Isotropic conduction

We write the 2-component of equation (2) in a medium with isotropic conductivity moving according to equation (1) dHz 3H, dt... 

The abbreviations mn and m L denote the longitudinal and transverse effective electron masses, respectively. m is the effective mass for isotropic conduction band minimum. 

Fig. 8.13 Equivalent distribution of conductive chains along the principal directions of a unit cube of an isotropic conducting mixture, defining the geometrical factor. Reproduced with permission of the Institute of Physics from Scarisbrick (1973).

Fig. 22 Schematic self-assembled transverse-witlzin-parallel aligned structure of PS-6-P4VP(TSA)i.o(PDP)i.o supramolecules and the direct-current conductivity as a fimction of temperature. Presented also is the isotropic conductivity of a nonaligned sample (4). In the aligned case (3) the conductivity is increased, probably due to fewer domain boimd-aries, and the nanoscale conductivity anisotropy is manifestly present [155]...

If we consider a spherical particle in equilibrium losing the heat absorbed from the beam by isotropic conduction into a surrounding medium of thermal conductivity k, the radial variation of the temperature T in the surrounding medium can easily be shown to be given by... 

Reduction does not stop at the ionic cluster level, but goes all the way to metallic particles. The latter is characterized by an isotropic conduction electron spin... 

Electrically conductive materials can be made to be either isotropically conductive (IC) or anisotropically conductive (AIC). IC materials are the most common and conduct electricity in all directions. AIC materials conduct materials in one axis when compressed between two contact points. 

Electrically conductive adhesives may be isotropic (conduction equally in all directions) or anisotropic (conduction in the z-direction only). Both types are widely used in the assembly and packaging of electronics. 

Lu D, Tong QK, Wong CP. Conductivity mechanisms of isotropic conductive adhesives. IEEE Trans Electron Package Mfg. 1999 22(3). 

There are two types of conductive adhesives conventional materials that conduct electricity equally in all directions (isotropic conductors) and those materials that conduct in only one direction (anisotropic conductors). Isotropically conductive materials are typically formulated by adding silver particles to an adhesive matrix such that the percolation threshold is exceeded. Electrical currents are conducted throughout the composite via an extensive network of particle-particle contacts. Anisotropically conductive adhesives are prepared by randomly dispersing electrically conductive particles in an adhesive matrix at a concentration far below the percolation threshold. A schematic illustration of an anisotropically conductive adhesive interconnection is shown in Fig. 1. The concentration of particles is controlled such that enough particles are present to assure reliable electrical contacts between the substrate and the device (Z direction), while too few particles are present to achieve conduction in the X-Y plane. The materials become conductive in one direction only after they have been processed under pressure they do not inherently conduct in a preferred direction. Applications, electrical conduction mechanisms, and formulation of both isotropic and anisotropic conductive adhesives are discussed in detail in this chapter. 

Neither isotropic conductive adhesives nor conventional solder interconnections, can easily satisfy these requirements. 

Conductive adhesives are one of the feasible alternatives to lead for electronics assembly. Isotropically conductive adhesives are suitable for standard pitch (50- to 100-mil) surface-mounted components and numerous commercial materials are available (see commercial suppher Ksting, Section VI.E). Anisotropically conductive adhesives are more suited to flex to rigid connections, fine pitch components (15- to 20-mil pitch), and flip-chip assembly (4- to 12-mil pitch) [22]. Adhesives are not ready to replace solder throughout the electronics industry, however, due to questions that remain concerning the reliability of electrical interconnections. Their implementation is currently limited to low-cost applications using polyester substrates and specialty appHcations where solder cannot be used. Additionally, the lack of equipment for large-volume assembly with anisotropically conductive adhesives, which require the simultaneous appUcation of heat and pressure, impedes the acceptance of these promising materials. 

Experimental [23] as well as theoretical [24-26] studies of percolation phenomena have been reported. In random and macroscopically homogeneous materials it has been demonstrated [27-29] that at concentrations of metal particles below the percolation threshold (p < Pc) a short-range percolation coherence length, exists. Electrical conductivity is probable for length scales less than Thus even if the metal-filled composite exhibits no bulk electrical conductivity, conduction can occur within domains that are smaller than As the concentration of metal particles approaches oo and the composite becomes isotropically conductive. 

Another factor that influences the value of pc is the aspect ratios of the metallic filler. Metal fibres, metal-plated glass fibers, and metal flakes can significantly lower the concentration required to achieve isotropic conduction as compared to spherical powders [3]. Values of pc as low as 1 vol % have been reported with stainless steel fibers having an aspect ratio of 750 [37]. 

IV. FORMULATION OF ISOTROPICALLY CONDUCTIVE ADHESIVES A. Requirements and Performance... 

Table 2 lists the requirements for a type I (electrically conductive) adhesive and test results of a typical current generation isotropically conductive adhesive as reported by Estes [44]. These requirements specify test ranges for characteristics that will establish processing, performance, and reliability. 

Materials for use as anisotropically conductive adhesives must satisfy requirements even more stringent than those defined previously for isotropically conductive adhesives. No specifications, however, have been defined specifically for these materials. When used for flip-chip applications, the adhesive not only serves as a physical and electrical interconnection between the device and the substrate, but also serves as the environmental protection and passivation layer. This fact, combined with high adhesive concentrations, makes the ionic contamination levels of these materials more critical than for isotropic conductive adhesives. In addition, the processing of these materials has a greater influence on joint reliability as the anisotropic electrical properties develop only after heat and pressure are applied to the joint. 

To lower the probability of conduction in the X Y plane (i.e., reduce the short-range percolation coherence length ), particles are used with an aspect ratio as close to 1 as possible. In contrast, isotropically conductive systems use flakes with high aspect ratios as fillers. Particle size distributions are minimized so that each particle can potentially serve as an electrical bridge between substrate and device. 

When using isotropically conductive adhesives, placement of components is performed by the same equipment as used for nonadhesive attachment techniques. Die bonders are similar to those used for eutectic bonding except for the type of adhesive dispenser. Surface-mounted placement machines developed for solder paste assembly can also be... 

Most conductive adhesive failures are accelerated by elevated temperature and humidity. In a study of 12 commercially available isotropically conductive adhesives, joint resistance increased between 160 and 35,000% when exposed to 65°C and 85% relative humidity (65/85) [56]. However, some adhesive manufacturers claim resistance change of less than 10% after 1000 h at 60°C and 90% relative humidity [57] and less than 4% after 1000 h at 85/85 [58]. Anisotropically conductive adhesive joints are even more susceptible to early failures under accelerated test conditions due to process variations [16]. Reliability screening tests can be used effectively to iteratively optimize process parameters. 

Isotropically conductive adhesive interconnections can be repaired using techniques similar to those used for solder rework. By application of heat locally at a temperature above the T value, a section of adhesive can be softened and the device can be removed... 

The aim of the present study was to find methods of obtaining such anisotropically conducting samples. Two approaches were used modification of the morphology of CT complex in solidified isotropically conducting films and modification of the solidification process in order to obtain the desired effect on the arising morphology. 

The first approach which could lead to breaking up of conductive paths at some preferred direction was effected by mechanical deformation of isotropically conducting films and by treating the conductive samples with high-voltage electrical pulses. It was expected that the conductive paths of CT complex can be destroyed in one direction mechanically or as a result of the Joule-Lentz heat of the electrical pulses. 

It was shown in a earlier paper that from such a solution a good isotropically conducting films can be obtained. 

Conductive adhesives have a wide range of applications. Wu et al. [2006] worked on high-conductivity isotropic conductive adhesives (ICAs) filled with Ag NWs (p 50). The authors found that when the filler content reached 56 wt%, the bulk resistivity was seven times lower than that of traditional ICAs filled with microsized Ag fillers. 

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