# Intermittent-Contact Heterodyne Force Microscopy

Authors: M. Teresa Cuberes
Journal: Journal of Nanomaterials
 (2009)

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## Abstract

Heterodyne Force Microscopy opens up a way to monitor nanoscale events with high temporal sensitivity from the quasistatic cantilever mechanical-diode response taking advantage of the beat effect. Here, a novel heterodyne ultrasonic force method is proposed, in which the cantilever is driven in amplitude-modulation mode, at its fundamental flexural eigenmode. Ultrasonic vibration in the megahertz range is additionally input at the tip-sample contact from the cantilever base and from the back of the sample. The ultrasonic frequencies are chosen in such a way that their difference is coincident with the second cantilever eigenmode. In the presence of ultrasound, cantilever vibration at the difference frequency is detected. Similarly as in heterodyne force microscopy, it is expected that the phase response yields information with increased sensitivity due to the beat effect.


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## Body

## 1.  Introduction

The mechanical-diode (MD)  approach is based on the detection of
the quasistatic response of an Atomic Force Microscopy (AFM) cantilever when
the forces actuating upon the tip vary nonlinearly in the ultrasonic time scale
[1, 2]. Up to now, the mechanical-diode response has been mostly exploited with
the AFM working in contact or near-contact mode [3, 4]. Heterodyne Force
Microscopy (HFM) [5] introduced a novel method, in which the cantilever tip is in
contact with the sample surface, and ultrasound is excited both at the tip
(from a transducer at the cantilever base) and at the sample surface (from a
transducer at the back of the sample) at adjacent frequencies, and mixed at the
tip-sample gap. By this procedure, the
tip-sample distance is modulated in beats, and extremely small phase shifts of
the sample ultrasonic vibration can be easily monitored via the much larger
phase shift of the cantilever vibration induced at the difference (beat)
frequency (beat effect). Here, I propose a novel heterodyne ultrasonic force
method, named hereafter Intermittent-Contact Heterodyne Force Microscopy
(IC-HFM) in which the cantilever is driven in tapping mode, at its fundamental resonance.
Ultrasonic vibration in the megahertz range is additionally input at the
tip-sample contact from the cantilever base and from the back of the sample.
The ultrasonic frequencies are so chosen that their difference is coincident
with the second-order cantilever resonance. Here, I demonstrate that in the
presence of ultrasound, cantilever vibration at the difference frequency is
detected. As explained below, the results can be attributed to the activation
of a mechanical-diode signal during the time that the tip and the sample are in
contact. The cantilever response can be controlled by varying the difference
frequency, which is kept nearest to the second-order cantilever resonance.
Phase data are expected to provide an increased sensitivity via the beat
effect.


## 2.  Principle of Measurement: Intermittent-Contact Heterodyne Force Microscopy (IC-HFM)

The principle of measurement in IC-HFM is illustrated in Figure1. The fundamental resonance of the cantilever ω0 is excited using a piezoelement at the
cantilever base. The AFM is operated in tapping mode, with the feedback keeping
constant the amplitude of the fundamental flexural cantilever resonance.
Additionally, ultrasonic vibration at frequencies ω1 and ω2 is input at the tip-sample contact from
ultrasonic piezos located at the cantilever base and at the back of the sample,
respectively. Frequencies ω1 and ω2 are chosen in such a way that |ω2−ω1| equals the second-order cantilever resonance.
As the cantilever is driven in its fundamental mode, it comes in contact with
the sample surface for a certain time every period. During this contact time,
the tip-sample distance is modulated in beats at the difference frequency |ω2−ω1| due to the tip and sample ultrasonic vibration
and, provided that the tip and sample ultrasonic vibration amplitudes are
sufficiently large, a mechanical-diode force will act upon the cantilever and resonantly
excite its second-order vibration mode. As in HFM [5], the phase cantilever
response at the difference frequency |ω2−ω1| is expected to provide information about
tip-sample interactions with increased time sensitivity due to the beat
effect.Figure 1
A schematic
diagram illustrating IC-HFM (see text).


## 3.  Experiment

The measurements have been implemented by appropriately
modifying a commercial AFM instrument (NANOTEC). The NANOTEC electronics was used for AFM operation
in tapping mode, with the feedback keeping constant the amplitude of fundamental
flexural cantilever resonanceω0.
Ultrasonic piezoelements were additionally attached to the sample and the tip
holders (see Figure 1). Function generators were used to simultaneously excite
the sinusoidal vibration of the sample surface and the cantilever tip at two
frequencies ω1 and ω2 in the megahertz range (≈4 MHz).
The difference frequency |ω2−ω1| was purposely chosen to be coincident with
the second-order cantilever resonance. Electronic mixing of the synchronous
signals from both generators provided the reference signal for a lock-in
amplifier to track the cantilever response at the difference frequency |ω2−ω1| in amplitude and phase. Rectangular Si cantilevers
were used: VISTA probes provided by Nanoscience Instruments, with nominal
spring constant 3 N m−1, and resonance frequencies ω0≈55KHz and ωsecond_mode≈350KHz.
The samples consisted in titanium nitride (TiN) coatings prepared by dc
magnetron sputtering onto polished AISI 304 stainless steel discs in a vacuum
chamber at room temperature using a water-cooled Ti target [6].


## 4.  Results and Discussion

Figures2(a) and  2(b) show the fundamental and the
second-free flexural cantilever resonances, respectively. Figure 2(c) shows the
spectral cantilever response measured with the FFT facility of our oscilloscope
(Agilent DSO6104A) with
the AFM operated in tapping  mode. Peaks at 333.65 KHz and 388.55 KHz are
apparent, which correspond to the 6th and 7th harmonics
of the fundamental cantilever resonance. As it is well known [7–12], in tapping
mode operation, a certain amount of power is shifted to higher harmonics due to
the distortion of the harmonic motion of the cantilever at the bottom of each
tapping oscillation cycle. Typically,
high-amplitude harmonics always appear close to the resonance frequencies of
higher  cantilever resonant  modes, indicating a dependence of harmonics generation
on cantilever resonances. In our case, the frequency corresponding to the
second-order cantilever resonant mode lies in between the 6th and 7th harmonics of the fundamental resonance, as indicated by the arrow in Figure 2(c).
In the absence of ultrasound, cantilever vibration in its second-order resonant
mode could not be observed from the FFT spectra (see Figure 2(c)). Nevertheless, in the presence of ultrasound,  when
ultrasonic signals of ω1=4.800MHz and ω2≈4.450MHz were simultaneously input to the cantilever
tip and sample surfaces, respectively, while keeping the AFM in tapping mode
operation (see Figure 1), a signal at |ω2−ω1|≈350KHz was clearly detected by means of the lock-in
amplifier (see Figure 3). The lock-in used for the detection of the difference
frequency was independent from the AFM electronics employed for tapping mode
operation. The reference signal for the lock-in amplifier to detect cantilever
vibration at the difference frequency of tip and sample ultrasonic vibrations
was provided by electronically mixing the synchronous signals from the ultrasonic
signal generators, using a simple mixer. A slight modification of the
difference frequency led to significant variations in the signal detected by
the lock-in amplifier. Figure 3 shows amplitude and phase outputs of the lock-in
amplifier in different cases, together with the simultaneously recorded
topographic image provided by the tapping-mode measurements.  A maximum amplitude value of the
signal detected by the lock-in amplifier was obtained when the difference
frequency of tip and sample ultrasonic vibrations was coincident with the second-order
cantilever resonance mode (Figures 3(b)–3(b′′), difference frequency of 350 KHz). Nevertheless, for this
frequency, the phase response could not be properly
measured. For difference frequency values slightly above or below the second
cantilever resonance (Figures 3(a)–3(a′′), difference frequency of 349 KHz, and Figures 3(c)–3(c′′), difference frequency of 351 KHz, respectively), the phase contrast is
reversed.(a) Fundamental and (b) second-order flexural
cantilever resonances measured with the cantilever tip out-of-contact with the
sample surface (free cantilever modes), in the absence of ultrasonic vibration.
(c) FFT of the AFM photodiode signal in tapping
mode operation: excitation frequencyω0=55.521KHz, set-point amplitude
V = 15% V0.
(a)(b)(c)Figure 3
Topography (a)–(c) and IC-HFM amplitude
(a′)–(c′) and Phase (a′′)–(c′′) images recorded over a same (700 × 700) nm2 surface region
of a TiN coating. Images with the same letter (i.e., (a), (a′), and (a′′)) were
simultaneously recorded. Tapping parameters: ω0 = 55.52 KHz, V = 31% V0. Ultrasonic parameters: (a)–(a′′) ω1 =  4.800 MHz, ω2 = 4.449 MHz; (b)–(b′′) ω1 =  4.800 MHz, ω2 = 4.450 MHz; (c)–(c′′) ω1 =  4.800 MHz, ω2 = 4.451 MHz. V1 and V2 were kept constant. Greyscale range: (a)–(c) 35 nm; (a′) 3.6 V, (b′)
6.5 V, (c′) 3.2 V; (a′′) 4.2 V, (b′′)
10 V (out-of-scale), (c′′) 5.0 V.The excitation of cantilever
vibration at the difference frequency of tip and surface ultrasonic vibrations is
attributed to the activation of the mechanical-diode effect during the
tip-sample contact time, as illustrated in Figure1, in the same manner that it
occurs in HFM [4, 5]. The procedures of Scanning Near Field Ultrasonic
Holography (SNFM) [13] and Resonant Difference Frequency Atomic Force
Ultrasonic [14] are similarly performed to HFM, with the difference (beat)
frequency chosen in the range of hundreds of KHz, above the first cantilever
resonance frequency in [13], and coincident with a high-order cantilever
contact resonance in [14]. Recently, it
has been demonstrated that GHz vibrations from an acoustic resonator can be
detected by operating the AFM in tapping mode using the amplitude of the
fundamental cantilever mode to control the feedback and collect the topography,
and the second-order mode to detect acoustic information [15]. In IC-HFM, the
operation mode is actually the same as in [15], save that here the resonant
excitation of the second-order cantilever mode is activated by mixing of
surface and tip ultrasonic vibrations via the nonlinearity of the tip-surface
interaction.The simultaneous
excitation of the first and second cantilever modes in amplitude modulation
(AM) AFM operation is currently attracting a great deal of interest [16–19]. It
has been demonstrated that the sensitivity of the AM- AFM to map compositional
changes can be enhanced by the simultaneous excitation of the first and second
flexural modes [18]. A theory has been developed that considers coupling of the
different eigenmodes of the cantilever by the virial of the tip-surface forces,
and explains the origin of the high force sensitivity observed in multifrequency
force microscopy experiments [19]. Here, it is demonstrated that it is possible
to detect and control cantilever vibration at frequencies near the second-order
cantilever resonance by simultaneously exciting ultrasonic vibration at the tip
and surface, while the AFM is driven in tapping mode. Tip-sample interactions
events that result in ultrasonic phase delays of surface versus tip vibration
should be easily detected with high sensitivity taking into account the beat
effect. The scope of the present work is limited to demonstrate the feasibility
of the procedure, rather than to provide a detail understanding of the observed
contrast. As it will be discussed elsewhere [20] TiN coatings may exhibit
important differences in elastic contrast due to strain, structural defects, or
coexistence of different phases. Contrast in IC-HFM images in Figure 3 may originate
because of elasticity inhomogeneities.


## 5.  Summary

The results
presented here demonstrate the detection of cantilever vibration at frequencies
coincident or next to its second-order resonant mode, excited by ultrasonic vibration
from the cantilever tip and from the sample surface mixed via the nonlinearity
of the tip-surface contact, while the AFM is operated in tapping mode. The
amplitude in the response is at a maximum when the difference frequency of
surface and tip ultrasonic vibration is exactly coincident with the second-order
cantilever resonance. Contrast in the phase images of the cantilever response is
reversed depending on whether the resulting difference frequency is above or
below the frequency of the second-order
cantilever resonance.



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