Amplitude-modulated AFM

Figure 13.9 Observation of a field-induced water bridge with amplitude modulation AFM. [a] Depicts the tip s oscillation before, during, and after the application of a voltage pulse for 20 ms that did not involve the formation of a water bridge [V = 10.4 V], [b] Depicts the tip s oscillation before, during, and after the application of a voltage pulse for 20 ms that involved the formation ofa water bridge [V = 11V], Step ill is indicative of the formation of a water bridge because the oscillation does not recover its initial value once the pulse is off. Each dot in the oscilloscope traces represents an instantaneous position of the atomic force microscope tip. [Data adapted from Refs. 19, 53, 69, and 81.]...

Figure 13.10 Measurement of the snap-off separation with an amplitude modulation AFM. [a] Piezo displacement Az vs. time, (b) Voltage pulse, (c) Tip oscillation. Zj represents the average tip-sample distance. The snap-ofF separation is given by Dsnap-off = Z -t- Azsnap-off- The zero position in the y-axis represents the position of the surface. Relative humidity, RH = 55%. Voltage pulse of 9 V and 1 ms. (Data adapted from Ref. 53.]...

In 1991, Albrecht et al. invented frequency modulation atomic force microscopy (FM-AFM) for operating d3mamic-mode AFM in vacuum environments. Before this invention, it was common to operate d3mamic-mode AFM with the amplitude detection method, which is referred to as amplitude modulation AFM (AM-AFM). In AM-AFM, the tip-sample distance is regulated such that the oscillation amplitude of the cantilever (A) is kept constant. 

Fig. 9. Block diagram of the frequency-modulation AFM feedback loop for constant amplitude control and frequency-shift measurement. Three physical observables are available frequency shift, damping signal, and (average) tunneling current.

The simple textbook solution of a harmonic damped oscillator becomes complex when the vibrating tip interacts with the surface of a sample, e.g., in tapping mode AFM. Although the different imaging modes and the experimental observables may vary, the underlying physics is similar. Amplitude and frequency modulated AFMs are most commonly used, labeled by AM-AFM (amplitude modulation or tapping) and FM-AFM. For a detailed review of this topic several reviews are available, e.g., [15]. 

For imaging in IC-AFM (see Fig. 3.29), the amplitude of cantilever oscillation is used for feedback control, and the set point. Asp. is less than the free oscillation amplitude, A . This mode of operation is also referred to as amplitude modulation (AM) AFM. A convenient way to standardize the description of tapping conditions for both stiff and compliant materials is to use Ao, Asp, and Asp/Ao [108]. This ratio is called the set-point ratio r p. 

This technique was first described in 1991 [153] and has since been reviewed [143,154]. It has been used to give molecular resolution images of electrically conductive polymers [155] and PS-h-PMMA block copolymers [156] in UHV. Because the technique is truly non-contact, it does not have the complexity of dual interaction paths (either repulsive or attractive) that are inherent to amplitude modulation IC-AFM. This makes the technique suitable for the study of metal-polymer bonding under controlled ambient conditions [157]. 

Most NC-AFMs use a frequency modulation (FM) teclmique where the cantilever is mounted on a piezo and serves as the resonant element in an oscillator circuit [101. 102]. The frequency of the oscillator output is instantaneously modulated by variations in the force gradient acting between the cantilever tip and the sample. This teclmique typically employs oscillation amplitudes in excess of 20 mn peak to peak. Associated with this teclmique, two different imaging methods are currently in use namely, fixed excitation and fixed amplitude. 

An alternative technique is noncontact AFM [18]. Figure 19 illustrates the concept. The tip oscillates above the surface, and the modulation in amplitude, phase, or frequency of the oscillating cantilever in response to force gradients from the sample can be measured to indicate the surface topography. Even without contact, the amplitude, phase, or frequency can be affected by the van der Waals forces of the sample within a nanometer range, which is the theoretical resolution however, this effect can be easily blocked by the fluid contaminant layer, which is substantially thicker than... 

The identification of phases in polymer blends can be accomplished in force modulation mode (FMM) AFM. Using FMM AFM the relative moduli (a convolution of storage and loss moduli) are mapped on the specimen surface. The rms amplitude of the FMM cantilever, driven in an oscillatory fashion, reflects directly the modulus of underlying polymer specimen. In the blend discussed below three phases can be differentiated. 

All AFM and STM topographic images were obtained in the mode of constant interaction. The distance modulation measurements were recorded by modulating the z-position of the piezo with a sinusoidal signal having an amplitude and frequency of 1 - 5 A and 1.5 kHz respectively. 

In the contact mode, there are static modes (de-modes), and dynamic modes (ac-modes). In the former, a cantilever-type spring bends in response to the force which acts on the probing tip until a static equilibrium is established [1]. In the dynamic mode, the lever oscillates close to its resonance frequency. A distance-dependence force shifts the resonance curve. Another technique is to modulate the position of the sample at a frequency below the cantilever resonance but above the feedback-response frequency and send the response signal to a lock-in amplifier to measure the signal s amplitude and phase [4]. The lock-in output is connected to the auxiliary data acquisition channels to form an image - this approach is popularly known as force modulation (FM-mode). FM-mode imaging or force cmve is an AFM technique that identifies and maps differences in surface stiffness or elasticity. 

Figure 2.13. Dependence of surface modulation amplitude (according to AFM measurements) on the number of deposited bilayers in PDADMAC/(Congo Red) LbL films. Source He et al., 2000. Reprinted with permission from American...

In FMM mode, the AFM tip is scanned in contact with the sample, while a constant cantilever deflection is maintained by the feedback system. In addition, a periodic signal is applied to either the sample or the tip. Any variation in the amplitude of cantilever modulation that results from the applied signal can be attributed to a change in the elastic properties of the sample. 

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