**1. Introduction**

28 Will-be-set-by-IN-TECH

98 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

Vairac, P., Cretin, B. & Kulik, A. J. (2003). Towards dynamical force microscopy using optical

Yacoot, A. & Koenders, L. (2008). Aspects of scanning force microscope probes and their effects on dimensional measurement, *J. Phys. D: Appl. Phys.* 41: 103001. Yamanaka, K. & Nakano, S. (1998). Quantitative elasticity evaluation by contact resonance in

probing of thermomechanical noise, *Appl. Phys. Lett.* 83: 3824.

an atomic force microscope, *Appl. Phys. A* 66: S313.

Friction and adhesion are two so related phenomena of the contact formed by two bodies. And due to the presence of friction and adhesion very often we have wear, i.e., third body presence generated by friction and adhesion. Likely, friction is one of the oldest phenomena in the history of humankind and of natural science, e.g., physics. Friction was the origin of first fire lit by human in early Stone Age, and of the many events Egyptians had faced while pulling huge blocks of stone needed for their pyramids. In fact, Egyptians were basically the first tribologists in history, even if the term tribology defined as "science and technology of interacting surfaces in relative motion", was suggested only in 1966 by Peter Jost.

Humanity needed to enter into Renaissance period in order to have Leonardo da Vinci (1452-1519) (Dowson, 1979) to introduce the first modern concepts of friction. Da Vinci came to two important conclusions:


In other words, these are today the two fundamental laws of friction, the friction force is proportional to the load (normal force), and independent of the apparent area of contact between the sliding body and the surface.

Two centuries later, Amonton (1663-1705) rediscovered and extended da Vinci's observations. Amonton confirmed these observations with further experiments, from which came Amonton's Law of Friction: *Ff* = *L*, which states that the friction force *Ff* is proportional to the applied load *L*. Thus, today the two fundamental laws of friction are called ''da Vinci-Amonton's laws''.

It took nearly an extra century, 1785, for the experiments of Coulomb (1736-1806) to distinguish between friction during sticking and sliding. He observed that the coefficient of kinetic friction was generally smaller than the coefficient of static friction. He also observed that *µ* was generally independent of sliding velocity. Investigating the origins of friction, Coulomb suggested that roughness (asperities) on the micrometer scale is responsible for the occurrence of friction, as depicted in Fig 1. However, there was experimental evidence against his hypothesis: highly polished surfaces did not exhibit low, but high friction.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 101

The Bowden-Tabor adhesion model explains the da Vinci-Amonton's laws of the macroscopic world. However, a basic understanding of friction is still lacking and many questions remain unanswered such as: i) What are the microscopic mechanisms of friction? ii) How is energy dissipated? iii) How do lubricants (third body presence) affect the shear properties? iv) Can

During the last two decades, the field of tribology at the atomic and nanometer scale became of interest to a bigger scientific community. These problems are beginning to be addressed by relative recent development of several experimental techniques (Krim, 1996). Instruments such as the surface forces apparatus (SFA) (Israelachvili, 1972) (Israelachvili et al., 1990), the quartz-crystal microbalance (QCM) (Krim et al., 1990) (Watts et al., 1990) (Krim et al., 1991), the atomic force microscope (AFM) (Mate et al., 1987) (Binnig et al., 1986a) and others are extending tribological investigations to atomic length and time scales. Furthermore, advances in computational power and theoretical techniques are now making sophisticated atomistic models and simulations feasible (Harrison & Brenner, 1995). Nanotribology, is the emerging field that attempts to use these techniques to establish an atomic- and nano-scale understanding of interactions between contacting surfaces in relative motion (Carpick et al., 1998a; Enachescu et al., 1998, 1999a, 1999b, 1999c, 2004; Park et al., 2005a; Carpick &

Nanotribology, and particularly AFM experiments, focusing on the fundamentals and basic understanding of friction, adhesion, and wear, is trying to do this in terms of chemical bonding and of the elementary processes that are involved in the excitation and dissipation

In AFM experiments, besides the obvious friction and wear obvious experiments, adhesion measurements are easily performed via so called pull-off experiments. A basic pull-off

Regarding the excitation and dissipation of energy modes during tribological experiments, several mechanisms have been investigated and proposed. One is related to coupling to the substrate (and tip) electron density that causes a drag force, similar to that causing an increase of electrical resistance by the presence of surfaces in thin films (Daly & Krim, 1996; Sokoloff, 1995; Persson & Volokitin, 1995; Persson & Nitzan, 1996). Another is related to excitation of surface phonon modes in atomic stick-slip events. Delocalization of the excited phonons by coupling to other phonon modes through nonharmonic effects and transport of the energy away from the excited volume leads to efficient energy dissipation (Sokoloff, 1993; Carpick & Salmeron, 1997). At high applied forces, an important event is the wear process leading to rupture of many atomic bonds, the creation of point defects near the

Another level of our understanding focus, and where AFM experiments may decisively contribute, includes questions such as the nature of relative motion between the two contacting bodies: is it continuous (smooth sliding) or discontinuous (stick-slip, e.g., atomic stick-slip)? How does friction depend upon the actual area of contact between two bodies? Are friction and adhesion related, and how? What is the behavior of lubricant molecules, including third bodies, at an interface? How are they compressed and displaced during loading and shear? How does their behavior depend upon their molecular structure and chemical identity?

It is our intent to partially address some of these questions in the work presented here.

the friction be calculated from molecular interaction potentials in a quantitative way?

Salmeron, 1997; Grierson &. Carpick, 2007; Szlufarska et al., 2008).

surface, displacement and creation of dislocations and debris particles.

of energy modes.

experiment is described in Fig. 2 below.

Fig. 1. A macroscopic contact that appears conforming and continuous is usually composed of multiple contact points between many microasperities. The frictional behavior of such a contact follows Amonton's Law. The friction law for a microscopic contact, a single asperity contact, is not known. A scanning probe instrument provides a well-defined single asperity contact (the tip) where interaction forces can be precisely measured with nanometer/atomic resolution. At this scale, macroscopic physical laws no longer apply. For example, the friction force (*Ff*) is no longer linearly proportional to the applied load (*L*).

An alternative explanation was given by Desaguliers, who suggested that molecular adhesion might be the relevant phenomenon. However, molecular adhesion was known to be proportional to contact area, whereas friction was found to be independent of contact area.

It is astonishing that wear phenomena, despite their obvious significance, were studied quite late. The reason for this delay may lie in the fact that the leading cause of wear is through the interactions of micro-contacts, which became an object of tribological research only after the work of Bowden and Tabor. It took about two centuries beyond Coulomb's work until this controversy was solved. Around 1950, Bowden and Tabor performed systematic, tribological experiments which showed that the contact of a macroscopic body is formed by a number of small asperities (Fig. 1). Thus, another contact area, the real area of contact had to be introduced. This new concept was extremely successful and is the basics of most present tribological studies. Essentially, the Bowden-Tabor model states that friction is proportional to the real area of contact.

From this point of view, Desaguliers was right to assume that adhesion, which is also proportional to the contact area, is more related to friction than roughness. Therefore, the model is also called Bowden-Tabor adhesion model. In first approximation, the real area of contact does not depend on the apparent contact area. By increasing the load, the number of contacting asperities also increases with load.

Fig. 1. A macroscopic contact that appears conforming and continuous is usually composed of multiple contact points between many microasperities. The frictional behavior of such a contact follows Amonton's Law. The friction law for a microscopic contact, a single asperity contact, is not known. A scanning probe instrument provides a well-defined single asperity contact (the tip) where interaction forces can be precisely measured with nanometer/atomic resolution. At this scale, macroscopic physical laws no longer apply. For example, the

An alternative explanation was given by Desaguliers, who suggested that molecular adhesion might be the relevant phenomenon. However, molecular adhesion was known to be proportional to contact area, whereas friction was found to be independent of contact area.

It is astonishing that wear phenomena, despite their obvious significance, were studied quite late. The reason for this delay may lie in the fact that the leading cause of wear is through the interactions of micro-contacts, which became an object of tribological research only after the work of Bowden and Tabor. It took about two centuries beyond Coulomb's work until this controversy was solved. Around 1950, Bowden and Tabor performed systematic, tribological experiments which showed that the contact of a macroscopic body is formed by a number of small asperities (Fig. 1). Thus, another contact area, the real area of contact had to be introduced. This new concept was extremely successful and is the basics of most present tribological studies. Essentially, the Bowden-Tabor model states that friction is

From this point of view, Desaguliers was right to assume that adhesion, which is also proportional to the contact area, is more related to friction than roughness. Therefore, the model is also called Bowden-Tabor adhesion model. In first approximation, the real area of contact does not depend on the apparent contact area. By increasing the load, the number of

friction force (*Ff*) is no longer linearly proportional to the applied load (*L*).

proportional to the real area of contact.

contacting asperities also increases with load.

The Bowden-Tabor adhesion model explains the da Vinci-Amonton's laws of the macroscopic world. However, a basic understanding of friction is still lacking and many questions remain unanswered such as: i) What are the microscopic mechanisms of friction? ii) How is energy dissipated? iii) How do lubricants (third body presence) affect the shear properties? iv) Can the friction be calculated from molecular interaction potentials in a quantitative way?

During the last two decades, the field of tribology at the atomic and nanometer scale became of interest to a bigger scientific community. These problems are beginning to be addressed by relative recent development of several experimental techniques (Krim, 1996). Instruments such as the surface forces apparatus (SFA) (Israelachvili, 1972) (Israelachvili et al., 1990), the quartz-crystal microbalance (QCM) (Krim et al., 1990) (Watts et al., 1990) (Krim et al., 1991), the atomic force microscope (AFM) (Mate et al., 1987) (Binnig et al., 1986a) and others are extending tribological investigations to atomic length and time scales. Furthermore, advances in computational power and theoretical techniques are now making sophisticated atomistic models and simulations feasible (Harrison & Brenner, 1995). Nanotribology, is the emerging field that attempts to use these techniques to establish an atomic- and nano-scale understanding of interactions between contacting surfaces in relative motion (Carpick et al., 1998a; Enachescu et al., 1998, 1999a, 1999b, 1999c, 2004; Park et al., 2005a; Carpick & Salmeron, 1997; Grierson &. Carpick, 2007; Szlufarska et al., 2008).

Nanotribology, and particularly AFM experiments, focusing on the fundamentals and basic understanding of friction, adhesion, and wear, is trying to do this in terms of chemical bonding and of the elementary processes that are involved in the excitation and dissipation of energy modes.

In AFM experiments, besides the obvious friction and wear obvious experiments, adhesion measurements are easily performed via so called pull-off experiments. A basic pull-off experiment is described in Fig. 2 below.

Regarding the excitation and dissipation of energy modes during tribological experiments, several mechanisms have been investigated and proposed. One is related to coupling to the substrate (and tip) electron density that causes a drag force, similar to that causing an increase of electrical resistance by the presence of surfaces in thin films (Daly & Krim, 1996; Sokoloff, 1995; Persson & Volokitin, 1995; Persson & Nitzan, 1996). Another is related to excitation of surface phonon modes in atomic stick-slip events. Delocalization of the excited phonons by coupling to other phonon modes through nonharmonic effects and transport of the energy away from the excited volume leads to efficient energy dissipation (Sokoloff, 1993; Carpick & Salmeron, 1997). At high applied forces, an important event is the wear process leading to rupture of many atomic bonds, the creation of point defects near the surface, displacement and creation of dislocations and debris particles.

Another level of our understanding focus, and where AFM experiments may decisively contribute, includes questions such as the nature of relative motion between the two contacting bodies: is it continuous (smooth sliding) or discontinuous (stick-slip, e.g., atomic stick-slip)? How does friction depend upon the actual area of contact between two bodies? Are friction and adhesion related, and how? What is the behavior of lubricant molecules, including third bodies, at an interface? How are they compressed and displaced during loading and shear? How does their behavior depend upon their molecular structure and chemical identity? It is our intent to partially address some of these questions in the work presented here.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 103

According to the classical law of friction, the friction force between two bodies in motion is proportional to the applied load and independent of the apparent area of contact (Dowson, 1998). However, a macroscopic contact between two apparently flat solid surfaces consists in practice of a large number of micro-contacts between the asperities that are present on both contacting surfaces (Fig. 1). The classical law of friction, which cannot be understood or deduced from first principles, is the result of many complex phenomena at the interface, in particular the specific interactions between contacting asperities, and the corresponding deformations of these asperities (Greenwood & Williamson, 1966). Although macroscopic tribological research can provide important empirical information about the frictional behavior of materials, it cannot explain friction at a fundamental level. Only detailed studies of friction at a single-asperity contact, under well-defined conditions and with nanometerscale or even atomic-scale resolution, can result in an understanding of friction at a fundamental level. Some ultra-high vacuum atomic force microscopy (UHV-AFM) experiments indicate that friction is proportional to the contact area for a nanometer-sized single-asperity contact (Carpick et al., 1996a, 1998a; Enachescu et al., 1998; Lantz et al., 1997a, 1997b). In some of these studies, the contact area was not directly measured but instead derived from continuum mechanics models, although, as discussed further below, it is generally not clear *a priori* which model is valid for a specific combination of materials. As well, most of these experiments were performed on layered materials, where it is unclear whether continuum mechanics models can be used quantitatively. Nevertheless, the continuum mechanics models generally provided convincing fits to the data. Carpick *et al.* (Carpick et al., 1996a) performed experiments on muscovite mica and found that friction was proportional to the contact area as described by the Johnson-Kendall-Roberts (JKR) model (Johnson et al., 1971). Experiments by Lantz *et al.* (Lantz et al., 1997a, 1997b) on NbSe2 and graphite resulted in a relation between friction and contact area as described by the Maugis-Dugdale (MD) model (Maugis, 1992; Johnson, 1997). Only one observation of the Derjaguin-Müller-Toporov (DMT) model (Derjaguin et al., 1975; Müller et al., 1983) has been reported so far by Enachescu *et al.* (Enachescu et al., 1998). The experiments were conducted with an extremely hard heterocontact, involving stiff materials with low adhesive forces, *i.e.* a tungsten-carbide AFM-tip in contact with a hydrogen-terminated diamond(111) sample. Both diamond and tungsten-carbide are extremely stiff, non-layered materials. Furthermore,

hydrogen passivates the diamond surface while carbides are generally quite inert.

carbide plays an important role in several types of hard coatings (Schwartz, 1990).

**2.1 Background** 

In this study, we discuss the results of a nanotribological study of a hydrogen-terminated diamond(111)/tungsten-carbide single asperity interface using UHV-AFM. Since the diamond sample is slightly boron-doped and the tungsten-carbide tip is conductive, we are able to measure the local contact conductance as a function of applied load. These experiments provide an independent way of determining the contact area, which can be directly compared to the corresponding friction force. Diamond and diamond-like films are important coating materials used in a wide variety of tools, hard disks, micro-machines, and aerospace applications. For micro-machine and hard disk applications in particular, the nanotribological properties are of great importance (Seki et al., 1987). Similarly, tungsten-

The AFM results (Carpick et al., 1996a, 1998a; Enachescu et al., 1998; Lantz et al., 1997a, 1997b) and surface forces apparatus (Homola et al., 1989) experiments indicate that the

Fig. 2. A typical pull-off, or force vs. displacement curve during an approach-retract experiment. The AFM lever deflection is recorded while tip and sample are brought into contact and separated again. As long as tip and sample are separated, the free lever is not deflected. When tip and sample are brought into close proximity (A) the lever "feels" an increasingly attractive force, caused by long range electrostatic or van der Waals forces, and is bent down towards the sample. When the force gradient exceeds the spring constant of the lever, an instability, the so called "jump-to-contact", occurs, and the tip abruptly contacts the surface. Upon further approach, the lever experiences a repulsive force and is bent upwards (B), for small deflections following Hook's law. Upon reversal of the piezo motion the deflection signal follows the previous path. But adhesive forces will keep the tip in contact with the sample until the elastic force of the lever exceeds the adhesion and the lever snaps out of contact (C).

As mentioned, friction and adhesion are related phenomena of the contact formed by two bodies. And due to the presence of friction and adhesion very often we have wear, i.e., third body presence generated by friction and adhesion. Also, the interface created under friction and adhesion plays a crucial role in the local electrical conductivity between the two bodies, besides the bodies' intrinsic conductivity properties. All of these, friction, adhesion, third body presence (wear) and local conductivity at nanometer scale are the goal of this work, that is trying to bring extra light in the emerging nanotribology field.

## **2. Atomic- and nano-scale friction experiments on a special interface**

The nanotribological properties of a hydrogen-terminated diamond(111)/tungsten-carbide interface have been studied using ultra-high vacuum atomic force microscopy. Both friction and local contact conductance were measured as a function of applied load. The contact conductance experiments provide a direct and independent way of determining the contact area between the conductive tungsten-carbide AFM-tip and the doped diamond sample. It was demonstrated that the friction force is directly proportional to the real area of contact at the nanometer-scale. Furthermore, the relation between the contact area and load for this extremely hard heterocontact is found to be in excellent agreement with the Derjaguin-Müller-Toporov continuum mechanics model.

According to the classical law of friction, the friction force between two bodies in motion is proportional to the applied load and independent of the apparent area of contact (Dowson, 1998). However, a macroscopic contact between two apparently flat solid surfaces consists in practice of a large number of micro-contacts between the asperities that are present on both contacting surfaces (Fig. 1). The classical law of friction, which cannot be understood or deduced from first principles, is the result of many complex phenomena at the interface, in particular the specific interactions between contacting asperities, and the corresponding deformations of these asperities (Greenwood & Williamson, 1966). Although macroscopic tribological research can provide important empirical information about the frictional behavior of materials, it cannot explain friction at a fundamental level. Only detailed studies of friction at a single-asperity contact, under well-defined conditions and with nanometerscale or even atomic-scale resolution, can result in an understanding of friction at a fundamental level. Some ultra-high vacuum atomic force microscopy (UHV-AFM) experiments indicate that friction is proportional to the contact area for a nanometer-sized single-asperity contact (Carpick et al., 1996a, 1998a; Enachescu et al., 1998; Lantz et al., 1997a, 1997b). In some of these studies, the contact area was not directly measured but instead derived from continuum mechanics models, although, as discussed further below, it is generally not clear *a priori* which model is valid for a specific combination of materials. As well, most of these experiments were performed on layered materials, where it is unclear whether continuum mechanics models can be used quantitatively. Nevertheless, the continuum mechanics models generally provided convincing fits to the data. Carpick *et al.* (Carpick et al., 1996a) performed experiments on muscovite mica and found that friction was proportional to the contact area as described by the Johnson-Kendall-Roberts (JKR) model (Johnson et al., 1971). Experiments by Lantz *et al.* (Lantz et al., 1997a, 1997b) on NbSe2 and graphite resulted in a relation between friction and contact area as described by the Maugis-Dugdale (MD) model (Maugis, 1992; Johnson, 1997). Only one observation of the Derjaguin-Müller-Toporov (DMT) model (Derjaguin et al., 1975; Müller et al., 1983) has been reported so far by Enachescu *et al.* (Enachescu et al., 1998). The experiments were conducted with an extremely hard heterocontact, involving stiff materials with low adhesive forces, *i.e.* a tungsten-carbide AFM-tip in contact with a hydrogen-terminated diamond(111) sample. Both diamond and tungsten-carbide are extremely stiff, non-layered materials. Furthermore, hydrogen passivates the diamond surface while carbides are generally quite inert.

In this study, we discuss the results of a nanotribological study of a hydrogen-terminated diamond(111)/tungsten-carbide single asperity interface using UHV-AFM. Since the diamond sample is slightly boron-doped and the tungsten-carbide tip is conductive, we are able to measure the local contact conductance as a function of applied load. These experiments provide an independent way of determining the contact area, which can be directly compared to the corresponding friction force. Diamond and diamond-like films are important coating materials used in a wide variety of tools, hard disks, micro-machines, and aerospace applications. For micro-machine and hard disk applications in particular, the nanotribological properties are of great importance (Seki et al., 1987). Similarly, tungstencarbide plays an important role in several types of hard coatings (Schwartz, 1990).

#### **2.1 Background**

102 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

Fig. 2. A typical pull-off, or force vs. displacement curve during an approach-retract experiment. The AFM lever deflection is recorded while tip and sample are brought into contact and separated again. As long as tip and sample are separated, the free lever is not deflected. When tip and sample are brought into close proximity (A) the lever "feels" an increasingly attractive force, caused by long range electrostatic or van der Waals forces, and is bent down towards the sample. When the force gradient exceeds the spring constant of the lever, an instability, the so called "jump-to-contact", occurs, and the tip abruptly contacts the surface. Upon further approach, the lever experiences a repulsive force and is bent upwards (B), for small deflections following Hook's law. Upon reversal of the piezo motion the deflection signal follows the previous path. But adhesive forces will keep the tip in contact with the sample until the elastic force of the lever exceeds the adhesion and the lever

As mentioned, friction and adhesion are related phenomena of the contact formed by two bodies. And due to the presence of friction and adhesion very often we have wear, i.e., third body presence generated by friction and adhesion. Also, the interface created under friction and adhesion plays a crucial role in the local electrical conductivity between the two bodies, besides the bodies' intrinsic conductivity properties. All of these, friction, adhesion, third body presence (wear) and local conductivity at nanometer scale are the goal of this work,

The nanotribological properties of a hydrogen-terminated diamond(111)/tungsten-carbide interface have been studied using ultra-high vacuum atomic force microscopy. Both friction and local contact conductance were measured as a function of applied load. The contact conductance experiments provide a direct and independent way of determining the contact area between the conductive tungsten-carbide AFM-tip and the doped diamond sample. It was demonstrated that the friction force is directly proportional to the real area of contact at the nanometer-scale. Furthermore, the relation between the contact area and load for this extremely hard heterocontact is found to be in excellent agreement with the Derjaguin-

that is trying to bring extra light in the emerging nanotribology field.

Müller-Toporov continuum mechanics model.

**2. Atomic- and nano-scale friction experiments on a special interface** 

snaps out of contact (C).

The AFM results (Carpick et al., 1996a, 1998a; Enachescu et al., 1998; Lantz et al., 1997a, 1997b) and surface forces apparatus (Homola et al., 1989) experiments indicate that the

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 105

is Ohmic, semiconductor-like, *etc.* For instance, in the case of a metal/semiconductor contact (Sze, 1981), which matches our tip-sample interface, the current is directly proportional to the area of contact, considering a constant metal/semiconductor barrier height and a constant temperature during the experiments. We do not expect to observe the current to change step-wise with load, *i.e.,* the well-known phenomena of quantized conductance occurring at contacts consisting of only a few atoms (Rubio et al., 1996), since in our

The experiments were performed in an UHV chamber (base pressure 7 x 10-11 Torr), since even in moderately evacuated chambers the residual oxygen and water vapor may combine with the sliding action to catalyze a phase change on diamond (Gardos, 1994). The UHVchamber is equipped with a home-built AFM (Dai et al., 1995), low-energy electron diffraction (LEED), and Auger electron spectroscopy (AES). The sample is an artificial type IIb diamond(111) single-crystal, which is terminated with hydrogen and slightly borondoped. The cleaning procedure used, as well as the single-crystal quality, are described in more detail by van den Oetelaar *et al.* (van den Oetelaar & Flipse, 1997). Fig 3 shows the LEED pattern taken after the cleaning procedure. This clear (1x1) LEED pattern supports the

Fig. 3. Our cleaning procedure gave rise to a clear hydrogen-terminated diamond(111)-(1x1)

Triangular silicon cantilevers with integrated tips, coated with approximately 20 nm tungsten-carbide, were used for all measurements. The tips were characterized by scanning electron microscopy (SEM) and AES. Two types of cantilevers were used, with a spring constant of 88 N/m and 0.23 N/m, respectively. The former cantilever was used for conductance measurements while the latter one was used for friction measurements. The tips were cleaned in UHV immediately prior to the measurements, by applying short voltage pulses and/or by rubbing them on the surface. Normal cantilever force constants were taken from the manufacturer, and the normal/lateral force ratio was calculated using the method described by Ogletree *et al.* (Ogletree et al., 1996). The absolute accuracy of the forces measured is limited due to significant uncertainty in the material properties of the cantilever and approximations used in the force constant calculations. However, relative changes in friction could be accurately determined by using the same cantilever and tip during a series of measurements. A flexible I-V converter, allowing current measurements

experiments the contact area contains many atoms.

surface, as shown in this LEED pattern.

spanning the range from pA to mA, was designed and built.

fact that we have a hydrogen-terminated diamond(111)-(1x1) surface.

**2.2 Experimental** 

friction force *Ff* varies with the applied load *L* in proportion to the tip-sample contact area *A*. Thus, *Ff* = *A* where is the shear strength, a fundamental interfacial property. In most cases, the relation between *A* and *L* is deduced from elastic continuum mechanics models, assuming a sphere (tip) in contact with a flat plane (sample) (Johnson, 1987). However, the correct relation between *A* and *L* not only depends on the exact geometry but also upon the strength of the adhesive forces compared to the elastic deformations (Maugis, 1992; Müller et al., 1980; Tabor, 1977; Greenwood, 1997; Johnson, 1996).

The JKR and DMT models mentioned above have been deduced for two extreme cases, namely for compliant materials with strong, short-range adhesive forces and for stiff materials with small, long-range adhesive forces, respectively. The empirical nondimensional parameter 1/3 2 \*2 3 *R Ez*<sup>0</sup> can be used to determine which of the two continuum mechanics models is most appropriate (Tabor, 1977; Johnson, 1996). In this expression, *R* is the sphere radius, is the work per unit area required to separate tip and surface from contact to infinity, and *E\** is a combined elastic modulus, given by the equation \* 2 21 11 22 *E EE* ((1 ) / (1 ) / ) , where *E1* and *E2* are the Young's moduli, and *1* and *2* are the Poisson's ratios of the sphere and plane, respectively. Finally, *z0* represents the equilibrium spacing for the interaction potential of the surfaces. If *µ* > 5, the JKR theory should be valid, while for < 0.1, the DMT theory should describe the relation between *A*  and *L* (Tabor, 1977; Johnson, 1996; Greenwood, 1997). Neither the JKR nor the DMT limit is appropriate for the intermediate cases (0.1 << 5). As discussed by Greenwood (Greenwood, 1997), it is difficult to calculate the exact area of contact for the continuum problem. Greenwood obtained a numerical solution using a Lennard-Jones potential and defined the contact edge as the point of maximum adhesive stress. Greenwood's solution closely resembles the Maugis-Dugdale model. In both cases, the variation of contact area with load then appears very close to the *shape* of the JKR curve for values of > 0.5. However, the JKR equation does not correctly predict the *actual* contact area, pull-off force, and thus the adhesion energy, unless > 5. Therefore, while a measurement of contact area versus load may resemble a JKR curve, quantitative analysis would be uncertain, as it would highly depend on a specific model for the tip-sample interaction potential.

In the case of the DMT model (< 0.1), the contact area *A* varies with the applied load *L* in a simple fashion: 2/3 2/3 2/3 <sup>2</sup> *<sup>R</sup> A LR K* , where K=(4/3)E\*. The pull-off force or critical load *Lc* is given by 2 *L R <sup>c</sup>* . The value of *Lc* can be obtained from AFM approach/retract displacements of the cantilever and sample, by measuring the (negative) normal force required to separate tip and sample. We note that the contact area goes to zero at pull-off, in contrast to the JKR model.

The contact radius in AFM experiments is generally in the nanometer-range and, consequently, much smaller than the electronic mean free path. In this limit, the contact conductance becomes directly proportional to the contact area, as described by Sharvin's equation for metallic contacts (Jansen et al., 1980): *G* = 3*a*2/4*l*, where is the resistivity, *l* is the mean free path of the conduction electrons, and *a* is the radius of the contact. We stress that this equation is only valid for nanometer-sized contacts, where *l* >> *a*. The linear relationship between the contact conductance and contact area is true whether the junction is Ohmic, semiconductor-like, *etc.* For instance, in the case of a metal/semiconductor contact (Sze, 1981), which matches our tip-sample interface, the current is directly proportional to the area of contact, considering a constant metal/semiconductor barrier height and a constant temperature during the experiments. We do not expect to observe the current to change step-wise with load, *i.e.,* the well-known phenomena of quantized conductance occurring at contacts consisting of only a few atoms (Rubio et al., 1996), since in our experiments the contact area contains many atoms.

#### **2.2 Experimental**

104 Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale

friction force *Ff* varies with the applied load *L* in proportion to the tip-sample contact area *A*.

cases, the relation between *A* and *L* is deduced from elastic continuum mechanics models, assuming a sphere (tip) in contact with a flat plane (sample) (Johnson, 1987). However, the correct relation between *A* and *L* not only depends on the exact geometry but also upon the strength of the adhesive forces compared to the elastic deformations (Maugis, 1992; Müller

The JKR and DMT models mentioned above have been deduced for two extreme cases, namely for compliant materials with strong, short-range adhesive forces and for stiff materials with small, long-range adhesive forces, respectively. The empirical

continuum mechanics models is most appropriate (Tabor, 1977; Johnson, 1996). In this

surface from contact to infinity, and *E\** is a combined elastic modulus, given by the equation

equilibrium spacing for the interaction potential of the surfaces. If *µ* > 5, the JKR theory

and *L* (Tabor, 1977; Johnson, 1996; Greenwood, 1997). Neither the JKR nor the DMT limit is

(Greenwood, 1997), it is difficult to calculate the exact area of contact for the continuum problem. Greenwood obtained a numerical solution using a Lennard-Jones potential and defined the contact edge as the point of maximum adhesive stress. Greenwood's solution closely resembles the Maugis-Dugdale model. In both cases, the variation of contact area

However, the JKR equation does not correctly predict the *actual* contact area, pull-off force,

versus load may resemble a JKR curve, quantitative analysis would be uncertain, as it would

displacements of the cantilever and sample, by measuring the (negative) normal force required to separate tip and sample. We note that the contact area goes to zero at pull-off, in

The contact radius in AFM experiments is generally in the nanometer-range and, consequently, much smaller than the electronic mean free path. In this limit, the contact conductance becomes directly proportional to the contact area, as described by Sharvin's

the mean free path of the conduction electrons, and *a* is the radius of the contact. We stress that this equation is only valid for nanometer-sized contacts, where *l* >> *a*. The linear relationship between the contact conductance and contact area is true whether the junction

with load then appears very close to the *shape* of the JKR curve for values of

highly depend on a specific model for the tip-sample interaction potential.

2/3 2/3

equation for metallic contacts (Jansen et al., 1980): *G* = 3*a*2/4

 

2/3 <sup>2</sup> *<sup>R</sup> A LR K* 

, where *E1* and *E2* are the Young's moduli, and

1/3 2 \*2 3

is the shear strength, a fundamental interfacial property. In most

*R Ez*<sup>0</sup> can be used to determine which of the two

< 0.1, the DMT theory should describe the relation between *A* 

is the work per unit area required to separate tip and

> 5. Therefore, while a measurement of contact area

< 0.1), the contact area *A* varies with the applied load *L* in a

, where K=(4/3)E\*. The pull-off force or critical load

*l*, where

is the resistivity, *l* is

. The value of *Lc* can be obtained from AFM approach/retract

< 5). As discussed by Greenwood

*1* and *2*

represents the

> 0.5.

Thus, *Ff* =

*A* where

nondimensional parameter

 

expression, *R* is the sphere radius,

\* 2 21 11 22 *E EE* ((1 ) / (1 ) / )

and thus the adhesion energy, unless

simple fashion:

In the case of the DMT model (

*Lc* is given by 2 *L R <sup>c</sup>*

contrast to the JKR model.

should be valid, while for

et al., 1980; Tabor, 1977; Greenwood, 1997; Johnson, 1996).

appropriate for the intermediate cases (0.1 <

 

are the Poisson's ratios of the sphere and plane, respectively. Finally, *z0*

The experiments were performed in an UHV chamber (base pressure 7 x 10-11 Torr), since even in moderately evacuated chambers the residual oxygen and water vapor may combine with the sliding action to catalyze a phase change on diamond (Gardos, 1994). The UHVchamber is equipped with a home-built AFM (Dai et al., 1995), low-energy electron diffraction (LEED), and Auger electron spectroscopy (AES). The sample is an artificial type IIb diamond(111) single-crystal, which is terminated with hydrogen and slightly borondoped. The cleaning procedure used, as well as the single-crystal quality, are described in more detail by van den Oetelaar *et al.* (van den Oetelaar & Flipse, 1997). Fig 3 shows the LEED pattern taken after the cleaning procedure. This clear (1x1) LEED pattern supports the fact that we have a hydrogen-terminated diamond(111)-(1x1) surface.

Fig. 3. Our cleaning procedure gave rise to a clear hydrogen-terminated diamond(111)-(1x1) surface, as shown in this LEED pattern.

Triangular silicon cantilevers with integrated tips, coated with approximately 20 nm tungsten-carbide, were used for all measurements. The tips were characterized by scanning electron microscopy (SEM) and AES. Two types of cantilevers were used, with a spring constant of 88 N/m and 0.23 N/m, respectively. The former cantilever was used for conductance measurements while the latter one was used for friction measurements. The tips were cleaned in UHV immediately prior to the measurements, by applying short voltage pulses and/or by rubbing them on the surface. Normal cantilever force constants were taken from the manufacturer, and the normal/lateral force ratio was calculated using the method described by Ogletree *et al.* (Ogletree et al., 1996). The absolute accuracy of the forces measured is limited due to significant uncertainty in the material properties of the cantilever and approximations used in the force constant calculations. However, relative changes in friction could be accurately determined by using the same cantilever and tip during a series of measurements. A flexible I-V converter, allowing current measurements spanning the range from pA to mA, was designed and built.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 107

The current versus load data was fitted using the JKR model. Treating *Lc* as a free parameter, the JKR fits, at all bias voltages, predict a critical load which is systematically and substantially too small compared to the independently measured pull-off force. If we apply the constraint *Lc* = -0.1 N to the JKR fit, the resulting fit is clearly incompatible with our data, as illustrated in Fig. 4(b) for a bias voltage of 4 V. In addition, we found from the fitting statistics that the mean square deviation of the JKR fit is more than one order of magnitude worse than that of the DMT fit. These local contact conductance results clearly show that the load dependence of the contact area for this single-asperity interface can be

A topographic AFM image is actually a convoluted image of the tip and surface features of the sample. Usually, one requires sharp AFM-tips to reveal the surface topography, but similarly, an extremely sharp feature on the surface can provide information about the shape of an AFM-tip (Atamny & Baiker, 1995). To determine the radius of curvature of the tungsten-carbide coated tip used in our friction experiments, we performed scans over the sharp edges of a faceted SrTiO3(305) sample (Sheiko et al., 1993) in air. The surface is terminated with a large number of (101) and (103) facets, which form long sharp ridges that are suitable for tip imaging (Carpick et al., 1996a; Ogletree et al., 1996; Sheiko et al., 1993). The thus obtained cross-sectional "image" of the AFM-tip actually provides an upper limit to the tip dimensions, but this upper limit appears to be very close to the real tip dimensions (Carpick et al., 1996a). The cross-sectional tip-profile can be fit by a hemisphere, as is shown in Fig. 5, resulting in a radius of curvature of 110 nm. Profile analysis using the SrTiO3(305) sample was performed before and after tip-sample contact, and no evidence of wear was

**-10 -5 0 5 10**

**Length [nm]**

Fig. 5. Hemispherical fit of the AFM-tip profile, resulting in a radius of curvature *R* = 110

described by the DMT continuum mechanics model.

**-0.1**

nm. Note the difference in vertical versus horizontal scale.

**0**

**0.1**

**0.2**

**Heigth [nm]**

**0.3**

**0.4**

**0.5**

discerned.

Friction versus load data were acquired by scanning the AFM-tip repeatedly back and forth over the same line on the surface, while linearly increasing or decreasing the externally applied load. The value of the friction force at a given load is half of the difference between the signals while scanning from left to right, and right to left, respectively (Carpick et al., 1996a; Hu et al., 1995).

#### **2.3 Results and discussions**

All of the results presented in this work were obtained on a hydrogen-terminated diamond(111) sample, consisting of atomically smooth and well-ordered islands of 150 - 250 Å in diameter (Enachescu et al., 1998; van den Oetelaar & Flipse, 1997). The friction and contact conductance data were acquired within the bounderies of a single island, thus avoiding multiple-contact points.

Fig. 4(a) shows a large number of I-V curves recorded at different loads up to 1.7 N, using an 88 N/m cantilever. The I-V characteristics are semiconductor-like and consistent with the *p*-type doping of the diamond sample. The shape of the I-V curves remains basically constant at all loads, strongly indicating that the applied load does not significantly affect the surface electronic properties of the interface. This observation supports our assumption that the current is proportional to the contact area.

Fig. 4. (a) Current measured through the tip-sample contact versus bias voltage (I-V curves) recorded as a function of increasing load up to 1.7 N. (b) Current versus applied load at three different constant bias voltages. The DMT fit is significantly better than the JKR fit, as illustrated for a bias voltage of 4 V, also indicated by the mean square deviation of the JKR fit, which is more than one order of magnitude worse for the JKR fit compared to the DMT fit.

Plotted in Fig. 4(b) is the load dependence of the current at several bias voltages applied to the sample, e.g., +3 V, +3.5 V and +4 V. The data can be fit by the DMT model, using Lc as a free parameter. The DMT model provides an excellent fit to the measured data, and the value of *Lc* deduced from the fits is in excellent agreement with the independently measured pull-off force of -0.1 N, obtained from cantilever-sample retract experiments for the same cantilever.

Friction versus load data were acquired by scanning the AFM-tip repeatedly back and forth over the same line on the surface, while linearly increasing or decreasing the externally applied load. The value of the friction force at a given load is half of the difference between the signals while scanning from left to right, and right to left, respectively (Carpick et al.,

All of the results presented in this work were obtained on a hydrogen-terminated diamond(111) sample, consisting of atomically smooth and well-ordered islands of 150 - 250 Å in diameter (Enachescu et al., 1998; van den Oetelaar & Flipse, 1997). The friction and contact conductance data were acquired within the bounderies of a single island, thus

Fig. 4(a) shows a large number of I-V curves recorded at different loads up to 1.7 N, using an 88 N/m cantilever. The I-V characteristics are semiconductor-like and consistent with the *p*-type doping of the diamond sample. The shape of the I-V curves remains basically constant at all loads, strongly indicating that the applied load does not significantly affect the surface electronic properties of the interface. This observation supports our assumption

> **4 V 3.5 V 3.0 V**

**JKR fit**

different constant bias voltages. The DMT fit is significantly better than the JKR fit, as

of -0.1 N, obtained from cantilever-sample retract experiments for the same cantilever.

(a) (b) Fig. 4. (a) Current measured through the tip-sample contact versus bias voltage (I-V curves) recorded as a function of increasing load up to 1.7 N. (b) Current versus applied load at three

illustrated for a bias voltage of 4 V, also indicated by the mean square deviation of the JKR fit, which is more than one order of magnitude worse for the JKR fit compared to the DMT fit.

Plotted in Fig. 4(b) is the load dependence of the current at several bias voltages applied to the sample, e.g., +3 V, +3.5 V and +4 V. The data can be fit by the DMT model, using Lc as a free parameter. The DMT model provides an excellent fit to the measured data, and the value of *Lc* deduced from the fits is in excellent agreement with the independently measured pull-off force

**Current [nA]**

**-0.5 0 0.5 1 1.5 2**

**Load [µN]**

**DMT fit**

**DMT fit**

1996a; Hu et al., 1995).

**Current [nA]**

**2.3 Results and discussions** 

avoiding multiple-contact points.

that the current is proportional to the contact area.

**-4 -3 -2 -1 0 1 2 3 4**

**Voltage [V]**

The current versus load data was fitted using the JKR model. Treating *Lc* as a free parameter, the JKR fits, at all bias voltages, predict a critical load which is systematically and substantially too small compared to the independently measured pull-off force. If we apply the constraint *Lc* = -0.1 N to the JKR fit, the resulting fit is clearly incompatible with our data, as illustrated in Fig. 4(b) for a bias voltage of 4 V. In addition, we found from the fitting statistics that the mean square deviation of the JKR fit is more than one order of magnitude worse than that of the DMT fit. These local contact conductance results clearly show that the load dependence of the contact area for this single-asperity interface can be described by the DMT continuum mechanics model.

A topographic AFM image is actually a convoluted image of the tip and surface features of the sample. Usually, one requires sharp AFM-tips to reveal the surface topography, but similarly, an extremely sharp feature on the surface can provide information about the shape of an AFM-tip (Atamny & Baiker, 1995). To determine the radius of curvature of the tungsten-carbide coated tip used in our friction experiments, we performed scans over the sharp edges of a faceted SrTiO3(305) sample (Sheiko et al., 1993) in air. The surface is terminated with a large number of (101) and (103) facets, which form long sharp ridges that are suitable for tip imaging (Carpick et al., 1996a; Ogletree et al., 1996; Sheiko et al., 1993). The thus obtained cross-sectional "image" of the AFM-tip actually provides an upper limit to the tip dimensions, but this upper limit appears to be very close to the real tip dimensions (Carpick et al., 1996a). The cross-sectional tip-profile can be fit by a hemisphere, as is shown in Fig. 5, resulting in a radius of curvature of 110 nm. Profile analysis using the SrTiO3(305) sample was performed before and after tip-sample contact, and no evidence of wear was discerned.

Fig. 5. Hemispherical fit of the AFM-tip profile, resulting in a radius of curvature *R* = 110 nm. Note the difference in vertical versus horizontal scale.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 109

premature pull-off of the tip. This premature pull-off is promoted by the tip-sample movement during scanning and is more likely to appear in this particular experiment due to

In an attempt to learn more about the relation between the friction force and the area of contact, we have plotted the friction force versus contact area, and the result is shown in Fig. 7. The friction force plotted in this figure is exactly the friction force measured during friction versus load experiments. The contact area was calculated using the DMT theory. The use of the DMT theory is supported by the three previous pieces of experimental evidence, namely: (i) the excellent DMT fit of the current versus load data using the stiff lever,

calculated after experimental determination of the radius of curvature *R* of the tip presented in Fig. 5, and of the pull-off force *Lc* presented in Fig. 6; (iii) the excellent DMT fit of the friction versus load experiments and the independent confirmation of the DMT fit by the experimental value of *Lc* presented in Fig. 6. Following the procedure suggested and supported above we found that a linear fit is the optimum fit for our friction force versus

free linear fit intercepts the origin, and the slope is a measure of the shear strength. We find

**0 2 4 6 8 10**

**]**

**Area of Contact [nm2**

Fig. 7. Friction force versus contact area, showing a clear linear relation. The corresponding

So, in contrast to the macroscopic law of friction, the friction force at the interface of a singleasperity is directly proportional to the contact area. Furthermore, since friction does not depend linearly upon the applied load for a single-asperity contact, one should be careful defining a friction coefficient, *i.e.* the friction force divided by the normal force, in AFM

< 0.1,

*A*. Consistently, this

= 238 MPa, a value which lies within the typical range for AFM

presented in Fig. 4(b); (ii) the excellent DMT prediction of the Tabor parameter,

contact area representation in Fig. 7, demonstrating that, indeed, *Ff* =

**0**

**0.5**

**1**

**1.5**

**2**

**2.5**

experiments (Carpick & Salmeron, 1997).

**Friction [nN]**

that the shear strength

shear strength

= 238 MPa.

experiments, as its value varies with load.

the very low adhesive force between the surfaces in contact.

Having obtained a value for the tip radius *R*, we can estimate the empirical parameter . Using *Lc* = -2*R*, can be obtained from the measured pull-off force. A typical normal force versus cantilever-sample displacement curve, during retraction of the cantilever, is shown in Fig. 6. The corresponding pull-off force is -7.3 nN, resulting in = 0.01 J/m2. Thus, using *z0* = 2 Å, *E*diamond = 1164 GPa (Klein, 1992), *E*WC = 700 GPa (Shackelford et al., 1994), diamond = 0.08 (Klein, 1992), and WC = 0.24 (Shackelford et al., 1994), we find that = 0.02. Indeed, this value is much smaller than the DMT condition < 0.1 discussed above, showing that the present tip-sample contact is firmly in the DMT regime.

Friction experiments were performed as a function of applied load using the soft lever (Enachescu et al., 1998). They were reproducible at different locations on the sample, and were obtained by decreasing the load from 12 nN to negative loads (unloading). Experiments where the load was increased (loading) exhibited the same behavior as the unloading results, indicating that the deformation of the contact is elastic for the range of loads investigated.

Friction versus load experiments could be fit very well by the DMT model, while treating both and the shear strength as free parameters (Enachescu et al., 1998). The mathematical fit results in a pull-off force of -7.3 nN and a shear strength of 238 MPa. Thus, the pull-off force predicted by the DMT fit is in excellent agreement with the pull-off value measured experimentally, as shown in Fig. 6.

Fig. 6. Typical normal force versus cantilever-sample displacement curve, during retraction of the cantilever. The corresponding pull-off force is –7.3 nN.

The measured pull-off force actually represents an *independent* verification of the DMT fit, since (and thus also the pull-off force) was treated as a free parameter in the DMT fit. Attempts to fit the JKR model to the friction versus load curves, using *Lc* both as a free parameter and as a constrained parameter, produced strongly inconsistent fits. Experimentally, no friction data for loads smaller than -2 nN could be obtained due to a

can be obtained from the measured pull-off force. A typical normal force

as free parameters (Enachescu et al., 1998). The mathematical

.

= 0.01 J/m2. Thus, using *z0* =

= 0.02. Indeed, this

diamond = 0.08

Having obtained a value for the tip radius *R*, we can estimate the empirical parameter

WC = 0.24 (Shackelford et al., 1994), we find that

value is much smaller than the DMT condition < 0.1 discussed above, showing that the

Friction experiments were performed as a function of applied load using the soft lever (Enachescu et al., 1998). They were reproducible at different locations on the sample, and were obtained by decreasing the load from 12 nN to negative loads (unloading). Experiments where the load was increased (loading) exhibited the same behavior as the unloading results, indicating that the deformation of the contact is elastic for the range of

Friction versus load experiments could be fit very well by the DMT model, while treating

fit results in a pull-off force of -7.3 nN and a shear strength of 238 MPa. Thus, the pull-off force predicted by the DMT fit is in excellent agreement with the pull-off value measured

**-50 0 50 100 150**

**Cantilever Displacement [nm]**

Fig. 6. Typical normal force versus cantilever-sample displacement curve, during retraction

The measured pull-off force actually represents an *independent* verification of the DMT fit,

 (and thus also the pull-off force) was treated as a free parameter in the DMT fit. Attempts to fit the JKR model to the friction versus load curves, using *Lc* both as a free parameter and as a constrained parameter, produced strongly inconsistent fits. Experimentally, no friction data for loads smaller than -2 nN could be obtained due to a

2 Å, *E*diamond = 1164 GPa (Klein, 1992), *E*WC = 700 GPa (Shackelford et al., 1994),

Fig. 6. The corresponding pull-off force is -7.3 nN, resulting in

present tip-sample contact is firmly in the DMT regime.

**-10**

of the cantilever. The corresponding pull-off force is –7.3 nN.

**-5**

**0**

**5**

**Force [nN]**

**10**

**15**

**20**

versus cantilever-sample displacement curve, during retraction of the cantilever, is shown in

Using *Lc* = -2

(Klein, 1992), and

loads investigated.

both 

since  *R*, 

and the shear strength

experimentally, as shown in Fig. 6.

premature pull-off of the tip. This premature pull-off is promoted by the tip-sample movement during scanning and is more likely to appear in this particular experiment due to the very low adhesive force between the surfaces in contact.

In an attempt to learn more about the relation between the friction force and the area of contact, we have plotted the friction force versus contact area, and the result is shown in Fig. 7. The friction force plotted in this figure is exactly the friction force measured during friction versus load experiments. The contact area was calculated using the DMT theory. The use of the DMT theory is supported by the three previous pieces of experimental evidence, namely: (i) the excellent DMT fit of the current versus load data using the stiff lever, presented in Fig. 4(b); (ii) the excellent DMT prediction of the Tabor parameter, < 0.1, calculated after experimental determination of the radius of curvature *R* of the tip presented in Fig. 5, and of the pull-off force *Lc* presented in Fig. 6; (iii) the excellent DMT fit of the friction versus load experiments and the independent confirmation of the DMT fit by the experimental value of *Lc* presented in Fig. 6. Following the procedure suggested and supported above we found that a linear fit is the optimum fit for our friction force versus contact area representation in Fig. 7, demonstrating that, indeed, *Ff* = *A*. Consistently, this free linear fit intercepts the origin, and the slope is a measure of the shear strength. We find that the shear strength = 238 MPa, a value which lies within the typical range for AFM experiments (Carpick & Salmeron, 1997).

Fig. 7. Friction force versus contact area, showing a clear linear relation. The corresponding shear strength = 238 MPa.

So, in contrast to the macroscopic law of friction, the friction force at the interface of a singleasperity is directly proportional to the contact area. Furthermore, since friction does not depend linearly upon the applied load for a single-asperity contact, one should be careful defining a friction coefficient, *i.e.* the friction force divided by the normal force, in AFM experiments, as its value varies with load.

Nanoscale Effects of Friction, Adhesion and Electrical Conduction in AFM Experiments 111

sample gave rise to periodic stick-slip friction behavior with a period equal to the atomic lattice constant of the Pt(111) surface. Local electrical conductivity measurements show a clear correlation between electronic and friction properties, with Ohmic behavior on clean regions of the Pt surface and semiconductor-like behavior on areas covered with adsorbates. Our results indicate that substantial material transfer may be an important and inevitable property of nanocontacts when one surface is highly reactive and the other surface is not thoroughly cleaned. Furthermore, this work establishes that stable STM imaging using a conductive cantilever is a reliable method for observing this effect, and for observing fine features on clean portions of a reactive surface. In addition, the correlation between adhesion, friction, and contact conductance allows one to discern the existence and certain properties of the transferred material, which demonstrates that multi-functional scanning probe techniques are desirable for third-body processes at the nanoscale and nanotribology

The sliding of materials in contact often involves the transfer of material from one surface to the other. This material, referred to sometimes as the third body, influences the transient behavior of the sliding contact and can completely dominate the steady-state sliding behavior of many interfaces, especially for low friction coatings (Singer, 1992; 1998). Studies of low-friction materials such as diamond-like carbon coatings, MoS2 coatings, and Tiimplanted steels indicate that chemically-modified transfer films are formed during initial

At small length scales third-bodies can also have a large impact on the contact properties. For example, hard disks and micro-electromechanical systems (MEMS) are critically limited by friction and adhesion-related failures due to the large surface-to-volume ratios of these devices (McFadden & Gellman, 1997). For such devices, an understanding of nano-scale third body behavior is important. Modeling work supports this notion. Robbins and co-workers have performed molecular dynamics simulations that indicate that molecular intermediate species in asperity contacts have a dramatic effect on friction (He et al., 1999; He & Robbins, 2001). They argue that contacts between crystalline or amorphous materials should, in general, exhibit very low friction due to the lack of interfacial lattice commensurability. The simulations show that molecules trapped at the interface, e.g. hydrocarbons, cause static

The role of third bodies and transferred species at small scales is clearly worthy of further experimental study, specifically through the use of scanning force microscopy techniques. Already, fundamental insights into many aspects of friction have been obtained through the use of scanning force microscopy (Carpick & Salmeron, 1997). These studies have addressed several important topics such as atomic-scale stick-slip behavior, friction in the wearless (low-load) regime, friction in the presence of molecular lubricant films, the role of interfacial contact area, and wear initiation. However, there have been few studies of third body effects and transferred species. One example is the work by Qian et al. (Qian et al., 2000) who showed that in atomic force microscope (AFM) experiments, friction measurements exhibit transient behavior, where several tens of scans were required before friction behavior become reproducible. They proposed that the phenomenon is due to transfer of

sliding, and these films determine the long-term frictional behavior of the interface.

friction that is consistent with observed macroscopic friction behavior.

studies of tip-sample material transfer.

**3.1 Background** 

The constant shear strength that we observe indicates that the mechanism of energy dissipation for this system does not change in this pressure range. Thus, the increase in friction with load is attributable to the increase in contact area, *i.e.* more atoms in contact, as opposed to a change in the frictional dissipation per interfacial atom. This may not be so surprising given that the nominal stress is only increasing as roughly *L1/3* (from the continuum mechanics models). The most likely mechanism of energy dissipation is thermalization of phonons generated at the contact zone during sliding. New modes of energy dissipation, resulting from inelastic processes, may activate at higher stresses (Carpick & Salmeron, 1997). For example, evidence of tip-induced atomic-scale wear has been reported for alkali-halide materials (Carpick et al., 1998b). Pressure-activated modes of energy dissipation are reported in organic thin films due to progressive molecular deformation (Barrena et al., 1999). These examples represent stress-dependent increases in the number of energy dissipation channels and are therefore manifested in increases in the shear strength compared with purely elastic, wearless friction.

Finally, we comment on the relative magnitude of the observed shear strength. The theoretical prediction for the shear strength of a crystalline material in the absence of dislocations is roughly given by *G*/30 (Cottrell, 1988), where *G* is the shear modulus. We can define an "effective" interfacial shear modulus 2 380 GPa *G GG G G eff WC diamond WC diamond* . This gives, for the diamond/tungsten-carbide contact, 1600 *Geff* . The shear strength of this system is thus far below the ideal material shear strength (Hurtado & Kim, 1998). Previous AFM results of Carpick *et al.* (Carpick et al., 1996a; 1998b) and Lantz *et al.* (Lantz et al., 1997a; 1997b) observed shear strengths near the ideal limit. An ideal shear strength in the range of *G*/30 suggests a "crystalline" or commensurate interface that is free of dislocations, where the commensurability may be brought about by atomic displacements induced by interfacial forces. Our measured shear strength indicates that there may be very little atomic commensurability for the diamond/tungsten-carbide interface, which is plausible considering the high stiffness of these materials. More importantly, the hydrogen passivation of the diamond surface strongly reduces the adhesive force, and also the friction force. In fact, removal of the hydrogen passivation would result in a value for the shear strength which is much larger than the ideal theoretical prediction of *G*/30 (van den Oetelaar & Flipse, 1997).

#### **3. Wear and third bodies in nanocontacts**

We have investigated the nanotribological properties of a tungsten carbide tip in contact with a clean Pt(111) single crystal surface under ultrahigh vacuum conditions using scanning probe techniques. Because of the conductive nature of the cantilever and tip, we could alternate between contact atomic force microscopy (AFM) and non-contact scanning tunneling microscopy (STM) using the same probe. Several types of interfaces were found depending on the chemical state of the surfaces. The first type is characterized by strong irreversible adhesion followed by material transfer between tip and sample. This resulted in substantial amounts of material being transferred from the tip to the sample upon contact. This material often covered areas far exceeding that of the contact region. Low adhesion and no material transfer characterize a second type of contacts, which is associated with the presence of passivating adsorbates in both (full passivation) or in one of the two contacting surfaces (half-passivation). Half-passivated contacts where the clean side is the Pt(111) sample gave rise to periodic stick-slip friction behavior with a period equal to the atomic lattice constant of the Pt(111) surface. Local electrical conductivity measurements show a clear correlation between electronic and friction properties, with Ohmic behavior on clean regions of the Pt surface and semiconductor-like behavior on areas covered with adsorbates.

Our results indicate that substantial material transfer may be an important and inevitable property of nanocontacts when one surface is highly reactive and the other surface is not thoroughly cleaned. Furthermore, this work establishes that stable STM imaging using a conductive cantilever is a reliable method for observing this effect, and for observing fine features on clean portions of a reactive surface. In addition, the correlation between adhesion, friction, and contact conductance allows one to discern the existence and certain properties of the transferred material, which demonstrates that multi-functional scanning probe techniques are desirable for third-body processes at the nanoscale and nanotribology studies of tip-sample material transfer.
