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

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 engineering components.

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 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).

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

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.

Measurement of the Nanoscale Roughness by

Fig. 9. AFM Scanner (Schitter et al., 2007).

measure different properties of the sample.

micrometers in thickness.

**4.2 Probes** 

data set is comprised of a dense, square grid of measurements.

Atomic Force Microscopy: Basic Principles and Applications 153

While the scanner is moving across a scan line, the image data are sampled digitally at equally spaced intervals. The data are the height of the scanner in z for constant-force mode (AFM) and the data are the cantilever deflection. The spacing between the data points is called the step size. The step size is determined by the full scan size and the number of data points per line. In a typical SPM, scan sizes run from tens of angstroms to over 100 microns and from 64 to 512 data points per line (some systems offer 1024 data points per line.) The number of lines in a data set usually equals the number of points per line. Thus, the ideal

The probe is a very important component of a SPM because different probes can measure different properties of the sample (Figure 10). In addition, the probe determines the force applied to the sample. Regarding AFM, the most common probes are the cantilevers that are highly suited to measure the topography of a sample. Different coatings on the cantilevers

The tip and the cantilever as an integrated component can be fabricated from silicon or silicon Nitride using photolithographic techniques. From a single silicon wafer it is possible to make more than 1000 probes. Regarding the physical properties, the cantilever ranges from 100 to 200 micrometers in length, 10 to 40 micrometers in width, and 0.3 to 2

Fig. 7. Waviness (adapted from B. C. MacDonald & Co., 2011).

The waviness height is also determined from the profile, which is just the height from the top of the peak to the bottom of the trough. It is usually at least three times the roughness average height.

Roughness is often described as closely spaced irregularities or with terms such as 'uneven', 'irregular', 'coarse in texture', 'broken by prominences', and other similar ones (Thomas, 1999) (Figure 8). Similar to some surface properties such as hardness, the value of surface roughness depends on the scale of measurement. In addition, the concept of roughness has statistical implications as it takes into consideration factors such as sample size and sampling interval. It is quantified by the vertical spacing of a real surface from its ideal form. If these spacing are large, the surface is rough; if they are small the surface is smooth.

Fig. 8. Roughness (adapted from B. C. MacDonald & Co., 2011).

#### **4. Basic components of AFM**

This topic will present some basic ideas about basic components of AFM.

#### **4.1 Scanner**

The movement of the tip or sample in the *x*, *y*, and *z*-directions is controlled by a piezoelectric tube scanner, similar to those used in STM. For typical AFM scanners, the maximum ranges are 80 µm x 80 µm in the *x*-*y* plane and 5 µm for the *z*-direction (Figure 9). The scanner moves across the first line of the scan, and back. It then steps in the perpendicular direction to the second scan line, moves across it and back, then to the third line, and so forth. The path differs from a traditional raster pattern in that the alternating lines of data are not taken in opposite directions ( Odom, 2004).

While the scanner is moving across a scan line, the image data are sampled digitally at equally spaced intervals. The data are the height of the scanner in z for constant-force mode (AFM) and the data are the cantilever deflection. The spacing between the data points is called the step size. The step size is determined by the full scan size and the number of data points per line. In a typical SPM, scan sizes run from tens of angstroms to over 100 microns and from 64 to 512 data points per line (some systems offer 1024 data points per line.) The number of lines in a data set usually equals the number of points per line. Thus, the ideal data set is comprised of a dense, square grid of measurements.

Fig. 9. AFM Scanner (Schitter et al., 2007).
