a) Strain rate of the silicon cantilever as a function of applied stress at 25 °C, 50 °C, and 100 °C and (b) comparison with literature values [19-21]

Grahic Jump Location
Fig. 6

(a) Strain rate of the silicon cantilever as a function of temperature and (b) comparison of results from this research and literatures [19-21]

Grahic Jump Location
Fig. 7

Stress exponent at 25 °C, 50 °C, and 100 °C

Grahic Jump Location
Fig. 8

(a) The effect of creep on Raman spectroscopy measurement and (b) comparison of near-surface stress and applied stress to the silicon cantilever



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In