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Quartz tuning forks have been widely used as force sensors in scanning probe microscopes. The anti-phase and in-phase eigenmodes of a tuning fork are involved during microscope operations. Dynamic characteristics of both eigenmodes are studied by experiments and finite element analysis simulations. It is demonstrated that elastic couplings exist between not only both the prongs but also two prongs and the base of the tuning fork. Experimental results show that the coupling between both the prongs increases the anti-phase mode eigenfrequency while the coupling between two prongs and the base of the tuning fork decreases the in-phase mode eigenfrequency. A mechanical model of the tuning fork is introduced and simplified. Parameters of the simplified model are calculated, which is described as a four-springs-three-point-masses system. The quantitative relation between the effective mass of one prong and the eigenfrequency of the anti-phase mode of the mechanical model is in good agreement with that of finite element simulations.
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Keywords:
- scanning probe microscope /
- quartz tuning fork /
- oscillation mode /
- mechanical model
[1] Günther P, Fischer U C, Dransfeld K 1989 Appl. Phys. B 48 89
[2] Edwards H, Taylor L, Duncan W, Melmed A J 1997 J. Appl. Phys. 82 980
[3] Naitou Y, Ookubo N 2004 Appl. Phys. Lett. 85 2131
[4] Kim K, Seo Y, Jang H, Chang S, Hong M H, Jhe W 2006 Nanotechnology 17 S201
[5] Labardi M, Allegrini M 2006 Appl. Phys. Lett. 89 174104
[6] Sandoz P, Friedt J M, Carry E 2008 Rev. Sci. Instrum. 79 086102
[7] Naber A 1999 J. Microsc. 194 307
[8] Seo Y, Jhe W, Hwang C S 2002 Appl. Phys. Lett. 80 4324
[9] Karrai K, Grober R D 1995 Appl. Phys. Lett. 66 1842
[10] Qin Y, Reifenberger R 2007 Rev. Sci. Instrum. 78 063704
[11] Giessibl F J 2000 Appl. Phys. Lett. 76 1470
[12] Seo Y, Choe H, Jhe W 2003 Appl. Phys. Lett. 83 1860
[13] Giessibl F J, Reichling M 2005 Nanotechnology 16 S118
[14] Liu J, Callegari A, Stark M, Chergui M 2008 Ultramicroscopy 109 81
[15] Ruiter A G T, Veerman J A, van der Werf K O,van Hulst N F 1997 Appl. Phys. Lett. 71 28
[16] Grober R D, Acimovic J, Schuck J, Hessman D, Kindlemann P J, Hespanha J, Morse A S, Karrai K, Tiemann I, Manus S 2000 Rev. Sci. Instrum. 71 2776
[17] Rensen W H J, van Hulst N F, Ruiter A G T, West P E 1999 Appl. Phys. Lett. 75 1640
[18] Seo Y, Cadden-Zimansky P, Chandrasekhar V 2005 Appl. Phys. Lett. 87 103103
[19] Wang X P, Liu L, Hu H L, Zhang K 2004 Acta Phys. Sin. 53 1008 (in Chinese) [王晓平、刘 磊、胡海龙、张 琨 2004 物理学报 53 1008]
[20] Rechen J 2001 Ph.D. Dissertation (Zurich: Swiss Federal Institute of Technology)
[21] Simon G H, Heyde M, Rust H P 2007 Nanotechnology 18 255503
[22] Castellanos-Gomez A, Agrait N, Rubio-Bollinger G 2009 Nanotechnology 20 215502
[23] García R, Pérez R 2002 Surf. Sci. Rep. 47 197
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[1] Günther P, Fischer U C, Dransfeld K 1989 Appl. Phys. B 48 89
[2] Edwards H, Taylor L, Duncan W, Melmed A J 1997 J. Appl. Phys. 82 980
[3] Naitou Y, Ookubo N 2004 Appl. Phys. Lett. 85 2131
[4] Kim K, Seo Y, Jang H, Chang S, Hong M H, Jhe W 2006 Nanotechnology 17 S201
[5] Labardi M, Allegrini M 2006 Appl. Phys. Lett. 89 174104
[6] Sandoz P, Friedt J M, Carry E 2008 Rev. Sci. Instrum. 79 086102
[7] Naber A 1999 J. Microsc. 194 307
[8] Seo Y, Jhe W, Hwang C S 2002 Appl. Phys. Lett. 80 4324
[9] Karrai K, Grober R D 1995 Appl. Phys. Lett. 66 1842
[10] Qin Y, Reifenberger R 2007 Rev. Sci. Instrum. 78 063704
[11] Giessibl F J 2000 Appl. Phys. Lett. 76 1470
[12] Seo Y, Choe H, Jhe W 2003 Appl. Phys. Lett. 83 1860
[13] Giessibl F J, Reichling M 2005 Nanotechnology 16 S118
[14] Liu J, Callegari A, Stark M, Chergui M 2008 Ultramicroscopy 109 81
[15] Ruiter A G T, Veerman J A, van der Werf K O,van Hulst N F 1997 Appl. Phys. Lett. 71 28
[16] Grober R D, Acimovic J, Schuck J, Hessman D, Kindlemann P J, Hespanha J, Morse A S, Karrai K, Tiemann I, Manus S 2000 Rev. Sci. Instrum. 71 2776
[17] Rensen W H J, van Hulst N F, Ruiter A G T, West P E 1999 Appl. Phys. Lett. 75 1640
[18] Seo Y, Cadden-Zimansky P, Chandrasekhar V 2005 Appl. Phys. Lett. 87 103103
[19] Wang X P, Liu L, Hu H L, Zhang K 2004 Acta Phys. Sin. 53 1008 (in Chinese) [王晓平、刘 磊、胡海龙、张 琨 2004 物理学报 53 1008]
[20] Rechen J 2001 Ph.D. Dissertation (Zurich: Swiss Federal Institute of Technology)
[21] Simon G H, Heyde M, Rust H P 2007 Nanotechnology 18 255503
[22] Castellanos-Gomez A, Agrait N, Rubio-Bollinger G 2009 Nanotechnology 20 215502
[23] García R, Pérez R 2002 Surf. Sci. Rep. 47 197
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