Noncontact Atomic Force Microscopy - Yale School of Engineering ...

Dual-Frequency-Modulation AFM Spectroscopy
Gaurav Chawla, C. Alan Wright, and Santiago D. Solares
Department of Mechanical Engineering, University of Maryland at College Park, USA
P.I-28
Force spectroscopy is an important application of atomic force microscopy (AFM),
whereby tip-sample interaction forces are measured with probes of varying geometry and
chemistry. Most methods rely on measuring either the instantaneous cantilever deflection
in static mode or the frequency shift in low-amplitude frequency-modulation mode. In
the first case the force is calculated directly from the cantilever deflection. In the second
case the frequency shift is used to compute the tip-sample force gradient, from which the
tip-sample force curve can be reconstructed after scanning a region for which a boundary
condition is known. In both cases, acquiring a 3D representation of the tip-sample forces
requires fine-grid scanning of a volume above the surface. Using computational
simulations, we have developed a dual-frequency-modulation AFM spectroscopy method
[1,2] in which the cantilever is simultaneously excited at the fundamental frequency and
at a higher-order eigenfrequency (with a much smaller amplitude), such that
topographical imaging is performed using the fundamental frequency response and force
spectroscopy is performed using the higher-order response. Our results suggest that this
method could enable measurement of the 3D tip-sample forces above the surface with a
single 2D scan. The procedure was originally developed for ambient air, but has been
extended to vacuum conditions, where we are evaluating the 3D imaging of atomic
orbitals by integrating quantum mechanics and cantilever dynamics calculations. We are
especially interested in the effect of tip apex geometry on the ability to image sub-atomic
features. The method’s experimental implementation in air is in progress.
1.85
a b
Dual-frequency tip response
ν 1 band
ν 2 band
imaging
spectroscopy
Effective frequency, MHz
1.75
1.65
1.55
1.45
0 20 40 60 80 100
Time, ms
Tip approach
Tip retract
Figure 1: (a) Illustration of the dual-frequency-modulation AFM concept, where the cantilever
vibrates at two eigenfrequencies such that the fundamental response is used to perform imaging
and the high-frequency response is used to perform force spectroscopy; (b) illustration of the
instantaneous frequency of the self-excited high-frequency response for one full oscillation of the
low-frequency response, under positive frequency shift for the fundamental frequency. Since the
frequency shift follows the tip-sample force gradient, it is in principle possible under ideal
conditions to extract the tip-sample force curve every low-frequency oscillation.
[1] G. Chawla and Solares, S.D., Measurement Science and Technology 20, No. 015501 (2009).
[2] S.D. Solares and G. Chawla, Measurement Science and Technology 19, No. 055502 (2008).
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