Study of Silicon Cantilevers by the Photoacoustic Elastic Bending Method

  • D. M. TodorovicEmail author
  • M. D. Rabasovic
  • D. D. Markushev
  • V. Jovic
  • K. T. Radulovic
Part of the following topical collections:
  1. ICPPP-18: Selected Papers of the 18th International Conference on Photoacoustic and Photothermal Phenomena


Rectangular silicon cantilevers are studied by the photoacoustic (PA) elastic bending method. Experimental signals versus modulation frequency of the excitation optical beam are measured and analyzed in a frequency range from 20 Hz to 50 000 Hz. The procedure for experimental signal correction to eliminate the frequency characteristics of the measuring system is given. The corrected experimental signal shows a good correlation with theoretically calculated PA signal at frequencies below 32 000 Hz. The corrected experimental PA elastic bending signals for cantilevers with different thicknesses are analyzed. The experimental results allow identifying the resonant frequency (the first resonant mode) of the cantilever vibrations. These values are in good agreement with the theoretically computed values. A theoretical model of the optically excited Si cantilever is derived, taking into account plasmaelastic, thermoelastic, and thermodiffusion mechanisms. Dynamic relations for the amplitude and phase of electronic and thermal elastic vibrations in optically excited cantilevers are derived. The theoretical model is compared to the experimental results.


Cantilever Photoacoustic Plasmaelastic Thermoelastic 



This work was supported by the Serbian Ministry of Education and Science within the framework of the project OI171016.


  1. 1.
    A. Mandelis (ed.), Photoacoustic and Thermal Wave Phenomena in Semiconductors (Elsevier, New York, 1987)Google Scholar
  2. 2.
    A. Mandelis, P. Hess (eds.), Semiconductors and Electronic Materials, Vol. IV in the Series: Progress in Photothermal and Photoacoustic Science and Technology (SPIE Press, Bellingham, 2000)Google Scholar
  3. 3.
    D.M. Todorovic, P.M. Nikolic, Semiconductors and Electronic Materials, Ch. 9, in the Series: Progress in Photothermal and Photoacoustic Science and Technology (Optical Engineering Press, New York, 2000), pp. 273–318Google Scholar
  4. 4.
    D.M. Todorovic, M.D. Rabasovic, D.D. Markushev, V. Jovic, K.T. Radulovic, Investigation of micromechanical structures by photoacoustic elastic bending method. Int. J. Thermophys. 33, 2222–2229 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    D.M. Todorovic, D.D. Markushev, M.D. Rabasovic, K.T. Radulovic, V. Jovic, Photoacoustic elastic bending method: study of the silicon membranes, in Proceedings of 28th International Conference on Microelectronics (MIEL 2012), Niš, Serbia, 13–16 May, 2012, pp. 169–172Google Scholar
  6. 6.
    D.M. Todorovic, M.D. Rabasovic, D.D. Markushev, M. Sarajlic, J. Appl. Phys. 116, 053506 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    M.D. da Silva, I.N. Bandeira, L.C.M. Miranda, Open-cell photoacoustic radiation detector. J. Phys. E Sci. Instrum. 20, 12 (1987)CrossRefGoogle Scholar
  8. 8.
    L.F. Perondi, L.C.M. Miranda, Minimal-volume photoacoustic cell measurement of thermal diffusivity. J. Appl. Phys. 62, 2955 (1987)ADSCrossRefGoogle Scholar
  9. 9.
    D.M. Todorović, B. Cretin, Y. Song, P. Vairac, Electronic and thermal generation of vibrations of optically excited cantilevers. J. Appl. Phys. 107, 023516 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Song, B. Cretin, D.M. Todorović, P. Vairac, Study of laser excited vibration of silicon cantilever. J. Appl. Phys. 104, 104909 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    D.M. Todorović, P.M. Nikolić, Investigation of carrier transport processes in semiconductors by the photoacoustic frequency transmission method. Opt. Eng. 36, 432–445 (1997)ADSCrossRefGoogle Scholar
  12. 12.
    G.S. Kino, R.G. Stearns, Effect of electronic strain on photoacoustic generation in silicon. Appl. Phys. Lett. 49, 926 (1985)ADSCrossRefGoogle Scholar
  13. 13.
    F. McDonald, G. Wetsel, Generalized theory of the photoacoustic effect. J. Appl. Phys. 49, 2313 (1978)ADSCrossRefGoogle Scholar
  14. 14.
    D.M. Todorović, P.M. Nikolić, A.I. Bojičić, K.T. Radulović, Thermoelastic and electronic strain contribution to the frequency transmission photoacoustic effect in semiconductors. Phys. Rev. B 55, 15631–15642 (1997)ADSCrossRefGoogle Scholar
  15. 15.
    A. Rosencwaig, A. Gersho, Theory of the photoacoustic effect with solids. J. Appl. Phys. 47, 64 (1976)ADSCrossRefGoogle Scholar
  16. 16.
    A.M. Mansanares, H. Vargas, F. Galembeck, J. Buijs, D. Bicanic, Photoacoustic characterization of a two-layer system. J. Appl. Phys. 70, 7047 (1991)ADSCrossRefGoogle Scholar
  17. 17.
    M.D. Dramicanin, P.M. Nikolic, Z.D. Ristovski, D.G. Vasiljevic, D.M. Todorovic, Photoacoustic investigation of transport in semiconductors: theoretical and experimental study of a Ge single crystal. Phys. Rev. B 51, 14226 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    J.A. Balderas-Lopez, A. Mandelis, Thermal diffusivity measurements in the photoacoustic open-cell configuration using simple signal normalization techniques. J. Appl. Phys. 90, 2273 (2001)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • D. M. Todorovic
    • 1
    Email author
  • M. D. Rabasovic
    • 2
  • D. D. Markushev
    • 2
  • V. Jovic
    • 3
  • K. T. Radulovic
    • 3
  1. 1.Institute for Multidisciplinary ResearchUniversity of BelgradeBelgradeSerbia
  2. 2.Institute of PhysicsUniversity of BelgradeBelgrade-ZemunSerbia
  3. 3.Institute for ChemistryTechnology and MetallurgyBelgradeSerbia

Personalised recommendations