Pressure-Dependent Thermal Characterization of Biporous ... · ﬂexibility to accommodate two...

568 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 10, NO. 4, APRIL 2020

Pressure-Dependent Thermal Characterization ofBiporous Copper Structures

Cheng-Hui Lin , Member, IEEE, and Yoonjin Won , Member, IEEE

Abstract— With the advance of modern semiconductor tech-nology, the power density of electronic devices continuouslyincreases. The performance of electronic devices is now governedby heat dissipation from the heat source to the heat sink, whichrequires new efficient thermal management solutions. Thermalinterface materials (TIMs), placed between heat source and heatsink, are designed to form a conduction pathway by providing alow thermal resistance conduit and by eliminating the air gapsbetween two contact surfaces. However, most TIMs commerciallyavailable show limited performances as they are either thermallyconductive but stiff (e.g., metals) or mechanically ductile withhigh thermal resistance (e.g., polymers), which motivates thesearch for new materials for the use in TIMs. In this article,we suggest a new type of metal/polymer composite-based TIMswith the aim of developing thermally conductive and mechani-cally compliant materials at a low cost. Metal/polymer composite-based TIMs are fabricated by using a hydrogen bubble-templatedelectrodeposition method that forms microscale cavities andnanoscale nanofeatures on copper substrate, called the biporouscopper (BPCu). The BPCu is then sintered to enhance thestructural strength and is infiltrated by polydimethylsiloxane(PDMS) to increase its structural flexibility and durabilityagainst mechanical or thermal stresses. We measure the pressure-dependent thermal resistances of TIMs by assuming 1-D thermalconduction. The average effective thermal conductivities are19.4 and 18.3 W/m K of 60% and 80% PDMS filling ratiosamples, respectively. In addition, enhancements in mechanicalstrength of BPCu/PDMS TIMs are confirmed through the smallerstructural deformation.

Index Terms— 3-D biporous copper (BPCu), packaging, hydro-gen bubble-templated electrodeposition, thermal interface mate-rials (TIMs).

I. INTRODUCTION

AS SEMICONDUCTOR devices reduce their vol-umes with increasing digital processing capabilities,

the increase in power density of modern electronics becomes achallenging issue from a perspective of thermal management.One method to resolve thermal issue is to enhance heat transferfrom heat source to heat spreader or heat sink through the useof additional materials, called the thermal interface materials(TIMs). TIMs are designed to provide thermal routes between

Manuscript received July 25, 2019; revised October 24, 2019; acceptedNovember 22, 2019. Date of publication December 3, 2019; date of currentversion April 1, 2020. The work of C.-H. Lin was supported by the Fellowshipof National Chung Shan Institute of Science and Technology, Taiwan. Recom-mended for publication by Associate Editor A. Bhattacharya upon evaluationof reviewers’ comments. (Corresponding author: Yoonjin Won.)

The authors are with the Department of Mechanical and AerospaceEngineering, University of California at Irvine, Irvine, CA 92617 USA(e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this article are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCPMT.2019.2956722

the hot and cold surfaces by creating conducting intermediarypathways [1]–[3]. In this process, it is important to accommo-date thermal expansion mismatch of two surfaces by attainingthe mechanical compliance [4], [5]. To do so, two types ofconventional TIMs are suggested; the first type is conductivematerials (e.g., metal or ceramic materials), and the other typeis mechanically compliant materials (e.g., polymers). Suchconventional TIMs’ performances have been limited due to thelarge stiffness (or low mechanical compliance) of conductivematerials or low thermal conductivities of compliant materials(which is typically lower than 0.4 W/m K) [6]–[8]. To fusethe advantages of those TIMs, past studies have suggested twodifferent strategies. The first strategy is to nanostructure con-ductive materials (i.e., metal-based materials or carbon-basedmaterials) to enhance their structural compliance. The exam-ples include the use of vertically aligned carbon nanotubes(CNTs) with a high intrinsic thermal conductivity (rangingfrom 3000 to 6600 W/m K [9], [10] for multiwalled and single-walled CNTs, respectively). In this effort, the vertical arrange-ment of CNTs is suggested to provide additional mechanicalflexibility to accommodate two surfaces that show differentthermal expansion coefficients [11]. The overall thermal resis-tances of CNT-metal bonding (e.g., silver, copper, and metaldeposited silicon [2], [12], [13]) are reported as low as ∼3.5 ×10−2 cm2K/W [14]. The second strategy is to begin with softmaterials with conductive nanoscale fillers in order to improvetheir effective thermal conductivity. For example, CNT parti-cles are dispersed in polymer matrices, enabling additionalconduction pathways [15]–[17]. Such CNTs/polymer compos-ites have several drawbacks, such as high fabrication costs[10], limited thermal conductivity enhancement due to poorpercolation [18], and strong dependence on their structuralmorphology [19]. Because of those limitations, there havebeen efforts to replace CNT particles with other nanoparticles(e.g., graphene and boron nitride) or metallic nanostructures(e.g., silver or copper nanowires). Sauciuc et al. [20] dis-cussed the mechanical properties and thermal characteristicsof vertically aligned graphite/polymer composite TIM. In thisarticle, the thermal degradation of the TIM caused by hard-ness was alleviated by introducing a mechanically compliantpolymer matrix. The measured effective thermal conductiv-ity was 30 W/m K in the out-of-plane direction. Kuanget al. [21] utilized the highly thermal conductive and ori-ented hexagonal boron nitride nanosheets (BNNs) dispersedin silicone rubber and natural rubber to form flexible TIMs,reporting a high effective thermal conductivity of 5.5 W/m K.

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LIN AND WON: PRESSURE-DEPENDENT THERMAL CHARACTERIZATION OF BPCu STRUCTURES 569

Chen et al. [22] proposed a novel method to fabricate circular,flexible and electroinsulated polyvinyl alcohol (PVA)/BNNScomposite TIMs via electrostatic spinning, and the through-plane thermal conductivity enhancement of polydimethyl-siloxane (PDMS)/PVA/BNNS TIM is measured to be tentimes compared to pure PDMS at 15.6 vol% BNNS load-ing. Vertically aligned copper nanowires are prepared byanodic aluminum oxide (AAO) porous membrane-templatedelectrodeposition [23] or using porous polycarbonate (PC)porous template [24], [25]. The resulting metallic nanowiresare further infiltrated by low viscosity PDMS to enhance themechanical strength, resulting in the thermal resistance of5 × 10−2 cm2 K/W, which is almost one magnitude lowerthan the commercial products. In addition to the aforemen-tioned two types of TIMs, soft alloy metal TIM is devel-oped [26]. The employment of soft metal matrix addressesthe delamination issue introduced by a paste-based matrix,which is commonly observed with the paste-based TIMs aftermultiple thermal and mechanical cycles.

While there have been numerous studies to fabricate the3-D porous structures in many applications such as catalysis,fuel cell electrodes, fluid delivery, and boiling heat transfer[27]–[30], a templated-electrodeposition method has drawnsignificant interest due to its simplicity. Among multiple meth-ods to create sacrificial templates, Shin et al. [31] and Shin andLiu [32] had reported a cost-effective method to create a 3-Dsacrificial, quasi-static template by using hydrogen bubbles’formation. In this process, acids are added in the electrolyte toprovide hydrogen ions, and the reaction at the cathode includesboth the formation of hydrogen bubbles and solid metal, whichcan be expressed as

Mn+ + ne− → M(s) (1)

2H+ + 2e− → H2(g). (2)

With a high current density, hydrogen bubbles continuouslyand dynamically form, and the low mass density of hydrogenallows bubbles to move upward or coalesce after formation,enabling an interconnected, highly porous, and coral-like metalstructure. As the pores are formed by gas departure and theinterconnection between pores provides additional water vaporroutes. Some of thermofluidic characteristics (e.g., boiling heattransfer coefficients) are reported in other studies [33], [34].However, the thermal conductivity for the use in TIMs is stillunderexplored.

In this article, we create a new type of 3-D porous cop-per structures by employing the hydrogen bubble-templatedelectrodeposition method. In order to enhance the struc-tural strength, the porous copper structures are sintered andinfiltrated with hexane-diluted PDMS, resulting in biporouscopper(BPCu)/PDMS composites. The thermal characteristicsof BPCu/PDMS composites as a function of pressure aremeasured based on the 1-D, steady-state thermal conductionmethodology.

II. PRESSURE-DEPENDENT THERMAL RESISTANCE

METROLOGY

In order to measure the thermal resistance of the samples,an experimental setup based on ASTM D5470-06 (Stand

Fig. 1. (a) Schematic of experimental setup showing two copper barsconnected to a heat source and heat sink, respectively. The TIM sampleis sandwiched between two copper bars, enabling 1-D heat conductionassumption. A set of load cells installed on the heat sink allow us to measurepressure-dependent thermal resistances. (b) Schematic of the 1-D thermalcircuits, including bulk thermal resistance and interface thermal resistances.

test method for thermal transmission properties of thermallyconductive electrical insulation materials) is prepared [25],[35]. As the scheme of the apparatus is shown in Fig. 1(a),a sample is placed between two symmetric square copper barsthat are connected to heat source and heat sink, respectively.The cross-sectional area of the copper bar is 10 mm× 10 mmwith a length of 35 mm. Because of the combination of smallcross-sectional area and high thermal conductivity of copper,we assume a 1-D, steady-state, thermal conduction by neglect-ing in-plane temperature differences. K-type thermocouplesare used to record the temperatures at three locations along thecopper bar. By using the temperature profile, the net heat fluxq” along the sample can be calculated based on Fourier’s law.To minimize heat losses, a ceramic fiber blanket and Teflonblock are used to insulate copper bars and heat source fromthe ambient. The convective heat loss is estimated at elevatedtemperature in the natural convection conditions where theconvective heat transfer coefficient of free air is set to be10 W/m2 K. The radiative heat loss is calculated based onthe temperature differences between the copper bars and theambient temperature with the emissivity of the copper barof 0.87. The calculated heat losses resulted from convection aswell as radiation are 930 and 780 W/m2, respectively, whichare responsible for 0.9% and 0.8% of the average net flux q”.

As the thermal circuit of the system is shown in Fig. 1(b),the thermal resistances are in series where the total interfaceresistance R”total (=R”Cu−Cu + R”Cu +R”TIM + R”TIM−Cu)can be acquired by dividing the temperature difference �Tbetween the surfaces of upper and lower copper bars by netheat flux q”. Before measuring the samples, R”total (=R”Cu−Cu



Fig. 2. (a) Total thermal resistance R”total (= R”Cu−Cu + R”Cu + R”Cu−Cu)for different thickness copper bricks. The thermal resistance distribution showsa linear trend with respect to the copper brick thickness. (b) Interface thermalresistances R”Cu−Cu under different applied pressures, and the scale bars onX-axis represent the deviations caused by the accuracy of load cells. R”Cu−Cuis less sensitive to the copper brick thickness, in particular, under the appliedpressure >2 MPa. The error bars on Y -axis are measured R”Cu−Cu deviationsafter three measurements with three different input powers.

+ R”Cu + R”Cu−Cu) of square copper bricks with fourdifferent thicknesses is tested to calibrate the setup. From thethermal conductivity of copper (∼400 W/m K) and thicknessesof different copper bricks, R”Cu of each copper brick canbe calculated. R”Cu−Cu can be identified by R”Cu−Cu =(R”total − R”cu)/2. By comparing to the literature value ofR”Cu−Cu (which are about 1–4 cm2 K/W) [36], we verify thevalidity of the measurement. The R”total values of the copperbricks for different thicknesses are plotted in Fig. 2(a). Thelinear fitting equation confirms uniform R”Cu−Cu as well asthickness dependence of R”Cu.

As the pressure is applied to the sample, the surface contactscreate more conduction pathways and thus decrease the ther-mal interface resistance between the surfaces [37]. Therefore,the pressure-dependent thermal interface resistances of thesamples are measured. In order to quantify the load pressure,four load cells are affixed in series and a threaded rod isemployed to provide the force exerted on the copper bar.

Fig. 3. Schematic of hydrogen template deposition illustrates the experi-mental layout of an anode and a substrate (cathode). The vertical distancebetween the anode and the cathode is fixed at 35 mm to ensure constantelectrical resistance, and the electricity is directly provided by a dc powersupply. The anode copper sheet is fixed at the position that only allows thebottom area to contact with the electrolyte.

The applied pressure is chosen to be 1–5 MPa (100–500-Napplied force on 100-mm2 area), limited by the capabilityof load cells. The results of the pressure-dependent thermalresistance tests in Fig. 2(b) show that the thermal interfaceresistances between cooper bricks and copper bars (R”Cu−Cu)decrease when the applied pressure increases. We can furtheruse pressure-inverse functional form: R”total = (C × P−1) +Y, where C is a fitting parameter, P is the applied pressure,and Y is the equation offset in the Y -direction, in order to fitthe data [25]. This relation equation can be utilized to predictand analyze the thermal interface resistances of BPCu/PDMSsamples. We also perform the uncertainty analysis of measuredR”total. Uncertainties for K-type thermal couples, power input,and machining tolerance are ±0.2 K, ±1 W, and ±10−4 m,respectively, eventuating in the effective R”total uncertaintyof 2.1%.

III. HYDROGEN BUBBLE-TEMPLATED

ELECTRODEPOSITION

The fabrication for the BPCu/PDMS process starts with acopper substrate, which is first cut into rectangular substratesof 15 mm × 10 mm × 1.8 mm by a metal shear. The coppersubstrate is placed in hydrochloric acid for 15 min to removeoxidation layers and is further purged by an isopropyl alcoholin an ultrasonic cleaner for 20 min and dried. As shownin Fig. 3, the substrate is placed in a stationary 0.4 M Cu2SO4+ 1.8 M H2SO4 electrolyte to conduct a bubble-templatedelectrodeposition. For this, the copper substrate is connectedto a cathode, while a copper sheet of 15 mm × 10 mm servesas an anode to dissipate copper ions. The substrate and theelectrode are placed horizontally in favor of bubble departurewith vertical distance fixed at 35 mm. The deposited area



Fig. 4. Schematic showing the fabrication process of BPCu/PDMS com-posite. (a) Copper electrochemically deposits on the copper substrate wherehydrogen bubbles are generated and serve as a template, simultaneously.(b) Void spaces due to the bubbles become interconnected microscale poresafter the electrodeposition process [31], [32]. (c) Hexane-diluted PDMS isinfiltrated to create BPCu/PDMS composite.

is 10 mm × 10 mm, and the current density is set to be1 A/cm2 in order to initiate not only copper deposition butalso hydrogen bubble formation. During this process, hydrogenbubbles are generated dynamically as a by-product due tothe high current density, which creates void portions in thedeposited copper and forms 3-D porous copper structures.

The chemical equations in the anode and cathode are listedas follows.

In the anode:

Cu = Cu2+ + 2e−. (3)

In the cathode:

Cu2+ + 2e− = Cu (4)

2H+ + 2e− = H2(↑). (5)

The deposition time varies from 1 to 3 min to control theBPCu samples’ thickness. After the electrodeposition process,as-fabricated BPCu samples are cleaned with deionized waterand dried. The samples are then sintered in the tube furnacefor 1 h at 500 ◦C in order to enhance the structural integrityof the BPCu samples. The furnace is vacuumed to preventoxidation during the sintering process.

We measure the structural thickness of BPCu samplesby obtaining cross-sectional scanning electronic microscope(SEM) images. In this process, a specific area (10 mm ×

Fig. 5. (a)–(c) Top-view SEM images of BPCu samples with electrodepo-sition time ranging from 1 to 3 min. The copper deposition templated withhydrogen bubbles creates porous copper with a coral-like surface morphology.(d)–(f) Cross-sectional images of BPCu samples. The length differencebetween each copper dendritic and the copper congregation at the upper layercan be both observed. Detailed images of copper dendritic (g)–(i) before and(j)–(l) after the sintering process. The sintering process improves the structuralintegrity without morphological change.

1 mm) is masked with a tape to provide a reference before theelectrodeposition. Note that it is challenging to mechanicallycleave the sample due to the combination of the substratethickness as well as the fragility of electrodeposited copper.

In order to increase the mechanical strength of BPCusamples, we infiltrate PDMS (Sylgard 184, Dow Corning Inc.,viscosity ν = 3500 cP and thermal conductivity kPDMS =0.16 W/m K) through the BPCu samples. For this, we mixthe PDMS monomer with a cross-link agent at 10:1 weightratio and dilute the mixture with hexane at 1:1 weight ratioto decrease its viscosity. The diluted PDMS is casted at theperimeter areas of BPCu. The volumetric filling ratios are cho-sen to be 60% and 80% where the filling volume is calculatedby VPDMS = casted area × structural thickness × structuralporosity × volumetric filling ratio. Then, the BPCu/PDMSsamples are cured in the atmosphere for 24 h.

IV. RESULT AND DISCUSSION

A. Morphology Details

The SEM images [see Fig. 5(a)–(c)] show the top viewof the BPCu samples with electrodeposition time rangingfrom 1 to 3 min. The growth of copper layer along withhydrogen bubbles creates highly interconnected micropore andnanopore with a coral-like surface morphology. Once theelectrodeposition time increases up to 2 or 3 min, the coppermolecules congregate at the copper dendritic tips, which leadsto thicker or blunt copper tips. The same phenomenon can alsobe observed from the cross-sectional SEM images. In Fig. 5(d),the 1-min BPCu sample shows relatively uniform morphologyover the sample, whereas the 2- or 3-min BPCu samples showspherical-shaped tips with larger diameters in Fig. 5(e) and (f).According to the previous study [34], the hydrogen bubblescoalesce at the upper layer as the electrodeposition timeincreases. The bubble diameter thereby increases, yet bubbledensity decreases. Due to the hydrogen bubbles coalescence,the copper dendritic diameter at the tips also increases as the



Fig. 6. (a) Relation between average structural thickness and electrode-position time. The average BPCu structural thickness increases at a rateof 50.8 μm/min. (b) Porosity as a function of electrodeposition time. As cop-per tips congregate, the porosity decreases when the deposition time increasesfrom 2 to 3 min.

structure grows. We further compare the copper dendritic mor-phology before and after the sintering process [see Fig. 5(g)and (l)], confirming similar morphologies.

For the detailed analysis, we calculate the average structuralthickness of the BPCu samples for different deposition timesbased on the cross-sectional images. Fig. 6(a) shows thestructural thickness of 65.2, 113.2, and 139.6 μm for varyingelectrodeposition time of 1–3 min, respectively. The lineartrend line estimates that the structural thickness increases at50.8 μm/min. The error bars represent the deviations in thestructural thickness of BPCu samples. The bubble-templatedelectrodeposition process naturally creates the deviations inthe structural thickness of BPCu samples, eventuating in largeerror bars.

After acquiring the average structural thickness of theBPCu samples, we calculate the overall porosity by using thefollowing expression:

∅ = 1 − m

ξδAC(6)

where m is the mass of porous structure, ξ is the copperdensity, δ is the average structural thickness, and AC is

Fig. 7. Top-view SEM images of the 1-min BPCu/PDMS TIM sampleswith (a) 60% and (b) 80% volumetric filling ratios. The density of protrudingcopper dendrites of 80% samples is less than that of 60% samples, so copperdendrites at lower layers will be encapsulated by the PDMS with 80%volumetric filling ratio. Cross-sectional view SEM images of BPCu/PDMssamples show the ability for the structure to survive the polymer infiltration,and the PDMS matrix is able to infiltrate the BPCu to the bottom of thestructure.

the projected area of porous structure. The resulting overallporosity with respect to electrodeposition time ranges from88% to 93%, as shown in Fig. 6(b). The overall porosity valuesare close to the values reported in previous studies [34], [35].As dendritic tips start to congregate, the porosity decreases,while the deposition time increases from 2 to 3 min.

To protect the porous copper, we infiltrate hexane-dilutedPDMS through the BPCu samples with two different con-stant volumetric filling ratios of 60% and 80%. Fig. 7(a)and (b) shows the top-view images of BPCu/PDMS sam-ples. The PDMS fills the microscale voids originated fromhydrogen bubbles and infiltrates the dendrite features at thetop through the wicking phenomena. Additionally, the cross-sectional images confirm the level of infiltration as well asstructural damage. The images in Fig. 7(c) and (d) showthat the hexane-diluted PDMS’s viscosity is low enough toreach the bottom of the BPCu structures and fill in microscaleand nanoscale pores. The structures are robust enough tosurvive the PDMS infiltration process. The images show thata filling ratio of 80% results in thicker PDMS layer, while theoverdeposited copper dendritic structures are minimized.

B. Pressure-Dependent Thermal Characteristics ofBPCu/PDMS Samples

Fig. 8 shows the measured R”total of the BPCu/PDMSsamples with different electrodeposition times and PDMSvolumetric filling ratios. In order to discuss the pressuredependence of thermal resistance, we apply the varying pres-sures of 1–5 MPa to the sample during the measurements.We repeat the measurement of each fabrication parameter forfive times (i.e., five samples with the same parameter andfive individual measurements for each sample) to calculatethe average thermal resistances as well as the standard devi-ations, represented as error bars in Fig. 8. The total thermalresistances are inversely proportional to the applied pressures:



Fig. 8. Pressure-dependent total interface resistances R”total of theBPCu/PDMS samples with (a) 60% and (b) 80% PDMS volumetric fillingratios.

R”total = (C × P−1) + Y, where C is 0.7 for both 60% and80% infiltrated BPCu/PDMS samples, which means that thesamples of both groups show similar sensitivity to the appliedpressure changes. On the other hand, the equation offsets in theY -direction for 60% infiltrated BPCu/PDMS samples are 2.3,3, and 3.65 for deposition time of 1–3 min, respectively. The Yvalues for 80% infiltrated BPCu/PDMS samples are 2.65, 3.4,and 4.23 for deposition time of 1–3 min, respectively. The Yvalues for both 60% and 80% infiltrated BPCu/PDMS samplesindicate regular total interface resistance R”totalincrementswith respect to sample thickness increments. Fig. 8(a) showsthe average total interface resistances R”total of the 60%infiltrated BPCu/PDMS samples. For 1-MPa applied pressure,total interface resistances are 3.6, 3.9, and 5.0 cm2 K/W,respectively, and the average increase is 18.3%. For 3- and5-MPa applied pressures, R”total is measured as 2.6, 3.1, and3.9 cm2 K/W and 2.3, 2.9, and 3.6 cm2 K/W, respectively.The average total thermal resistance increases are 23.0% and25.3%. With higher applied pressure (3 MPa), the averagethermal resistances show smaller deviations from the equationpredicted values. This can be explained by the fact that whenthe structure deformation increases, a higher degree of copperdendrite bend or collapse is generated and, thus, creates a

more uniform as well as solid contact interface between theBPCu/PDMS samples and the copper bar. Fig. 8(b) showsthe average total interface resistances R”total of the 80%infiltrated BPCu/PDMS samples versus applied pressures andelectrodeposition time. R”total of 1-, 2-, and 3-min depositedsamples is 4.0, 5.3, and 5.9 cm2 K/W, respectively. Theaverage thermal resistance increase is 21.2% as the depositiontime increases with the increments of 1 min. When the appliedpressures increase up to 3 and 5 MPa, R”total of the 1–3-minBPCu/PDMS samples increases from 2.9 to 4.3 cm2 K/Wand 2.6 to 3.8 cm2 K/W, respectively. Therefore, the averageinterface resistance increases are 22.8% and 20.0%. The samephenomena can be observed for R”total of the 80% infiltratedBPCu/PDMS samples at high applied pressure regime, whichshows lower measured value deviation under lower structuredeformation. After analyzing the experimental data, the resultcan be divided into two parts. First, due to higher structuralreinforcement, with 80% filling ratio, the measured R”total islarger than that with 60% filling ratio under the same deposi-tion time and applied pressure. On the other hand, with higherapplied pressure (>2 MPa), i.e., larger sample deformation, theerror bars of R”total of each deposition time become smaller,which means more consistent measured values of each datapoint.

We estimate the effective thermal conductivity of theBPCu/PDMS samples by using the values of the total thermalinterface resistance R”total and other parameters where thetotal thermal resistance R”total can be expressed as a series ofthermal resistances: R”Cu−Cu + R”Cu + R”TIM + R”TIM−Cu.Once we can apply two different pressures to the samples,we measure the R”total,1 and R”total,2 for pressures 1 and 2,respectively,

R”total,1 =R”Cu-Cu,1+R”Cu,1+R”TIM,1+R”TIM-Cu,1

(7)

R”total,2 =R”Cu-Cu,2+R”Cu,2+R”TIM,2+R”TIM-Cu,2.

(8)

As mentioned in the previous discussion, applied pressurefacilitates copper dendrite deformation or collapse and enablesmore uniform and solid contacts between BPCu/PDMS sam-ples and the copper bar. Thus, we assume that R”TIM−Cuwill remain constant during the measurement. Since R”Cu andR”TIM−Cu are independent for different pressures, R”Cu andR”TIM−Cu can be eliminated by subtracting (8) from (7)

R”total,1 − R”total,2 = R”TIM,1 − R”TIM,2

+R”Cu-Cu,1 − R”Cu-Cu,2 (9)

�R”total = �R”TIM + �R”Cu-Cu (10)

and the values of R”Cu−Cu are 1.42, 1.07, 0.82, 0.63, and0.53 cm2 K/W under 1–5-MPa applied pressure, respectively,from the equipment calibration step [see Fig. 2(b)]. Thedifference of thermal resistance of TIMs for different pressures�R”TIM can be further rewritten by using the effective thermalconductivity keff

�R"TIM = �δ

keff(11)



Fig. 9. Pressure-dependent structural thickness of the BPCu/PDMS sampleswith different electrodeposition times of (a) 1, (b) 2, and (c) 3 min. Thesamples with a larger PDMS volumetric filling ratio have better mechanicalstrength augmentation and thus show less structural deformation under a givenapplied pressure.

where �δ represents the thickness difference of BPCu/PDMSsamples under different pressures. The average effective ther-mal conductivity keff is calculated as 19.4 and 18.3 W/m Kfor 60% and 80% filling ratio samples, respectively.

The effective thermal conductivity can be compared to thetheoretical values, predicted by a simple effective medium

TABLE I

COMPRESSION RATIO OF AS-FABRICATED BPCU, 60%, AND 80%INFILTRATED BPCU/PDMS SAMPLES

Fig. 10. Cross-sectional view SEM images of (a) as-fabricated BPCu and (b)80% BPCu/PDMS after compression. Copper dendrite of as-fabricated BPCusample is collapsed and sectioned into coppers bits by applied pressure. On theother hand, 80% BPCu/PDMS shows deformed and tilted copper dendrite aftercompression, so the integrity of the continuous heat transfer pathway is betterpreserved due to the PDMS encapsulation.

theory (EMT) [19]

keff,EMT = kp∅+km(1 − ∅) (12)

where kp is the thermal conductivity of polymer (kPDMS =0.16 W/m K), km is the thermal conductivity of metal (kCu =400 W/m K), and ø is the structural porosity. The BPCu/PDMSsamples with the porosity of 88%–93% result in the effectivethermal conductivity of 20 to 60 W/m K, which is larger thanthe values from the pressure-dependent measurements. Thediscrepancy might be explained by the following reasons.

1) The equation simulates two thermal resistances in parallelintroduced by two different materials; however, it does notaccount for the tortuosity of 3-D porous structures. Suchtortuosity results in the twists of heat flux vectors along eachcopper dendrites as well as the increase in the heat conductionpath [38].

2) The grains of electrodeposited copper create addi-tional contacts and corresponding contact thermal resistancesbetween thermally conductive fillers [39], [40].

3) The creation of nanoscale features after the electrode-position, which can be comparable to the mean free path ofcopper (∼39 nm), facilitates heat transfer carriers’ scatteringat the nanoscale and further decreases the effective thermalconductivity of the porous copper samples [38], [41].

Previous research had revealed that Maxwell’s EMT modelprovides better prediction for thermal conductivity of 3-D het-erogeneous composite media with spherical diluent particles[42], [43] where the effective conductivity can be written as

keff Maxwell = 2 (1 − ∅)

3 − (1 − ∅)km. (13)

The Maxwell effective thermal conductivities of BPCu/PDMSsamples with 88%–93% porosities are in the range of 19.11–33.3 W/m K, which are closer to our experimental valuesbecause of the consideration of 3-D dispersed spherical pores



as diluents. However, Maxwell’s EMT model neglects theinteractions between diluent particles [44], [45], so effectivethermal conductivity could be overestimated by Maxwell’smodel. Fig. 5(a)–(c) shows that as-fabricated BPCu structureshave interconnected pores, so the porosities of BPCu structureswill be higher than the closed-pack limit (no connectionbetween each pore) simulated in Maxwell’s EMT model.Bhattacharya et al. [46] proposed an empirical correlation toevaluate the thermal properties of metal-foam-based compositestructures with different porosities and pore sizes, and the cor-relation showed accurate evaluations of thermal conductivities,especially for ultrahigh porosity foam-based structures

keff= A

⎛⎝kp∅+km (1 − ∅) +

⎛⎝ 1 − A

∅kp

+ 1−∅km

⎞⎠

⎞⎠ (14)

where A is the empirical coefficient, and the value is 0.35. Thecalculated effective thermal conductivities of the BPCu/PDMSsamples are in the range of 14.1–16.9 W/m K, which showsbetter thermal conductivity evaluation than the previous twoEMT models due to the consideration of 3-D structure as wellas interconnections between the pores. The calculated thermalconductivities are slightly lower than the experimental values,because the empirical correlation is designated for foam-basedstructures with higher porosities (∅ = 90.5%–97.8%) andlarger pore sizes (300–500 μm) [47].

We further discuss the mechanical strength enhancementthat can be available through the PDMS infiltration by mea-suring the structural thickness before and after the pressuresapplied to the samples. As shown in Fig. 9, the resultsconfirm that thickness variations with respect to applied pres-sures attend to be smaller for 80% volumetric filling ratiocompared to 60% volumetric filling ratio. We quantify thecompression ratios of pure BPCu, 60% BPCu/PDMS sam-ples, and 80% BPCu/PDMS samples with applied pressuresranging from 0 to 5 MPa where the compression ratio =(δ0mpa − δ5 mpa)/(δ0 mpa). The calculated compression ratiovalues are listed in Table I. Without the PDMS infiltration,compression ratios of pure BPCu samples are 12%–14%higher than those of 60% BPCu/PDMS samples and 13%–20% higher than those of 80% BPCu/PDMS samples. Thiscomparison clearly indicates that the PDMS infiltration mini-mizes the deformation of BPCu/PDMS structure with a largerfilling ratio for a given applied pressure. Although the sinteringprocess can enhance the mechanical strength of the structures[34], [48], as-fabricated BPCu remains fragile against appliedpressures because of highly porous characteristics as wellas weak structural strength caused by high electrodepositionrates. The PDMS infiltration process not only enhances theoverall structural strength but also preserves the integrityof copper dendrite (that provides continuous heat transferpathway) under different pressures via encapsulating BPCustructure with elastic polymer matrix. The cross-sectional viewSEM images of as-fabricated BPCu and 80% BPCu/PDMSafter the compression in Fig. 10(a) show that as-fabricatedBPCu is fragmented into copper bits after compression.On the other hand, Fig. 10(b) shows better copper dendritepreservation as well as thicker structural thickness for 80%

BPCu/PDMS due to the PDMS encapsulation. Furthermore,the infiltration of PDMS into BPCu system could deceleratethe oxidation process of Cu particles, which might survivedespite thermal cycling at elevated temperature and humidity,which can be further confirmed in the future work.

V. CONCLUSION

In summary, this article studies the pressure-dependentthermal characteristics of 3-D BPCu structures. We employa cost-effective method to fabricate 3-D BPCu structuresand improve their mechanical strength by infiltrating poly-mer matrix, creating BPCu/PDMS composite. The pressure-dependent thermal properties of the BPCu/PDMS samples aremeasured by using 1-D thermal resistance analysis for varyingstructural thicknesses and filling ratios. Therefore, the effectivethermal conductivities of the BPCu/PDMS with 60% and 80%filling ratios are measured to be 19.4 and 18.3 W/m K, respec-tively. The mechanical strength enhancement of BPCu/PDMSsamples can be verified by examining the compression ratio,which confirms the strength augmentation with larger fillingratios. To prove the thermal reliability of suggested materials,the mechanical testing, chemical stability introduced by PDMSinfiltration, and degradation of BPCu/PDMS composite withrespect to loading cycles should be addressed.

REFERENCES

[1] R. Prasher, “Thermal interface materials: Historical perspective, status,and future directions,” Proc. IEEE, vol. 94, no. 8, pp. 1571–1586,Aug. 2006.

[2] B. A. Cola, P. B. Amama, X. Xu, and T. S. Fisher, “Effects of growthtemperature on carbon nanotube array thermal interfaces,” J. HeatTransf., vol. 130, no. 11, 2008, Art. no. 114503.

[3] K. M. Razeeb and S. Roy, “Thermal diffusivity of nonfractal and fractalnickel nanowires,” J. Appl. Phys., vol. 103, no. 8, 2008, Art. no. 084302.

[4] E.-C. Cho et al., “Graphene-based thermoplastic composites and theirapplication for LED thermal management,” Carbon, vol. 102, pp. 66–73,Jun. 2016.

[5] H. Jiang, Z. Wang, H. Geng, X. Song, H. Zeng, and C. Zhi, “Highlyflexible and self-healable thermal interface material based on boronnitride nanosheets and a dual cross-linked hydrogel,” ACS Appl. Mater.Interfaces, vol. 9, no. 11, pp. 10078–10084, 2017.

[6] Y. Agari and T. Uno, “Estimation on thermal conductivities of filledpolymers,” J. Appl. Polym. Sci., vol. 32, no. 7, pp. 5705–5712, 1986.

[7] Z. Han and A. Fina, “Thermal conductivity of carbon nanotubes andtheir polymer nanocomposites: A review,” Prog. Polym. Sci., vol. 36,no. 7, pp. 914–944, Jul. 2011.

[8] X. Huang, C. Zhi, P. Jiang, D. Golberg, Y. Bando, and T. Tanaka,“Polyhedral oligosilsesquioxane-modified boron nitride nanotube basedepoxy nanocomposites: An ideal dielectric material with high thermalconductivity,” Adv. Funct. Mater., vol. 23, no. 14, pp. 1824–1831, 2013.

[9] S. Berber, Y.-K. Kwon, and D. Tománek, “Unusually high thermalconductivity of carbon nanotubes,” Phys. Rev. Lett., vol. 84, p. 4613,May 2000.

[10] A. M. Marconnet, M. A. Panzer, and K. E. Goodson, “Thermal con-duction phenomena in carbon nanotubes and related nanostructuredmaterials,” Rev. Mod. Phys., vol. 85, no. 3, pp. 1295–1326, 2013.

[11] M. M. J. Treacy, T. W. Ebbesen, and J. M. Gibson, “Exceptionally highYoung’s modulus observed for individual carbon nanotubes,” Nature,vol. 381, no. 6584, pp. 678–680, 1996.

[12] B. A. Cola, X. Xu, and T. S. Fisher, “Increased real contact in thermalinterfaces: A carbon nanotube/foil material,” Appl. Phys. Lett., vol. 90,no. 9, 2007, Art. no. 093513.

[13] B. A. Cola, J. Xu, and T. S. Fisher, “Contact mechanics and thermalconductance of carbon nanotube array interfaces,” Int. J. Heat MassTransf., vol. 52, nos. 15–16, pp. 3490–3503, 2009.



[14] J. R. Wasniewski, “Characterization of metallically bonded carbonnanotube-based thermal interface materials using a high accuracy 1Dsteady-state technique,” J. Electron. Packag., vol. 134, no. 2, 2012,Art. no. 020901.

[15] A. Yu, P. Ramesh, X. Sun, E. Bekyarova, M. E. Itkis, and R. C. Haddon,“Enhanced thermal conductivity in a hybrid graphite nanoplatelet—Carbon nanotube filler for epoxy composites,” Adv. Mater., vol. 20,no. 24, pp. 4740–4744, 2008.

[16] W. Lin, K. S. Moon, and C. P. Wong, “A combined process of in situfunctionalization and microwave treatment to achieve ultrasmall thermalexpansion of aligned carbon nanotube–polymer nanocomposites: Towardapplications as thermal interface materials,” Adv. Mater., vol. 21, no. 23,pp. 2421–2424, 2009.

[17] A. M. Marconnet, N. Yamamoto, M. A. Panzer, B. L. Wardle, andK. E. Goodson, “Thermal conduction in aligned carbon nanotube–polymer nanocomposites with high packing density,” ACS Nano, vol. 5,no. 6, pp. 4818–4825, 2011.

[18] J. Xu, A. Munari, E. Dalton, A. Mathewson, and K. M. Razeeb, “Sil-ver nanowire array-polymer composite as thermal interface material,”J. Appl. Phys., vol. 106, no. 12, 2009, Art. no. 124310.

[19] F. Lian, J. P. Llinas, Z. Li, D. Estrada, and E. Pop, “Thermal conduc-tivity of chirality-sorted carbon nanotube networks,” Appl. Phys. Lett.,vol. 108, no. 10, 2016, Art. no. 103101.

[20] I. Sauciuc et al., “Carbon based thermal interface material for high per-formance cooling applications,” in Proc. Intersociety Conf. Thermomech.Phenom. Electron. Syst., 2014, pp. 426–434.

[21] Z. Kuang et al., “Fabrication of highly oriented hexagonal boron nitridenanosheet/elastomer nanocomposites with high thermal conductivity,”Small, vol. 11, no. 14, pp. 1655–1659, 2015.

[22] J. Chen, X. Huang, B. Sun, Y. Wang, Y. Zhu, and P. Jiang, “Verti-cally aligned and interconnected boron nitride nanosheets for advancedflexible nanocomposite thermal interface materials,” ACS Appl. Mater.Interfaces, vol. 9, no. 36, pp. 30909–30917, 2017.

[23] J. Chow and S. K. Sitaraman, “Electroplated copper nanowires asthermal interface materials,” in Proc. 15th Intersociety Conf. Ther-mal Thermomech. Phenom. Electron. Syst. (ITherm), May/Jun. 2016,pp. 151–155.

[24] M. T. Barako et al., “Thermal conduction in vertically aligned coppernanowire arrays and composites,” ACS Appl. Mater. Interfaces, vol. 7,no. 34, pp. 19251–19259, 2015.

[25] M. T. Barako et al., “Dense vertically aligned copper nanowire compos-ites as high performance thermal interface materials,” ACS Appl. Mater.Interfaces, vol. 9, no. 48, pp. 42067–42074, 2017.

[26] R. N. Jarrett and C. K. Merritt, “Technique for forming a thermallyconductive interface with patterned metal foil,” U.S. Patent 7 593 228 B2,Sep. 22, 2009.

[27] M. E. Davis, “Ordered porous materials for emerging applications,”Nature, vol. 417, no. 6891, pp. 813–821, 2002.

[28] A. Stein, “Advances in microporous and mesoporous solids—Highlightsof recent progress,” Adv. Mater., vol. 15, no. 10, pp. 763–775, 2003.

[29] Q. N. Pham, M. T. Barako, J. Tice, and Y. Won, “Microscale liquidtransport in polycrystalline inverse opals across grain boundaries,” Sci.Rep., vol. 7, no. 1, 2017, Art. no. 10465.

[30] C. M. Patil and S. G. Kandlikar, “Pool boiling enhancement throughmicroporous coatings selectively electrodeposited on fin tops of openmicrochannels,” Int. J. Heat Mass Transf., vol. 79, pp. 816–828,Dec. 2014.

[31] H.-C. Shin, J. Dong, and M. Liu, “Nanoporous structures prepared byan electrochemical deposition process,” Adv. Mater., vol. 15, no. 19,pp. 1610–1614, 2003.

[32] H.-C. Shin and M. Liu, “Copper foam structures with highly porousnanostructured walls,” Chem. Mater., vol. 16, no. 25, pp. 5460–5464,2004.

[33] S. Li, R. Furberg, M. S. Toprak, B. Palm, and M. Muhammed,“Nature-inspired boiling enhancement by novel nanostructured macro-porous surfaces,” Adv. Funct. Mater., vol. 18, no. 15, pp. 2215–2220,2008.

[34] Y.-Q. Wang, J.-L. Luo, Y. Heng, D.-C. Mo, and S.-S. Lyu, “Wettabilitymodification to further enhance the pool boiling performance of themicro nano bi-porous copper surface structure,” Int. J. Heat MassTransf., vol. 119, pp. 333–342, Apr. 2018.

[35] K. M. Razeeb, A. Munari, E. Dalton, J. Punch, and S. Roy, “Thermalproperties of carbon nanotube-polymer composites for thermal interfacematerial applications,” in Proc. ASME/JSME Thermal Eng. Summer HeatTransf. Conf. (HT), 2009, pp. 817–823.

[36] M. M. Yovanovich, “Four decades of research on thermal contact, gap,and joint resistance in microelectronics,” IEEE Trans. Compon. Packag.Technol., vol. 28, no. 2, pp. 182–206, Jun. 2005.

[37] J. P. Gwinn and R. L. Webb, “Performance and testing of thermalinterface materials,” in Microelectron. J., vol. 34, no. 3, pp. 215–222,2003.

[38] M. T. Barako et al., “Quasi-ballistic electronic thermal conductionin metal inverse opals,” Nano Lett., vol. 16, no. 4, pp. 2754–2761,2016.

[39] A. A. Balandin, D. L. Nika, S. Ghosh, and P. E. Pokatilov, “Lattice ther-mal conductivity of graphene flakes: Comparison with bulk graphite,”Appl. Phys. Lett., vol. 94, no. 20, 2009, Art. no. 203103.

[40] M.-H. Bae et al., “Ballistic to diffusive crossover of heatflow in graphene ribbons,” Nature Commun., vol. 4, Apr. 2013,Art. no. 1734.

[41] W. Zhang et al., “Influence of the electron mean free path on theresistivity of thin metal films,” Microelectron. Eng., vol. 76, nos. 1–4,pp. 146–152, 2004.

[42] S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielec-tric constant of periodic composite structures,” Phys. Rev. B, Condens.Matter, vol. 48, no. 20, pp. 14936–14943, 1993.

[43] H. T. Aichlmayr and F. A. Kulacki, “The effective thermal conductivityof saturated porous media,” Adv. Heat Transf., vol. 39, pp. 377–460,Oct. 2006.

[44] R. B. Bird et al., Transport Phenomena, vol. 7, no. 2. New York, NY,USA: Wiley, 1961.

[45] J. Canny, “A computational approach to edge detection,” IEEETrans. Pattern Anal. Mach. Intell., vol. PAMI-8, no. 6, pp. 679–698,Nov. 1986.

[46] A. Bhattacharya, V. V. Calmidi, and R. L. Mahajan, “Thermophysicalproperties of high porosity metal foams,” Int. J. Heat Mass Transf.,vol. 45, no. 5, pp. 1017–1031, 2002.

[47] L. Zhang et al., “Thermal conductivity enhancement of phasechange materials with 3D porous diamond foam for thermalenergy storage,” Appl. Energy, vols. 233–234, pp. 208–219,Jan. 2019.

[48] P. Xu, Q. Li, and Y. Xuan, “Enhanced boiling heat transfer on compositeporous surface,” Int. J. Heat Mass Transf., vol. 80, pp. 107–114,Jan. 2015.


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