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W. Richard Bowen and Nidal Hilal 4

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24 1. BAsIC PRINCIPLEs OF ATOMIC FORCE MICROsCOPy<br />

T Absolute temperature K<br />

v 0 Unloaded resonant frequency Hz<br />

v 1 Loaded resonant frequency Hz<br />

w Cantilever width m<br />

x Deflection of cantilever m<br />

� Inside angle of V-shaped cantilever °<br />

� i Imaginary component of hydrodynamic function –<br />

� hard Contact slope versus hard surface nm V �1<br />

� ref Contact slope measured versus reference cantilever nm V �1<br />

� f Density of surrounding fluid Pa s<br />

ϕ Angle between cantilever <strong>and</strong> reference lever °<br />

� f Fundamental resonant frequency of lever Hz<br />

references<br />

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J. Gurley, An atomic resolution atomic force microscope implemented using an optical<br />

lever, J. Appl. Phys. 65 (1) (1988) 164–167.<br />

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with sputtered silicon tip, Sensors Actuat. A 92 (2001) 96–101.<br />

[7] M. Tortonese, R.C. Barrett, C.F. Quate, Atomic resolution with an atomic force microscope<br />

using piezoresistive detection, Appl. Phys. Lett. 62 (8) (1993) 834–836.<br />

[8] T. Gotszalk, P. Grabiec, F. Shi, P. Dumania, P. Hudek, I.W. Rangelow, Fabrication of<br />

multipurpose AFM/SCM/SEP microprobe with integrated piezoresistive deflection<br />

sensor <strong>and</strong> isolated conductive tip, Microelectron. Eng. 41/42 (1998) 477–480.<br />

[9] P.-F. Indermuhle, G. Schurmann, G.-A. Racine, N.F. De Rooij, Fabrication <strong>and</strong> characterization<br />

of cantilevers with integrated sharp tips <strong>and</strong> piezoelectric elements for<br />

actuation <strong>and</strong> detection for parallel applications, Sensors Actuat. A 60 (1997) 186–190.<br />

[10] T. Itoh, T. Suga, Self-excited force-sensing microcantilevers with piezoelectric thin<br />

films for dynamic scanning force microscopy, Sensors Actuat. A 54 (1996) 477–481.<br />

[11] C. Lee, T. Itoh, T. Suga, Self-excited piezoelectric PZT microcantilevers for dynamic SFM<br />

– with inherent sensing <strong>and</strong> actuating capabilities, Sensors Actuat. A 72 (1999) 179–188.<br />

[12] Y. Su, A. Brunnschweiler, A.G.R. Evans, G. Ensell, Piezoresistive silicon V-AFM cantilevers<br />

for high-speed imaging, Sensors Actuat. A 76 (1999) 139–144.<br />

[13] H. Takahashi, K. Ando, Y. Shirakawabe, Self-sensing piezoresistive cantilever <strong>and</strong> its<br />

magnetic force microscopy applications, Ultramicroscopy 91 (2002) 63–72.

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