《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_j.1744-7402.2009.02482.x[1]

Int/ Appl Ceram. Technol, 714)415-434(2010) DO:1O.I11744-74022009.02482x International Journal o pplied Ceramic TECHNOLOGY ceramic Product D Polymer-Ceramic Composites of 0-3 Connectivity for Circuits in electronics: a review Mailadil t sebastian National Institute for interdisciplinary Science and Technology, CSIR-NIIST, Trivandrum 695019, india Heli Jantunen Microelectronics and Materials Physics Laboratory and EMPART Research Group of Infotech Oulu, FI 90014 Oulu, Finland Composite technology, where a novel artificial material is fabricated by combining, for example, ceramic and polymer materials in an ordered manner or just by mixing, was earlier used widely for sonar, medical diagnostics, and NDT purposes However, in recent decades, large numbers of ceramic-polymer composites have been introduced for telecommunication and microelectronic applications. For these purposes, composites of 0-3 connectivity (a three-dimensionally connected polymer phase is loaded with isolated ceramic particles)are the most attractive from the application point of view Composites of0-3 connectivity enable flexible forms and very different shapes with very inexpensive fabrication methods including simply mixing and molding. In this brief review, we gather together the research carried out within 0-3 ceramic-polymer composites for microwave substrates, also including embedded capacitor, inductor, or microwave-absorbing performances Introduction low thermal dependence of permittivity (tEr),moisture absorption resistance, low coefficient of thermal expan- Materials used in microelectronic packaging have to sion(CTE), and high dimensional stability and me- simultaneously fulfill diverse requirements, such as low chanical stiffness. Ceramic-polymer composites, espe dielectric loss(tan 8), moderate relative permittivity(Er), cially type 0-3, are a potential material group suitable for producing demanding and functional packages that combine the electrical properties of ceramics and the mechanical Flexibility, chemical stability, and processing

Polymer–Ceramic Composites of 0–3 Connectivity for Circuits in Electronics: A Review Mailadil T. Sebastian* National Institute for Interdisciplinary Science and Technology, CSIR-NIIST, Trivandrum 695019, India Heli Jantunen Microelectronics and Materials Physics Laboratory and EMPART Research Group of Infotech Oulu, FI 90014 Oulu, Finland Composite technology, where a novel artificial material is fabricated by combining, for example, ceramic and polymer materials in an ordered manner or just by mixing, was earlier used widely for sonar, medical diagnostics, and NDT purposes. However, in recent decades, large numbers of ceramic–polymer composites have been introduced for telecommunication and microelectronic applications. For these purposes, composites of 0–3 connectivity (a three-dimensionally connected polymer phase is loaded with isolated ceramic particles) are the most attractive from the application point of view. Composites of 0–3 connectivity enable flexible forms and very different shapes with very inexpensive fabrication methods including simply mixing and molding. In this brief review, we gather together the research carried out within 0–3 ceramic–polymer composites for microwave substrates, also including embedded capacitor, inductor, or microwave-absorbing performances. Introduction Materials used in microelectronic packaging have to simultaneously fulfill diverse requirements, such as low dielectric loss (tan d), moderate relative permittivity (er), low thermal dependence of permittivity (ter), moisture absorption resistance, low coefficient of thermal expan￾sion (CTE), and high dimensional stability and me￾chanical stiffness.1 Ceramic–polymer composites, espe￾cially type 0–3, are a potential material group suitable for producing demanding and functional packages that combine the electrical properties of ceramics and the mechanical flexibility, chemical stability, and processing Int. J. Appl. Ceram. Technol., 7 [4] 415–434 (2010) DOI:10.1111/j.1744-7402.2009.02482.x Ceramic Product Development and Commercialization *mtsebastian@niist.res.in r 2010 The American Ceramic Society

416 International ournal of Applied Ceramic Technolog-Sebastian and Jantunen Vol.7,No.4,2010 possibilities of polymers. It is well known that the con- wavelength travelling though the medium is inversely nectivity between the phases in the composite materials proportional to the square root of the permittivity. In is very important in achieving the desired properties. many cases, this leads to products not possible in any The preparation of 0-3 type composite materials by other way, also with a low production cost. Although combining a dielectric or a ferroelectric ceramic and a many ceramic materials with a high Er and low loss are polymer for suitable properties means not only choosing available, they are generally brittle in nature. This leads to a difficulty in the fabrication of complex shapes or also coupling them with the best possible design struc- machining the ceramic substrates during circuit fabri- ture. This concept of connectivity, first reported by cation. These difficulties can be avoided by using 0-3 Newnham et al, describes the interspatial relationships polymer-ceramic composites as an alternative, which in a multiphase material controlling the mechanical and offer excellent material characteristics such as low-tem electrical pro and thermal fluxes between the perature processability, fexibility, machinability, chem- phases. Additionally, the filler particle size, interfacial ical resistance, tailored dielectric properties, etc. Such properties, percolation level, and porosity effects can composites include glass- or ceramic-reinforced epoxy, lso play a role in the composite properties. Interfacial PTFE, and various types of thermoset hydrocarbons effects can occur between the ic grains and the Among these, PTFE is the most preferred host matrix polymer matrix, leading to large dielectric relaxations that exhibits excellent dielectric properties such as low normally at low frequencies( called Maxwell-Wagner permittivity, extremely low loss tangent, and is stable relaxations). However, the response of the composite across a wide range of frequencies. The loss tangent of ay have a property that isplayed in the indi- PTFE at a high frequency maintains the signal integrity vidual phases. The feasibility of these composites for and minimizes radiation effects during data transfer use in piezoelectric and pyroelectric applications, flexible The properties of PTFE such as chemical inertness, low sensors,transducers, thick film dielectrics, embedded moisture absorption, high service temperatures,etc capacitors, and other multilayer RF devices has been are also important for many microwave applications cher gated6-8 The research was mainly focused on Although PTFE-based substrates are well accepted for mose thermoplastic poly and elastomers like microwave circuit applications, their wide usage is PVDF, P(VDF-TrFe), silicon-rubber, stricted because of the processing difficulties. Unlike polyimide, 6 pVC, 7cyanoet lated cellulose polymer, 8 other polymers, PTFE cannot be processed through in- polydimethylsiloxane, polystyrene, benzocycobu- jection molding or melt extrusion because of its very chough polymer-bas olefin copolymers, polyphenylene sulfide, poly- substrates are very common in use, the lite erature re- olefin elastomer(POe), polypropelene,and polyure- garding the preparation and characterization of these thane. The properties of the ceramic-polymer technologically and commercially important materials is composites are determined by the number of phases very limited. Most of the works in this line are focused and the way in which the phases are interconnected. on the developments of commercial products and are The response of a ceramic-polymer composite to an ex- protected by patent laws. Ceramic-filled polymers are ternal excitation(electric field, temperature, stress, etc. used in electronic packaging for device encapsulation depends on the response of individual phases, their Encapsulation of electronic devices protects them from interfaces as well as the connectivity concept. Polymer- an adverse environment and increases their long-term ezoelectric ceramic Fexible ferroelectric composites reliabilit have been extensively investigated.u for piezoelectric With the recent progress in nanoscience and tech- and pyroelectric transducer applications and hence will nology, there is an increasing interest in polyn not be discussed in the present review. composites both in scientific research and in engineering applications. For example, the epoxy-silica nanocom- posite has been used in electronic and optical packag Microwave Substrate ing. The epoxy nanofiller composite has good optical Materials with a high relative permittivity (er) Properties due to the smaller filler particle size. The electrical characteristics of microelectronic devices, such reduce the size of the microwave devices because the propagation velocity, and cross

possibilities of polymers. It is well known that the con￾nectivity between the phases in the composite materials is very important in achieving the desired properties.2,3 The preparation of 0–3 type composite materials by combining a dielectric or a ferroelectric ceramic and a polymer for suitable properties means not only choosing the right materials, processed in a particular way, but also coupling them with the best possible design struc￾ture. This concept of connectivity, first reported by Newnham et al.,2 describes the interspatial relationships in a multiphase material controlling the mechanical and electrical properties and thermal fluxes between the phases. Additionally, the filler particle size, interfacial properties, percolation level, and porosity effects can also play a role in the composite properties.4 Interfacial effects can occur between the ceramic grains and the polymer matrix, leading to large dielectric relaxations normally at low frequencies (called Maxwell–Wagner relaxations). However, the response of the composite may have a property that is not displayed in the indi￾vidual phases.5 The feasibility of these composites for use in piezoelectric and pyroelectric applications, flexible sensors, transducers, thick film dielectrics, embedded capacitors, and other multilayer RF devices has been investigated.6–8 The research was mainly focused on thermoset, thermoplastic polymers and elastomers like epoxy,9–12 PVDF,13 P(VDF-TrFe),14 silicon-rubber,15 polyimide,16 PVC,17 cyanoethylated cellulose polymer,18 polydimethylsiloxane,19 polystyrene,20 benzocyclobu￾tene,21 polymethyl methocrylate,22 metallocene cyclic olefin copolymers,23,24 polyphenylene sulfide,25,26 poly￾olefin elastomer (POE),27 polypropelene,28 and polyure￾thane.29 The properties of the ceramic–polymer composites are determined by the number of phases and the way in which the phases are interconnected. The response of a ceramic–polymer composite to an ex￾ternal excitation (electric field, temperature, stress, etc.) depends on the response of individual phases, their interfaces as well as the connectivity concept. Polymer– piezoelectric ceramic flexible ferroelectric composites have been extensively investigated6,30 for piezoelectric and pyroelectric transducer applications and hence will not be discussed in the present review. Microwave Substrates Materials with a high relative permittivity (er) reduce the size of the microwave devices because the wavelength travelling though the medium is inversely proportional to the square root of the permittivity. In many cases, this leads to products not possible in any other way, also with a low production cost. Although many ceramic materials with a high er and low loss are available, they are generally brittle in nature. This leads to a difficulty in the fabrication of complex shapes or machining the ceramic substrates during circuit fabri￾cation. These difficulties can be avoided by using 0–3 polymer–ceramic composites as an alternative, which offer excellent material characteristics such as low-tem￾perature processability, flexibility, machinability, chem￾ical resistance, tailored dielectric properties, etc.31 Such composites include glass- or ceramic-reinforced epoxy, PTFE, and various types of thermoset hydrocarbons. Among these, PTFE is the most preferred host matrix that exhibits excellent dielectric properties such as low permittivity, extremely low loss tangent, and is stable across a wide range of frequencies. The loss tangent of PTFE at a high frequency maintains the signal integrity and minimizes radiation effects during data transfer. The properties of PTFE such as chemical inertness, low moisture absorption, high service temperatures, etc. are also important for many microwave applications. Although PTFE-based substrates are well accepted for microwave circuit applications, their wide usage is re￾stricted because of the processing difficulties. Unlike other polymers, PTFE cannot be processed through in￾jection molding or melt extrusion because of its very high melt viscosity. Although polymer-based composite substrates are very common in use, the literature re￾garding the preparation and characterization of these technologically and commercially important materials is very limited. Most of the works in this line are focused on the developments of commercial products and are protected by patent laws. Ceramic-filled polymers are used in electronic packaging for device encapsulation. Encapsulation of electronic devices protects them from an adverse environment and increases their long-term reliability. With the recent progress in nanoscience and tech￾nology, there is an increasing interest in polymer nano￾composites both in scientific research and in engineering applications. For example, the epoxy–silica nanocom￾posite has been used in electronic and optical packag￾ing.32 The epoxy nanofiller composite has good optical properties due to the smaller filler particle size. The electrical characteristics of microelectronic devices, such as signal attenuation, propagation velocity, and cross 416 International Journal of Applied Ceramic Technology—Sebastian and Jantunen Vol. 7, No. 4, 2010

wwceramics. org/ACT Composites of 0-3 Connectivity talk, are influenced by the dielectric properties of the 4D1 iportant re materials is to ensure the electrical insulation of the sil- 载LDU8 chip and circuit pins. a low conductivity is needed roid leakage current, a low E, to minimize the ca- 06 itive coupling effects, and a low loss factor to reduce y un et investigated the dielectric prop 0D4 erties of epoxy composites with micrometer-sized and nanosized silica fillers. The epoxy-nanosilica composite had higher dielectric loss at a low frequency and 0.002 was attributed to the increased ionic conductivity caused by the contaminants from the sok-gel-synthesized nanosized silica. Chen et al. investigated the effect of properties of PTFE/SiO2 composites. They found that the loss factor and water absorption increase with decreasing filler particle size. The PTFE/silica composite, when treated with a 4.006 phenyltriethoxysilane coupling agent, increase tensile strength and CTE and the water absorption de creases without significant changes in the dielectric properties. Murali et al. prepared PTFE with nano and micrometer-sized silica composites and reported that the PTFE/silica nanocomposites have lower den- sity and higher losses and higher E, for <30 wt of fll ler. However, the composites prepared by filling silica Volume fraction of Sm2 07 are able to achieve only moderate relative permittivity Fig. 1. Variation of relative permittivity and loss tangent (a) cause d by its low Er (3.8-5.4). In order to obtain a Polbystyrene-Sm2Si 0,(6) Polyetbhylene-Sm2Si20r composites with higher Er for miniaturization of devices, the four possi different wolume fractions of the filler at I MHz(afier Thomas et al ") ble ways are to use fillers of a high En, increase the vol ume fraction of the filler, modify the polymer-ceramic filler materials with disk- or needle-type grains instead interfaces, dry the materials before processing, or change of spherical ones. These calculations estimated that the morphology of the filler grains. However, the first under mixture conditions where inclusion has 50 times approach with a higher filler concentration results in higher permittivity than the matrix, disk- and needle- oor Auidity and poor fexibility and low strength in the type fillers could produce 5 and 3. 4 times higher composite. Hu et al. for example could increase the mittivity than the spherical ones. However, the avail permittivity value of PpS polymer up to 13.5(1 GHz) ability of these kinds of ceramic fillers is very limited by addition of 70 wt% of Ba. 55Sro45TiO3(BST) pow- Furthermore, the chosen polymer exerts an effect on the der. It was reported that the mechanical properties de- achieved electrical properties. Figure I shows the vari- grade with increased filler loading 36.37 This problem ation of relative permittivity and tan 8 at 1 MHz for an be overcome by modifying the filler materials. Re- different volume fractions of the filler in the polyethyl- cently, Che et al. reported that a spherical powder ene/Sm2Si2O, and polystyrene/Sm2 Si2O, compos- with optimized particle size can increase Auidity and ites. The e. and tan s increase with an increase in cking. They reported that by using a composite di- the filler content. The polyethylene with a 0.4 volume electric from spherical powder of Cao.65Sro35 TiO3 and fraction of Sm2S2O7 showed an Er of 5.28 and a tan 8 of a thermoplastic polymer could increase the filler con- 0.005 at 8 GHz, whereas for the same volume fraction centration by over 5 vol% for a higher Er. On the other in polystyrene had values of 4.34 and 0.010, respec hand,theoretical calculations proposed that composites tively. The same kind of extrinsic reason, nar h very high E, values could be prepared by selecting polymer, ceramic, chemical, and mechanical coupling

talk, are influenced by the dielectric properties of the packaging materials. An important role of the packaging materials is to ensure the electrical insulation of the sil￾icon chip and circuit pins. A low conductivity is needed to avoid leakage current, a low er to minimize the ca￾pacitive coupling effects, and a low loss factor to reduce signal loss. Sun et al. 33 investigated the dielectric prop￾erties of epoxy composites with micrometer-sized and nanosized silica fillers. The epoxy–nanosilica composite had higher dielectric loss at a low frequency and was attributed to the increased ionic conductivity caused by the contaminants from the sol–gel-synthesized nanosized silica. Chen et al. 34 investigated the effect of filler particle size on the properties of PTFE/SiO2 composites. They found that the loss factor and water absorption increase with decreasing filler particle size. The PTFE/silica composite, when treated with a phenyltrimethoxysilane coupling agent, increased the tensile strength and CTE and the water absorption de￾creases without significant changes in the dielectric properties. Murali et al. 35 prepared PTFE with nano￾and micrometer-sized silica composites and reported that the PTFE/silica nanocomposites have lower den￾sity and higher losses and higher er for o30 wt % of filler as compared with the use of a micrometer-sized filler. However, the composites prepared by filling silica are able to achieve only moderate relative permittivity caused by its low er (3.8–5.4). In order to obtain a higher er for miniaturization of devices, the four possi￾ble ways are to use fillers of a high er, increase the vol￾ume fraction of the filler, modify the polymer–ceramic interfaces, dry the materials before processing, or change the morphology of the filler grains. However, the first approach with a higher filler concentration results in poor fluidity and poor flexibility and low strength in the composite. Hu et al. 26 for example could increase the permittivity value of PPS polymer up to 13.5 (1 GHz) by addition of 70 wt% of Ba0.55Sr0.45TiO3 (BST) pow￾der. It was reported that the mechanical properties de￾grade with increased filler loading.36,37 This problem can be overcome by modifying the filler materials. Re￾cently, Che et al. 38 reported that a spherical powder with optimized particle size can increase fluidity and packing. They reported that by using a composite di￾electric from spherical powder of Ca0.65Sr0.35TiO3 and a thermoplastic polymer could increase the filler con￾centration by over 5 vol% for a higher er. On the other hand, theoretical calculations proposed that composites with very high er values could be prepared by selecting filler materials with disk- or needle-type grains instead of spherical ones.39 These calculations estimated that under mixture conditions where inclusion has 50 times higher permittivity than the matrix, disk- and needle￾type fillers could produce 5 and 3.4 times higher per￾mittivity than the spherical ones. However, the avail￾ability of these kinds of ceramic fillers is very limited. Furthermore, the chosen polymer exerts an effect on the achieved electrical properties. Figure 1 shows the vari￾ation of relative permittivity and tan d at 1 MHz for different volume fractions of the filler in the polyethyl￾ene/Sm2Si2O7 and polystyrene/Sm2Si2O7 compos￾ites.40 The er and tan d increase with an increase in the filler content. The polyethylene with a 0.4 volume fraction of Sm2S2O7 showed an er of 5.28 and a tan d of 0.005 at 8 GHz, whereas for the same volume fraction in polystyrene had values of 4.34 and 0.010, respec￾tively. The same kind of extrinsic reason, namely polymer, ceramic, chemical, and mechanical coupling, Fig. 1. Variation of relative permittivity and loss tangent (a) Polystyrene–Sm2Si2O7 (b) Polyethylene–Sm2Si2O7 composites with different volume fractions of the filler at 1 MHz (after Thomas et al.40). www.ceramics.org/ACT Polymer–Ceramic Composites of 0–3 Connectivity 417

418 International ournal of Applied Ceramic Technolog-Sebastian and Jantunen Vol.7,No.4,2010 to the dielectric properties of 0-3 ceramic-polymer com- different polymers were used with the same ceramic filler 0.008 It has been reported recently that there exist inter Er(Modified Lichtenecker 20 phase regions at polymer-filler interfaces in particulate- 0.006 filled polymer composites. The interphase consists of polymer molecules that are bonded or ori- Eg ented at the filler-Particle interface, giving rise to unique electrical and physical properties. The interphase region of the composite can have E, significantly differ- 00001暑 ent from that of the polymer phase due to the nature of the chemical bonding of the polymer molecules to the 0102030405060 Volume Percentage of BsT urface of the filler particles. Chemical coupling agents and surfactants such as silanes, organometallic chelating agents, etc. are generally used to enhance the compat ibility between the polymer phase and the dispersed 0.008 filler phase of Ite systems. Thus, in the r Modified Lichtenecker che interphase region of a polymer-ceramic composite is 0.006 comprised of polymer molecules and/or additives mo- cularly bonded to the surface of the filler, creating a 80.004 material with chemical, mechanical, and electrical char- acteristics different from those of the constituent phases Additionally, Kobune et al. /reported that vacuum dry- 0.000L 2 ng with silane surface treatment of the filler( BaZrO3 aTiO3-Ba(Fe1/Ta1)O3 )improved Er and tan 8 when a 0-3 epoxy composite was prepared. Volume Percentage of nano BST It has been reported that the use of nanosized filler Fig. 2. Variation of relative permitivity and los tangent(a) BSTc- particles in 0-3 type polymer-ceramic composites in- COC composites(b)BSTa-COC composite at I GHZ as a finction of structure. #8. 4s mposite loading and improves the micro- creases BST loading (after Hu et al. 2. BST, BaassSrods TrO Recently hu et al. investigated the effect of particle size of the filler on the dielectric properties and cies, but has hardly any effect at microwave frequencies ites. The composites with the BST nanopowder showed a mediate frequency, indicating the relaxation behavior of higher Er and loss factor at BST loading over 10 vol% the polymer matrix. The dielectric properties of the compared with using a normal BST powder as shown in composites are influenced not only by the relative per- Fig. 2. Figure 3 shows the microstructure of the compos- mittivity of the components but also by other factors The use of nanopowders yielded a more uniform and between the two phases. Therefore, the prediction of crostructure but in general the use of der increased the loss facto ative permittivity of the components and the volume fraction of the filler is very important but is a difficult task for electronic packaging applications. The follow Dielectric Properties of Polymer-Ceramic ing equations are commonly used to calculate the Er of the composites with a low filler content. 1. Jayasundere-Smith It was found that for the same filler ceramic load- g, the dielectric characteristics Em(1-)+6+2后 trongly depend on the type of polymer. Polar poly- celt mers increase the Er of the composites at low frequen 1-+3m-12+3(-m)

to the dielectric properties of 0–3 ceramic–polymer com￾posites was reported by Teirikangas et al. 41 when three different polymers were used with the same ceramic filler. It has been reported recently that there exist inter￾phase regions at polymer–filler interfaces in particulate- filled polymer composites.42–46 The interphase region consists of polymer molecules that are bonded or ori￾ented at the filler–particle interface, giving rise to unique electrical and physical properties. The interphase region of the composite can have er significantly differ￾ent from that of the polymer phase due to the nature of the chemical bonding of the polymer molecules to the surface of the filler particles. Chemical coupling agents and surfactants such as silanes, organometallic chelating agents, etc. are generally used to enhance the compat￾ibility between the polymer phase and the dispersed filler phase of composite systems. Thus, in these cases, the interphase region of a polymer–ceramic composite is comprised of polymer molecules and/or additives mo￾lecularly bonded to the surface of the filler, creating a material with chemical, mechanical, and electrical char￾acteristics different from those of the constituent phases. Additionally, Kobune et al. 47 reported that vacuum dry￾ing with silane surface treatment of the filler (BaZrO3– BaTiO3–Ba(Fe1/2Ta1/2)O3) improved er and tan d when a 0–3 epoxy composite was prepared. It has been reported that the use of nanosized filler particles in 0–3 type polymer–ceramic composites in￾creases the composite loading and improves the micro￾structure.48,49 Recently, Hu et al. 24 investigated the effect of particle size of the filler on the dielectric properties and microstructure of cyclic olefin copolymer–BST compos￾ites. The composites with the BST nanopowder showed a higher er and loss factor at BST loading over 10 vol% compared with using a normal BST powder as shown in Fig. 2. Figure 3 shows the microstructure of the compos￾ites with 10 vol% BST nano and normal powder loadings. The use of nanopowders yielded a more uniform and homogeneous microstructure but in general the use of nanopowder increased the loss factor. Dielectric Properties of Polymer–Ceramic Composites It was found that for the same filler ceramic load￾ing, the dielectric characteristics of the composites strongly depend on the type of polymer. Polar poly￾mers increase the er of the composites at low frequen￾cies, but has hardly any effect at microwave frequencies. The loss tangent of the composites peaks at an inter￾mediate frequency, indicating the relaxation behavior of the polymer matrix. The dielectric properties of the composites are influenced not only by the relative per￾mittivity of the components but also by other factors such as the morphology, dispersion, and the interactions between the two phases.39 Therefore, the prediction of the relative permittivity of the composite from the rel￾ative permittivity of the components and the volume fraction of the filler is very important but is a difficult task for electronic packaging applications. The follow￾ing equations are commonly used to calculate the er of the composites with a low filler content. 1. Jayasundere–Smith equation50: eeff ¼ emð1 vfÞ þ ei vf 3em eiþ2em h i 1þ3 vf ðeiemÞ eiþ2em h i 1 vf þ vf 3em eiþ2em h i 1þ3 vf ðeiemÞ eiþ2em h i ð1Þ 0 10 20 30 40 50 60 0.000 0.002 0.004 0.006 0.008 (a) (b) Dielectric loss εr(Modified Lichtenecker) εr(Experimental) Volume Percentage of BST Loss tangent 5 10 15 20 Relative Permittivity 0 5 10 15 20 25 30 35 0.000 0.002 0.004 0.006 0.008 Volume Percentage of nano BST Dielectric loss εr(Modified Lichtenecker) εr(Experimental) Los tangent 2 4 6 8 10 Relative permittivity Fig. 2. Variation of relative permittivity and loss tangent (a) BSTc￾COC composites (b) BSTa-COC composite at 1 GHZ as a function of BST loading (after Hu et al.24). BST, Ba0.55Sr0.45TiO3. 418 International Journal of Applied Ceramic Technology—Sebastian and Jantunen Vol. 7, No. 4, 2010

wwceramics. org/ACT Polymer-Ceramic Composites of 0-3 Connectivity 419 gm角C0 )C composites with BST loading100,组a%,的60m% and(d) BSTa-COC with BST Fig 3. SEM images Hu et al). BST, BaossSross Tio 2. Modified Lichtnecker equation lar. 33 among these equations, the Lichtnecker equation is the most com- log er =log Em +ur(l-m)log(=i)(2) monly used relation for predicting the permittivity of the composites. The Lichtnecker logarithmic rule con- 3. Series mixing formulas siders the composites as a random mixture of nearly spherical inclusions. In general, the theoretical predic (3) tions are valid for low filler contents and deviations from predictions increase with increasing filler contents. This 4. Maxwell-Wagner equation: ramic particles at higher filler contents and also due to 2Em +Ei+2 ur(E-Em) 2cm+1-(1-Em) (4) porosity or air enclosed by the composite. The theoret- ical predictions do not consider the matrix-filler inter 5. Effective medium theory(EMT) hase interactions and are valid for a composite made of a filler and a matrix with nearly the same relative per- tr(E-Em) mittivity values. The modified Lichtnecker eq Em 1+ Em +n(1-urEi-Em (5) cludes a fitting factor n, which repr between the filler and the matrix. In polyethelene- where Eeff, E;, and Em are the permittivity of the com- Sm2 Si2O, and polystyrene-Sm2Si2O7, the relative per posites, filler, and matrix, respectively, Ve is the volume mittivity calculated using the modified Lichtnecker fraction of the ceramic, and n is the fitting parameter or equation showed good agreement with experimental the morphology factor. The Jayasundere-Smith equa- data as shown in Fig. 4 for a filler up to 0.4 vol% tion is only valid for a filler content up to 0.3 vol%. This The deviations at higher volume fractions can be attrib is due to the fact that it considers the interactions be- uted to inhomogeneity in the filler distribution in the tween neighboring spheres. The Maxwell-Wagner polymer matrix and air entrapment in the composite In rule is generally valid when the properties of the two addition, it has been reported that the fitting fact

2. Modified Lichtnecker equation51: log eeff ¼ log em þ vfð1 nÞlog ei em ð2Þ 3. Series mixing formula51: 1 eeff ¼ vf ei þ ð1 vfÞ em ð3Þ 4. Maxwell–Wagner equation33: eeff ¼ em 2em þ ei þ 2 vf ðei emÞ 2em þ ei vf ðei emÞ ð4Þ 5. Effective medium theory (EMT)51 eeff ¼ em 1 þ vf ðei emÞ em þ nð1 vfÞðei emÞ   ð5Þ where eeff, ei, and em are the permittivity of the com￾posites, filler, and matrix, respectively, Vf is the volume fraction of the ceramic, and n is the fitting parameter or the morphology factor. The Jayasundere–Smith equa￾tion is only valid for a filler content up to 0.3 vol%. This is due to the fact that it considers the interactions be￾tween the neighboring spheres. The Maxwell–Wagner rule is generally valid when the properties of the two phases in the composite are similar.33 Among these equations, the Lichtnecker equation is the most com￾monly used relation for predicting the permittivity of the composites. The Lichtnecker logarithmic rule con￾siders the composites as a random mixture of nearly spherical inclusions. In general, the theoretical predic￾tions are valid for low filler contents and deviations from predictions increase with increasing filler contents. This is mainly due to the imperfect dispersion of filler ce￾ramic particles at higher filler contents and also due to porosity or air enclosed by the composite. The theoret￾ical predictions do not consider the matrix–filler inter￾phase interactions and are valid for a composite made of a filler and a matrix with nearly the same relative per￾mittivity values. The modified Lichtnecker equation in￾cludes a fitting factor n, which represents the interaction between the filler and the matrix. In polyethelene– Sm2Si2O7 and polystyrene–Sm2Si2O7, the relative per￾mittivity calculated using the modified Lichtnecker equation showed good agreement with experimental data as shown in Fig. 440 for a filler up to 0.4 vol%. The deviations at higher volume fractions can be attrib￾uted to inhomogeneity in the filler distribution in the polymer matrix and air entrapment in the composite. In addition, it has been reported that the fitting factor n is Fig. 3. SEM images of BSTc-COC composites with BST loading (a) 10 vol%, (b) 40 vol%, (c) 60 vol%, and (d) BSTa-COC with BST loading of 10 vol% (after Hu et al.24). BST, Ba0.55Sr0.45TiO3. www.ceramics.org/ACT Polymer–Ceramic Composites of 0–3 Connectivity 419

International ournal of Applied Ceramic Technolog-Sebastian and Jantunen Vol.7,No.4,2010 Licht 0-S2 △-S3 EMt 7S4 Modified Lichteneck -o- S5 10203040506070 BaTiO3 powder(vol%) Variation of relative Permittivity with BaTiO3 poud loading and their particle size (S1=0.151um, S2=0.254um S3=0319μm,S=08321um,S5=0916μum, after Cho et al.3 shape of the filler used in the polymer-ceramic com- posites. A small value of n indicates a near-spherical shape for the filler, while a high value of n shows a largely nonspherically shaped particle. However, the particle size should be small for a better fitting with the theoretical prediction. The EMT model fits well for the polymer-Sm2Si2O7 composites as shown in Fig. 4 However, Teirikangas et al. reported that in som cases, the morphology factor n used in EMT is not in- Volume fraction of Sm2 Si207 dependent of the selection of the polymer. Several quan titative rules of mixture models had been proposed for permitivity(a) polystyrene- Si 07(6) polyethylene-Sm25i207 each componen. s of the dielectric properties of Fig. 4. Comparison of theoretical and experimental relative redictions of the However, the theoretical composites at 8 GHz(after Thomas et al) models do not completely agree with the experimental somewhat sensitive to both the polymer and the ce- that it is difficult to obtain the correct Er of the powders ramic, thus reducing the feasibility of the Lichtnecker Instead, E, of the bulk ceramic is used. The er of the equation for different materials. The relative permit- powder may be different from that of the bulk. In fer- tivity of composites also depends on the distribution of roelectric BaTiO3 powders, Er varies with particle of the filler, shape, and size of the fillers and the interfac between ceramics and polymers. Recently, Rao et al. ace grain sizes. Figure 5 shows the variation of Er with proposed a model(Effective Medium Theory, EMT)to The number of theoretical models available for pre predict the relative permittivity of the composite in listing loss tangent is relatively less, as it is more com which the dielectric property of the composite is treated plicated. 4 The following relations are used to model the as an effective medium whose relative permittivity is dielectric loss tangent of the composites btained by averaging the permittivity values of the constituents. The emt model is a self-consistent model that assumes a random unit cell consisting of each filler an8)2=∑m(tan)2 surrounded by a concentric matrix layer. The model includes a morphology factor"n, "which is determined where tan 8 and tan 8; are the loss tangent of the com- empirically. This correction factor compensates for th osite, the loss tangent of ith material, a is a constant

somewhat sensitive to both the polymer and the ce￾ramic, thus reducing the feasibility of the Lichtnecker equation for different materials.41 The relative permit￾tivity of composites also depends on the distribution of the filler, shape, and size of the fillers and the interface between ceramics and polymers. Recently, Rao et al. 51 proposed a model (Effective Medium Theory, EMT) to predict the relative permittivity of the composite in which the dielectric property of the composite is treated as an effective medium whose relative permittivity is obtained by averaging the permittivity values of the constituents. The EMT model is a self-consistent model that assumes a random unit cell consisting of each filler surrounded by a concentric matrix layer. The model includes a morphology factor ‘‘n,’’ which is determined empirically. This correction factor compensates for the shape of the filler used in the polymer–ceramic com￾posites. A small value of n indicates a near-spherical shape for the filler, while a high value of n shows a largely nonspherically shaped particle. However, the particle size should be small for a better fitting with the theoretical prediction. The EMT model fits well for the polymer–Sm2Si2O7 composites as shown in Fig. 4. However, Teirikangas et al. 41 reported that in some cases, the morphology factor n used in EMT is not in￾dependent of the selection of the polymer. Several quan￾titative rules of mixture models had been proposed for predictions of the basis of the dielectric properties of each component.6,50,52,53 However, the theoretical models do not completely agree with the experimental observations. One of the reasons for the poor fitting is that it is difficult to obtain the correct er of the powders. Instead, er of the bulk ceramic is used. The er of the powder may be different from that of the bulk. In fer￾roelectric BaTiO3 powders, er varies with particle or grain sizes.53 Figure 5 shows the variation of er with vol% of BaTiO3 powder having different grain sizes. The number of theoretical models available for pre￾dicting loss tangent is relatively less, as it is more com￾plicated.54 The following relations are used to model the dielectric loss tangent of the composites. General mixing model55,56 ðtan dcÞ a ¼ Xvfiðtan diÞ a ð6Þ where tan dc and tan di are the loss tangent of the com￾posite, the loss tangent of ith material, a is a constant, Fig. 4. Comparison of theoretical and experimental relative permittivity (a) polystyrene–Sm2Si2O7 (b) polyethylene–Sm2Si2O7 composites at 8 GHz (after Thomas et al.40). Fig. 5. Variation of relative permittivity with BaTiO3 powder loading and their particle size (S1 5 0.151 mm, S2 5 0.254 mm, S3 5 0.319 mm, S4 5 0.832 mm, S5 5 0.916 mm, after Cho et al.53). 420 International Journal of Applied Ceramic Technology—Sebastian and Jantunen Vol. 7, No. 4, 2010

wwceramics. org/ACT Polymer-Ceramic Composites of 0-3 Connectivity 一 Experimental Parallel Serial ewwwM 0.03 Bruggmen “日: Volume Percentage of SCT Fig on of the experimental dielectric loss with the 4 predicted values(afier Subodh et al. 5) 4.5 and vg is the volume fraction of the ith material. The 24.0 value of the constant a determines the mixing rule where a=-1 means serial mixing, a= 1 parallel mix d a=0 gives the logarithmic The Bruggeman model Em)(E+2e/)e Temperature(C) +e-sa)(e+28) (7) polystyrene-Sm i207(b) polyethylene-Sm2i207composites(after Thomas where the e, em,E,e"i, e"m, e" are the real and imag- inary parts of the permittivity of the filler, matrix, and the temperature variation of the relative permittivity the composite, respectively. Figure 6 shows the com- reasonably small and the material is thus useful for parison of the predicted and experimental loss tangent practical applications. Results for other properties im for epoxy/Srg Ce?Ti12O3 composites. The Bruggeman portant for microwave substrates have been reported less model gives a relatively good fit with the experimental frequently. Walpata et al obtained a temperature results for lower filler contents. The dielectric loss de- compensated thermoplastic composite with a high E, by pends on intrinsic and extrinsic factors. The intrinsic using a second filler with contrasting thermal depen are mainly due to the interaction of the ac elec- dence of permittivity(tEr). They prepared a polyp ld with phonons. The extrinsic factors such henylene sulfide/SrTiO3/mica composite. The use of as defects, interfaces, size and shape of the filler, and one ceramic with a positive ter and the other with a micropores also contribute to dielectric loss negative ter allowed to obtain a temperature-compen- is The temperature coefficient of relative permittivity sated compensate figure 8 shows the variation of E, of one of the important properties that control the over- the composite 38/8/54(mica/SrTiO, /PPS)measured at all performance of the substrate materials. Some groups 2 GHz. The same procedure was also followed by Xiang have reported fabrication and calculation methods et al. to modify ter. Table I gives a list of the dielectric perature-compensated composites properties polym Figure 7 shows the temperature dependence of the Among the many reported composites given in Table relative permittivity of polystyrene and polyethylene I, polystyrene-Sr2Ce2TisO1s has a very loss tangent of composites with Sm2Si2O7. In many cases, however, 0.0004 relatively high permittivity of 13.6 at

and vfi is the volume fraction of the ith material. The value of the constant a determines the mixing rule where a 5 1 means serial mixing, a 5 1 parallel mix￾ing, and a 5 0 gives the logarithmic mixing rule.55 The Bruggeman model57 e00 ¼ ðe0 i e0 Þðe0 i þ 2e0 mÞe0 ðe0 i e0 mÞðe0 i þ 2e0 Þe0 m e00 m þ 3ðe0 e0 mÞ ðe0 i e0 mÞðe0 i þ 2e0 Þ e00 i ð7Þ where the e0 i, e0 m, e0 , e00 i, e00 m, e00 are the real and imag￾inary parts of the permittivity of the filler, matrix, and the composite, respectively. Figure 6 shows the com￾parison of the predicted and experimental loss tangent for epoxy/Sr9Ce2Ti12O36 composites. The Bruggeman model gives a relatively good fit with the experimental results for lower filler contents. The dielectric loss de￾pends on intrinsic and extrinsic factors. The intrinsic factors are mainly due to the interaction of the ac elec￾tric field with phonons. The extrinsic factors such as defects, interfaces, size and shape of the filler, and micropores also contribute to dielectric loss. The temperature coefficient of relative permittivity is one of the important properties that control the over￾all performance of the substrate materials. Some groups have reported fabrication and calculation methods to enable temperature-compensated composites.38,59 Figure 7 shows the temperature dependence of the relative permittivity of polystyrene and polyethylene composites with Sm2Si2O7. 40 In many cases, however, the temperature variation of the relative permittivity is reasonably small and the material is thus useful for practical applications. Results for other properties im￾portant for microwave substrates have been reported less frequently. Walpata et al. 60 obtained a temperature￾compensated thermoplastic composite with a high er by using a second filler with contrasting thermal depen￾dence of permittivity (ter). They prepared a polyp￾henylene sulfide/SrTiO3/mica composite. The use of one ceramic with a positive ter and the other with a negative ter allowed to obtain a temperature-compen￾sated compensate. Figure 8 shows the variation of er of the composite 38/8/54(mica/SrTiO3/PPS) measured at 2 GHz. The same procedure was also followed by Xiang et al. 59 to modify ter. Table I gives a list of the dielectric properties of several polymer–ceramic composites. Among the many reported composites given in Table I, polystyrene–Sr2Ce2Ti5O15 has a very loss tangent of 0.0004 with a relatively high permittivity of 13.6 at 0 10 20 30 40 0.01 0.02 0.03 0.04 tan δ Volume Percentage of SCT Experimental Parallel Serial Logarithmic Bruggmen Fig. 6. Comparison of the experimental dielectric loss with the predicted values (after Subodh et al.58). Fig. 7. Variation of relative permittivity with temperature (a) polystyrene–Sm2Si2O7 (b) polyethylene–Sm2Si2O7 composites (after Thomas et al.40). www.ceramics.org/ACT Polymer–Ceramic Composites of 0–3 Connectivity 421

International ournal of Applied Ceramic Technolog-Sebastian and Jantunen Vol.7,No.4,2010 8 GHz. The Taclampus of Taconic has a loss tangent of 0.0004 with a low relative permittivity of 2. 1 at 10 GHz. Frequency The low E, facilitates in faster signal transmission, whereas a higher value of Er aids miniaturization of the devices. Thermal Conductivity Dielectrie constant Epoxy-silica composites have been used widely as because of their excal material for the last 35 years the electronic packagi ellen mechanical and electrical properties, low cost, and ease of processing. Silica has a low thermal conductivity of 1.5 W/mK. In order rmal COl Temperature(c) Bollampally used thermally conducting fillers such Fig. 8. Variation of relative permittivity and frequency of patch as alumina and aluminum nitride Figure 9 shows the antenna comprised of a mica/Sr/PPS (38/8/54/96)composite variation of thermal conductivity as a function of with temperature measured at 2 GHe(after Walpata et al o) volume loading of alumina, silica, and silica-coated alu- minum nitride. Addition of 50 vol% silica-coated alu- minum nitride increased the thermal conductivity 10 Table I. Dielectric Properties of Polymer-Ceramic Composites Polymer Filler Er Tan s Ref n2Si2O7 4.81 0.0055 8Ghz Thomas et al40 Ca(ILil3Nby/3)o.8Tio. 2JO3 0.4 7 8GHz George and Sebastian Li2MgSiO A 4 0.0032 8 GHz George 4 0.004 8 ghz Subodh et aL58 HDPE Sr2Ce2TisO1 0.4 11.0 8GHz Subodh et al. 63 Polystyrene Li2△ MgSio4 0.4 3.84 12 8GHz George et al. Polyester Sm,,o 0.4 4.34 0.0101 8 GHz Thomas et al. 40 P Sr2Ce2TisO15 13.6 8GHz Subodh et al 641 Polystyrene Ca(LilNbz/3).sTio.21O3 0.4 8 GHz George and Sebastian PTFE CeO2 7 GHz Anjana et al. PTFE 60wt% 8 GHz Chen and colleagu PTFE ZnAl2OA-TiOz 7 GHz Thomas et ai PTFE SrTiO3 0.63 13.1 10 GHz Rajesh PTFE TiO 10.2 8 GHz Rajesh et al.8 PTFE 2MgO-2Al2O3-5SiO2 60 wt% 3.1 10GHz Murali et al PTFE 2MgO-2Al2O3-5SiO2 10 2.17 10GHz Murali et aL.6 PTFE Bi2O3-ZnO-Nb20 0.6 12.5 PTFE A 0.66 4.3 800 MHz Xiang et a,35 PTFE 0.56 3.35 10GHz Murali et al35 PTFE 11.8 10 GHz Rajesh et al. PTFE aNdSmTi,O1 67wt% 8.0 PTFE LSCO 0.3 25,000 I MHz Deepa et al. PTFE Sr,CenT 0.4 772 7GHz Subodh et al. 74 POE SrTiO3 0.4 11.0 0.9 GHz Xiang et al. POE SrTiO -NiZn ferrite 5.4 0.0018 100Hz Yang et al75 PEEK TiO2 25 499 8GHz Raiesh et al Poly(methymetho Bao. Sro 4TiO3 0.416 1212 0.026 10 KHz Xiang et al. Metallocene cyclic Soda lime borosilicate 0.36 192 0.0009 I MHz yang et al23

8 GHz. The Taclampus of Taconic has a loss tangent of 0.0004 with a low relative permittivity of 2.1 at 10 GHz. The low er facilitates in faster signal transmission, whereas a higher value of er aids miniaturization of the devices. Thermal Conductivity Epoxy–silica composites have been used widely as the electronic packaging material for the last 35 years because of their excellent mechanical and electrical properties, low cost, and ease of processing.97 Silica has a low thermal conductivity of 1.5 W/mK. In order to increase the thermal conductivity, Wong and Bollampally98 used thermally conducting fillers such as alumina and aluminum nitride. Figure 9 shows the variation of thermal conductivity as a function of volume loading of alumina, silica, and silica-coated alu￾minum nitride. Addition of 50 vol% silica-coated alu￾minum nitride increased the thermal conductivity 10 Fig. 8. Variation of relative permittivity and frequency of patch antenna comprised of a mica/SrTiO3/PPS (38/8/54 vol%) composite with temperature measured at 2 GHz (after Walpata et al.60). Table I. Dielectric Properties of Polymer–Ceramic Composites Polymer Filler Vf er Tan d Fo Ref Polyethylene Sm2Si2O7 0.4 4.81 0.0055 8 GHz Thomas et al. 40 Polyethylene Ca([Li1/3Nb2/3)0.8Ti0.2]O3 0.4 7.72 0.004 8 GHz George and Sebastian61 Polyethylene Li2MgSiO4 0.4 3.54 0.0032 8 GHz George et al. 62 Polyethylene Sr9Ce2Ti12O36 0.4 12.1 0.004 8 GHz Subodh et al. 58 HDPE Sr2Ce2Ti5O15 0.4 11.0 0.006 8 GHz Subodh et al. 63 Polystyrene Li2MgSiO4 0.4 3.84 0.012 8 GHz George et al. 62 Polyestyrene Sm2Si2O7 0.4 4.34 0.0101 8 GHz Thomas et al. 40 Polystyrene Sr2Ce2Ti5O15 0.5 13.6 0.0004 8 GHz Subodh et al. 64 Polystyrene Ca([Li1/3Nb2/3)0.8Ti0.2]O3 0.4 7.4 0.003 8 GHz George and Sebastian61 PTFE CeO2 0.6 5.0 0.0064 7 GHz Anjana et al. 65 PTFE SiO2 60 wt% 2.9 0.0024 8 GHz Chen and colleagues34,35 PTFE ZnAl2O4–TiO2 0.6 4.8 0.008 7 GHz Thomas et al. 66 PTFE SrTiO3 0.63 13.1 0.0055 10 GHz Rajesh et al. 67 PTFE TiO2 0.67 10.2 0.022 8 GHz Rajesh et al. 68 PTFE 2MgO–2Al2O3–5SiO2 60 wt% 3.17 0.0034 10 GHz Murali et al. 69 PTFE 2MgO–2Al2O3–5SiO2 10 wt% 2.17 0.0007 10 GHz Murali et al. 69 PTFE Bi2O3–ZnO–Nb2O5 0.6 12.5 0.001 800 MHz Xiang et al. 70 PTFE Al2O3 0.66 4.3 0.0021 10 GHz Murali et al. 35 PTFE MgO 0.56 3.35 0.015 10 GHz Murali et al. 35 PTFE CaTiO3 11.8 0.0036 10 GHz Rajesh et al. 71 PTFE BaNdSmTi4O12 67 wt% 8.04 0.009 Jacob et al. 72 PTFE LSCO 0.3 25,000 1 MHz Deepa et al. 73 PTFE Sr2Ce2Ti5O16 0.4 7.72 0.08 7 GHz Subodh et al. 74 POE SrTiO3 0.4 11.0 0.010 0.9 GHz Xiang et al. 27 POE SrTiO3–NiZn ferrite 5.4 0.0018 100 Hz Yang et al. 75 PEEK TiO2 25 wt% 4.99 0.0087 8 GHz Rajesh et al. 76 Poly(methymetho crylate) Ba0.6Sr0.4TiO3 0.416 1212 0.026 10 KHz Xiang et al. 22 Metallocene cyclic olefin coploymer Soda lime borosilicate 0.36 1.92 0.0009 1 MHz Yang et al. 23 422 International Journal of Applied Ceramic Technology—Sebastian and Jantunen Vol. 7, No. 4, 2010

wwceramics. org/ACT Polymer-Ceramic Composites of 0-3 Connectivity Table l. continued Polymer Ref PMN-PT/BaTiO3(3: 1) 0.7 0.017 10 KHz Bhalla et aL.77 PZ 0.4 Bhalla et aL77 EEEEEEEEEE PMN-PT 805 ooooooooooooo Windlass et aL7 0.6 Ramajo and colleagues BaTio 5 Lee et alsl SrTiO3 00 5 10 GHz Lee et al SroCezT112O36 0.4 14.1 0.022 8GHz subodh et aL.74 BaTiO3 0.45 13.1 I GHz lee et al8 PMN-PT-BT 07 110 Rao et al82 a(li, Nb)TiO3 0.3 8.0 I MHz George and Sebastian Ca(Li, Nb)TiO3-Ag 0.3Ag818,000 I MHz George and Sebastian Ca(Li, Nb)TiO3-Ag 0.26Ag I MHz George and Sebastian (BaosRo. 1)(Tio. Zro.1)O3 70 wt% 25.2 0.035 I MHz Yang et al. Batio Amin et a PVDF TGS ng e PVDF bTiO 0.62 Yamazaki and PVDF ZT 05 100Hz Yao et aL89 PVDF Batio T P(VDF/TrFe) 05 118 Abdullah and Das P(VDF/TrFe 05 Dias and Das Gupta P(VDF/TrFe) bTiO:: Ca Dias and Das gupta° Nio.. 2,OA 2 Y TMPTA Cdo 0.2 2200 Popielarz and Chiang COC 0.25 0.0023 Polyphenelene sulfide BST 13.5 0.0025 Hu et aL26 Mica/SrTiO3 0.38 6.4 0.0052 38 Batio Batio 0.1 0.0082 u er RT Duroid 6010 LM PTFE-ceramic 10.24 0.0018 RT Duroid 5880 PTFE-glass microfibers 2 GHz Rogers RT Duroid 5870 PTFE-glass microfibers 2.33 0.0023 GHz Roge RT Duroid 6002 10GHz Rogers RO4533 3 RO4534 RO4535 RO4350 3.45 10GHz Rogers FR4 10 GHz Roge TFG 3.2 0.003 10G TPG30 2.87 10 GHz Taconic TLG-29, TLG-30 287-3.50.0024-0.002910 GHz Taconic TLG-32. TLG-33 TLG-34, TLG-35 TLT PTFE-fiber glass 2 0.0006 I MHz Taconic TLP PTFE→ fber glass 0.0009 10GHz Taconic TLC 2.75-3.200.0030 10 GHz Taconic 2.95-3.00 0.0028 10 GHz Taconic RF-35 10 GHz Taconic RF-35P 0.0035 10GHz Taconic TSM-30 0.0012 10 GHz Taconic

Table I. Continued Polymer Filler Vf er Tan d Fo Ref Epoxy PMN-PT/BaTiO3 (3:1) 0.7 89 0.017 10 KHz Bhalla et al. 77 Epoxy PZT 0.4 110 Bhalla et al. 77 Epoxy PMN-PT 135 Windlass et al. 78 Epoxy BaTiO3 0.6 45 0.035 Ramajo and colleagues79,80 Epoxy BaTiO3 0.5 24 Lee et al. 81 Epoxy SrTiO3 0.5 21 10 GHz Lee et al. 81 Epoxy Sr9Ce2Ti12O36 0.4 14.1 0.022 8 GHz Subodh et al. 74 Epoxy BaTiO3 0.45 13.1 0.025 1 GHz Lee et al. 81 Epoxy PMN-PT-BT 0.7 110 0.016 Rao et al. 82 Epoxy Ca(Li,Nb)TiO3 0.3 8.0 0.009 1 MHz George and Sebastian83 Epoxy Ca(Li,Nb)TiO3–Ag 0.3 Ag 818,000 2.6 1 MHz George and Sebastian83 Epoxy Ca(Li,Nb)TiO3–Ag 0.26 Ag 72.3 0.065 1 MHz George and Sebastian83 Epoxy (Ba0.9Sr0.1)(Ti0.9Zr0.1)O3 70 wt% 25.2 0.035 1 MHz Yang et al. 84 Rubber BaTiO3 0.3 17 Amin et al. 85 PVDF TGS 0.8 12 Fang et al. 86 PVDF PbTiO3 0.62 54 Yamazaki and Kitayama87 PVDF PZT 0.5 90 Abdullah88 PVDF PZT 0.7 140 0.3 100 Hz Yao et al. 89 PVDF BaTiO3 0.2 20 Tripathi et al. 90 P(VDF/TrFe) PZT 0.5 118 Abdullah and Das Gupta91 P(VDF/TrFe) PZT 0.5 80 Dias and Das Gupta92 P(VDF/TrFe) PbTiO3:Ca 0.6 66 Dias and Das Gupta6 HDPE Ni0.8Zn0.2Fe2O4 0.4 4.2 0.01 Yang et al. 93 TMPTA CdO 0.2 2200 0.1 1 KHz Popielarz and Chiang94 COC BST 0.25 6 0.0023 1 GHz Hu et al. 24 Polyphenelene sulfide (PPS) BST 0.7 13.5 0.0025 1 GHz Hu et al. 26 PPS Mica/SrTiO3 0.38 6.4 0.0052 210GHz Che et al. 38 Polyimide BaTiO3 0.9 117 1 MHz Devaraju et al. 95 Polyimide BaTiO3 0.1 35 0.0082 10 KHz Devaraju et al. 95 RT Duroid 6010 LM PTFE–ceramic — 10.24 0.0018 Rogers RT Duroid 5880 PTFE–glass microfibers — 2.2 — 2 GHz Rogers RT Duroid 5870 PTFE–glass microfibers — 2.33 0.0023 10 GHz Rogers RT Duroid 6002 2.94 0.0012 10 GHZ Rogers RO 4533 3.3 0.0020 Rogers RO 4534 3.4 0.0022 Rogers RO 4535 3.5 0.0032 Rogers RO 4350 3.45 0.004 10GHz Rogers FR4 Fiber glass reinforced epoxy 4.2 0.020 10 GHz Rogers TFG 3.2 0.003 10 GHz Rogers TPG30 2.87 0.0027 10 GHz Taconic TLG-29, TLG-30, TLG-32, TLG-33, TLG-34, TLG-35 2.87–3.5 0.0024–0.0029 10 GHz Taconic TLT PTFE–fiber glass fabric 2.5 0.0006 1 MHz Taconic TLP PTFE–fiber glass fabric 2.17 0.0009 10 GHz Taconic TLC 2.75–3.20 0.0030 10 GHz Taconic TLE 2.95–3.00 0.0028 10 GHz Taconic RF-35 3.5 0.0028 10 GHz Taconic RF-35P 3.5 0.0035 10 GHz Taconic TSM-30 2.94 0.0012 10 GHz Taconic www.ceramics.org/ACT Polymer–Ceramic Composites of 0–3 Connectivity 423

International ournal of Applied Ceramic Technolog-Sebastian and Jantunen Vol.7,No.4,2010 Table l. continued ef TLY PTFE woven glass 2.17-2 0.0009 10GHz Taconic TLX PTFE woven glass 2.45-2.65 0.0019 10 GHz Taconic 0.0004 10 GHz Taconic RF-60A 10 GHz Taconic RF-41,RF-43,RF-45 4.10-1.500.0033-0.003810 GHz Taconic TRF-4l, TRF-43, PTFE woven glass 4.1-4.5 00035 10GHz Taconic TRF-45 RF.30 3.00 0.0014 1.9 GHz Taconic HyRelex 0.0020 10GHz Taconic Cer-10 10.0 0.0035 10 GHz Taconic Arlon 25FR and 25N 3.38 0.0025 10 GHz Arlon SPEEDBOARD C 0.004 10GHz Barnes FASTRISE 27 10GHZ Taconic TSM29 10GHz Taconic CLTE 294-3.000.0012-0.0023 AD320 2.55-4.30.0015-0.0035 AD410A 0.0023 Arlon 6.00 AR1000 0.003 25N DiClad 880-PIM 2.17 0.0009 Iso Clad 91 2.17 CuClad 250 GT Nelco N4000-13 Nelco 4000-13 SI 0.008 10GHZ Nelo elco-400013SI 3.30 times as compared with the pure epoxy. Additionally, determine the precise value of the thermal conductivity polymer-ceramic composites are commonly used of composite materials. The following models are used electronic substrates and for packaging to dissipate to calculate the effective thermal conductivity of poly he heat generated in the electronic devices. The mer-ceramic composites thermal conductivity of the polymer is generally very l Geometric mean model. low. It was reported that the addition of a high thermal It is a simple model to predict the thermal conduc conductivitymaterial such as aluminum nitride tivity of a two-component composite. 00 The thermal as a filler effectively increases the thermal con- conductivity is given by of polymers or polymer-ceramic comp 3298.99 kerr=k ikI-w Determining the thermal conductivity of o materials is crucial in a number of industrial processes. where kef, kb, and km are the thermal conductivities of The effective thermal conductivity of a heterogeneous the composite, filler, and matrix, respectively material is strongly affected by its composition, crystal 2. EMT model: structure, distribution within the medium. and contact The EMT assumes that the composite system is a he between the particles. Several models and experimental m us medium and the EMT equation for thermal onductivity can be derived through the Laplace equation

times as compared with the pure epoxy. Additionally, polymer–ceramic composites are commonly used as electronic substrates and for packaging to dissipate the heat generated in the electronic devices. The thermal conductivity of the polymer is generally very low. It was reported that the addition of a high thermal conductivity material such as aluminum nitride as a filler effectively increases the thermal con￾ductivity of polymers or polymer–ceramic compos￾ites.32,98,99 Determining the thermal conductivity of composite materials is crucial in a number of industrial processes. The effective thermal conductivity of a heterogeneous material is strongly affected by its composition, crystal structure, distribution within the medium, and contact between the particles. Several models and experimental approaches have been reported100–111 to predict and determine the precise value of the thermal conductivity of composite materials. The following models are used to calculate the effective thermal conductivity of poly￾mer–ceramic composites: 1. Geometric mean model: It is a simple model to predict the thermal conduc￾tivity of a two-component composite.100 The thermal conductivity is given by keff ¼ kVf f k1Vf m ð8Þ where keff, kf, and km are the thermal conductivities of the composite, filler, and matrix, respectively. 2. EMT model: The EMT assumes that the composite system is a ho￾mogeneous medium and the EMT equation for thermal conductivity can be derived through the Laplace equation Table I. Continued Polymer Filler Vf er Tan d Fo Ref TLY PTFE woven glass 2.17–2.4 0.0009 10 GHz Taconic TLX PTFE woven glass 2.45–2.65 0.0019 10 GHz Taconic Taclamplus 2.1 0.0004 10 GHz Taconic RF-60A 6.15 0.0038 10 GHz Taconic RF-41, RF-43, RF-45 4.10–4.50 0.0033–0.0038 10 GHz Taconic TRF-41, TRF-43, TRF-45 PTFE woven glass reinforced 4.1–4.5 0.0035 10 GHz Taconic RF-30 3.00 0.0014 1.9 GHz Taconic HyRelex 2.6 0.0020 10 GHz Taconic Cer-10 10.0 0.0035 10 GHz Taconic Arlon 25FR and 25 N 3.38 0.0025 10 GHz Arlon SPEEDBOARD C 2.6 0.004 10 GHz Barnes et al. 96 FASTRISE 27 2.7 0.0020 10 GHZ Taconic TSM29 2.94 0.0014 10 GHz Taconic CLTE 2.94–3.00 0.0012–0.0023 Arlon TC350 3.5 0.0020 Arlon TC600 6.15 0.0020 Arlon AD255A, AD260, AD300A, AD320A, AD350A, AD410A, AD430A 2.55–4.3 0.0015–0.0035 Arlon AD1000A 10.2 0.0023 Arlon AD600 6.00 0.003 Arlon AR1000 9.8 0.003 Arlon 25N 3.38 0.0025 Arlon 25FR 3.58 0.0035 Arlon DiClad 880-PIM 2.17 0.0009 Arlon IsoClad 917 2.17 0.0013 Arlon CuClad 250 GT 2.40 0.001 Arlon Nelco N4000-13 3.70 0.008 Nelco Nelco 4000-13 SI 3.4 0.008 10 GHZ Nelco Nelco-400013SI 3.30 0.007 Nelco 424 International Journal of Applied Ceramic Technology—Sebastian and Jantunen Vol. 7, No. 4, 2010