**2. General aspects of the Atomic Force Microscope (AFM)**

In Binnig et al. (1986) the atomic force microscope ("AFM") was presented. The AFM has been described as one of the most efficient tools for obtaining high-resolution images of the samples, by exploiting its surface, both in air and in liquid media. At the core of the "AFM", there is a tip, mounted on the end of a micro cantilever, while the tip vibrates to scan the sample, its vibration is detected by a laser system, which emit signals to a photo detector that generate images of the object under examination at high resolution. This movement may vary depending on the need and on the type of material being analyzed. These variations include techniques such as static contact mode and dynamic techniques, such as non-contact mode and intermittent or tapping mode. The principle of operation of the "AFM" is to the measure the deflection of the microcantilever on whose free end the probe is mounted. The deflections (analyzed during the scan) are caused by forces acting between the tip and sample. These forces act on medium to large distances - typically ≥ 100 Å – such as attractive Van der Waals forces, magnetic forces and Coulomb forces (Eisenschitz, 1930). It can be said that when the tip approaches to the sample, it is first attracted by the surface, due to a wide range of attractive forces in the region. This attraction increases when the probe is very close to the sample. However, when the atoms of the tip and sample become very close, the orbital electrons begin to repel. The forces are canceled when the distance between the atoms is of the order of several angstroms (the distance of the order characteristic of a chemical bond). When the forces become positive, it can be said that the atoms of the tip and the sample are in contact and ultimately the repulsive forces dominate.

In Figures: 1,2 and 3, the main characteristics and the operation of an AFM can be observed. Figure 3; display the basic configuration of an AFM. The micro cantilever is V-shaped or rectangular with a sharp tip. This tip is usually of pyramidal or conical shape (Figure 2).

**Figure 1.** AFM photo (source: Bowen and Hilal 2009)

for the Atomic Force Microscope.

"MEMS" and "NEMS" the proper tools of mathematical modeling and simulations as well as qualitative dynamic analysis. It should be considering a macro-model, which agrees with the simulation results on a physical level, and with the experimental results, obtained from test structures in a lab. Many surveys have been developed in major research centers in Brazil and throughout the world in this direction. It is announced that several research groups in Brazil are involved with this theme, but most of the research carried out or in development focuses on experimentation or in the use of the numerical method - called finite element method. It is known that the nonlinear phenomena are prevalent in MEMS

The main idea of this chapter lies in the study of "State of the Art" of non-linear dynamic models and the design of their controls, since this new area of research is of paramount importance. This chapter deals with two boundary problems belonging to this line of research, in development at the university of Rio Claro and Bauru UNESP, for us, through research groups and development projects for Graduate (Masters) and Post–Doctor. Mainly

In Binnig et al. (1986) the atomic force microscope ("AFM") was presented. The AFM has been described as one of the most efficient tools for obtaining high-resolution images of the samples, by exploiting its surface, both in air and in liquid media. At the core of the "AFM", there is a tip, mounted on the end of a micro cantilever, while the tip vibrates to scan the sample, its vibration is detected by a laser system, which emit signals to a photo detector that generate images of the object under examination at high resolution. This movement may vary depending on the need and on the type of material being analyzed. These variations include techniques such as static contact mode and dynamic techniques, such as non-contact mode and intermittent or tapping mode. The principle of operation of the "AFM" is to the measure the deflection of the microcantilever on whose free end the probe is mounted. The deflections (analyzed during the scan) are caused by forces acting between the tip and sample. These forces act on medium to large distances - typically ≥ 100 Å – such as attractive Van der Waals forces, magnetic forces and Coulomb forces (Eisenschitz, 1930). It can be said that when the tip approaches to the sample, it is first attracted by the surface, due to a wide range of attractive forces in the region. This attraction increases when the probe is very close to the sample. However, when the atoms of the tip and sample become very close, the orbital electrons begin to repel. The forces are canceled when the distance between the atoms is of the order of several angstroms (the distance of the order characteristic of a chemical bond). When the forces become positive, it can be said that the atoms of the tip and the sample are in contact and ultimately the repulsive forces dominate.

In Figures: 1,2 and 3, the main characteristics and the operation of an AFM can be observed. Figure 3; display the basic configuration of an AFM. The micro cantilever is V-shaped or rectangular with a sharp tip. This tip is usually of pyramidal or conical shape (Figure 2).

and NEMS, which is a strong motivation for the work of our research group.

**2. General aspects of the Atomic Force Microscope (AFM)** 

**Figure 2.** (source: Bowen and Hilal 2009)

**Figure 3.** Control of the positioning of the scanner. Adapted from : (Cidade et al. 2003)

Typically, probes are made predominantly of silicon nitride (Si3N4); its upper surface is coated with a thin reflective surface, generally gold (Au) or aluminum (Al). The probe is brought to inside and out of contact with the sample surface, by using a piezo-crystal (Hilal and Bowen, 2009). In the illustration of a typical micro-manipulator, shown in Figure 3, it is possible to observe that it consists of a movable stage mounted under an optical microscope. The movement of the base can be controlled by an electronic control console. Large deflections are required to achieve high sensitivity. Therefore, the spring should be very "soft" (slightly stiff).
