APPLIED PHYSICS LETTERS 92, 153106 共2008兲

Intermodulation atomic force microscopy
Daniel Platz, Erik A. Tholén, Devrim Pesen, and David B. Havilanda兲Nanostructure Physics, Royal Institute of Technology, SE-10691 Stockholm, Sweden

共Received 21 January 2008; accepted 26 March 2008; published online 15 April 2008兲
A mode of atomic force microscopy 共AFM兲 is demonstrated where an oscillating AFM cantilever
having linear response is driven with two frequencies in the vicinity of a resonance. New
frequencies in the response, known as intermodulation products, are generated when the linearity of
the cantilever response is perturbed by the nonlinear tip-surface interaction. A rich structure of theintermodulation products is observed as a function of the probe-surface separation, indicating that
it is possible to extract much more detailed information about the tip-surface interaction than ispossible with the standard amplitude and phase imaging methods. © 2008 American Institute ofPhysics. 关DOI: 10.1063/1.2909569兴
The sensitivity and utility of atomic force microscopy
共AFM兲 were considerably enhanced by the introduction ofresonant detection1,2 or “tapping mode” AFM.3 In the standard realization of tapping mode AFM, a probe consisting ofa cantilever with a sharp tip is driven near the fundamental
eigenmode of the cantilever at frequency f 0. When the probe
is brought close to a surface, the atomic forces between the
tip and the surface are detected by measuring a change in theamplitude and phase of the cantilever oscillation at the frequency that the cantilever is driven. Attempts to extend tapping mode AFM and extract more information regarding thesurface properties include analyzing the cantilever oscillation
for higher harmonics of the drive frequency.4–6 These harmonics do not generally coincide with higher order eigenmodes of the cantilever, and therefore, response is verysmall. Special cantilevers with flexural eigenmodes at or near
the harmonics of the fundamental,7 or higher frequency torsional eigenmodes have also been investigated.8 Other techniques employ two drive frequencies, one at each of the twolowest eigenmodes of the cantilever while measuring the response at both drive frequencies.9,10 Here, we demonstrate amethod to probe the tip-surface interaction using only thefundamental eigenmode of a cantilever, where a highly linear
response of free cantilever oscillation is weakly perturbed by
the nonlinear tip-surface interaction, causing new frequencies to appear in the response.
The sensitivity of resonant detection is improved when
the resonator 共oscillating cantilever兲 has a weak damping, sothat a high quality factor Q is achieved.11 High Q resonatorsbuild up large amplitude oscillation on resonance, which implies that the restoring force should be a highly linear function of the coordinate describing the displacement from equilibrium. The tip-surface force, on the other hand, is not a
linear function of this coordinate. When this nonlinearity isstrong enough 共i.e., probe close enough to the surface兲,strong distortion of the resonance curve and bifurcation, orthe appearance of multi-valued oscillation states, occur.12,13
However, a very weak nonlinearity, which barely distorts theresonance curve, can be detected by measuring intermodulation products 共IMPs兲.14 Intermodulation is a phenomenon in
nonlinear systems driven with more than one frequency,
where the nonlinearity causes the generation of new frequena兲

Electronic mail: haviland@kth.se.

cies in the response, which are not present in the drive. In
many engineering contexts, intermodulation is considered anundesirable effect and intermodulation measurements areused for characterization of signal distortion due to nonlinearity. Here, we use intermodulation in an advantageous
way to realize a very sensitive, high information bandwidthmode of AFM, which we call intermodulation AFM
共IMAFM兲.15In Fig. 1, we compare the response of a linear resonatorand a nonlinear resonator when driven with two frequencies.
The linear resonator 关Fig. 1共a兲兴 shows response only at thetwo drive frequencies, f 1 and f 2. In the nonlinear resonator关Fig. 1共b兲兴, new frequencies are present in the response,
which are the IMPs. Following the usual convention, wedenote the IMPs by their order as described in Fig. 1共b兲. For
the realization of IMAFM demonstrated here, we study theodd order IMPs, which form a series of peaks near the resonance with spacing n⌬f = n共f 2 − f 1兲 from the two drive frequencies 共n is an integer兲.
To realize IMAFM, we used a Veeco multimode AFM
and Nanoscope IV controller equipped with a signal accessmodule together with several pieces of auxiliary equipment.
The signal used to drive the cantilever consisting of twofrequencies was synthesized with two arbitrary waveform

FIG. 1. 共a兲 The linear response of the resonator away from the surface.
When driven with two frequencies, f 1 and f 2, the linear system respondswith oscillation at f 1 and f 2. 共b兲 When close to the surface, nonlinear tipsurface interactions generate IMPs of many orders.

0003-6951/2008/92共15兲/153106/3/$23.00
92, 153106-1© 2008 American Institute of Physics
Downloaded 19 Mar 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

153106-2

Platz et al.

FIG. 2. 共Color online兲 The frequency spectra of the cantilever response areplotted as the surface is approached. Many intermodulation peaks of higherorder can be seen, where the amplitude of each peak is uniquely dependent
on the tip-surface separation.

generators 共AWGs兲 and a summing preamplifier. A data acquisition card 共DAC兲 was used to measure the cantileverresponse by capturing the raw detector signal from the split
quadrant photodiode in the AFM head. The clocks of both
AWGs and the DAC were phase locked to the same 10 MHz
signal. While scanning, lines of data were captured on thetrace, and during the retrace they were parsed and Fouriertransformed to extract the IMP amplitudes at different tip
positions. When scanning the test samples, our IMAFM system was run in parallel with the Nanoscope system, using thefeedback and scanning controls of the Nanoscope IV controller. In this way, we could compare IMAFM with the standard
amplitude and phase imaging methods. The AFM probe usedhere was a relatively stiff Si tapping mode probe with abeam-type cantilever 共RTESP-300, nominal spring constant
40 N / m兲 having a resonant frequency f 0 = 330.8 kHz and Q= 633, or mechanical bandwidth B = f 0 / Q = 523 Hz. It wasdriven by a small piezostack built into the probe holder. TheAFM probe was cleaned in an oxygen plasma prior to measuring. Measurements were performed at room temperaturein air on Si chips with a special surface chemistry described
below.
Figure 2 is a three-dimensional plot showing the spectraof the cantilever response 共log amplitude versus frequency兲
as the cantilever is approaching the surface. When the tip isfar from the surface, at the right hand side of Fig. 2, theresponse spectrum has two dominant peaks, which are thetwo drive frequencies f 1 and f 2. At this distance from thesurface, the cantilever is undergoing free oscillation, unperturbed by the tip-surface interaction. The free oscillation response spectrum also shows a background of intermodulation peaks of many orders, which are visible above the noisefloor. These background peaks are due to nonlinearities in theDAC and could be reduced with better quality electronics.
To clarify the origin of these background IMPs, we madea detailed study of the free cantilever response as a functionof the drive amplitude. Sweeping two equal amplitude drive

Appl. Phys. Lett. 92, 153106 共2008兲

signals f 1 and f 2 with fixed ⌬f through the cantilever resonance, we recorded the amplitude of the response at f 1, f 2,
and f IM3 共data not shown here兲. When the cantilever wasdriven near the resonance and undergoing large amplitude
oscillations 共detector signal amplitude ⬎0.8 V兲, a third order
IMP could be seen above the background, which was generated by the nonlinear dynamics of the cantilever itself. However, at the oscillation amplitude levels used in the following
共detector signal amplitude ⬍0.4 V兲, IMPs due to the cantilever itself were well below the background level of our detection system.
As the surface is approached 共moving from the right toleft in Fig. 2兲, the response spectra show a large increase in
the measured IMPs, and the measured amplitude of theseIMPs show much variation with the average probe-surface
separation. By making ⌬f ⯝ B, a large number of IMPs canbe measured in the response spectrum. In Fig. 2 with ⌬f= 600 Hz 共B = 523 Hz兲, one can count as many as nine measurable IMPs, each with a unique dependence on probesurface separation, and presumably containing a great deal of
information about the exact nature of the tip-surface interaction. However, at this time, we lack a general theory of how
to extract the tip-surface potential from this data.
Note that the optimal measurement bandwidth of
IMAFM is given by ⌬f, which can be chosen smaller orlarger than the mechanical bandwidth B = f 0 / Q of the resonator. Smaller ⌬f will result in longer measurement timeand, therefore, slower scanning speed, but small ⌬f will also
give a larger number of IMPs within the frequency band offinite cantilever response. Here, we see how IMAFM optimally uses frequency space to extract information from theoscillator regarding the nonlinear perturbation. IMAFM has
a much larger information bandwidth than standard tapping
mode AFM, which records response at only one frequency.
Thus, IMAFM represents an ideal approach to dynamic force
microscopy, where the goal is to determine the functional
form of the tip-surface interaction by analysis of the cantilever response.13
To more clearly show the structure of the IMPs versus
probe-surface separation, we plot the amplitude of the cantilever response 共linear scale兲 at the two drive frequencies andthe first three odd IMPs 共Fig. 3兲. Here, we see the response
for both the approach and the retracting of the probe from thesurface, which was done in one continuous ramp toward andaway from the surface. The strong similarity of approach andretract for each curve demonstrates that the measured change
in cantilever response is reversible, or nonhysteretic. Important for the sensitivity of AFM is the responsivity 共i.e., slopeof curves in Fig. 3兲 at first contact with the surface, which issimilar in magnitude for the drive frequencies and the IMPs.
However, the IMPs start from a low signal level and, therefore, a small change in IMP amplitude can be detected without saturation by using higher gain electronic amplifiers withappropriate filtering. The responsivity of the IMPs will depend on the choice of f 1 and f 2 relative to f 0, which was not
optimized in this measurement.
To demonstrate the utility of IMAFM in imaging mode,
we show an image of a special sample consisting of a protein
monolayer adsorbed on to a smooth Si surface 共Fig. 4兲. On
this surface, a stripe pattern is exposed with a low energy
共5 keV兲 electron beam in an electron beam lithography system. The exposure causes a chemical change in the surface
where the electrons strike the protein monolayer but noDownloaded 19 Mar 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

153106-3

Appl. Phys. Lett. 92, 153106 共2008兲

Platz et al.

FIG. 3. 共Color online兲 The amplitude of response at the two drive frequencies, f 1 and f 2, and the first three odd IMPs. The f 2, f IM5, and f IM7 curves
have been offset on the vertical axis for clarity.

change in topography.16 We performed standard tapping
mode height and phase imaging, where the feedback regulated the probe-surface separation to keep a constant amplitude of the cantilever response at the drive frequency as thetip was scanned over the surface. While scanning, the height
image 共i.e., feedback signal兲 was featureless, but we see inFig. 4共a兲 how the exposed striped pattern can be seen in thephase image. Phase imaging is a well established technique
for sensing very subtle changes in surface chemistry,17 whichcause a change in resonator damping.18

FIG. 4. A comparison of the phase image 共a兲 of standard tapping mode AFM
and the IM3 image 共b兲 collected with identical feedback setup. The sample
is a protein monolayer adsorbed on to a smooth SiOx surface. A striped
pattern exposed with an electron beam causes a chemical change, but nochange in surface topography. The histograms 共c兲 and 共d兲 show the distribution of grayscale values in 共a兲 and 共b兲, respectively. The scan width is100 ␮m.

In a second sweep over the same area using IMAFM, wesimultaneously gathered several images by recording the amplitude of IMPs of higher orders. Figure 4共b兲 shows the image generated from the amplitude of IM3, which is somewhat noisier than the phase image, due to the lower signal
level of IM3 in comparison with the phase. However, a comparison of the grayscale histograms 关Figs. 4共c兲 and 4共d兲兴
shows that the IM3 image has slightly better contrast thanthe phase image. We also found that imaging on IM3 wasmore stable and easier to use than phase imaging. Whenphase imaging, the contrast would often jump, presumably
due to a small change in the cantilever resonance when impurities get stuck to the cantilever. The IM3 image appeared
to be immune to such jumps.
These experiments demonstrate that IMAFM is an attractive alternative to tapping mode AFM. With further optimization of the technique, images can be acquired in a single
scan with higher sensitivity and greater information content
than the standard tapping mode AFM. In closing, we notethat IMAFM can be performed by running the feedback directly from one or a combination of the IMPs, and that
implementation of IMAFM can be greatly simplified in thepresent generation of AFMs where the modern controllers
have a larger capacity for digital signal synthesis andprocessing.
This work was supported by the Swedish VR,
Wennergren Foundation and used the Albanova Nano FabLaboratory with equipment donated by the K A Wallenberg
Foundation.
1

Y. Martin, C. C. Williams, and H. K. Wickramasinghe, J. Appl. Phys. 61,4723 共1987兲.
T. R. Albrecht, P. Grütter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668
共1991兲.
3
Q. Zhong, D. Inniss, K. Kjoller, and V. B. Elings, Surf. Sci. Lett. 290,L668 共1993兲; US Patent No. RE36,488 2000.
4
R. W. Stark and W. M. Heckl, Rev. Sci. Instrum. 74, 5111 共2003兲.
5
M. Balantekin and A. Atalar, Appl. Phys. Lett. 87, 243513 共2005兲.
6
S. Crittenden, A. Raman, and R. Reifenberger, Phys. Rev. B 72, 235422
共2005兲.
7
O. Sahin, G. Yaralioglu, R. Grow, S. F. Zappe, A. Atalar, C. Quate, and O.
Solgaard, Sens. Actuators, A 114, 183 共2004兲.
8O. Sahin, S. Magonov, C. Su, C. F. Quate, and O. Solgaard, Nat.
Nanotechnol. 2, 507 共2007兲.
9N. F. Martinez, S. Patil, J. R. Lozano, and R. Garcia, Appl. Phys. Lett. 89,153115 共2006兲.
10R. Proksch, Appl. Phys. Lett. 89, 113121 共2006兲.
11J. Tamayo, J. Appl. Phys. 97, 044903 共2005兲.
12
P. Gleyzes, P. K. Kuo, and A. C. Boccara, Appl. Phys. Lett. 58, 2989
共1991兲.
13R. Garcia and R. Perez, Surf. Sci. Rep. 47, 197 共2002兲.
14
D. E. Oates, S. H. Park, and G. Koren, Phys. Rev. Lett. 93, 197001
共2004兲.
15
D. B. Haviland, D. Platz, and E. A. Tholén, Patent Pending 共2007兲.
16
D. Pesen, A. Erlandsson, M. Ulfendahl, and D. B. Haviland, Lab Chip 7,1603 共2007兲.
17
W. F. Heinz and J. H. Hoh, J. Chem. Educ. 82, 695 共2005兲.
18
J. P. Cleveland, B. Anczykowski, A. E. Schmid, and V. B. Elings, Appl.
Phys. Lett. 72, 2613 共1998兲.
2Downloaded 19 Mar 2009 to 133.28.47.30. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp