Measuring adhesion energy between MEMS structures using an adhered cantilever

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Abstract

Spontaneous stiction of MEMS elements during fabrication or operation is a serious problem. Capillary or electrostatic forces causing stiction can be eliminated, but dispersion forces are always present due to their fundamental nature and should be investigated in detail. In this paper, dispersion forces are studied experimentally for Si-Au and Si-Ru systems using a test structure – an adhered cantilever. Long (12 mm) and thin (10 μm) cantilevers allow measurements with high accuracy. The paper discusses in detail the fabrication procedure of the cantilevers and the measuring chip. Information on the adhesion energy is extracted from the cantilever shape, which is registered by a scanning interferometer. The roughness of the contacting surfaces is carefully studied and the equilibrium average distance between the surfaces during contact is obtained. The work is of interest not only for MEMS, but also allows one to gain fundamental knowledge about dispersion forces at small distances, which is inaccessible for other experimental methods.

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About the authors

I. V. Uvarov

Centre for Scientific and Information Technologies of the Valiev Department of Physics and Technology Research of the Kurchatov Institute

Author for correspondence.
Email: i.v.uvarov@bk.ru
Russian Federation, Yaroslavl

O. V. Morozov

Centre for Scientific and Information Technologies of the Valiev Department of Physics and Technology Research of the Kurchatov Institute

Email: i.v.uvarov@bk.ru
Russian Federation, Yaroslavl

A. V. Postnikov

Centre for Scientific and Information Technologies of the Valiev Department of Physics and Technology Research of the Kurchatov Institute

Email: i.v.uvarov@bk.ru
Russian Federation, Yaroslavl

V. B. Svetovoy

Frumkin Institute of Physical Chemistry and Electrochemistry of the Russian Academy of Sciences

Email: i.v.uvarov@bk.ru
Russian Federation, Moscow

References

  1. Maboudian R., Howe R.T. Critical review: Adhesion in surface micromechanical structures // J. Vacuum Sci. Technol. B. 1997. V. 15. P. 1–20. https://doi.org/10.1116/1.589247
  2. Mastrangelo C., Hsu C. A simple experimental technique for the measurement of the work of adhesion of microstructures // Technical Digest IEEE Solid-State Sensor and Actuator Workshop. 1992. P. 208–212. https://doi.org/10.1109/SOLSEN.1992.228291
  3. Legtenberg R., Tilmans H.A., Elders J., Elwenspoek M. Stiction of surface micromachined structures after rinsing and drying: model and investigation of adhesion mechanisms // Sens. Actuators A. 1994. V. 43. P. 230–238. https://doi.org/10.1016/0924-4247(93)00654-M
  4. Tas N., Sonnenberg T., Jansen H., Legtenberg R., Elwenspoek M. Stiction in surface micromachining // J. Micromech. Microeng. 1996. V. 6. 385. https://doi.org/10.1088/0960-1317/6/4/005
  5. London F. Zur theorie und systematik der molekularkräfte // Zeitschrift für Physik. 1963. V. 63. P. 245–279. https://doi.org/10.1007/BF01421741
  6. Boinovich L.B. Long-range surface forces and their role in the progress of nanotechnology // Russian Chemical Reviews. 2007. V. 76(5). P. 471–488. https://doi.org/10.1070/RC2007v076n05ABEH003692
  7. Derjaguin B.V., Churaev N.V., Muller V.M. Surface forces. Springer. New York, 2013, ISBN: 1475766416.
  8. Churaev N.V. Surface forces in wetting films // Adv. Colloid Interface Sci. 2003. V. 103. P. 197–218. https://doi.org/10.1016/S0001-8686(02)00074-X
  9. Lifshitz E.M. Theory of molecular attractive forces between solids // JETP. 1956. V. 2. P. 73–83.
  10. Dzyaloshinskii I.E., Lifshitz E.M., Pitaevskii L.P. General theory of van der Waals’ forces // Soviet Physics Uspekhi. 1961. Vol. 4. P. 153–176. https://doi.org/10.1070/PU1961v004n02ABEH003330
  11. Lifshitz E.M., Pitaevskii L.P. Statistical Physics, Part 2, Pergamon Press. Oxford, ISBN: 0750626364.
  12. Casimir H.B.G. On the attraction between two perfectly conducting plates // Proc. Kon. Ned. Akad. Wet. 1948. V. 51. P. 793–795.
  13. Klimchitskaya G.L., Mohideen U., Mostepanenko V.M. The Casimir force between real materials: Experiment and theory // Rev. Mod. Phys. 2009. V. 81. 1827. https://doi.org/10.1103/RevModPhys.81.1827
  14. Rodriguez A.W., Capasso F., Johnson S.G. The Casimir effect in microstructured geometries // Nat. Photonics. 2011. V. 3. P. 211. https://doi.org/10.1038/nphoton.2011.39
  15. Palasantzas G., Sedighi M., Svetovoy V.B. Applications of Casimir forces: Nanoscale actuation and adhesion // Appl. Phys. Lett. 2020. V. 117. 120501. https://doi.org/10.1063/5.0023150
  16. Harris B.W., Chen F., Mohideen U. Precision measurement of the Casimir force using gold surfaces // Phys. Rev. A. 2000. V. 62. 052109. https://doi.org/10.1103/PhysRevA.62.052109
  17. Chan H.B., Aksyuk V.A., Kleiman R.N., Bishop D.J., Capasso F. Quantum mechanical actuation of microelectromechanical systems by the Casimir force // Science. 2001. V. 291. P. 1941–1944. https://doi.org/10.1126/science.1057984
  18. van Zwol P.J., Palasantzas G., De Hosson J.T.M. Influence of random roughness on the Casimir force at small separations // Phys. Rev. B. 2008. V. 77. 075412. https://doi.org/10.1103/PhysRevB.77.075412
  19. Sedighi M., Svetovoy V.B., Palasantzas G. Casimir force measurements from silicon carbide surfaces // Phys. Rev. B. 2016. V. 93. 085434. https://doi.org/10.1103/PhysRevB.93.085434
  20. Mastrangelo C.H., Hsu C.H. Mechanical stability and adhesion of microstructures under capillary forces. I. Basic theory // J. Microelectromech. Syst. 1993. V. 2. P. 33–43. https://doi.org/10.1109/84.232593
  21. Mastrangelo C.H., Hsu C.H. Mechanical stability and adhesion of microstructures under capillary forces. II. Experiments // J. Microelectromech. Syst. 1993. V. 2. P. 44–55. https://doi.org/10.1109/84.232594
  22. de Boer M.P., Michalske T.A. Accurate method for determining adhesion of cantilever beams // J. Appl. Phys. 1999. V. 86. P. 817–827. https://doi.org/10.1063/1.370809
  23. Knapp J.A., de Boer M.P. Mechanics of microcantilever beams subject to combined electrostatic and adhesive forces // J. Microelectromech. Syst. 2002. V. 11. P. 754–764. https://doi.org/10.1109/JMEMS.2002.805047
  24. DelRio F.W., Dunn M.L., Phinney L.M., Bourdon C.J., de Boer M.P. Rough surface adhesion in the presence of capillary condensation // Appl. Phys. Lett. 2007. V. 90. 163104. https://doi.org/10.1063/1.2723658
  25. van Zwol P.J., Palasantzas G., De Hosson J.T.M. Influence of random roughness on the adhesion between metal surfaces due to capillary condensation // Appl. Phys. Lett. 2007. V. 91. 101905. https://doi.org/10.1063/1.2768919
  26. DelRio F.W., de Boer M.P., Knapp J.A., Reedy E.D., Clews P.J., Dunn M.L. The role of van der Waals forces in adhesion of micromachined surfaces // Nat. Mater. 2005. V. 4. P. 629–634. https://doi.org/10.1038/nmat1431
  27. Svetovoy V., Postnikov A., Uvarov I., Stepanov F., Palasantzas G. Measuring the dispersion forces near the van der Waals–Casimir transition // Phys. Rev. Appl. 2020. V. 13. 064057. https://doi.org/10.1103/PhysRevApplied.13.064057
  28. Morozov O.V. Dynamics of deposition and removal of a fluorocarbon film in the cyclic process of plasma-chemical etching of silicon // Bulletin of the Russian Academy of Sciences: Physics. 2024. V. 88. P. 447–453. https://doi.org/10.1134/S1062873823706050
  29. Morozov O.V., Amirov I.I. Aspect-ratio-independent anisotropic silicon etching in a plasma chemical cyclic process // Russ. Microelectron. 2007. V. 36. P. 333–341. https://doi.org/10.1134/S1063739707050071
  30. Soldatenkov I.A., Stepanov F.I., Svetovoy V.B. Dispersion forces and equilibrium distance between deposited rough films in contact // Phys. Rev. B. 2022. V. 105. 075401. https://doi.org/10.1103/PhysRevB.105.075401
  31. van Zwol P.J., Svetovoy V.B., Palasantzas G. Distance upon contact: Determination from roughness profile // Phys. Rev. B. 2009. V. 80. 235401. https://doi.org/10.1103/PhysRevB.80.235401
  32. Muravyeva T.I., Uvarov I.V., Naumov V.V., Palasantzas G., Svetovoy V.B. Excessive number of high asperities for sputtered rough films // Phys. Rev. B. 2021. V. 104. 035415. https://doi.org/10.1103/PhysRevB.104.035415
  33. Postnikov A.V., Uvarov I.V., Svetovoy V.B. Experimental setup for measuring the dispersion forces by the adhered cantilever method // Rev. Sci. Instrum. 2023. V. 94. 043907. https://doi.org/10.1063/5.0147016
  34. Hopcroft M.A., Nix W.D., Kenny T.W. What is the Young’s modulus of silicon? // J. Microelectromech. Syst. 2010. V. 19. P. 229–238. https://doi.org/10.1109/JMEMS.2009.2039697
  35. Soldatenkov I.A., Svetovoy V.B. Adhesion energy for a nonideal cantilever and its relation to the Casimir-Lifshitz forces // Physics. 2024. V. 6. 1204. https://doi.org/10.3390/physics6040074
  36. Derjaguin B. Untersuchungen über die Reibung und Adhäsion, IV // Kolloid-Zeitschrift. 1934. V. 69. P. 155–164. https://doi.org/10.1007/BF01433225

Supplementary files

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2. Fig. 1. Schematic representation of a stuck cantilever. The gap h (x) is calculated from the average distance between the surfaces h0 in the contact area

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3. Fig. 2. Stages of fabrication of a micromechanical chip with cantilevers

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4. Fig. 3. AFM scans of silicon (a), gold (b), and ruthenium (c) surfaces showing the RMS roughness σ and colour scale. Graphs (d-e) show the density function of the roughness distribution function over height for the three scans on each material. The black dashed curve shows the normal distribution for the data corresponding to the black markers and the indicated values of σ

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5. Fig. 4. Results of measuring the shape of stuck cantilevers: (a) cantilever shape for Si-Au (light brown curve) and Si-Ru contact (blue curve); (b) shape near the fixed end for the Si-Ru system, markers indicate experimental data, blue curve corresponds to a 4th order polynomial; (c) the same but for the stuck end; (d) height difference between the left and right edge of the cantilever; (e) schematic representation of the twisted cantilever cross section

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6. Fig. 5. (a) Adhesion energy between parallel surfaces. Yellow and blue curves correspond to calculations for Si-Au and Si-Ru systems, respectively. The blue and pink markers correspond to measurements for Si-Au and Si-Ru. (b) Relative contact area of surfaces at angle φ = Δh / w for Au4 (yellow curve) and Ru2 (blue curve) samples. The dashed lines show the average distance and the corresponding Reff value

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