Optimized detection of normal vibration modes of atomic force microscope cantilevers with the optical beam deflection method

Recently, higher-order normal vibration modes of atomic force microscope cantilevers were utilized for functional imaging applications. Here, we present a detailed theoretical investigation of the sensitivities with which these modes are detected using the optical beam deflection method. The detection sensitivities depend strongly on the size and position of the focused optical spot. Optimization of the sensitivities is performed for the individual (transverse) normal modes. For the case that multiple normal modes need to be detected simultaneously, a universal sensitivity function is constructed. This function generates accurate values for the detection sensitivity as a function of spot diameter and mode number. Finally, different optimization strategies for the simultaneous detection of multiple normal modes are presented.

[1]  Jan Greve,et al.  A detailed analysis of the optical beam deflection technique for use in atomic force microscopy , 1992 .

[2]  M. Ohta,et al.  Defect Motion on an InP(110) Surface Observed with Noncontact Atomic Force Microscopy , 1995, Science.

[3]  Martin Stark,et al.  Higher-harmonics generation in tapping-mode atomic-force microscopy: Insights into the tip–sample interaction , 2000 .

[4]  U. Dürig,et al.  Relations between interaction force and frequency shift in large-amplitude dynamic force microscopy , 1999 .

[5]  F. Giessibl,et al.  Atomic Resolution of the Silicon (111)-(7x7) Surface by Atomic Force Microscopy , 1995, Science.

[6]  Gus Gurley,et al.  Short cantilevers for atomic force microscopy , 1996 .

[7]  Robert W. Stark,et al.  Tapping-mode atomic force microscopy and phase-imaging in higher eigenmodes , 1999 .

[8]  N. Amer,et al.  Novel optical approach to atomic force microscopy , 1988 .

[9]  Ricardo Garcia,et al.  Compositional mapping of surfaces in atomic force microscopy by excitation of the second normal mode of the microcantilever , 2004 .

[10]  Tilman E. Schäffer,et al.  Calculation of thermal noise in an atomic force microscope with a finite optical spot size , 2005 .

[11]  Hans-Jürgen Butt,et al.  Calculation of thermal noise in atomic force microscopy , 1995 .

[12]  Deron A. Walters,et al.  Atomic force microscope for small cantilevers , 1997, Photonics West.

[13]  Ute Rabe,et al.  Vibrations of free and surface‐coupled atomic force microscope cantilevers: Theory and experiment , 1996 .

[14]  Jason Cleveland,et al.  Finite optical spot size and position corrections in thermal spring constant calibration , 2004 .

[15]  Paul K. Hansma,et al.  Characterization and optimization of the detection sensitivity of an atomic force microscope for small cantilevers , 1998 .

[16]  D. Rugar,et al.  Frequency modulation detection using high‐Q cantilevers for enhanced force microscope sensitivity , 1991 .

[17]  Tilman E. Schäffer,et al.  Force spectroscopy with a large dynamic range using small cantilevers and an array detector , 2002 .

[18]  J. Parlebas,et al.  Growth, electronic, magnetic and spectroscopic properties of transition metals on graphite , 1999 .

[19]  M. Gustafsson,et al.  Scanning force microscope springs optimized for optical‐beam deflection and with tips made by controlled fracture , 1994 .

[20]  P. Hansma,et al.  An atomic-resolution atomic-force microscope implemented using an optical lever , 1989 .

[21]  H. Hölscher,et al.  Quantitative analysis of dynamic-force-spectroscopy data on graphite(0001) in the contact and noncontact regimes , 2000 .

[22]  Paul K. Hansma,et al.  Tapping mode atomic force microscopy in liquids , 1994 .

[23]  Oleg Kolosov,et al.  Ultrasonic force microscopy for nanometer resolution subsurface imaging , 1994 .

[24]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[25]  Abdullah Atalar,et al.  Contact imaging in the atomic force microscope using a higher order flexural mode combined with a new sensor , 1996 .

[26]  Martin Stark,et al.  Inverting dynamic force microscopy: From signals to time-resolved interaction forces , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  M. Viani,et al.  Small cantilevers for force spectroscopy of single molecules , 1999 .

[28]  Yan Liu,et al.  Relationship between Stiffness and Force in Single Molecule Pulling Experiments , 1999 .

[29]  H. Gaub,et al.  Force spectroscopy with single bio-molecules. , 2000, Current opinion in chemical biology.

[30]  Robert W. Stark,et al.  Fourier transformed atomic force microscopy: tapping mode atomic force microscopy beyond the Hookian approximation , 2000 .

[31]  Ute Rabe,et al.  Acoustic microscopy by atomic force microscopy , 1994 .

[32]  Robert W. Stark,et al.  Optical lever detection in higher eigenmode dynamic atomic force microscopy , 2004 .

[33]  Paul K. Hansma,et al.  Studies of vibrating atomic force microscope cantilevers in liquid , 1996 .