RESEARCH ARTICLE | MARCH 30 2022 Thermal transport in silver-coated polymer sphere composites by the bidirectional 3ω method Susanne Sandell; Thorstein Wang; Emigdio Chávez-Ángel; ... et. al Journal of Applied Physics 131, 125107 (2022) https://doi.org/10.1063/5.0080682 CrossMark   View Export Online Citation Articles You May Be Interested In Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf Exploring non-linear correlators on AGP J. Chem. Phys. (February 2021) Construction of linearly independent non-orthogonal AGP states J. Chem. Phys. (March 2021) AGP: Search for the consistent RPA reference state AIP Conference Proceedings (June 2012) Journal of METHOD scitation.org/journal/jap Applied Physics Thermal transport in silver-coated polymer sphere composites by the bidirectional 3ω method Cite as: J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 Submitted: 2 December 2021 · Accepted: 12 March 2022 · View Online Export Citation CrossMark Published Online: 30 March 2022 Susanne Sandell,1 Thorstein Wang,1 Emigdio Chávez-Ángel,2 Helge Kristiansen,1,3 Zhiliang Zhang,1 and Jianying He1,a) AFFILIATIONS 1 NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf 7491 Trondheim, Norway 2 Catalan Institute of Nanoscience and Nanotechnology (ICN2), (ICN-CSIC) Barcelona, Campus UAB, E08193 Bellaterra, Spain 3 Conpart AS, NO-2013 Skjetten, Norway a) Author to whom correspondence should be addressed: jianying.he@ntnu.no ABSTRACT The bidirectional 3ω method is an electrothermal technique that is commonly used to obtain the thermal conductivity of materials such as liquids, biological samples, and pastes. In this work, an epoxy-based adhesive was filled with monodisperse 10 μm polymethyl methacrylate spheres coated with silver thin films (AgPS), such that a metallic network that dominated the thermal transport was formed through the composite. The bidirectional 3ω method was used to obtain the thermal conductivity of the conductive adhesive at different volume frac- tions of AgPS. For 50 vol.% AgPS, corresponding to 3.4 vol.% silver, the thermal conductivity was 2:03 + 0:21 W m−1 K−1. The results show that the thermal conductivity is strongly correlated with the AgPS volume fraction, while maintaining a volume fraction of silver far below the commercial silver paste, which has typical filler fractions of 40 vol.% silver. The results of this work were compared to thermal measure- ments of the same material by other techniques, and advantages and disadvantages of the methods were finally discussed. Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0080682 I. INTRODUCTION fraction is high enough to form an electrically conductive percolat- Thermal management is critical to the lifetime, performance, ing network in all directions through the matrix, the composite is and reliability of electronic devices.1–4 In order to avoid overheat- called an isotropic conductive adhesive (ICA). ICAs are an environ- ing, it is desirable to increase the heat dissipation, both at the mentally friendly alternative to soldering as they are lead-free, and “local” single transistor level as well as at the “global” electronic they are typically used for material systems that require lower pro- packaging levels.5 Polymers are widely used in electronic packaging cessing temperatures. They can also be applied to materials that are as the matrix material in composites, such as thermal interface difficult to wet with traditional solders, such as glass and ceramics. materials6 and conductive adhesives.7 The bulk thermal conductiv- Conventional ICAs are composed of an adhesive matrix with ity of most polymers is very low, on the order of 0.1– embedded metal flakes or particles for both electrical and thermal 0.5 W m−1 K−1 , which limits their heat dissipation capabilities.8 To conductivity. Due to their excellent electrical and thermal proper- increase the thermal and/or electrical conductivity of conductive ties, silver particles are often used. Although increased electrical adhesives, conductive fillers are often added to the polymer matrix. conductivity (σ) is often the goal when optimizing ICA processes, These fillers can be carbon-based, metallic, ceramic or, more this article will focus solely on increasing thermal conductivity (κ). recently, boron nitride-based.7 The electrically conductive filler par- Conventional ICAs require a high silver content, up to 40 vol.%, to ticles form a percolating network through the polymer adhesive achieve thermal conductivities at around κ  3 W m−1 K−1 using matrix, significantly increasing the electrical and thermal conduc- the laser flash (LF) technique.10 tivity.9 In order to form the percolating network, a filler fraction of In order to reduce the silver content, monodisperse micron- between 25 and 40 vol.% is usually required. When the filler sized polymer spheres coated with thin silver films (AgPS) J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 131, 125107-1 Published under an exclusive license by AIP Publishing Journal of METHOD scitation.org/journal/jap Applied Physics embedded in epoxy have proven themselves as a viable alternative The thermal conductivity κ of the substrate is then given by23,24 to the conventional ICAs.11–20 This material system, hereafter referred to as AgPS-ICA, has a large advantage over the conven- ðb ð1 1 Pl sin2 (kb) tional ICAs due to the significant reduction in costly silver. ΔT2ω ¼ ΔT2ω (x)dx ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dk, (3) 2b b πκ 0 (kb)2 k2 þ q2 AgPS-ICAs have yielded thermal conductivities similar to the conventional ICAs at Ag filler fractions of around 3 vol.% measured where b is the half-width of the heater, κ is the substrate’s thermal using both steady state (SS) and LF techniques.21,22 For both conductivity, and Pl is the AC power per unit length of the heater. methods, a clear correlation was observed between AgPS volume qffiffiffiffiffi fraction and thermal conductivity. However, for larger AgPS The integration variable, k, is the wavenumber. q ¼ i2ω α , and α is volume fractions (.40 vol.%), values measured by the SS method the thermal diffusivity. The quantity lth ¼ j 1q j is the thermal penetra- are consistently around 35% higher than those measured by the tion depth, which is the depth at which the thermal wave propagates transient LF method. This discrepancy is possibly due to the volu- into the substrate during one cycle of AC heating. κ is found by least metric constraint exerted on the sample during curing and mea- squares fitting of the measured temperature drop in Eqs. (1)–(3). surement by the SS method. However, the thermal transport The conventional 3ω method requires microfabrication of the mechanisms of this novel AgPS-ICA need further investigation,22 heater on top of the sample to be measured, which requires the and the best suited thermal characterization technique is yet to be sample to be solid, dry, and flat. While useful for thin films and found. Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf rigid substrates, it is impractical for a wide range of samples. The In this work, we measured the thermal conductivity of bidirectional 3ω method was developed26–29 in order to measure AgPS-ICAs using a self-built electrothermal characterization tech- thermal conductivity for samples such as nanofluids,30 biological nique, commonly referred to as the 3ω method. To the best of our tissues,31 and thermal pastes.32 It allows for the sample to be knowledge, this is the first attempt at thermal characterization of deposited onto a platform where the heater is already deposited this novel ICA by 3ω. The results obtained here are discussed in [Fig. 2(a)]. It has the additional advantage of requiring only a small the context of the previous measurements by SS and LF, and finally droplet of the sample material in order to accurately measure the these techniques are compared in terms of advantages and thermal conductivity. disadvantages. The bidirectional 3ω method extends the conventional meth- odology by considering heat transfer through two semi-infinite media above and below the heater line, as indicated schematically in Fig. 2(b). The main principles are given here, and the reader is II. 3ω METHOD referred to the work by Oh et al.28 and the supplementary informa- The 3ω method is a thermal characterization technique widely tion in Rodríguez-Laguna et al.30 for a more detailed description. used for the determination of thermal conductivity. It was devel- The sample of interest is placed on a quartz substrate with a passiv- oped in the 1990s by Cahill23,24 and is a transient electrothermal ated heater line, the reference, as shown in Figs. 2(a) and 2(b). The technique which induces a temperature fluctuation by applying a relation between the temperature oscillations is as follows:28 transient (AC) current to a thin microfabricated metal line, Iapp (t) ¼ I0 cos(ωt). The metal line acts as both heater and sensor. 1 1 1 ¼ þ , (4) Hereafter, for convenience, the metal line will be referred to as the ΔTeff ΔTref ΔTsam heater. Due to the applied AC current, the heater temperature oscil- lates at an angular frequency of 2ω. The temperature fluctuation in where ΔTeff is the measured temperature oscillation of the heater. the heater, in turn, induces a fluctuation in the electrical resistance, ΔTref is the temperature oscillation of the heater in a system con- Re , which is detected by measuring the voltage, V, across the sisting of only the reference substrate. The temperature spread in heater. This signal relates to the temperature fluctuation, ΔT2ω . the thin dielectric layer is also included in ΔTref . ΔTsam is the tem- ΔT2ω can then be used to determine the thermal properties of the perature oscillation in the heater in a system consisting only of the substrate. The measured temperature oscillation is given by23,24 sample. The thermal resistance at the sample/reference interface is neglected. First, a calibration measurement of the reference is per- 2 V3ω,RMS formed to determine ΔTref . Then, the sample is applied, and a new ΔT2ω ¼ (1) thermal measurement is done. The sample’s temperature rise is β V0,RMS then given by rewriting Eq. (4), where V0 and V3ω are total and third harmonic voltages, respec-  1 tively, across the heater. As a rule of thumb, V3ω is typically three 1 1 orders of magnitude larger than V0 .25 β is the temperature coeffi- ΔTsam ¼  : (5) ΔTeff ΔTref cient of electrical resistivity, Here, ΔTsam is then taken as ΔT2ω in Eq. (1) from which the 1 dRe (T) thermal conductivity of the sample, κ, is found by least squares β¼ , (2) Re,0 dT fitting to Eq. (3). V0 measured between the inner voltage pads of the metal strip where Re,0 is the electrical resistance at a reference temperature T0 . is a sum of the 1ω and 3ω components, with the latter being three J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 131, 125107-2 Published under an exclusive license by AIP Publishing Journal of METHOD scitation.org/journal/jap Applied Physics FIG. 1. (a) SEM image of the cross section of an ICA containing 35 vol.% AgPS (2.2 vol.% silver), and (b) SEM image of a commercial ICA with 31 vol.% silver flakes. (b) was adapted from Ref. 11. Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf orders of magnitude smaller than the first. A conditioning circuit configuration to a NI9217 module. The data acquisition modules (Fig. 3) is able to cancel out the V1ω signal, leaving only the V3ω are all from National Instruments (Austin, TX, USA). signal to be detected by the lock-in amplifier. To remove the fundamental (1ω) component, the voltage The current source, a Keithley 6221 (OH, USA), outputs a amplitude measured across the variable resistance RD is adjusted high-purity sinusoidal current Iapp (t) of frequency ω that is applied iteratively. This is done by varying the resistance RD until the across the metal line. In order to make sure that the heating power amplitude of the measured voltage Vω matches the amplitude of is always constant at 2 mW, the magnitude of Iapp (t) is adjusted the voltage measured across the heater line, Vωþ3ω . The resistance iteratively by measuring the voltage across a 10 Ω resistor element, is varied using a M642 programmable resistance decade (Meatest, and calculating the current I0 ¼ VI0 =(10 Ω), as indicated in Fig. 3. Brno, Czech Republic). When the voltages are matched, the final Also shown in the figure is V0 , which is measured between the operational amplifier subtracts Vω from Vωþ3ω , outputting V3ω , voltage pads. I0 and V0 , along with the temperature T of a PT100 which is then measured using a DSP7265 lock-in amplifier (Signal element placed in close proximity to the sample, are measured Recovery, Oak Ridge, TN, USA). The operational amplifiers are using a data aquisition box (DAQ) of type NI cDAQ-9174. The polarized using a BP3002 DC power supply (Digimess, Leicester, voltages associated with I0 and V0 are measured using BNC con- UK). The measured signal is averaged by 10 measurements at each nections to a NI9215 module, whereas T is measured in a 4-wire frequency. The choice of heating frequency is an important source of uncertainty, since it determines the thermal penetration depth (or thermal wavelength) in the sample. If the frequency is too high, the measured signal will be dominated by the interface between the heater and sample. If too small, the signal will be dominated by the substrate or the interface between the substrate and platform. Other important sources of uncertainty in the measurement are the heater dimensions (film thickness, width, and length). For a more thorough discussion on measurement design rules for reducing uncertainty sources, see work by Dames.33 In these measurements, the heating frequency is ffi chosen to pffiffiffiffiffiffiffiffiffiffi ensure that the thermal penetration depth (lth ¼ α=2ω) is several times smaller than the substrate and sample thickness. In this case, it was calculated that the sample was 3.4 times thicker than the penetration depth. This is to ensure that the oscillating temperature is localized well within the media of interest, and is insensitive to the boundary condition between them and the surroundings. However, we want to have a frequency low enough so that the FIG. 2. (a) The reference chip for 3ω measurements, showing the applied thermal wave penetrates well into the sample and substrate, to not current Iapp (t) and the measured voltage V1ω,3ω between the pads. The sample be affected by the thermal resistances associated with the interfaces placement is shown in purple. (b) The reference chip with sample in the cross- near the heater. Also, the substrate and sample should “see” the sectional view. The bidirectional heat flow is illustrated schematically. (c) heater as a 1D source, that is b ! 0. This is ensured by choosing Measured temperature rise ΔTeff of the reference chip and reference þ sample, frequencies such that lth =b . 5, which is a design criteria for 1% respectively. error for this assumption.33,34 J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 131, 125107-3 Published under an exclusive license by AIP Publishing Journal of METHOD scitation.org/journal/jap Applied Physics FIG. 3. The conditioning circuit of the 3ω setup. Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf III. SAMPLE FABRICATION PY-302 epoxy resin with Jeffamine D-230 curing agent (both from The reference chip was made by dicing a 0.5 cm thick fused Huntsman, Lindberg & Lund AS, Norway) in a 3:1 ratio by weight. quartz glass slide (SPI Supplies, PA, USA) into 1 cm2 chips and AgPS was added to the matrix at 35, 40, 45, and 50 vol.%, respec- tively (see Fig. 1 and Table I). A small droplet (approximately microfabricating a 3ω structure on the chip. The 3ω structure was 2.5 μl) of sample was applied to the 3ω reference chip in the sensor deposited through a hard mask by electron beam evaporation (AJA International, Inc., Scituate, MA, USA) of a Ti(2 nm)/Au(100 nm) area as indicated by Figs. 2(a) and 2(b). Then, the sample-chip layer. The hard mask is a 0.5 mm thick Ti plate with cut-outs cor- system was cured in a vacuum oven (Binder, Tuttlingen, Germany) responding to the 3ω structure, custom ordered from Veco (Veco at 150 ∘C for 40 min. The electrical connections to the voltage pads were made by manually wire bonding Au wires (diameter of B.V, Eerbeeck, The Netherlands). Since the sample in this case is electrically conductive, a dielectric layer of 50 nm Al2 O3 was depos- 20 μm) between the pads and a chip holder with connections to ited by sputtering on top of the thin metal lines connecting the BNC-cable inputs. voltage pads. The typical heater width is 20 μm, and its length (measured IV. RESULTS AND DISCUSSION between the inner voltage pads) is 1 mm. The substrate material, The thermal conductivities of the AgPS-ICA are plotted in fused quartz, has a thermal conductivity of 1.4 W m−1 K−1 and a Fig. 4 and shown in Table II. The reported error margins represent thermal diffusivity of 0.95 mm2 s−1, according to the supplier’s the standard error of the four individual measurements performed technical datasheet.35 for each sample. A progressive, near-linear enhancement of The AgPS were prepared by a two-step swelling process, pro- thermal conductivity is seen as a function of AgPS volume fraction. ducing crosslinked PMMA particles with Diameters of 10 μm.36 For the largest AgPS volume fraction, 50 vol.%, a thermal conduc- The 145 nm Ag shell was deposited by an electroless plating tivity of 2:03 + 0:21 W m−1 K−1 is reported from the 3ω measure- process. The adhesive matrix was prepared by mixing Araldite ment. From Table I, this corresponds to 3.4 vol.% silver. According to Kim et al., a conventional silver flake ICA would need almost 20 vol.% silver to achieve a similar thermal conductivity.37 Also shown in Fig. 4 are thermal conductivity measurements of the TABLE I. Volume and weight fractions of AgPS, calculated pre-cure density of AgPS-ICA and Ag volume and weight fraction of the four samples. The calculations same AgPS-ICA from Kristiansen et al.21 by the SS method and the are based on measured weight fractions and nominal densities given by the manu- LF method. In the SS method, the sample is cured at different facturers of the constituents, and the nominal diameter and Ag film thickness of the thicknesses between two Cu rods and measured the thermal con- AgPS. ductivity as κ ¼ Q=∇T, where Q is the heat flow through the sample and ∇T is the temperature gradient across the sample. The Density LF is a transient method used to measure the thermal diffusivity α AgPS AgPS AgPS-ICA Ag Ag of the sample, the density ρ is measured by the immersion method, Sample (vol.%) (wt.%) (g/cm3) (vol.%) (wt.%) and the specific heat Cp is measured using differential scanning cal- 35AgPS 35 47.7 1.40 2.2 16.3 orimetry (DSC). Then, the thermal conductivity is given by 40AgPS 40 53.1 1.44 2.6 18.6 κ ¼ αρCp . 45AgPS 45 58.1 1.48 3.0 29.9 From Fig. 4, it is evident that the two transient methods (3ω 50AgPS 50 62.5 1.52 3.4 33.3 and LF) are in good agreement, following a similar trendline. However, the 3ω measurements yield thermal conductivities on J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 131, 125107-4 Published under an exclusive license by AIP Publishing Journal of METHOD scitation.org/journal/jap Applied Physics TABLE III. Using the Wiedemann–Franz law, the electronic contribution to the thermal conductivity κe is calculated. The ratio κe/κ is calculated from the thermal conductivity measurements by the 3ω method. Sample σ (S/m) κe (W m−1 K−1) κe/κ 4 40AgPS 4.54×10 0.33 0.24 45AgPS 1.54×105 1.12 0.70 50AgPS 2.00×105 1.46 0.72 could result in closer contact between the Ag shells, which conduct a large portion of the heat above the percolation threshold. This is in contrast to the curing method for the transient methods, in which the AgPS-ICA samples are allowed unconstrained thermal expansion. It can be argued that the SS method measures the thermal conductivity of AgPS-ICAs for a more realistic curing con- Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf dition, as ICAs usually are cured between two bodies at a fixed BLT. In order to measure thermal properties under more realistic operating conditions, the 3ω sample curing process could be modi- fied such that the sample is cured at a given BLT. FIG. 4. Thermal conductivity of AgPS-ICAs for varying volume fractions of AgPS measured by 3ω, SS,21 and LF22 methods. The 3ω and LF measure- The results support the thermally conductive path theory, in ments were done at room temperature, whereas the SS measurements were which the filler particles at these high fill fractions are in contact done at 40  C. The error bars represent the standard error of the four data with each other, as shown in Fig. 1(a). Thus, they form a thermally points for each sample. conductive network through the polymeric matrix material. We can calculate the electronic contribution to the total thermal con- ductivity using the Wiedemann–Franz law.38 It states that the ratio average 11% above the LF measurements. The SS measurements of electronic contribution to thermal conductivity κe and electrical give a thermal conductivity 16% below the 3ω measurements for conductivity σ of a metal is proportional to temperature T, the 40AgPS. For the 45 and 50AgPS sample, the SS measurements give thermal conductivities that are 46% and 38% above the 3ω κe ¼ L0 T, (6) measurements, respectively. Pettersen et al.22 did LF measurements σ of AgPS-ICAs and showed that the technique for measuring the specific heat had a significant effect on the measured thermal con- where the proportionality constant L0 is called the Lorentz number ductivity for this sample system. However, this effect alone cannot and has the value of L0 = 2.44×10-8 W Ω K−2. From electrical con- explain the large discrepancies observed between the transient and ductivity measurements of the AgPS-ICA,39 κ e is calculated in steady state methods. Kristiansen et al.21 pointed out that the large Table III. It is worth mentioning here, that the increase in thermal discrepancy in the values reported by the SS method occur for 45 conductivity resulting from a higher concentration of AgPS-ICA and 50AgPS, which is above the percolation threshold. The also increases the electrical conductivity of the samples.40 increased thermal conductivity measured by the SS method could From Table III, we see that the κ e =κ ratio is 0.24 for the be due to the fixed bond line thickness (BLT) between the reference 40AgPS sample, and 0.70 and 0.72 for the 45AgPS and 50AgPS bodies during curing of the AgPS-ICA sample, which exerts a sample, respectively. Although the silver thin films conduct a sig- contact pressure on the sample due to thermal expansion. This nificant portion of the heat compared to their low volume fraction, the phonon contribution from the PMMA cores and the epoxy matrix still comprises a substantial part of the total effective thermal conductivity of the AgPS-ICA, especially for the 40AgPS TABLE II. Thermal conductivity results for AgPS-ICAs from 3ω, SS, and LF methods. sample. The thermal transport by electrons is limited to occur within the silver thin films or by tunneling across ultrathin epoxy vol.% 0 35 40 45 50 layers between two AgPS. The thermal transport of the AgPS-ICA AgPS system has been discussed previously in the context of LF measure- vol.% Ag 0 2.2 2.6 3.0 3.4 ments,22 which concluded that the thermal transport in the AgPS −1 −1 is dominated by the electronic heat transfer in the Ag layer. We Thermal conductivity (W m K ) believe a minor thermal transport mechanism deserves mention, 3ω … 1.08 ± 0.11 1.39 ± 0.12 1.60 ± 0.12 2.03 ± 0.21 which is the possibility of electron–phonon interactions across the SS 0.2 … 1.16 ± 0.09 2.33 ± 0.20 2.81 ± 0.20 Ag–polymer interfaces. When the heat is transported between the LF … … 1.20 ± 0.060 1.48 ± 0.074 1.86 ± 0.093 silver thin films and the nonconductive cores and matrix, this process is indeed believed to be dominated by phononic J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 131, 125107-5 Published under an exclusive license by AIP Publishing Journal of METHOD scitation.org/journal/jap Applied Physics TABLE IV. Comparison of thermal measurement techniques. Accuracy of 3ω based on the standard error of the measurements performed in this work. Measurement Technique Heating time Accuracy Advantages Disadvantages 3ω Transient 10 min ≈10% Small sample size (μl) Unrealistic curing conditions current κ measured directly Time consuming sample preparation and calibration Heating principle similar to operating conditions <1 ∘C temperature gradient SS Steady state 2h ≈2%1 Standardized method (ASTM Time-consuming to reach steady state D5470)44 Simple experimental setup Radiation loss and thermal contact resistance and data reduction κ measured directly Requires specific size and shape of sample Sample is cured at a given Typically large (>20 °C) temperature gradient BLT Downloaded from http://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/5.0080682/16456448/125107_1_online.pdf LF Transient <1 min 3–5%1 Standardized method (ASTM Measures κ indirectly by measuring α laser E1461-13)45 <1 ∘C temperature gradient Graphite coating, absolute planarity and accurate sample thickness measurements required Non-contact method interactions. The process of heat transfer across metal–dielectric characteristic size of the heater geometry. Even at 1000 K, the calcu- interfaces have been widely studied by pulsed femtosecond laser lated error due to radiation is 2%,46 which means that in our case heating, such as the study by Lyeo and Cahill.41 They concluded with ΔT , 1 K, this error source can be neglected. A drawback of that electrons contribute negligibly to heat transfer across a metal– the 3ω method is that the calibration of the β parameter is very dielectric interface. This gives us some insight into the heat transfer time consuming, usually taking 3–4 h. This drawback can be over- process between the silver thin films and the surrounding poly- come, however, either by (1) making the 3ω sensor reusable, or (2) meric material. First, the hot electrons in the silver film thermalize standardizing the fabrication process of the 3ω sensor chips by by electron–phonon scattering within the metal film, a process using photolithography. It is then expected that two sensors from which occurs on the picosecond timescale.42 Then, the thermal the same batch process should have the same β value. The option energy of the metal’s phonons is distributed to the polymer mate- of making the sensor reusable could be realized by applying a thin rial through phonon–phonon scattering processes. The nonstick layer on top of the sensor, such that the sample can be electron-phonon thermalization process is so rapid that it will not easily removed after measurement. affect the 3ω measurements. This is because the heating events Contact thermal resistance is a major source of error in induced by the AC current are on the millisecond timescale, which contact techniques. In 3ω, this is omitted by the choice of fre- is set by the frequency of the current (< 150 Hz). In conclusion, quency band, avoiding the higher frequencies where the interface the measurement’s timescale is much larger than the timescale resistance contributes to the result. In the SS method, measure- associated with Electron–phonon thermalization events, which ments of different sample thicknesses will eliminate the interface occur within picoseconds. resistance, however, at the expense of longer time needed for There is still no uniform testing standard for thermal conduc- testing. In this comparison, LF is the only non-contact method, tivity measurements of polymer composites. Therefore, the since it uses a laser pulse to heat the front side of the sample and obtained experimental values from different instruments are diffi- an IR detector to read the time-dependent temperature on the cult to compare.43 However, some advantages and disadvantages of sample’s backside. Radiation losses are accounted for by the the testing methods discussed here have been gathered in Table IV. thermal model used to fit the results. However, the sample prepara- A main difference between the transient and steady state tion is not straightforward. The sample needs to be a specific size methods is the measurement time. In a steady-state measurement, and shape, and is usually prepared by spraying a layer of graphite the system as a whole must reach thermal equilibrium before mea- to act as an absorber. Accurate measurements of sample thickness surements are done, which may take two hours. Furthermore, para- are critical, as well as absolute planarity. The thickness of the sitic heat loss and thermal conduction through the thermocouples sample is limited by the timescales associated with the heating and must be accounted for in steady state measurement, which is a IR sensing. Commercial instruments can measure samples down to major drawback for this technique. A significant advantage of 3ω around 100 μ m depending on the thermal diffusivity of the mate- over the SS method is that the error due to radiation loss is greatly rial, and for thinner films, the 3ω method or thermoreflectance reduced, due to the fact that thermal radiation scales with the methods are needed.47 A clear drawback of the LF technique, is J. Appl. Phys. 131, 125107 (2022); doi: 10.1063/5.0080682 131, 125107-6 Published under an exclusive license by AIP Publishing Journal of METHOD scitation.org/journal/jap Applied Physics that it is an indirect way of measuring κ, by measuring the thermal DATA AVAILABILITY diffusivity α and calculating the thermal conductivity by κ ¼ ραCp , Data sharing is not applicable to this article as no new data where the density ρ and specific heat Cp must be measured from were created or analyzed in this study. separate experiments. 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Kumar, “Making strong fibers,” Science 319, 908–909 that can achieve similar thermal and electrical conductivities as (2008). 9 conventional ICAs with only a small fraction of the silver content. Advanced Flip Chip Packaging, edited by H.-M. Tong, Y.-S. Lai, and C. Wong We measured the thermal conductivity of AgPS-ICAs using the (Springer US, Boston, MA, 2013). bidirectional 3ω method. A progressive, near-linear enhancement 10 M. Inoue, H. Muta, T. Maekawa, S. Yamanaka, and K. Suganuma, “Physical of thermal conductivity was seen as a function of AgPS factors determining thermal conductivities of isotropic conductive adhesives,” volume fraction. For 50 vol.% AgPS, corresponding to 3.4 vol.% J. Electron. Mater. 38, 430–437 (2009). 11 H.-V. Nguyen, E. Andreassen, H. Kristiansen, and K. E. Aasmundtveit, “Die silver, the thermal conductivity of the AgPS-ICA was shear testing of a novel isotropic conductive adhesive–epoxy filled with metal- 2:03 + 0:21 W m−1 K−1. For conventional silver flake ICAs, the coated polymer spheres,” IEEE Trans. Compon. Packag. Manuf. Technol. 3, volume fraction of silver would be nearly 20 vol.% silver in order to 1084–1093 (2013). achieve a similar thermal conductivity. The results were discussed 12 S. Jain, “Isotropically conductive adhesive filled with silver metalised polymer and compared to measurements by SS and LF, and the methods spheres,” Ph.D. thesis (Loughborough University, United Kingdom, 2016). 13 were compared in terms of applicability to AgPS-ICAs. H.-V. Nguyen, H. Kristiansen, J. Gakkestad, R. Johannessen, N. Høivik, and K. E. Aasmundtveit, “Spherical polymer particles in isotropic conductive adhe- sives a study on rheology and mechanical aspects,” in 3rd Electronics System ACKNOWLEDGMENTS Integration Technology Conference ESTC (IEEE, 2010), pp. 1–6. 14 H.-V. Nguyen, H. Kristiansen, R. Johannessen, E. Andreassen, A. Larsson, The NTNU authors wish to acknowledge the Research and K. E. Aasmundtveit, “Temperature dependence of mechanical properties Council of Norway for the support to this project through the of isotropic conductive adhesive filled with metal coated polymer spheres,” in FRINATEK Project No. 251068 with the title “Engineering IEEE 61st Electronic Components and Technology Conference (ECTC) (IEEE, Metal-Polymer Interface for Enhanced Heat Transfer (HEFACE)” 2011). 15 and also for supporting the NTNU NanoLab through the H.-V. Nguyen, J. He, T. Helland, H. Kristiansen, and K. E. Aasmundtveit, Norwegian Micro- and Nano-Fabrication Facility, NorFab, Project “Electrical characterization of individual metal-coated polymer spheres used in No. 245963. ICN2 is supported by the Severo Ochoa program from isotropic conductive adhesives,” J. Appl. Polym. Sci. 133, 43764–43773 (2016). 16 the Spanish Research Agency (AEI, Grant No. SEV-2017-0706) S. Jain, D. Whalley, M. Cottrill, H. Kristiansen, K. Redford, C. Nilsen, T. Helland, and C. Liu, “Electrical properties of an isotropic conductive adhesive and by the CERCA Programme/Generalitat de Catalunya. E.C.- Á filled with silver coated polymer spheres,” in 18th European Microelectronics acknowledges the support from the Spanish MICINN project SIP Packaging Conference (IEEE, 2011), pp. 1–7. (No. PGC2018-101743-B-I00) and from EU Project NANOPOLY 17 S. Jain, D. C. Whalley, M. Cottrill, T. Helland, H. Kristiansen, K. Redford, and (No. GA 289061). C. Liu, “The effect of coating thickness on the electrical performance of novel isotropic conductive adhesives prepared using metallised polymer micro- spheres,” in 2013 IEEE 63rd Electronic Components and Technology Conference AUTHOR DECLARATIONS (IEEE, 2013), pp. 796–802. 18 H.-V. Nguyen, K. E. Aasmundtveit, H. Kristiansen, and T. Helland, “An over- Conflict of Interest view of isotropic conductive adhesives filled with metal-coated polymer spheres,” The authors have no conflicts to disclose. 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