**2. Basic principles**

SPM is defined as a specific type of microscopy that uses the basic principle of scanning a surface with a very sharp probe to image and measure properties of material, chemical and

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biological surfaces. According to the tip-sample interaction the microscopy has a specific name. The two primary forms of SPM are STM and AFM.

The AFM provides a 3D profile on a nanoscale, by measuring forces between a sharp probe (radius less than 10nm) and surface at very short distance (0.2-10nm probe-sample separation). The probe is supported on a flexible cantilever and the AFM tip gently touches the surface and records the small force between the probe and the surface (Wilson & Bullen, 2007). This force can be described using Hooke`s law:

$$\mathbf{F} = -\mathbf{k}.\mathbf{x}\tag{1}$$

Measurement of the Nanoscale Roughness by

type of interaction tip/sample.

Fig. 3. Contact Mode.

on the surface (Wisendanger, 1994)

Atomic Force Microscopy: Basic Principles and Applications 149

Fig. 2. Force as function of the tip/sample distance. Imaging modes of the AFM based on the

The intermittent mode (Figure 4) is similar to contact but in this mode the cantilever makes intermittent contact with the surface in a resonant frequency (hundreds of KHz). The probe slightly "taps" on the sample surface during scanning, contacting the surface at the bottom of its swing. Because the contact time is a small fraction of its oscillation period, the lateral forces are reduced dramatically. Intermittent mode is usually preferred to image samples with structures that are weakly bound to the surface or samples that are soft (polymers, thin films). There are also two other types of image contrast mechanisms in intermittent mode. *Amplitude imaging*: It's an image contrast mechanism where the feedback loop adjusts the z – piezo so that the amplitude of the cantilever oscillation remains (nearly) constant. The voltages needed to keep the amplitude constant can be compiled into an (error signal) image, and this imaging can often provide high contrast between features

 *Phase imaging*: The main characteristic of this mode is that the phase difference between the driven oscillations of the cantilever and the measured oscillations can be attributed to different material properties. For example, the relative amount of phase lag between the freely oscillating cantilever and the detected signal can provide qualitative information

about the differences in chemical composition, adhesion, and friction properties.

Where F = Force; k = Spring constant; x = Cantilever deflection.

The basic components of an AFM are the probe, the cantilever, the scanner, the laser, a data processor and a photodetector as shown in figure 1.

Fig. 1. Principle of AFM.

Forces involved in the tip-sample interaction affect how the probe interacts with the sample. If the probe experiences repulsive forces the probe will be in contact mode otherwise as the probe moves further away from the surface, attractive forces dominate and the probe will be in non-contact mode (Figure 2).

There are three primary imaging modes in AFM: the contact mode where the probe-surfaceseparation is less than 0.5 nm, the intermittent contact that occurs in a range of 0.5 and 2nm and the non-contact mode where the probe-surface-separation ranges from 0.1 to 10nm.

In contact mode (repulsive regime), if the spring constant of cantilever is less than surface, then the cantilever bends. The force on the tip is repulsive (Figure 3). The forces between the probe and the sample remain constant by maintaining a constant cantilever deflection then an image of the surface is obtained. The advantages of this imaging mode are: fast scanning, good for rough samples and it can be used in friction analysis (Wilson & Bullen, 2007). On the flip side however, forces can damage/deform soft samples (this can be solved by imaging in liquids).

biological surfaces. According to the tip-sample interaction the microscopy has a specific

The AFM provides a 3D profile on a nanoscale, by measuring forces between a sharp probe (radius less than 10nm) and surface at very short distance (0.2-10nm probe-sample separation). The probe is supported on a flexible cantilever and the AFM tip gently touches the surface and records the small force between the probe and the surface (Wilson & Bullen,

F k.x (1)

The basic components of an AFM are the probe, the cantilever, the scanner, the laser, a data

Forces involved in the tip-sample interaction affect how the probe interacts with the sample. If the probe experiences repulsive forces the probe will be in contact mode otherwise as the probe moves further away from the surface, attractive forces dominate and the probe will be

There are three primary imaging modes in AFM: the contact mode where the probe-surfaceseparation is less than 0.5 nm, the intermittent contact that occurs in a range of 0.5 and 2nm and the non-contact mode where the probe-surface-separation ranges from 0.1 to 10nm.

In contact mode (repulsive regime), if the spring constant of cantilever is less than surface, then the cantilever bends. The force on the tip is repulsive (Figure 3). The forces between the probe and the sample remain constant by maintaining a constant cantilever deflection then an image of the surface is obtained. The advantages of this imaging mode are: fast scanning, good for rough samples and it can be used in friction analysis (Wilson & Bullen, 2007). On the flip side however, forces can damage/deform soft samples (this can be solved by

name. The two primary forms of SPM are STM and AFM.

2007). This force can be described using Hooke`s law:

processor and a photodetector as shown in figure 1.

Fig. 1. Principle of AFM.

imaging in liquids).

in non-contact mode (Figure 2).

Where F = Force; k = Spring constant; x = Cantilever deflection.

Fig. 2. Force as function of the tip/sample distance. Imaging modes of the AFM based on the type of interaction tip/sample.

Fig. 3. Contact Mode.

The intermittent mode (Figure 4) is similar to contact but in this mode the cantilever makes intermittent contact with the surface in a resonant frequency (hundreds of KHz). The probe slightly "taps" on the sample surface during scanning, contacting the surface at the bottom of its swing. Because the contact time is a small fraction of its oscillation period, the lateral forces are reduced dramatically. Intermittent mode is usually preferred to image samples with structures that are weakly bound to the surface or samples that are soft (polymers, thin films). There are also two other types of image contrast mechanisms in intermittent mode.


Measurement of the Nanoscale Roughness by

**3. Surface texture: Roughness, waviness and spacing** 

surface. On a surface, the lay is in the front-to-back direction (Figure 6).

Fig. 6. Surface lay (adapted from B. C. MacDonald & Co., 2011).

roughness sampling length (Oberg et al., 2000).

retraction of the tip.

engineering components.

Atomic Force Microscopy: Basic Principles and Applications 151

mode for imaging soft surfaces, but its sensitivity to external vibrations and the inherent water layer on samples in ambient conditions often causes problems in the engagement and

Surface texture is an important issue when the main interest is to understand the nature of material surfaces and it plays an important role in the functional performance of many

The American National Standards Institute's B46.1 specification defines surface texture as the repetitive or random deviation from the normal surface that forms the three dimensional topography of a surface. Before 1990's the measurement of sample surface was obtained by a contact stylus profiler (Whitehouse et al., 1975) that had limitations including a large stylus radius, a large force and low magnification in the plane and may have misrepresented the real surface topography owing to the finite dimension of the stylus tip (Vorburguer & Raja, 1990). On the ultramicroscopic scale of surface, atomic force microscopy (AFM) has been developed to obtain a three-dimensional image of a material surface on a molecular scale. "Lay" is the term used to indicate the direction of the dominant pattern of texture on the

Waviness (Figure 7) is the measure of the more widely spaced component of surface texture. It is a broader view of roughness because it is more strictly defined as the irregularities whose spacing, defined as the average spacing between waviness peaks, is greater than the

There are many parameters for measuring waviness. One of the most important is the waviness evaluation length, which is the length in which the waviness parameters are determined. Within this length the waviness profile is determined. This is a surface texture profile that has the shorter roughness characteristics filtered out, or removed; it also does not include any profile changes due to changes in workpiece geometry. So when it comes to waviness it's important to understand that it's always related to roughness. From this profile the waviness spacing, the average spacing between waviness peaks, is determined.

Fig. 4. Intermittent-Contact Mode.

Non-contacting mode (attractive VdW) is based on the knowledge that the probe does not touch the sample but oscillates above it during scanning (Figure 5).

The majority of the samples, unless the ones that are in a controlled UHV (Ultra High Vacuum) or in a environmental chamber have some liquid adsorbed on the surface so the surface topography can be measured by using a feedback loop to monitor changes in the amplitude due to the attractive forces between the probe and the sample.

The advantages of this mode are: very low forces exerted on the samples (10-12 N) and extend probe lifetime. The disadvantages of this mode are: generally lower resolution; contaminant layer on surface can interfere with oscillation; usually need UHV to have best imaging.

The choice as to which AFM mode to use depends on the surface characteristics of interest and on the hardness/stickiness of the sample. Contact mode is most useful for hard surfaces; a tip in contact with a surface, however, is subject to contamination from removable material on the surface.

Excessive force in contact mode can also damage the surface or blunt the probe tip. Intermittent mode is well-suited for imaging soft biological specimen and for samples with poor surface adhesion (DNA and carbon nanotubes). Non-contact mode is another useful

Non-contacting mode (attractive VdW) is based on the knowledge that the probe does not

The majority of the samples, unless the ones that are in a controlled UHV (Ultra High Vacuum) or in a environmental chamber have some liquid adsorbed on the surface so the surface topography can be measured by using a feedback loop to monitor changes in the

The advantages of this mode are: very low forces exerted on the samples (10-12 N) and extend probe lifetime. The disadvantages of this mode are: generally lower resolution; contaminant

The choice as to which AFM mode to use depends on the surface characteristics of interest and on the hardness/stickiness of the sample. Contact mode is most useful for hard surfaces; a tip in contact with a surface, however, is subject to contamination from

Excessive force in contact mode can also damage the surface or blunt the probe tip. Intermittent mode is well-suited for imaging soft biological specimen and for samples with poor surface adhesion (DNA and carbon nanotubes). Non-contact mode is another useful

layer on surface can interfere with oscillation; usually need UHV to have best imaging.

touch the sample but oscillates above it during scanning (Figure 5).

amplitude due to the attractive forces between the probe and the sample.

Fig. 4. Intermittent-Contact Mode.

Fig. 5. Non-Contact Mode.

removable material on the surface.

mode for imaging soft surfaces, but its sensitivity to external vibrations and the inherent water layer on samples in ambient conditions often causes problems in the engagement and retraction of the tip.
