Size-dependent effective Young's modulus of silicon nitride cantilevers

Applied Physics Letters

Volumn 94, Issue 23, 2009, Pages

  Babaei Gavan, Khashayar ^a   Westra, Hidde J R ^a   Van Der Drift, Emile W J M ^a   Venstra, Warner J ^a   Van Der Zant, Herre S J ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BULK VALUE; EXPERIMENTAL DATA; RESONANCE FREQUENCIES; RESONANCE MODE; SURFACE ELASTICITIES; SURFACE STRESS; THICKNESS DEPENDENCE; YOUNG'S MODULUS;

ELASTIC MODULI; ELASTICITY; RESONANCE; SILICON NITRIDE;

NANOCANTILEVERS;

EID: 67649083892     PISSN: 00036951     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3152772     Document Type: Article

References (27)

1. M. Li, H. X. Tang, and M. L. Roukes, Nat. Nanotechnol. 1748-3387 2, 114 (2007). 10.1038/nnano.2006.208
2. M. E. Gurtin, X. Markenscoff, and R. N. Thursten, Appl. Phys. Lett. 0003-6951 29, 529 (1976). 10.1063/1.89173
3. J. Lagowski, H. C. Gatos, and E. S. Sproles, Appl. Phys. Lett. 0003-6951 26, 493 (1975). 10.1063/1.88231
4. P. Lu, H. P. Lee, C. Lu, and P. Q. Zhang, J. Appl. Phys. 0021-8979 99, 073510 (2006). 10.1063/1.2189213
5. S. H. Park, J. S. Kim, J. H. Park, J. S. Lee, Y. K. Choi, and O. M. Kwon, Thin Solid Films 0040-6090 492, 285 (2005). 10.1016/j.tsf.2005.06.056
6. P. Sharma, S. Ganti, and N. Bhate, Appl. Phys. Lett. 0003-6951 82, 535 (2003). 10.1063/1.1539929
7. Y. Tsukamoto, H. Yamaguchi, and M. Yanagiswa. Thin Solid Films 0040-6090 154, 171, 1987. 10.1016/0040-6090(87)90362-2
8. L. Zhang and H. Huang, Appl. Phys. Lett. 0003-6951 89, 183111 (2006). 10.1063/1.2374856
9. X. Li, T. Ono, Y. L. Wang, and M. Esashi, Appl. Phys. Lett. 0003-6951 83, 3081 (2003). 10.1063/1.1618369
10. G. Y. Jing, H. L. Duan, X. M. Sun, Z. S. Zhang, J. Xu, Y. D. Li, J. X. Wang, and D. P. Yu, Phys. Rev. B 0163-1829 73, 235409 (2006). 10.1103/PhysRevB.73.235409
11. S. Cuenot, C. Fŕtigny, S. Demoustier-Champagne, and B. Nysten, Phys. Rev. B 0163-1829 69, 165410 (2004). 10.1103/PhysRevB.69.165410
12. P. Lu, H. P. Lee, C. Lu, and S. J. O'Shea, Phys. Rev. B 0163-1829 72, 085405 (2005). 10.1103/PhysRevB.72.085405
13. J. E. Sader, J. Appl. Phys. 0021-8979 89, 2911 (2001). 10.1063/1.1342018
14. G. F. Wang and X. Q. Feng, Appl. Phys. Lett. 0003-6951 90, 231904 (2007). 10.1063/1.2746950
15. Y. Zhang, Q. Ren, and Y. P. Zhao, J. Phys. D: Appl. Phys. 0022-3727 37, 2140 (2004). 10.1088/0022-3727/37/15/014
16. K. Babaei Gavan, E. W. J. M. van der Drift, W. J. Venstra, M. R. Zuiddam, and H. J. S. van der Zant, J. Micromech. Microeng. 0960-1317 19, 035003 (2009). 10.1088/0960-1317/19/3/035003
17. X. F. Li and B. L. Wang, Appl. Phys. Lett. 0003-6951 94, 101903 (2009). 10.1063/1.3094130
18. A. Khan, J. Philip, and P. Hess, J. Appl. Phys. 0021-8979 95, 1667 (2004). 10.1063/1.1638886
19. P. J. French, P. M. Sarro, R. Malĺe, E. J. M. Fakkeldij, and R. F. Wolffenbuttel, Sens. Actuators, A 0924-4247 58, 149 (1997). 10.1016/S0924-4247(96)01397-0
20. For the thinnest cantilevers, h=20 nm, the number of samples was too low to obtain a reliable fit; Eeff could not be determined accurately.
21. J. He and M. Lilley, Appl. Phys. Lett. 0003-6951 93, 263108 (2008). 10.1063/1.3050108
22. M. J. Lachut and J. E. Sader, Phys. Rev. Lett. 0031-9007 99, 206102 (2007). 10.1103/PhysRevLett.99.206102
23. G. G. Stoney, Proc. R. Soc. London, Ser. A 0950-1207 82, 172 (1909). 10.1098/rspa.1909.0021
24. R. L. Edwards, G. Coles, and W. N. Sharpe, Exp. Mech. 0014-4851 44, 49 (2004). 10.1007/BF02427976
25. R. Buchner, K. Rohloff, W. Benecke, and W. Lang, Proceedings of the 13th International Conference on Solid-state Sensors, Actuators, and Microsystems, June 2005 (unpublished), p. 575.
26. J. M. Gere and S. P. Timoshenko, Mechanics of Materials (Wadsworth International, CA, 1985).
27. A two-layer composite beam theory is used to describe the observed trend in Eeff. We used Eeff = (k+l) / [(h+ h1) 3 (Eh+ E1 h1)] with k= E2 h4 + E12 h14 and l=2E E1 h h1 (2 h2 +2 h12 +3h h1). Here, h1 and E1 are the thickness and Young's modulus, respectively, of the first layer.