CMP/MIC - March 2002

Kristan G. Bahten

Rippey Corporation
5000 Hillsdale Circle
El Dorado Hills, CA 95762

T. Zhang, E. Estragnat, H. Liang and J. Lee

University Of Alaska
Fairbanks

Introduction
As device dimensions dramatically decrease with rapidly advancing technologies, micrometer and sub-micrometer particle removal from the device's surface becomes critical to both its quality and durability. After the device's surface has been through chemical-mechanical-polishing (CMP), particles with very complex composition remaining on the surface can cause damage to the device and eventually lead to failure and low products yield. These remains include slurry particles in micrometer or sub-micrometer scale, pieces of polishing pad used in CMP, and particles of surface material removed during polishing. Post-CMP cleaning is therefore a necessary process to minimize various particle contaminations to the surface. To develop an optimal and effective Post-CMP cleaning process, an improved understanding of the interactions between a particle and a substrate surface is important. Because the complex composition and size variation of the remain particles, the adhesion force may be a combination of several bounding forces such as long range van der Waals forces, chemical or hydrogen bound, and electrostatic forces. Among those forces, van der Waals forces are significant in particle-surface interaction and will be studied in this paper.

Several theoretical models [1,2,3,4] have been developed and used by researchers to study the interactions (adhesion and deformation) between a particle and a substrate surface. Adhesion force between a particle and a substrate surface has been extensively studied theoretically and compared with AFM contact mode test results for some materials. Most researchers have attributed removal force to adhesion or pull-out force. However, in Post-CMP cleaning process, the removal of a particle from a surface involves not only the adhesion force that separates a particle from a surface but also a frictional force that is related to particle sliding and rolling along the surface. In our current work, frictional force and coefficient of friction will be studied based on van der Waals interaction potential energy and compared with experimental results.

System Idealization
The system to be modeled is idealized from a Post-CMP cleaning process. This process consists of a contaminated wafer surface and a nodule of a cleaning brush made of polymer foam. The rubbing action of the brush on wafer surface will remove those remain particles from the surface. The system consists of a single rough spherical colloid particle representing the particle contamination and a smooth, hard, and flat wafer surface as shown in Fig. 1. The van der Waals interaction model is derived based on the following assumptions: 1. the contact surface of the substrate is atomically smooth. 2. the roughness of the colloidal particle with radius R is represented by uniformly distributed hemispherical hard asperities that have es height and separate from each other by a distance s. 3. The substrate possesses infinite volume. The molecule-to-molecule interactions follow the macroscopic, pair-wise additivity approach. 4. The van der Waals interactions are non-retarded and therefore separation between the colloid and the substrate is less than 10 nm [4].

Potential and Force
A schematic of a single particle interacting with a flat surface is illustrated in Fig. 2. Assume that the pair potential energy between two molecules (atoms) is purely attractive [4, 5] and in the form of

(1.)

where C is a constant and is the distance between the two particles. With the pair additivity assumption, the sum of net interaction potential energy between the particle and the planar surface of the solid substrate can be integrated as below

(2.)

where and is the molecular number density and the volume of the substrate, respectively. For a solid ring of cross-section area dxdz and of radius x, the volume of the infinitesimal ring within the substrate is . Introduce r and into Eq. (2), the net interaction energy for the particle at a distance D away from the surface therefore is

(3.)

Adhesion and Frictional Force
Based on the interaction potential energy given in Eq. (3), the adhesion force can be obtained by differentiating with respect to z and is given below after integration with n=6.

(4.)

The adhesion force for a smooth sphere can also be obtained from Eq. (3) as below

(5.)

where R is the radius of the smooth sphere. Equations (4) and (5) can also be found elsewhere [4]. Follow the similar procedure, the frictional force is derived from Eq. (3) by differentiating with respect to x and is expressed as

(6.)

for a single asperity and

(7.)

for a smooth sphere, where A is Hamaker constant.

Removal Forces
Traditionally, the removal force of a contaminating particle from a surface is defined as the total adhesion forces of all the asperities in contact with the substrate surface [4]. However, the frictional force also plays an important role along with adhesion force during cleaning process. Therefore, both of the two forces will be discussed in the following. To determine the total adhesion and frictional forces of all the asperities in contact with the surface, we have to firstly determine the adhesion induced deformation and contact area between particle and the surface. Different models for adhesion induced deformation and contact area have been developed elsewhere [6-9]. The generalization of the models that calculate the contact radius is given as

(8.)

where a is the adhesion induced contact radius, R is the colloid radius, and C and n are the model parameters [4]. From the contact area, adhesion induced indentation deformation can be calculated if we assume the colloid is rigid as shown in Fig. 4, that is,

(9.)

From the indentation deformation d, the spherical contact surface area can be calculated and is given by

(10.)

If we define P3 as the number of asperities per unit contact surface area, the total number of asperity in contact with the substrate surface then is N = S P3. Therefore, the total adhesion and frictional forces can be calculated by the following equations

(11.)

and

(12.)

The ratio of the frictional force to the adhesion force is

(13.)

Eq. (13) shows that frictional force is about more than 50% of adhesion force and therefore cannot be ignored in the removal force in Post-CMP cleaning process.

As we focus our attention on the cleaning process, the frictional force is actually the major force in removal of contaminating particles because the relative motion of the two contact surfaces is along the tangential direction. During cleaning process, the applied cleaning force has to be greater than the frictional force given by Eq. (12) such that the particle is able to slide along the substrate surface. The magnitude of the applied cleaning force depends on both the cleaning pressure and the roughness of the brush surface. On the other hand, a rolling mechanism is also possible. Consider all the forces applied on an isolated particle as shown in Fig. 5. The cleaning force and the frictional force form a moment that will rotate the particle clockwise and travel along the substrate. However, as the particle rotates the substrate will deform under the pressure force P such that the reaction force FN will shift toward right. The shifting of the reaction force will induce a moment formed by FN and P, which will counteract the moment caused by Q and Fr. The critical state is reached when the two moments are in equilibrium, i. e.

(14.)

where is the distance between and P. Equation (14) is obtained by assuming that the cleaning force is applied at the mass center of the particle. Therefore the applied cleaning force Q is equal to frictional force pending the rolling begins. If, however, the cleaning force is applied at the top of the particle, the extreme case, then Eq. (14) will become

(15.)

which implies that Q = FT/2. In this case, particle rolling will occur under rather smaller applied cleaning force than particle sliding does. Based on the above analysis, it can be assumed that both particle rolling and sliding mechanism will coexist during cleaning process under consideration of particle irregularities.

Results and Discussions
Experiments that simulate the Post-CMP cleaning process have been conducted in our laboratory. Those tests results are plotted in Figs. 6 and 7. Comparing the experimental measured data with the theoretical adhesion coefficient of friction value 0.589 given by Eq. (13), it is found that the theoretical value is higher than that for dry cleaning and much higher for wet cleaning. The differences can be attributed to: 1. The theoretical value is for static coefficient of friction while the values measured by experiments are kinetic coefficients in principle. Universally speaking, kinetic coefficient is usually lower than static coefficient. 2. Effects of both the colloidal particle and substrate surface roughness. Although the formula used to calculate adhesion and frictional forces include the influence of roughness of the colloid particle surface, the coefficient of friction does not include such parameters. Therefore, it is obvious that current simple approach could not include roughness as well as material properties influences on friction coefficient. However, studies have shown that surface smoothness and atomic structure have great influence on adhesion coefficient of friction [10]. 3. Influence of presenting water molecules as well as chemical ingredient such as pH value. When water molecules adsorb to the substrate surface the adhesion friction will drop because surface sites will be covered with these atoms or layers of oxide.

Equation (13) gives the coefficient of friction for pure adhesion. As the particle slides along the substrate surface, the substrate will deform both elastically and plastically. These deformations create an additional part of friction. Therefore, the total coefficient of friction contains contributions from both the adhesion and the deformation. A continuum model that fully accounts of both the adhesion and deformation in the coefficient of friction is given by Johnson [11] and Challen et al. [12]. In this model, the coefficient of friction is derived based on an idealized system that consists of a single hard asperity and a plastic wedge in plane strain condition and is given by

(16.)

where , f is the normalized strength of the interfacial film and is defined in the usual way as the ratio of the shear strength of the film t to the shear flow stress of the substrate material k, that is, . The m value in Eq. (16) may be thought as representing adhesion coefficient of friction at a=0. For a typical value of f=0.8 at ox=0, Eq. (16) gives u=0.21 less than ½ of the current derived coefficient of friction value.

Lubrication Effect
The experimental results show that the overall coefficient of friction for dry cleaning is higher than that for wet cleaning. The difference in the coefficients indicates that water may play a role of lubrication during cleaning and therefore reduce the friction between the two surfaces. To study the low friction phenomenon with wet cleaning from point of view of tribology, we develop a "Stribeck curve" that relates the coefficient of friction with dimensionless number Sc. The "Stribeck coefficient" is calculated by where h is the absolute viscosity of the liquid, V is the relative surface speed, and is the normal force. From test data, Sc is calculated with correspondent to the coefficient of friction and plotted in Fig. 7. The Stribeck curve in Fig. 7 show the variation of the coefficient of friction with Sommerfeld grouping, Sc. A standard Stribeck curve for rigid materials is plotted in Fig.8, which characterizes different lubrication regimes. A low speed and high load region represents a boundary lubrication (BL) regime; a high speed and low load region represents a hydrodynamic lubrication (HL) regime; the region in the between is the elasto-hydrodynamic lubrication (EHL) regime. By comparing Fig. 7 and Fig. 8, we could identify which lubrication regime the cleaning system could fit into. It can be seen from Fig. 7 that the friction behavior of the cleaning system may be characterized by BL and EHL regimes. The HL regime does not show up in the cleaning process. This may be attributed to the roughness of the cleaning pad.

Conclusions
Based on van der Waals interaction potential energy, formulation to calculate frictional force is derived along with adhesion force for a rough colloidal particle and a smooth substrate surface. From the forces applied on a particle, two possible mechanisms of particle removal, sliding and rolling, that involved in cleaning process are analyzed. Under consideration of the irregularities of the contaminating particles on the substrate surface, both the two mechanisms could involve in the cleaning process. From the derived adhesion and frictional forces, the coefficient of adhesion friction is calculated by dividing the frictional force by the adhesion force. This adhesion coefficient is compared with the coefficient of friction obtained from cleaning experiments for the dry and wet condition. The derived adhesion friction is higher than the maximum friction value under dry cleaning and much higher than the average friction value of wet cleaning condition. Several factors that may contribute to the differences have been discussed. These factors, among others, are assumed to have major influence on the difference. The difference between the friction under dry and wet conditions are analyzed from the point of view of tribology. By comparing the "Stribeck curve" from cleaning experiments with standard Stribeck curve, the difference could be interpreted by different lubrication regimes. It is concluded that current approach to calculate the adhesion coefficient of friction is not able to take into account of surface roughness of the contact body as well as material properties although the roughness of the particle can be accounted into the adhesion force and frictional force evaluations. A more complicated model should be proposed to include the roughness and material properties. On the other hand, a model to calculate friction caused only by substrate deformation is also needed.






Figure 1. A schematic of the interaction of a flat, smooth surface and rough spherical colliod.





Figure 2. A schematic of the interaction between a single molecule and a smooth flat surface with infinite volume.





Figure 3. A schematic of the interaction between a single asperity of radius Es a substrate surface with infinite volume.


Figure 4. Adhesion induced indentation deformation.






Figure 5. Forces applied on a particle at verge state of rolling.






Figure 6. Friction coefficient as a function of surface speed.






Figure 7. The "Cleaning Stribeck Curve".



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