Frequency-modulated AFM

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]. 

Umeda, K. Fukui, K. 2010. Observation of redox-state-dependent reversible local structural change of ferrocenyl-terminated molecular island by electrochemical frequency modulation AFM. Langmuir 26 9104-9110. 

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. 

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. 

Dielectric relaxation of supported polymer films was measured for dry as well as wet samples by using the LDS method. A Veeco Multimode AFM (Nanoscope Ilia with ADC5 extension) was adapted to a frequency-modulated electrostatic force microscope (FM-EFM) and operated in lift mode (details are reported in Refs. [41, 47]) FM-EFM with improved bandwidth was here implemented through a RHK Technology PLLProll phase-locked-loop (PLL) frequency detector, having a nominal response bandwidth of 4 kHz that could be extended to about 10 kHz by... 

Pulsed-force mode AFM (PFM-AFM) is a method introduced for fast mapping of local stiffness and adliesion with lower required data storage than recording force-distance curves at each point on the x-y plane [115]. A sinusoidal or triangular modulation is applied between the tip and sample (either via lever or sample piezo) at a lower frequency than that of either the piezo or cantilever resonance frequency. Tip and sample then come... 

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... 

In the so-called pulsed force mode AFM technique developed by Marti and coworkers [124], the data acquisition rates are increased. In this mode, as outlined in Sect. 3.2, the sample is modulated sinusoidally ( 1 kHz) during a conventional contact mode AFM scan to cause that the tip contacts, indents, and breaks free from the surface with a frequency of 1 kHz during scanning. Instead of recording the complete f-d curve, pull-off forces and stiffness are acquired parallel to sample topography at useful scan rates that become possible (Fig. 3.54). 

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