**1. Introduction**

Scanning probe microscopes (SPMs) were invented by Binnig and Rohrer in 1980s and have been one of the key methods for measurements and manipulations in nanotechnologies since then [1, 2]. The first SPMs were a scanning tunnelling microscope (STM), which uses a tunnelling current. The vertical resolution of sub‐nm comes from the extremely short length of interaction between the probe and sample surface. If a sharp tip can be prepared, the lateral resolution of sub‐nm is possible. STM can see sample surfaces at an atomic resolution and manipulate a single atom. The concept of STM can be extended to various fields and wide varieties of properties can be measured on the nano scale by changing the interaction between the probe and sample. It should be noted that micro fabrication techniques based on micro‐ machining techniques has been indispensable to the development of SPMs. Atomic force microscopes (AFM) are one of the most successful microscopes in SPMs [3]. As a probe, they use micro cantilevers with a tiny tip, whose apex radius is around several nm. Typical dimensions of the cantilever are 100‐μm long and a few‐μm thick. Micro structures at these dimensions are not easy to fabricate for conventional machining. Therefore, micro fabrication methods have been developed. Micromaching not only improved the performance of SPMs but also made them a popular technology because the fabrication methods were suitable for mass production.

SPM have been extending its application to mechanical fields. One of the successful applica‐ tions is a friction force microscope (FFM), which has been a key technology of micro/nano tribology [4]. FFM can measure the local frictional or rheological properties at a micro/nano scale although AFM is limited to measurement of the topography. The performance of micro/ nano mechanical devices, such as micro/nano electro mechanical systems (MEMS/NEMS), computer hard disk drives (HDDs), is dominated by surface forces such as friction and viscous forces rather than volume forces such as gravitational forces. Therefore, the measurement of the local frictional properties is very important for the performance analysis and design of

© 2013 Fukuzawa; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Fukuzawa; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

micro/nano mechanical devices. FFM is also applied to local characterization of the sample surface by using that different materials usually have different frictional properties. If the sample consists of composite materials such as laminated materials or carbon‐fiber‐reinforced materials, the local composition can be evaluated at a nanometer scale by measuring the frictional property distribution. Recently, the local chemical composition and properties such as hydrophobicity can be mapped by measuring friction force distribution with a chemically functionalised probe. In this chapter, the basis and drawbacks of FFM are briefly reviewed and recent trials to overcome the drawbacks are described.

**2.1. Measurement principle of conventional FFM**

vertical direction, *F*<sup>V</sup> are respectively given by

When the probe is scanned under a constant load condition as shown in Figure 1, the micro cantilever twists along its long axis due to the friction force applied to the probe tip. FFM measures the friction forces by detecting this torsion of the cantilever. In addition to the friction force, the load, the force in the vertical direction, is simultaneously applied to the tip. This causes the vertical deflection of the micro cantilever. Lettering *θ* and *∆z* be torsion angle and vertical deflection, respectively. The friction force in lateral direction, *F*<sup>L</sup> and the load in the

where *k*<sup>l</sup> and *k*<sup>v</sup> are to the tensional rigidity and spring constant of the cantilever. In addition, *l* is the length of the cantilever. The friction force and load can be simultaneously obtained from measured torsion angle *θ* and vertical deflection *∆z* by using Eqs. (1) and (2). If the sharp tip whose apex radius is around one nanometer is prepared and the probe is scanned on the sample surface with a piezo scanner, the friction coefficient, which is the most fundamental frictional properties, can be mapped on a nanometer scale. Next, a method for measuring the torsion angle *θ* and vertical deflection *∆z* is explained. This is based on the method for measuring the vertical deflection in AFM, which is called optical lever method. A schematic setup is shown in Figure 1. The light from the laser diode is focused on to the micro cantilever surface and the reflected light forms the light spot on the four‐segmented PD. The four PDs detects the light intensities separately and the difference in PD signals, (*I*A+*I*B)‐(*I*C+*I*D) and (*I*<sup>A</sup> +*I*C)‐(*I*B+*I*D) are obtained. Here, *I*A, *I*B, *I*C, and *I*<sup>D</sup> are the signals from PD of A, B, C, and D, respectively. When the load is applied to the probe and micro cantilever deflects vertically, the light spot moves in the vertical direction. This causes the change in the differential signal (*I*<sup>A</sup> +*I*B)‐(*I*C+*I*D). In a similar fashion, the friction force is applied, the differential signal (*I*A+*I*C)‐(*I*<sup>B</sup> +*I*D) changes due to the lateral displacement of the light spot, which is generated by the torsion of the micro cantilever. The mode of probe scanning in FFM is the same as the contact AFM mode. In this mode, the probe is scanned under a constant load condition, which is achieved by controlling the probe height with a piezo actuator so that the vertical deflection signal (*I*<sup>A</sup> +*I*B)‐(*I*C+*I*D) keeps a set value. Typical probes for FFM are I‐ and V‐shaped microcantilevers as shown in Figure 2. Usually, I‐shaped cantilever is made of single crystal silicon and V‐shaped one is made of silicon nitride. Typical spring constant in vertical direction, *K*<sup>V</sup> is around 1 N/m. Both probes are basically designed for contact mode AFM. Thus, only the introduction

*<sup>l</sup> <sup>θ</sup>* (1)

Measurement of Frictional Properties on the Micro/Nanometer Scale 191

*FV* =*kvΔz* (2)

*FL* = *kl*

of the four‐segmented PD can provide FFM measurement with usual AFM setups.

Conventional FFM probes have been very useful for mapping friction properties and produc‐ ing fruitful results in various fields, however, it has a fundamental problem to be solved. It

**2.2. Drawbacks of conventional FFM probes**

**Figure 1.** Schematic of conventional micro-cantilever-based FFM.

### **2. Conventional FFM**

Conventional FFMs use a micro cantilever as a probe, which is used in AFM. By slightly modifying an AFM setup, replacing a two‐segmented photodiode (PD) as a position sensitive detector (PSD) with a four‐segmented one, FFM measurement become possible. Because of this convenience, many of the commercial AFMs have a four‐segmented photodiode and can make a FFM measurement with a micro cantilever probe for AFM. However, probes are designed for AFM, not for FFM. This limits the performance of FFM. In SPMs, the development of the probe is significant as described above. Although many trials have been done to overcome the drawbacks, a standard probe for FFM has not been established yet. Here, measurement principle of conventional FFMs and then their drawbacks are explained.

#### **2.1. Measurement principle of conventional FFM**

micro/nano mechanical devices. FFM is also applied to local characterization of the sample surface by using that different materials usually have different frictional properties. If the sample consists of composite materials such as laminated materials or carbon‐fiber‐reinforced materials, the local composition can be evaluated at a nanometer scale by measuring the frictional property distribution. Recently, the local chemical composition and properties such as hydrophobicity can be mapped by measuring friction force distribution with a chemically functionalised probe. In this chapter, the basis and drawbacks of FFM are briefly reviewed and

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Four segmented photodiode (PD)

by twist

Laser spot B A

<sup>D</sup> <sup>C</sup> Movement

Detection plan of PD

Movement by deflection

recent trials to overcome the drawbacks are described.

Laser for optical lever method

Tip Friction force (Lateral force) Load

(vertical froce)

Conventional FFMs use a micro cantilever as a probe, which is used in AFM. By slightly modifying an AFM setup, replacing a two‐segmented photodiode (PD) as a position sensitive detector (PSD) with a four‐segmented one, FFM measurement become possible. Because of this convenience, many of the commercial AFMs have a four‐segmented photodiode and can make a FFM measurement with a micro cantilever probe for AFM. However, probes are designed for AFM, not for FFM. This limits the performance of FFM. In SPMs, the development of the probe is significant as described above. Although many trials have been done to overcome the drawbacks, a standard probe for FFM has not been established yet. Here, measurement principle of conventional FFMs and then their drawbacks are explained.

Sample

**Figure 1.** Schematic of conventional micro-cantilever-based FFM.

Micro-cantilever

Susbstrate (Probe base)

Biomedical Engineering

190

**2. Conventional FFM**

When the probe is scanned under a constant load condition as shown in Figure 1, the micro cantilever twists along its long axis due to the friction force applied to the probe tip. FFM measures the friction forces by detecting this torsion of the cantilever. In addition to the friction force, the load, the force in the vertical direction, is simultaneously applied to the tip. This causes the vertical deflection of the micro cantilever. Lettering *θ* and *∆z* be torsion angle and vertical deflection, respectively. The friction force in lateral direction, *F*<sup>L</sup> and the load in the vertical direction, *F*<sup>V</sup> are respectively given by

$$F\_L = \frac{k\_l}{l} \Theta \tag{1}$$

$$F\_V = k\_v \Delta z \tag{2}$$

where *k*<sup>l</sup> and *k*<sup>v</sup> are to the tensional rigidity and spring constant of the cantilever. In addition, *l* is the length of the cantilever. The friction force and load can be simultaneously obtained from measured torsion angle *θ* and vertical deflection *∆z* by using Eqs. (1) and (2). If the sharp tip whose apex radius is around one nanometer is prepared and the probe is scanned on the sample surface with a piezo scanner, the friction coefficient, which is the most fundamental frictional properties, can be mapped on a nanometer scale. Next, a method for measuring the torsion angle *θ* and vertical deflection *∆z* is explained. This is based on the method for measuring the vertical deflection in AFM, which is called optical lever method. A schematic setup is shown in Figure 1. The light from the laser diode is focused on to the micro cantilever surface and the reflected light forms the light spot on the four‐segmented PD. The four PDs detects the light intensities separately and the difference in PD signals, (*I*A+*I*B)‐(*I*C+*I*D) and (*I*<sup>A</sup> +*I*C)‐(*I*B+*I*D) are obtained. Here, *I*A, *I*B, *I*C, and *I*<sup>D</sup> are the signals from PD of A, B, C, and D, respectively. When the load is applied to the probe and micro cantilever deflects vertically, the light spot moves in the vertical direction. This causes the change in the differential signal (*I*<sup>A</sup> +*I*B)‐(*I*C+*I*D). In a similar fashion, the friction force is applied, the differential signal (*I*A+*I*C)‐(*I*<sup>B</sup> +*I*D) changes due to the lateral displacement of the light spot, which is generated by the torsion of the micro cantilever. The mode of probe scanning in FFM is the same as the contact AFM mode. In this mode, the probe is scanned under a constant load condition, which is achieved by controlling the probe height with a piezo actuator so that the vertical deflection signal (*I*<sup>A</sup> +*I*B)‐(*I*C+*I*D) keeps a set value. Typical probes for FFM are I‐ and V‐shaped microcantilevers as shown in Figure 2. Usually, I‐shaped cantilever is made of single crystal silicon and V‐shaped one is made of silicon nitride. Typical spring constant in vertical direction, *K*<sup>V</sup> is around 1 N/m. Both probes are basically designed for contact mode AFM. Thus, only the introduction of the four‐segmented PD can provide FFM measurement with usual AFM setups.

#### **2.2. Drawbacks of conventional FFM probes**

Conventional FFM probes have been very useful for mapping friction properties and produc‐ ing fruitful results in various fields, however, it has a fundamental problem to be solved. It

uses the torsion angle *θ* and vertical deflection *∆z* for detecting the friction force *F*<sup>L</sup> and load *F*V. Two deformations have to be independent of each other for accurate measurement of the friction force and load. Considering that both deformations occur at the end of the micro cantilever, they are possible to interfere with each other. The independent deformations are valid only when the deformations are small enough, which means that the friction force and load are small enough. This mechanical interference cause significant drawbacks in FFM.

*k*<sup>l</sup> and reduce the torsion of the cantilever. This leads to the decrease of the sensitivity of the friction force. In order to measure the friction force accurately, the vertical spring constant *k*<sup>v</sup> has to be higher, which decreases the load sensitivity. Thus, the design for the high force sensitivities of both the friction force and load is difficult for conventional cantilever probe due to the mechanical interference.In conventional FFMs, since probes are designed for AFM, most of the probe is set so as to reduce torsion of the cantilever. Therefore, friction force sensitivity

Measurement of Frictional Properties on the Micro/Nanometer Scale 193

In addition to the drawbacks due to the mechanical interference, conventional FFMs have anotherfundamental drawback. As described in Section 2.1, the torsion of the micro cantilever is detected to obtain the friction force. This is implemented by the optical lever method. The optical lever method can provide the differential signal (*I*A+*I*C)‐(*I*B+*I*D) corresponding to the torsion angle *θ* in Eq. (1). For quantitative measurement, the relationship between the signal (*I*A+*I*C)‐(*I*B+*I*D) and angle *θ* has to be known. For this purpose, the torsion angle *θ* of the micro cantilever has to be measured. In addition, this measurement has to be done for the micro cantilever installed in AFM setup because the signal (*I*A+*I*C)‐(*I*B+*I*D) may change for the setup to setup. This torsion angle measurement is not easy in usual setups. Therefore, the standard calibration method for the friction force has not been established yet. This is one of the reasons

Many trials have been done in order to overcome the above drawbacks of the conventional FFM. One promising candidate is a dual‐axis probe. The mechanical interference problem in the conventional probe is caused by the fact that the probe uses the two deformations of the same part, the probe end. If the different parts of the probe deform due to the friction force and load, the mechanical interference can be reduced or eliminated. Dual‐axis probe is based on this idea. Chui et al. presented the probe that serially connected an array of cantilevers to a V‐shaped cantilever with a tip [8]. The schematic structure is shown in Figure 3. The surface of the cantilever array is set vertically to the V‐shaped cantilever one. The double cantilever array laterally deflects for the friction force and V‐shaped cantilever vertically deforms for the load. The friction force and load is obtained from these lateral and vertical deflections. Ando et al. presented the concept of another type of dual‐axis probe, where the two double cantile‐ vers that rotate by 90 degrees to each other are serially connected as shown in Figure 4 [9]. The double cantilever with its surface normal to the sample surface deflects for the friction force

The detection method for vertical deflection of the probe for conventional FFM can be applied to the dual‐axis probe whereas that forlateral one cannot because the probe does not twist and deflects laterally. In the optical lever method, which is widely used in conventional FFMs, the light does not move on the PD even if the probe deflects laterally. Therefore, the optical lever method cannot be applied to dual‐axis probes directly. Moreover, in the both dual‐axis probes, the deformation parts are serially connected as shown in Figures 3 and 4. The displacement of

why FFM remains at the level of qualitative evaluation means [7].

is made victim of that of the load.

**3. Dual‐axis FFM probes**

and another double cantilever does for the load.

**Figure 2.** Typical types of micro cantilever for FFM. (a) I-shaped and (b) V-shaped cantilevers. The figures are viewed from the tip side.

The first drawback is the decrease of the measurement accuracy [5, 6]. As described in Section 2.1, in Eqs.(1) and (2),the tensionalrigidity *k*<sup>l</sup> and spring constant *k*<sup>v</sup> are assumed to be constant. However, when the friction force is large, the torsional rigidity *k*<sup>l</sup> and the spring constant *k*<sup>v</sup> depends on the load and friction force. These limit FFM applications for conventional probe. Therefore, conventional FFMs remain at the level of qualitative evaluation means in many applications.

The second drawback is the decrease of the measurement performance. The fundamental equations, Eqs. (1) and (2) indicate that the improvement of the force sensitivity requires the decrease of the rigidity, *k*<sup>l</sup> or *k*v. In contrast, the reduction of the mechanical interference requires the high rigidity for the counterpart deformation. For example, the torsional rigidity has to be set high in order to measure the load accurately. Since the V‐shaped cantilevers are designed for a contact AFM mode, crossed cantilever structure is adopted in order to increase *k*<sup>l</sup> and reduce the torsion of the cantilever. This leads to the decrease of the sensitivity of the friction force. In order to measure the friction force accurately, the vertical spring constant *k*<sup>v</sup> has to be higher, which decreases the load sensitivity. Thus, the design for the high force sensitivities of both the friction force and load is difficult for conventional cantilever probe due to the mechanical interference.In conventional FFMs, since probes are designed for AFM, most of the probe is set so as to reduce torsion of the cantilever. Therefore, friction force sensitivity is made victim of that of the load.

In addition to the drawbacks due to the mechanical interference, conventional FFMs have anotherfundamental drawback. As described in Section 2.1, the torsion of the micro cantilever is detected to obtain the friction force. This is implemented by the optical lever method. The optical lever method can provide the differential signal (*I*A+*I*C)‐(*I*B+*I*D) corresponding to the torsion angle *θ* in Eq. (1). For quantitative measurement, the relationship between the signal (*I*A+*I*C)‐(*I*B+*I*D) and angle *θ* has to be known. For this purpose, the torsion angle *θ* of the micro cantilever has to be measured. In addition, this measurement has to be done for the micro cantilever installed in AFM setup because the signal (*I*A+*I*C)‐(*I*B+*I*D) may change for the setup to setup. This torsion angle measurement is not easy in usual setups. Therefore, the standard calibration method for the friction force has not been established yet. This is one of the reasons why FFM remains at the level of qualitative evaluation means [7].
