^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Conductive adhesives are widely used in electronic packaging applications such as die attachment and solderless interconnections, component repair, display interconnections, and heat dissipation. The effects of film thickness as functions of filler volume fraction, conductive filler size, shape, as well as uncured adhesive matrix viscosity on the electrical conduction behavior of epoxy-based adhesives are presented in this work. For this purpose, epoxy-based adhesives were prepared using conductive fillers of different size, shape, and types, including Ni powder, flakes, and filaments, Ag powder, and Cu powder. The filaments were 20 μm in diameter, and 160 or 260 μm in length. HCl and H_{3}PO_{4} acid solutions were used to etch and remove the surface oxide layers from the fillers. The plane resistance of filled adhesive films was measured using the four-point method. In all cases of conductive filler addition, the planar resistivity levels for the composite adhesive films increased when the film thickness was reduced. The shape of resistivity-thickness curves was negative exponential decaying type and was modeled using a mathematical relation. The relationships between the conductive film resistivities and the filler volume fractions were also derived mathematically based on the experimental data. Thus, the effects of surface treatment of filler particles, the type, size, shape of fillers, and the uncured epoxy viscosity could be included empirically by using these mathematical relations based on the experimental data. By utilizing the relations we proposed to model thickness-dependent and volume fraction-dependent conduction behaviors separately, we were able to describe the combined and coupled volume fraction-film thickness relationship mathematically based on our experimental data.

Over the past decades, the use of electrically conductive adhesive (ECA's) has expanded rapidly in the microelectronics industry. The major applications for ECA's are die attachment, liquid crystal display (LCD), and surface-mounted assembly of packaged components on printed wiring board (PWB's). ECA's can be used as solder replacement, interconnection, sealing, electrical shielding, various electronic components bonding, fastening and brazing [

Unlike other types of adhesives, electrically conductive adhesives perform two primary functions. First, conductive adhesives form joints with sufficient strength so that they can bond two surfaces, and second, an electrical interconnection is formed between the two bonded surfaces. This dual functionality is usually achieved in composite form by dispersion of particles in an insulating adhesive matrix [^{4} Ω-cm (Ohm-cm), which is about two orders of magnitude higher than the best metallic conductors. The metal fillers, which are added to the epoxy resin usually improve its other properties such as strength, thermal conductivity

Compared to traditional tin/lead (Sn/Pb) soldering technology, conductive adhesive joining technology offers many advantages, such as: (i) lower sensitivity to thermo-mechanical stresses, due to higher flexibility than solder; (ii) lower cure temperature enabling the use of heat sensitive or non-solderable materials; (iii) high resolution capability for fine-pitch interconnections due to smaller particle size than solder pastes; (iv) simple processing, and thereby lower cost; and (v) environmental compatibility [

Despite the achievements so far, the conductive adhesive joining technology still has some problems. The major ones being conductivity lower than solder, sensitivity to type and quality of component and board metallization, longer curing times, and the question of durability in various climatic environments. The processing parameters, such as temperature, pressure, cure time, pot and shelf life are critical to the success of making reliable electrical and mechanical interconnections. A conductive adhesive joint may fail in many different ways [

Composite material properties, which result when conductive particles are dispersed into a polymer matrix, are influenced by the particle volume fraction. The main interest has been focused on the critical volumetric concentration of filler at which the composite resistivity drops suddenly from the high value of matrix to a value orders of magnitude lower [

In ECA's, the conductive paths are formed by metal particles. These particles must initially make intimate contact (physical and tunneling) and form a conductive chain, which transports electrons [

Several factors are known to affect the magnitude of the threshold volume fraction, such as particle size distribution, particle shape, and pre-treatment of particle. For different conductive adhesive systems, different fillers result in different adhesive resistivity behavior, along with the limitation imposed by the adhesive film thickness.

This work is concerned with the modeling of thickness-dependent conduction behavior of epoxy adhesives with different volume fractions of particle fillers, which have different size, shape, and type.

In metal-polymer composite systems, three situations are possible: no contact, close proximity and physical contact between the conductive particles [

When a sufficient amount of conductive filler is loaded into an insulating polymer matrix, the composite transforms from an insulator to a conductor, the result of continuous linkages of filler particles. Assuming a random dispersion of the conductive filler, as its concentration increases, no significant change occurs until a critical concentration (volume fraction) V_{c} is reached. This point where the electrical resistivity decreases dramatically, called the

The probability of a continuous network being formed by filler particles in a matrix is related to the statistical average number of contacts each particle makes with neighboring particles and the maximum number of contacts per particle that are possible [_{c} is the critical probability of network formation, and Z is the maximum number of possible contacts, or coordination number (see _{p} for a random dispersion of spheres in a matrix is 1.5. For spherical particles, C_{p} is apparently a constant.

The volume percentage of metal filler, P, in a matrix can be related to the average number of contacts per filler particle _{p} = f (P_{c}). We assume a linear relationship [_{m} is the maximum packing fraction of the filler in the matrix. Combining the above two equations, we get:

For a random mixture of spheres, we have: C_{p} = 1.5, Z = 6, and P_{m} = 0.637. Therefore, P_{c} is 0.159. This value is much lower than the experimental values. Based on this observation, Jantzen proposed [

At the critical loading for network formation, we have:

For the random sphere case as above, P_{c} is 0.305, which also represents the critical concentration (volume fraction), V_{c}, for the filler particles. This represents the point at which network formation begins and the sharp drop in resistivity starts. These equations do not adequately account for preparation technique, particle size distribution, or particle-particle interaction effects.

Network formation theories for flakes, fibers, and other irregular shapes are even less well developed. For irregular fillers with a completely random distribution, the critical value of P_{c} is assumed to be the same as that for spherical fillers [

Wei and Sancaktar [_{i}) of conductive adhesive paths between the conductive particles incorporated in the adhesive matrix. The average length of conductive paths can be defined as:
_{i} is the directional variable. Statistically, the conductive path factor is inversely proportional to the volume fraction. This implies that the average conductive path's length increases with decreasing volume fraction.

The resistivity of the filled adhesives containing spherical particles can be expressed by:
_{s} is the contact resistance, and m is the average contact number, which is a function of the particle volume fraction. Using computer simulation, Wei and Sancaktar determined the following functional relation between m and Φ [

The contact resistance R_{s} can be determined [

The constriction resistance is given by
_{1}, and ρ_{2} are resistivities of the two particles in contact, and a is the contact area. The tunnel resistance, R_{t} is given by,
_{σ} (Ω m^{2}) defines the tunnel resistivity.

In our research, epoxy resins (Epon 815C and Epon 830), and the curing agent (Diethylenetriamine DETA), obtained from Shell Chemical Company (Houston, Texas) were used. Epon 830, which is a DGEBA type epoxy, had an epoxide equivalent weight of 190–198, and viscosity of 170–225 poise. Epon Resin 815C is liquid bisphenol A based epoxy resin containing n-butyl glycidyl ether. It had an epoxide equivalent weight of 180–195, and viscosity of 5–7 poise.

The following conductive particles were used in experiments: Ag powder (4–7 μm), Ni powder (3–7 μm, see

HCl and H_{3}PO_{4}, provided by EM Science (Gibbstown, NJ) were used for etching purposes.

The preparation of the conductive adhesive was done as follows: First, the required amount of conductive particles was thoroughly mixed manually with epoxy resin. Then, as recommended by Turgut and Sancaktar [

In order to remove the surface oxide layer, the nickel and copper particles were etched with 10% Hydrochloric acid (HCl) and 20% Phosphoric acid (H_{3}PO_{4}) respectively [

Electrical resistances of conductive adhesive were measured by employing the standard four-point probe method under laboratory conditions. The apparatus used was Micro-ohmmeter (Model 580, Keithley Instruments, Inc., Cleveland, Ohio). Resistivity was calculated from the bulk resistance of the ECA specimen. Two strips of an adhesive tape were applied (as a mold) onto a precleaned glass slide with a gap between these two strips. A conductive paste was then spread within the space by means of a doctor blade. The narrow sides of the film were covered with aluminum foils to facilitate measurement with the four-point probe. After cure, the bulk resistance of this ECA strip was measured by using a Keithley Micro-ohmmeter with a four-point probe. The effect of the mixture of different metal fillers, volume fraction, and thickness on the resistivity of the ECA was observed.

The film resistivity (ρ) was calculated by using the relation,

Experimental results for the thickness dependent conduction behavior are shown in _{c}, increases (see

The shape of resistivity-thickness curves is negative exponential decaying type. To describe this behavior, the function,

Based on the adhesive thickness-resistivity data, and

The thickness dependent resistivity behavior of conductive adhesive films containing three different volume fractions of nickel flakes are shown in

Comparison of

As mentioned before, two kinds of Epoxy resin were used in the experiments.

For the behavior of approximately spherical shaped powder particles, the results are shown in

For the nickel and copper powders, oxide removal treatment also has a significant effect in reducing adhesive resistivity. Especially for untreated copper particles, no conduction can be obtained in the adhesive films without etching the particles. Comparison of

For the same volume fraction of nickel powder loading, the Epon 815C resin has a higher resistivity level than Epon 830 resin. Comparison of

For the case of nickel filament addition,

For the same amount of 160 μm filaments loading, the resistivity level is less with the Epon 830 resin than the Epon 815C resin. Comparison of

For nickel filaments with 260 μm length, comparison of

For the same amount of 260 μm filaments loading, the resistivity level is less with the Epon 830 resin in comparison to the Epon 815C resin. Comparison of

Our results on the thickness-dependent resistivity behavior of conductive particle filled epoxy resins reveal that the values of the governing

Examination of

Volume fraction-thickness dependent resistivity behaviors of etched nickel flake filled conductive adhesive films of three different thicknesses are shown in

By comparing

The results for film resistivity behavior with powder particles are shown in

For unetched Ni powder with Epon 815C resin, increasing the film thickness from 0.04 cm to 0.06 cm, results in 9% and 6% decreases in A and n values, respectively, and a further increase to 0.14 cm, results in 27% and 26% reductions, respectively (

When we use Ag powder with Epon 815C resin, increasing the film thickness from 0.04 cm to 0.06 cm, results in 11% and 17% decreases in A and n values, respectively, and a further increase to 0.14 cm, results in 25% and 40% reductions in parameters A and n (

The effects of powder particle etching can be further illustrated by comparison of

For the nickel powder (

For the case of nickel filament addition,

When we use unetched nickel filaments of 160 μm length in Epon 815C resin, increasing the film thickness from 0.06 cm to 0.19 cm, results in 78% decrease in the A value, and 27% increase in the n value (

For the nickel filaments of 260 μm length, when we use unetched particles with Epon 815C resin, increasing the film thickness from 0.06 cm to 0.19 cm, results in 79% decrease in the A value, and 22% increase in the n value (

At equal concentration, the unetched nickel filaments produce higher resistivity compare to the etched filaments. For the nickel filaments of 160 μm length, the values of the parameter A with the etched particles dropped dramatically by as much as 94% (t = 0.19 cm) for the Epon 815C system (

Comparing Epon 830 resin with 815C, for the same thickness of adhesive film, the 260 μm nickel filaments approximately follow the same trend as nickel flakes, nickel powder, and silver powder. The parameter A has lower values with Epon 815C resin than Epon 830 resin. The average difference is as much as 17% with unetched filaments, and 4% with etched filaments. On the other hand, Epon 815C has higher values for exponent n in comparison to Epon 830. The average difference is as much as 16% with unetched filaments, and 6% with etched filaments. As for 160 μm nickel filaments, the results display a mixed trend. Going from Epon resin 815C to 830, the values of parameter A increase by as much as 22% (average), and exponent n increase by as much as 4% (average) with the unetched filaments. For the etched 160 μm Ni filaments, again going from Epon 815C to 830, the values of parameter A increase by as much as 45% (t = 0.08 cm), and the values of exponent n decrease by 13% (t = 0.19 cm).

In all, we can conclude that the values of the parameters A and n are affected by the thickness of adhesive film, etch treatment, pre-polymer viscosity, particle type and particle shape.

Earlier, we discussed the thickness dependent conduction behavior (Section 3.1). To describe that behavior,

Since a, b, and c are functions of the volume fraction Φ, and A and n are functions of thickness t,

In order to model the volume fraction-film thickness behavior mathematically based on our experimental data, we assumed that each parameter can be represented by an equation of the type:

This particular mathematical form was chosen, because it is the simplest function which efficiently represents the data available. For example, with etched nickel flakes in Epon 815C system, we get 3 data points from

The calculation procedure can be illustrated by the following set of quadratic equations representing the volume fraction (Φ) dependent behavior of parameter a (

Simultaneous solution of equation set (19) results in: e = 39, f = −38, g = 9.3. Therefore, we have, ^{2} − 38*Φ + 9.3. The functions, b(Φ), c(Φ), A(t) and n(t) can be obtained similarly.

Subsequent to these calculations,

The parameters e, f and g of

The major objective of this work was to study the conduction behavior of epoxy conductive adhesives with different volume fraction of particle fillers of different size, shape, and type. Two different epoxy adhesives (Epon 815C and Epon 830) of viscosities with 30-fold difference were used as the matrix material. As for conductive fillers, the following conductive particles of various shapes were used: Ag powder (4–7 μm), Ni powder (3–7 μm), Ni flakes (1–5 μm), Cu powder (6–7 μm), Ni filaments (20 μm diameter with 160 μm or 260 μm length). The effects of etching the filler particles were also considered. The results of this work lead to the following conclusions:

For the film thickness dependent conduction behavior, the resistivity levels are reduced as the adhesive film thickness increases. Conversely, when the thickness is reduced significantly, the effective coordination number, Z is reduced, and therefore, the critical volume fraction requirement for network formation, P_{c}, increases. Therefore, a significant increase in resistivity is observed coupled with a significant increase in the slope of the resistivity-thickness curve. The shapes of the resistivity-thickness curves are similar and typical, presenting a negative exponential shape.

For the particle volume-fraction dependent conduction behavior, the resistivity levels were reduced with increasing volume fraction. The shapes of resistivity-volume fraction curves are typical and display a negative power function curve.

Due to the presence of non-conducting nickel oxide, the unetched nickel particles always have higher resistivity than the etched ones. Similarly, the presence of copper oxide results in high resistivity for copper particles.

For the three different types of metal powders investigated, the order of film conductivity, from high to low was: silver, copper and nickel.

As for the effect of particle shape on the adhesive film resistivity, we found that the order from high to low conductivity was: nickel filaments of 260 μm length, nickel filaments of 160 μm length, nickel flakes, and nickel powder. Thus, we can conclude that the particle aspect ratio is an important parameter in affecting the adhesive film resistivity; as the aspect ratio increases, the filled adhesive film resistivity decreases. Obviously, when the particle aspect ratio increases, the effective coordination number, Z also increases, and therefore, the critical volume fraction requirement for network formation, P_{c}, decreases.

The parameters a, b and c, which are the coefficients of the exponentially decaying fitting function for the thickness-dependent conduction behavior, were found to be dependent on the particle filler volume fraction, etch treatment, prepolymer viscosity, particle type, and particle shape. For the unique case for nickel flakes, the coefficient c remained almost constant.

The values of A and n, which are the parameters of the mathematical relation used for describing the volume fraction-dependent conduction behavior, were found to depend on the thickness of the adhesive film, etch treatment, prepolymer viscosity, particle type, and particle shape. The values of the parameter A were found to be more sensitive to these factors than the exponent n.

By utilizing the mathematical relations we proposed to model thickness-dependent and volume fraction-dependent conduction behaviors separately, we were able to describe the combined and coupled volume fraction-film thickness relationship mathematically based on our experimental data.

Contact configuration of spheres in hexagonal packing.

SEM photomicrographs of Ni powder (3–7 μm), as received (

Thickness-dependent resistivity of Epon 815C films filled 35%, 42% and 50% by volume with unetched nickel flakes (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Thickness-dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

Volume fraction-thickness dependent resistivity of Epon 815C (

The material parameters of the decaying exponential function ρ=a+b × Exp (−ct) thickness-dependent conduction behavior with various conductive particles in Epon 815C resin.

^{−1}) |
|||||
---|---|---|---|---|---|

Unetched Ni flake | 35 | 537.2 | 21,456 | 44.2 | 87.8 |

42 | 460.7 | 19,830 | 47.7 | 91.5 | |

50 | 360.4 | 12,370 | 46.6 | 92.1 | |

Etched Ni flake | 35 | 0.80 | 13.9 | 46.8 | 95.1 |

42 | 0.25 | 3.5 | 47.6 | 91.3 | |

50 | 0.09 | 1.2 | 43.2 | 92.6 | |

Unetched Ni powder | 35 | 454.2 | 43,436.4 | 53.6 | 90.1 |

50 | 196.2 | 35,054.8 | 50.4 | 87.1 | |

60 | 7.61 | 18,490.3 | 44.5 | 84.4 | |

Etched Ni powder | 35 | 60.7 | 8,483.9 | 45.9 | 96.5 |

50 | 43.3 | 3,038.9 | 42.7 | 90.4 | |

60 | 4.31 | 1,399.5 | 36.8 | 89.1 | |

Ag powder | 35 | 2.9 | 250.9 | 85 | 94.2 |

50 | 0.8 | 10.1 | 49.3 | 84.5 | |

60 | 0.1 | 0.8 | 23.9 | 97.7 | |

Etched Cu powder | 40 | 36.2 | 395 | 50.5 | 98.0 |

50 | 3.9 | 50.4 | 25.9 | 92.3 | |

60 | 0.1 | 12.6 | 23.1 | 91.8 | |

Unetched Ni filament (160 μm) | 35 | 0.27 | 1.37 | 17.9 | 98.2 |

50 | 0.07 | 0.52 | 14.1 | 97.9 | |

60 | 0 | 0.11 | 5.6 | 63.4 | |

Etched Ni filament (160 μm) | 35 | 0.0063 | 0.1 | 25.5 | 94.5 |

50 | 0.0045 | 0.08 | 19.4 | 91.6 | |

60 | 0.0003 | 0.02 | 17.4 | 96.1 | |

Unetched Ni filament (260 μm) | 35 | 0 | 1.03 | 14.2 | 80.6 |

50 | 0 | 0.41 | 6.4 | 75.3 | |

60 | 0 | 0.26 | 6.5 | 75.3 | |

Etched Ni filament (260 μm) | 35 | 0.0036 | 0.039 | 21.9 | 95.9 |

50 | 0.0026 | 0.016 | 17.7 | 94.7 | |

60 | 0.0001 | 0.011 | 14.6 | 94.8 |

The material parameters of the decaying exponential function ρ=a+b × Exp (−ct) thickness-dependent conduction behavior with various conductive particles in Epon 830 resin.

^{−1}) |
|||||
---|---|---|---|---|---|

Unetched Ni flake | 50 | 515.8 | 10,215 | 44.6 | 98.1 |

Etched Ni flake | 25 | 0.57 | 15.4 | 47.2 | 93.5 |

35 | 0.19 | 1.24 | 41.7 | 92.4 | |

50 | 0.05 | 0.96 | 42 | 88.0 | |

Unetched Ni powder | 35 | 270.9 | 15,064.8 | 54.2 | 93.6 |

50 | 230.2 | 13,980.7 | 54.4 | 96.6 | |

60 | 0 | 678.3 | 15.5 | 59.9 | |

Etched Ni powder | 35 | 46.5 | 6,355.9 | 43 | 97.6 |

50 | 39.8 | 2,088.8 | 41 | 66.1 | |

60 | 0 | 41.9 | 10.3 | 59.5 | |

Ag powder | 35 | 0 | 2.3 | 4.1 | 57.1 |

50 | 0 | 0.8 | 0.9 | 96.5 | |

60 | 0 | 0.1 | 0.5 | 61.7 | |

Etched Cu powder | 40 | 19.1 | 3,217.6 | 83.4 | 92.9 |

50 | 0.01 | 37 | 23.7 | 88.0 | |

60 | 0 | 3.8 | 18.8 | 85.0 | |

Unetched Ni filament (160 μm) | 35 | 0.22 | 0.79 | 19.1 | 96.0 |

50 | 0.05 | 0.29 | 9.52 | 99.1 | |

60 | 0.02 | 0.26 | 8.4 | 94.4 | |

Etched Ni filament (160 μm) | 35 | 0.0042 | 0.049 | 21.2 | 93.8 |

50 | 0.0021 | 0.038 | 18.2 | 92.3 | |

60 | 0.0001 | 0.011 | 16.4 | 95.1 | |

Unetched Ni filament (260 μm) | 35 | 0.16 | 0.52 | 10.5 | 97.9 |

50 | 0 | 0.23 | 5.4 | 85.2 | |

60 | 0 | 0.21 | 4.8 | 94.7 | |

Etched Ni filament (260 μm) | 35 | 0.0027 | 0.035 | 14.8 | 93.2 |

50 | 0.0001 | 0.016 | 11.1 | 93.0 | |

60 | 0 | 0.004 | 9.4 | 77.3 |

The material parameters of the 2-parameter power function ρ = A/Φ^{n}, describing the volume fraction (Φ)-dependent conduction behavior with various conductive particles in Epon 815C resin.

Etched Ni flake | 0.04 | 0.0015 | 7.24 | 93.4 |

0.06 | 0.0012 | 6.88 | 92.8 | |

0.14 | 0.0008 | 6.69 | 91.9 | |

Unetched Ni powder | 0.04 | 19.9000 | 4.84 | 98.4 |

0.06 | 18.2000 | 4.57 | 81.8 | |

0.14 | 14.5000 | 3.55 | 79.6 | |

Etched Ni powder | 0.04 | 12.9000 | 4.38 | 93.4 |

0.06 | 5.3000 | 4.50 | 88.5 | |

0.14 | 5.2000 | 2.55 | 64.2 | |

Ag powder | 0.03 | 0.0650 | 5.47 | 79.1 |

0.05 | 0.0580 | 4.53 | 83.7 | |

0.13 | 0.0490 | 3.28 | 77.3 | |

Cu powder | 0.04 | 1.1100 | 4.66 | 80.5 |

0.06 | 0.9600 | 4.50 | 73.5 | |

0.15 | 0.7000 | 4.41 | 76.6 | |

Unetched Ni filament (160 μm) | 0.06 | 0.0500 | 2.51 | 98.6 |

0.08 | 0.0430 | 2.55 | 99.6 | |

0.19 | 0.0106 | 3.20 | 82.9 | |

Etched Ni filament (160 μm) | 0.06 | 0.0038 | 1.85 | 83.2 |

0.08 | 0.0014 | 2.64 | 98.2 | |

0.19 | 0.0006 | 2.35 | 73.9 | |

Unetched Ni filament (260 μm) | 0.06 | 0.0340 | 2.80 | 94.2 |

0.08 | 0.0270 | 2.97 | 93.9 | |

0.19 | 0.0071 | 3.60 | 84.9 | |

Etched Ni filament (260 μm) | 0.06 | 0.0013 | 2.52 | 96.3 |

0.08 | 0.0011 | 2.57 | 94.5 | |

0.19 | 0.0005 | 2.46 | 76.3 |

The material parameters of the 2-parameter power function ρ = A/Φ^{n}, describing the volume fraction (Φ)-dependent conduction behavior with various conductive particles in Epon 830 resin.

Etched Ni flake | 0.04 | 0.0069 | 4.33 | 77.2% |

0.06 | 0.0067 | 3.90 | 80.5% | |

0.14 | 0.0046 | 3.55 | 92.6% | |

Unetched Ni powder | 0.04 | 551.7000 | 1.57 | 92.4% |

0.06 | 362.3000 | 1.23 | 93.1% | |

0.14 | 97.6000 | 1.21 | 90.9% | |

Etched Ni powder | 0.04 | 49.1000 | 3.02 | 92.6% |

0.06 | 25.8000 | 2.88 | 97.0% | |

0.14 | 7.8400 | 2.34 | 74.0% | |

Ag powder | 0.03 | 0.1200 | 3.94 | 68.2% |

0.05 | 0.1100 | 3.91 | 38.5% | |

0.13 | 0.0100 | 1.54 | 62.5% | |

Cu powder | 0.04 | 0.1200 | 6.58 | 75.0% |

0.06 | 0.1100 | 6.03 | 77.4% | |

0.15 | 0.0800 | 5.90 | 64.9% | |

Unetched Ni filament (160 μm) | 0.06 | 0.0370 | 2.41 | 92.7% |

0.08 | 0.0290 | 2.51 | 87.0% | |

0.19 | 0.0099 | 3.03 | 81.6% | |

Etched Ni filament (160 μm) | 0.06 | 0.0023 | 1.95 | 80.5% |

0.08 | 0.0016 | 2.11 | 81.2% | |

0.19 | 0.0003 | 2.96 | 77.7% | |

Unetched Ni filament (260 μm) | 0.06 | 0.0420 | 2.21 | 90.5% |

0.08 | 0.0360 | 2.29 | 89.5% | |

0.19 | 0.0071 | 3.36 | 87.5% | |

Etched Ni filament (260 μm) | 0.06 | 0.0014 | 2.29 | 90.5% |

0.08 | 0.0011 | 2.49 | 92.0% | |

0.19 | 0.0002 | 2.91 | 80.7% |

The parameters e, f and g of

Epon 815C | Etched Ni flake | e | 39.00 | 799.0 | −443.0 |

f | −38.00 | −764.0 | 352.0 | ||

g | 9.30 | 183.0 | −22.3 | ||

Epon 815C | Unetched Ni powder | e | 342.1 | 226,000 | 77.7 |

f | −2,262.2 | −415,000 | −144.4 | ||

g | 1,241.8 | 186,000 | 103.2 | ||

Etched Ni powder | e | 560 | −41,000 | 77.7 | |

f | −1,010 | 29,000 | −144.4 | ||

g | 410 | −1,000 | 95.5 | ||

Epon 815C | Ag powder | e | −14.4 | −3,100 | 33 |

f | 8.9 | 3,300 | −290.3 | ||

g | −0.03 | −880 | 186.2 | ||

Epon 815C | Etched Cu powder | e | 1,430 | 15,300 | 1.09 |

f | −1,610 | −17,300 | −1.23 | ||

g | 450 | 4,800 | 0.37 | ||

Epon 815C | Unetched Ni filament (160 μm) | e | −1.3 | −3.2 | 123 |

f | 0.7 | −0.55 | −220.3 | ||

g | 0.03 | 1.6 | 93.5 | ||

Etched Ni filament (160 μm) | e | 0.06 | 27.1 | 1,680 | |

f | −0.11 | −38 | −2,360 | ||

g | 0.04 | 13.1 | 830 | ||

Epon 815C | Unetched Ni filament (260 μm) | e | 0 | −3 | −77 |

f | 0 | 2.7 | 124.7 | ||

g | 0 | −0.4 | −40.6 | ||

Etched Ni filament (260 μm) | e | 0.05 | −0.17 | −129.9 | |

f | −0.08 | 0.14 | −173.9 | ||

g | 0.03 | −0.01 | 72.2 |

The parameters e, f and g of

Epon 830 | Etched Ni flake | e | 11.50 | 559.0 | 228.0 |

f | −107.00 | −447.0 | −191.8 | ||

g | 2.52 | 99.7 | 80.9 | ||

Epon 830 | Unetched Ni powder | e | 4,190 | 259,000 | 800 |

f | −6,910 | −418,000 | −1,300 | ||

g | 2,640 | 158,000 | 490 | ||

Etched Ni powder | e | 730 | −16,500 | 611.7 | |

f | −1,200 | −2,400 | −982.9 | ||

g | 460 | 7,400 | 379.5 | ||

Epon 830 | Ag powder | e | 0 | −6.2 | −35.7 |

f | 0 | −0.2 | 35.3 | ||

g | 0 | 2.4 | −7.82 | ||

Epon 830 | Etched Cu powder | e | 950 | 1.57 | 2,740 |

f | −1,050 | −1.73 | −3,060 | ||

g | 290 | 0.47 | 870 | ||

Epon 830 | Unetched Ni filament (160 μm) | e | −1.72 | −10.4 | −521 |

f | 1.59 | 13.1 | 761.9 | ||

g | −0.32 | −3.67 | −241.2 | ||

Etched Ni filament (160 μm) | e | 0.012 | 0.89 | 339.5 | |

f | −0.034 | −1.39 | −491.5 | ||

g | 0.016 | 0.52 | 189.1 | ||

Epon 830 | Unetched Ni filament (260 μm) | e | −2.41 | −4.4 | −284.5 |

f | 2.75 | 5.04 | 417 | ||

g | 0.77 | −1.19 | −132 | ||

Etched Ni filament (260 μm) | e | −0.03 | −0.014 | −15.8 | |

f | 0.04 | −0.105 | 0.39 | ||

g | −0.01 | 0.72 | 14.9 |

The parameters e, f and g of

Etched Ni flake | Epon 815 | e | 0.1000 | 156.3 |

f | −0.0250 | −33.6 | ||

g | 0.0020 | 8.3 | ||

Unetched Ni powder | Epon 815 | e | 387.5000 | 7.5 |

f | −123.8000 | −14.3 | ||

g | 24.2000 | 5.4 | ||

Etched Ni powder | Epon 815 | e | 3790.0000 | −303.80 |

f | −760.0000 | 36.40 | ||

g | 40.0000 | 3.41 | ||

Ag powder | Epon 815 | e | 2.3800 | 313.80 |

f | −0.5400 | −72.10 | ||

g | 0.0800 | 7.40 | ||

Etched Cu powder | Epon 815 | e | 41.9000 | 63.60 |

f | −11.7000 | −14.40 | ||

g | 1.5000 | 5.13 | ||

Unetched Ni filament (160 μm) | Epon 815 | e | 0.4300 | 30.10 |

f | −0.4100 | −2.21 | ||

g | 0.0700 | 2.53 | ||

Etched Ni filament (160 μm) | Epon 815 | e | 0.8700 | −324.10 |

f | −0.2400 | 84.90 | ||

g | 0.0200 | −2.08 | ||

Unetched Ni filament (260 μm |
Epon 815 | e | 1.3000 | −21.30 |

f | −0.5300 | 11.50 | ||

g | 0.0600 | 2.19 | ||

Etched Ni filament (260 μm) | Epon 815 | e | 0.0350 | −26.90 |

f | −0.0150 | 6.30 | ||

g | 0.0020 | 2.24 |

The parameters e, f and g of

Etched Ni flake | Epon 830 | e | −0.0630 | 171.3 |

f | 0.0060 | −38.6 | ||

g | 0.0070 | 5.6 | ||

Unetched Ni powder | Epon 830 | e | 61,600.0000 | 167.5 |

f | −15,600.0000 | −33.8 | ||

g | 1,100.0000 | 2.65 | ||

Etched Ni powder | Epon 830 | e | 9,410.0000 | 2.50 |

f | −2,110.0000 | −7.30 | ||

g | 120.0000 | 3.30 | ||

Ag powder | Epon 830 | e | −7.5000 | −281.30 |

f | 0.1000 | 21.00 | ||

g | 0.1200 | 3.56 | ||

Etched Cu powder | Epon 830 | e | 1.5100 | 236.90 |

f | −0.6500 | −51.20 | ||

g | 0.1400 | 8.24 | ||

Unetched Ni filament (160 μm) | Epon 830 | e | 1.7400 | −2.10 |

f | −0.6400 | 5.30 | ||

g | 0.0700 | 2.10 | ||

Etched Ni filament (160 μm) | Epon 830 | e | 0.1800 | −2.20 |

f | −0.0600 | 8.30 | ||

g | 0.0050 | 1.50 | ||

Unetched Ni filament (260 μm) | Epon 830 | e | 0.2900 | 44.10 |

f | −0.3400 | −2.20 | ||

g | 0.0600 | 2.20 | ||

Etched Ni filament (260 μm) | Epon 830 | e | 0.0520 | −47.60 |

f | −0.0220 | 16.70 | ||

g | 0.0030 | 1.46 |