The conductive filler particles can only provide electrical conductivity through chains of contact between them. At a lower volume fraction of filler particles the resistivity of an ICA is very high i.e. the material behaves as an insulator because the conductive particles are isolated within the polymer matrix, as shown in Figure 2.6.
Chapter 2: Literature Review
Figure 2.6 Change of conductivity of ICAs based on percolation theory (after Morris et al.
(2007))
Conduction occurs only when the volume fraction of filler is more than a certain value, called the percolation threshold (ϕc). At this volume fraction sufficient particles are in contact to form initial conductive pathways between the electrodes i.e. at the percolation threshold, at least one chain, forms a conductive path between the measuring electrodes (Li et al. 1995; Morris et al. 2007). As formation of conductive path is a stochastic process, therefore for the same filler and matrix systems different percolation thresholds could be obtained (Ruschau et al. 1992a; Ruschau et al. 1992b).
On further increasing the volume fraction of filler, the number of chains increases and the conductivity of adhesive increases (Li et al. 1997). It is believed that a point is reached where most of the conductive particles contact their neighbours to form a three-dimensional network and the conductivity then increases only slightly with any further increase in the filler concentration. This point is called ϕsat as shown in Figure 2.6 (Morris 1999).
The percolation threshold (ϕc) and the conductivity of an ICA has been found to depend upon the filler geometry/shape, size, size distribution and on sample dimensions (Edward 2008). Non-spherical fillers have been found to have lower percolation thresholds and higher conductivities (Ruschau et al. 1992b; Li et al. 1997; Morris 1999;
Su 2006). This is because spherical fillers tend to pack much more densely whereas
122 4 Isotropically Conductive Adhesives (ICAs)
Fig. 4.1. Effect of filler volume fraction on the resistivity of ICA systems
Fig. 4.2. Schematic illustration of how electrical conduction paths are established by uninterrupted particle-to-particle contact between the component and the chip carrier terminal pads in an ICA joint
Vc
1224 Isotropically Conductive Adhesives (ICAs) Fig. 4.1. Effect of filler volume fraction on the resistivity of ICA systems Fig. 4.2. Schematic illustration of how electrical conduction paths are established by uninterrupted particle-to-particle contact between the component and the chip carrier terminal pads in an ICA joint Vc
Volume Fraction of Filler
Conductive filler Polymer matrix Electrical conduction (particle-to-particle contact)
122 4 Isotropically Conductive Adhesives (ICAs)
Fig. 4.1. Effect of filler volume fraction on the resistivity of ICA systems
Fig. 4.2. Schematic illustration of how electrical conduction paths are established by uninterrupted particle-to-particle contact between the component and the chip carrier terminal pads in an ICA joint
Vc
non-spherical filler normally show a greater tendency for bridging, which enables connectivity at lower volume fractions, leading to their lower packing densities and hence their lower percolation threshold and higher conductivities. The bridging become especially significant when fibre or flake fillers are used (Ruschau et al. 1992a; Li et al.
1997). However, it has been found that with the use of such irregular shaped fillers, the viscosity of the system rises more rapidly with filler content, which can reduce the ease of processing (Morris 1999; Petrie 2008; Licari et al. 2011). The effect of the filler on viscosity of an ICA is important factor to be taken into consideration when selecting the filler as it can affect printing or dispensing (Edward 2008). The relative viscosity for suspensions of non-spherical (irregular shaped) particles was given by Krieger et al.
(1959) as:
𝜼𝒓= 𝜼𝜼
𝒎= (𝟏 − 𝝓𝝓𝒇
𝒎𝒆𝒇𝒇)−𝟐 2.1 where ηr is the relative viscosity of a suspension;
η the steady-state viscosity of a suspension with particles (Pa.s);
ηm is the viscosity of the suspending medium without particles (Pa.s);
ϕf is the volume fraction of filler; and
ϕmeff is the effective maximum packing fraction of filler above which no flow is possible.
For non-spherical fillers with length to diameter ratios (L/D) between 6 to 27, ϕmeff varies between 0.44 to 0.18, whereas for mono-sized spheres (L/D = 1), ϕmeff = ϕmax= 0.63 (Kitano et al. 1981). Equation 2.1 shows that for a given volume fraction of filler, the relative viscosity increases with increasing aspect ratio (non-sphericity) of the particles, thus mono-sized spheres offers lower relative viscosities than flakes for similar volume fraction. Furthermore, deformable spheres have been found to result in lower relative viscosities than solid spheres (Genovese 2012).
In addition, flakes have a tendency to become oriented parallel to the adhered surfaces during application processes and under the influence of gravity. This results in a better conductivity in the plane of the substrate compared to conductivity normal to this plane.
This can be beneficial for printed conductors but for bonding applications, where
Chapter 2: Literature Review
electrical conductivity is required perpendicular to the bond line, this type of orientation can reduce conductivity and be a disadvantage (Morris et al. 2007).
Ruschau et al. (1992a) and Li et al. (1997) found that the percolation threshold for an ICA depends on the measurement geometry. They also found that the resistivity across thickness differed from the resistivity through the thickness. Ruschau et al. postulated that the important variables that determine the degree of anisotropy in conduction are the geometry factor, G ( = area of contact electrode / distance between electrodes) and Γ ( = particle size / the smallest sample dimension). As G and Γ increased, the percolation probabilities increased/decreased from bulk samples of the same composite. Li et al.
showed that as the sample thickness increases to ten times the particle size percolation become independent of the thickness (Li et al. 1997).
Ruschau et al. (1992a), Li et al. (1997) and (Su 2006) have shown that for the same filler shape, smaller filler particles offer a lower percolation threshold and lower resistivity as compared to larger fillers. Ruschau et al. identified the reason for this lower percolation threshold for smaller particles as their lower packing density. This decrease in packing density for smaller particles was attributed to an increase in surface area, lower particle mass, and therefore the greater significance of weak short-range forces leading to agglomeration. These short-range forces include electrostatic fields and surface adsorption of moisture and other wetting liquids. They have also shown that fillers with a larger particle size distribution offer lower percolation thresholds and lower resistivity compared to mono-sized fillers as particles with a larger size distribution pack less densely than particles with a narrow size distribution. Further, fillers with a wider size distribution has been found to reduce the viscosity. This is mainly because for a wider particle size distribution, the smaller particles may occupy spaces between the larger particles such that the maximum packing fraction ϕmeff
thereby decreasing the relative viscosity (Genovese 2012). However, increasing the effective packing fraction will increase the amount of filler and may have an adverse effect on mechanical strength (Ogunjimi et al. 1992b; Morris et al. 2007).