title: Interpreting motion and force for narrow-band intermodulation atomic force microscopy.
abstract: Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple modes in a frequency comb. A high-quality factor cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show, by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time-domain perspective, we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with the tip motion (F(I)) and quadrature to the motion (F(Q)). Traditionally, these force components have been considered as a function of the static-probe height only. Here we show that F(I) and F(Q) actually depend on both static-probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of F(I) and F(Q) from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe-height dependence of the force components F(I) and F(Q), providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.
authors: Royal Institute of Technology (KTH), Section for Nanostructure Physics, Albanova University Center, SE-106 91 Stockholm, Sweden.
authors: Daniel
authors: D
authors: Platz
authors: Daniel
authors: D
authors: Forchheimer
authors: Erik A
authors: EA
authors: Tholén
authors: David B
authors: DB
authors: Haviland
keywords: AFM; atomic force microscopy; force spectroscopy; frequency combs; high-quality-factor resonators; intermodulation; multifrequency
references: Ultramicroscopy. 2010 May;110(6):573-7
references: 20227182
references: Phys Rev Lett. 2010 Feb 5;104(5):050801
references: 20366757
references: Nanotechnology. 2008 Sep 17;19(37):375704
references: 21832558
references: Nat Nanotechnol. 2007 Aug;2(8):507-14
references: 18654349
references: Nanotechnology. 2012 Jul 5;23(26):265705
references: 22699717
references: Phys Rev Lett. 2009 Nov 27;103(22):220801
references: 20366084
references: Nat Mater. 2005 Feb;4(2):156-9
references: 15654346
references: Science. 1995 Jan 6;267(5194):68-71
references: 17840059
references: Phys Rev Lett. 2006 Jul 21;97(3):036104
references: 16907516
references: Proc Natl Acad Sci U S A. 2002 Sep 17;99(19):12006-10
references: 12198180
references: Nanotechnology. 2009 Apr 22;20(16):165703
references: 19420576
references: Proc Natl Acad Sci U S A. 2002 Jun 25;99(13):8473-8
references: 12070341
references: Proc Natl Acad Sci U S A. 2006 Mar 28;103(13):4813-8
references: 16551751
references: Science. 1993 Jun 4;260(5113):1451-6
references: 17739801
references: Phys Rev Lett. 1986 Mar 3;56(9):930-933
references: 10033323