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Thermal gap conductance at low contact pressures (<1 MPa): Effect of gold plating and plating thickness
International Journal of Heat and Mass Transfer 53 (2010) 5373–5379
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal gap conductance at low contact pressures (<1 MPa): Effect of gold plating and plating thickness Prashant Misra, J. Nagaraju * Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
a r t i c l e
i n f o
Article history: Received 26 May 2009 Received in revised form 12 May 2010 Accepted 20 June 2010 Available online 5 August 2010 Keywords: Thermal gap conductance OFHC Cu Brass Thin gold plating
a b s t r a c t Thermal contact conductance (TCC) measurements are made on bare and gold plated (60.5 lm) oxygen free high conductivity (OFHC) Cu and brass contacts in vacuum, nitrogen, and argon environments. It is observed that the TCC in gaseous environment is significantly higher than that in vacuum due to the enhanced thermal gap conductance. It is found that for a given contact load and gas pressure, the thermal gap conductance for bare OFHC Cu contacts is higher than that for gold plated contacts. It is due to the difference in the molecular weights of copper and gold, which influences the exchange of kinetic energy between the gas molecules and contact surfaces. Furthermore, the gap conductance is found to increase with increasing thickness of gold plating. Topography measurements and scanning electron microscopy (SEM) analysis of contact surfaces revealed that surfaces become smoother with increasing gold plating thickness, thus resulting in smaller gaps and consequently higher gap conductance. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Engineering surfaces are never absolutely smooth and the surface irregularities become apparent when observed under a microscope. As a result, when two solids are pressed together, actual contact is made only at a few discrete points separated by relatively large gaps. Due to the reduction in heat transfer area at the interface, there exists an extra resistance to heat flow, known as thermal contact resistance. A more popular term for it is the thermal contact conductance (TCC), defined as the inverse of thermal contact resistance. Heat transfer across the interface can take place by means of conduction through solid-to-solid contact spots and conduction through the gaps. Heat transfer through the interfacial gaps gives rise to thermal gap conductance (hg ), which together with the conductance of contact spots (hc ) decides the overall joint conductance (hj ) of a thermal contact. Therefore, for all thermal contacts
hj ¼ hc þ hg
ð1Þ
In vacuum environment, the thermal gap conductance is negligible and the joint conductance is predominantly the conductance of contact spots only (hj hc ). Radiative heat transfer across the gaps is insignificant at moderate temperatures, and needs to be considered only if interface temperatures are above 300 °C [1]. In a gaseous environment, heat transfer through gas filled interfacial gaps is possible by either conduction or convection. Considering the small * Corresponding author. Tel./fax: +91 80 22932273. E-mail address: [email protected] (J. Nagaraju). 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.06.052
thickness of interfacial gaps (typically less than 10 lm), possibility of convective heat transfer is also neglected due to the fact that the Grashof number (the ratio of buoyant to viscous forces) is generally below 2000 [2]. Therefore, conduction remains the dominant mode of heat transfer across the gas filled interfacial gaps. Conduction across the gaps is particularly important when the contact pressure is relatively low, and/or the interstitial gaseous medium is relatively good thermal conductor [3]. It has been shown that, at low contact pressures (<1 MPa), very little heat passes through the solid contact spots, and the major portion of heat transfer occurs through the gas even when the solids are relatively soft and good thermal conductors such as aluminum [4]. In many practical applications, especially in electronic components, the operating contact pressures are in low or moderate range (for instance, average contact pressure in the case of a bolted thermal contact between the base plate and the heat sink of a multiple chip unit (MCU) in a computer is about 0.9 MPa). As a result, in such cases, the gaseous gap conductance plays a more significant role than the solid spot conductance. The thermal resistance at the interface can often lead to thermally induced failure of a component or a system as has been frequently observed in the case of electronic systems. As a result, enormous research has been done in this field and a substantial amount of data is available on the solid spot conductance [5–7]. However, there is comparatively little information on thermal gap conductance, especially of an experimental nature. Gaseous heat transfer across the interfacial gaps depends upon a number of parameters, such as, thermal properties of solids and gases, surface roughness characteristics, applied contact load, micro-hardness of
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Nomenclature erfc–1 H h k M Mg Ms Mg P Pr T TAC TCC Y
Greek symbols ratio of specific heats of gas K mean free path l ratio of molecular weights of gas and solid (=Mg/Ms) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r combined rms roughness ¼ r21 þ r22
inverse complementary error function Vickers micro-hardness thermal conductance thermal conductivity gas parameter molecular weight of gas molecular weight of solid for monoatomic gases Mg ; ¼ 1:4M g ; for dia=polyatomic gases contact pressure Prandtl number temperature thermal accommodation coefficient thermal contact conductance mean surface plane separation
c
Subscripts 1, 2 contact surfaces 1 and 2 c contact g gas j joint s solid
solids, etc. Because of the large number of parameters involved, numerous attempts by various researchers to model the thermal gap conductance have not been completely successful. While analytical models tend to neglect some of the important parameters, experimental correlations are valid only for limited ranges of these parameters. Song [8] and Hegazy [9] studied the gap conductance in N2, Ar and He environments across nickel and stainless steel contacts. Yovanovich et al. [10] developed a sophisticated statistical model (popularly known as the integral model) to predict thermal gap conductance between conforming rough surfaces, which was later presented in a simplified form by Song [8]. Bahrami et al. [11] presented a new approximate comprehensive, yet simple model for determining the heat transfer through the gap between conforming rough surfaces. The model is based on the general expression for heat transfer between two isothermal parallel plates proposed by Yovanovich [12], and covers the four regimes of heat conduction of gas, i.e., continuum, temperature-jump or slip, transition, and free molecular. It is easy to evaluate and accounts for gas and solid mechanical and thermal properties, gas pressure and temperature, surface roughness, and the applied load. According to this model, the thermal gap conductance is expressed as a function of the thermal conductivity of gas, gas parameter, and mean surface plane separation
kg hg ¼ MþY
ð2Þ
Where the gas parameter depends on the properties of gas and the mean plane separation depends on the properties of contact surfaces and applied contact pressure. The simple relationship for thermal gap conductance expressed in Eq. (2) is obtained by simplifying the gap thermal resistance problem with the help of the following assumptions: (i) the gas and microcontacts thermal resistances are in parallel at the interface; (ii) the gap heat transfer area is identical to the apparent area; (iii) temperatures for the contacting surfaces are uniform; and (iv) heat transfer through the interstitial gas in the gaps occurs by conduction. Bahrami et al. [11] compared his model (Eq. (2)) with the experimental data of Song [8] and Hegazy [9], obtained from SS 304 and Ni 200 contacts in Ar, He and N2 gases. The data covered a wide range of surface characteristics, applied load, thermal and mechanical properties, and the gas pressure. The model showed good agreement with the data over entire range of comparison with the rms relative difference between the data and the model to be approximately 7.8%. Techniques for enhancement of thermal performance of contacts are continuously being researched to overcome some of the challenging thermal problems posed by the progressive miniaturi-
zation of electronic components and systems. Use of soft surface coatings is one such technique that has been suggested for better thermal management in electronics [13,14]. Chung [15] studied the variation of contact resistance with indium, lead, and aluminum coatings on metals. Fletcher et al. [16] used both the vapor deposited silver and electroplated silver coatings in electronic components for the enhancement of TCC. Kang et al. [17] experimentally studied the enhancement in contact conductance across aluminum contacts coated with materials such as lead, tin, and indium. Antonetti and Yovanovich [18] gave a thermomechanical model according to which the thermal contact conductance across metallic coated contacts depends on the effective hardness and thermal conductivity ratio of that substrate–layer combination. Present work deals with experimental measurements of thermal gap conductance across bare and gold plated (with different plating thickness) OFHC Cu and brass (Cu/Zn 30) contacts. Gold is a relatively softer material with a reasonably high value of thermal conductivity. It offers a stiff resistance to oxidation in normal conditions. The obtained experimental data is analyzed with the help of surface topography, micro-hardness, and SEM measurements conducted on the contact surfaces. 2. Experimentation The test setup developed for simultaneously measuring electrical contact resistance and thermal contact conductance [19] is used for the experimentation. However, only thermal contact conductance measurements are made in the present study. Schematic of the setup is shown in Fig. 1a. It consists of various subsystems including a contact conductance cell, a vacuum system, a loading system, heating–cooling systems, and sophisticated instrumentation for temperature and low level electrical resistance measurements. The contact conductance cell can either be evacuated with the help of vacuum system, or can be pressurized by introducing a gas. The cell houses the contact specimens in a triangular frame attached to its lid. The top half of the triangular frame stays outside the contact conductance cell and holds a hydraulic jack and a compression type load cell. Hydraulic jack is a part of the hydraulic loading system, with which specimens are subjected to different contact loads. The axial contact load acting on the specimens is measured with the help of the load cell. The bottom half of the frame, which stays inside the contact conductance cell, accommodates the contact specimens in the form of a stacked assembly known as the test column. Fig. 1b shows the details of the test column. It consists of two contact specimens, two identical heat-flux meters, and two identical heater–cooler blocks. Heater–cooler
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Fig. 1a. Schematic of test setup.
blocks have vacuum compatible heaters powered by a stable output voltage from a variac, as well as cooling coils connected to a constant temperature liquid bath. The heater and the cooler blocks act as heat source and sink, respectively, and maintain a steady heat flow through the test column. Heat-flux meters are used for measuring the heat flow rate in the test column. The test column is balanced on a pair of ball and conical seating arrangements placed at both ends to ensure that the compressive load is always applied parallel to the axis of the test column. Instrumentation for temperature measurement includes multiple T-type thermocouples connected to a multi-channel DAQ hardware interfaced with a PC. These thermocouples measure temperatures at different axial locations in the heat-flux meters and contact specimens, and the collected data is used for heat flow rate and interface temperature drop estimations. Steady state temperature data obtained from the heat-flux meters is used for calculating the heat flow rate (Q) by using the Fourier’s law of heat conduction. Temperature data obtained from the contact specimens is used for estimating the temperature drop (DT) at the contact interface. Thermal conductance of the joint is then calculated as hj ¼ Q =ADT, where A is the apparent area of the contact. Uncer-
tainty in any single TCC measurement can be calculated from the relative uncertainties associated with the heat flow rate (±5%, obtained from the uncertainties in thermal conductivity and temperature measurements), apparent contact area (±0.13%), and interface temperature drop measurements (±3.4%). Therefore, the relative uncertaintyp inffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a typical TCC measurement made with the ffi present setup is 0:052 þ 0:00132 þ 0:0342 ffi 0:06 ¼ 6%. A complete description of the setup, its functioning, methodology used for TCC measurements, and detailed uncertainty analysis is provided elsewhere [19,20]. All the experiments are conducted on OFHC Cu and brass specimens prepared from respective single bar stocks to ensure identical material properties. Cylindrical specimens of 40 mm length and 16 mm diameter are prepared. To insert the thermocouples, three holes (1.2 mm diameter, 8 mm deep, and 10 mm apart) are drilled in each specimen along its length. All contact surfaces are optically polished to have a smooth surface finish. Three different thicknesses of gold layers (0.1, 0.3, and 0.5 lm) are obtained on three pairs of specimens by electrodeposition technique. A 2 lm thick nickel underlayer is given between the OFHC Cu/brass substrate and the gold layer in all the gold plated specimens. A nickel under-
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different experiments. On each specimen pair, measurements are made in vacuum, followed by nitrogen and argon environments (gas pressure of 2 bar). Properties of the used gases are given in Table 2. Detailed experimentation and data reduction procedure is provided in [20]. 3. Results and discussion
Fig. 1b. Details of test column.
plate in gold coated contacts is very common in commercial contacts as it acts as a diffusion barrier, provides mechanical backing, and improves the adhesion of the gold coating. Topography measurements on contact surfaces are made with the help of a stylus based profilometer (Taylor–Hobson Form Talysurf Intra). Microhardness measurements on bare and plated contact surfaces are made with the help of a Vicker’s micro-hardness tester (Zwick Roell ZHV1), at a constant indenter load of 10 gf. These measurement results from all the specimens are summarized in Table 1. SEM images of contact surfaces are taken after conducting the experiments. TCC measurements on all specimen pairs are made at different contact pressures in the range of 0–1 MPa. Interface temperature is maintained constant for facilitating easy comparison of data from
Table 1 Properties of contact surfaces. Contact
Bare OFHC Cu 0.1 lm Au plated 0.3 lm Au plated 0.5 lm Au plated 0.1 lm Au plated 0.3 lm Au plated 0.5 lm Au plated
OFHC Cu OFHC Cu OFHC Cu brass brass brass
Combined rms roughness qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ r21 þ r22 [lm]
Vicker’s micro-hardness [kg/mm2]
0.55 0.50 0.37 0.22 0.59 0.39 0.28
130 380 349 312 390 352 319
Fig. 2 shows the comparison of thermal conductance for bare OFHC Cu contacts in different environments. For vacuum environment, the plotted conductance is the measured joint conductance, which is nothing but the conductance of contact spots. For gaseous environments, the plotted conductance is the thermal gap conductance, which is obtained by subtracting the conductance of contact spots (thermal conductance in vacuum) from the measured joint conductance in these environments (according to Eq. (1)). Experimentally obtained gap conductance data is compared with the theoretical model [11]. The data agrees well with the model and the rms relative difference between the present experimental data and the model is less than 7%. It can be observed from Fig. 2 that the magnitude of thermal gap conductance for both N2 and Ar is higher than that of contact spot conductance, thus confirming that heat transfer through gas filled interfacial gaps is dominant in thermal contacts operating at low or moderate contact pressures. Furthermore, the thermal gap conductance for a given gas pressure is higher in N2 compared to that in Ar, because of relatively higher thermal conductivity of N2 (Table 2). A similar trend of gap conductance has been reported by other researchers [21–23] at higher contact pressures (few MPa) too. This validates the assumption that conduction is the dominant mode of heat transfer across the interfacial gaps. Figs. 3a and 3b show the comparison of thermal gap conductance in bare and gold plated OFHC Cu contacts in N2 and Ar environment, respectively. In both environments, it is observed that the thermal gap conductance for bare OFHC Cu contacts is higher than that for all the gold plated contacts. The magnitude of gap conductance is governed by the amount of thermal energy exchanged between the gas molecules and contact surfaces. For a given gas–solid combination, the degree to which the kinetic energy of a gas molecule is exchanged while in collision with the solid wall depends on a parameter known as the thermal accommodation coefficient (TAC), which depends on the molecular weights of the gas and the solid. A correlation for predicting the TAC for a given gas–solid combination is given by Song and Yovanovich [24], as
! Mg T s 273 TAC ¼ exp 0:57 273 6:8 þ Mg
2:4l T s 273 1 exp 0:57 þ 273 ð1 þ lÞ2
ð3Þ
It can be seen from Eq. (3) that the TAC strongly depends on the factor 2.4l/(1 + l)2, which is a function of the ratio of molecular weights of gas and solid (l). Higher the value of l, higher is this factor and consecutively, higher will be the value of TAC. Now; for N2 —OFHC Cu :
l¼
M N2 28 2:4l ffi 0:44 ) ¼ ffi 0:51 2 M OFHC Cu 64 ð1 þ lÞ
and; for N2 —Au :
l¼
M N2 28 2:4l ffi 0:14 ) ¼ ffi 0:26 M Au 197 ð1 þ lÞ2
Assuming that all other conditions are same, the TAC for N2–OFHC Cu combination should be more than for N2–Au. Using the same approach, it can be shown that the TAC for Ar–OFHC Cu is more than that for Ar–Au combination (l = 0.63 and 0.20 for Ar–OFHC Cu and Ar–Au, respectively). As a result, transfer of thermal energy
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Table 2 Properties of gaseous media. Property Thermal conductivity (kg) [W/mK] Molecular weight (Mg) Mean free path (K) [nm] @ 288 K and 760 torr Ratio of specific heats (c) Prandtl number (Pr)
N2
Ar 5
kg(T) = 0.028 + 5.84 10 27 6 T 6 400 °C 28 62.8 1.41 0.69
T;
kg(T) = 0.018 + 4.05 105T; 27 6 T 6 400 °C 40 66.6 1.67 0.67
Fig. 2. Contact spot conductance and gap conductance in OFHC Cu contacts.
Fig. 3b. Thermal gap conductance in bare and gold plated OFHC Cu contacts in Ar.
Fig. 3a. Thermal gap conductance in bare and gold plated OFHC Cu contacts in N2.
Fig. 4a. Thermal gap conductance in gold plated brass contacts in N2.
across the gaps will be relatively more in OFHC Cu contacts. This explains the observed high thermal gap conductance for bare OFHC Cu contacts compared to gold plated ones in both environments. It is also observed in Figs. 3a and 3b that the gap conductance for gold plated contacts increases with increasing thickness of gold plating. Gold plated brass contacts also exhibit an exactly similar kind of behavior, as shown in Figs. 4a and 4b in N2 and Ar environments, respectively. The transfer of heat from one solid surface to another through a gas filled gap depends on the thickness of the gap. As discussed earlier, given the very small size of interfacial gaps, the prevailing mode of heat transfer through the gas is
conduction. Under such circumstances, smaller be the thickness of gap, more efficient is the heat transfer through it. The thickness of interfacial gaps is estimated by a parameter known as the mean surface plane separation (Y), given as [11]
Y¼
pffiffiffi 1 2P 2rerfc H
ð4Þ
For a given contact pressure, the mean surface plane separation depends on the inherent roughness and hardness of contacting surfaces. Rougher be the contacting surfaces, higher is the mean plane separation. Similarly, for a given roughness and contact pressure,
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[25]. SEM images of various contact surfaces shown in Fig. 5 clearly indicate that the gold plated surfaces become smoother with increasing plating thickness. With decreasing surface roughness the mean surface plane separation or the thickness of interfacial gaps decreases, thus resulting in increased heat transfer through gaps and thereby an enhanced thermal gap conductance. Micro-hardness measurements on contact surfaces indicate that the surface micro-hardness also decreases with increasing gold plating thickness. This also has an effect on the enhancement of thermal gap conductance observed in Figs. 3 and 4 (in accordance with Eq. (4)). However, as discussed earlier this effect of hardness will be very small compared to that of surface roughness. Similarly, higher micro-hardness of gold plated surfaces (due to the underlying layer of nickel) is also responsible for the reduced thermal gap conductance observed in gold plated contacts compared to bare OFHC Cu contacts.
4. Conclusions Fig. 4b. Thermal gap conductance in gold plated brass contacts in Ar.
lower be the surface micro-hardness, smaller is the mean plane separation. However, by evaluating Eq. (4) using the approximate expressions given for erfc–1 [11], it can be easily seen that the roughness is the dominant term in Eq. (4). This indicates that the thickness of interfacial gaps is highly influenced by the roughness of contacting surfaces, while surface micro-hardness has a relatively smaller effect. Topography measurements on contact surfaces reveal that the roughness of gold plated surfaces decreases as gold plating thickness increases (Table 1). This is particularly true for thin gold coatings, which tend to be porous and discontinuous
Thermal conductance data obtained at low contact pressures in vacuum and gaseous environments shows that the conductance of gaps is much higher than the conductance of contacting spots, asserting the fact that bulk of heat transfer across the interface takes place through gas filled interfacial gaps. The thermal gap conductance in gold plated OFHC Cu contacts is lower than that in bare contacts because of the higher molecular weight of gold compare to OFHC Cu. For a given gas–solid combination, a higher gas to solid molecular weight ratio results in higher gap conductance. In gold plated contacts, thermal gap conductance shows an increase with increasing gold plating thick-
Fig. 5. SEM images of different contact surfaces showing the effect of gold plating thickness on surface topography.
P. Misra, J. Nagaraju / International Journal of Heat and Mass Transfer 53 (2010) 5373–5379
ness. Topography measurements and SEM analysis of contact surfaces indicate that thin gold platings tend to become smooth as plating thickness increases, resulting in smaller interfacial gaps and thereby enhanced thermal gap conductance.
References [1] C.V. Madhusudana, Thermal Contact Conductance, Springer-Verlag, New York, 1996. pp. 1-8. [2] W.H. McAdams, Heat Transmission, McGraw–Hill, New York, 1954. [3] S.M.S. Wahid, C.V. Madhusudana, Gap conductance in contact heat transfer, Int. J. Heat Mass Transfer 43 (2000) 4483–4487. [4] C.V. Madhusudana, Thermal contact conductance and rectification at low joint pressures, Int. J. Heat Mass Transfer 20 (1) (1993) 123–132. [5] B. Snaith, S.D. Probert, P.W. O’Callaghan, Thermal resistances of pressed contacts, Appl. Energy 22 (1) (1986) 31–84. [6] M.A. Lambert, L.S. Fletcher, Review of models for thermal contact conductance of metals, J. Thermophys. Heat Transfer 11 (2) (1997) 129–140. [7] M.M. Yovanovich, Four decades of research on thermal contact, gap, and joint resistance in microelectronics, IEEE Trans. Compon. Packag. Technol. 28 (2) (2005) 182–206. [8] S. Song, Analytical and experimental study of heat transfer through gas layers of contact interfaces, PhD Thesis, University of Waterloo, Canada, 1988. [9] A.A. Hegazy, Thermal joint conductance of conforming rough surfaces: effect of surface micro-hardness variation, PhD Thesis, University of Waterloo, Canada, 1985. [10] M.M. Yovanovich, J.W. DeWaal, A.A. Hegazy, A statistical model to predict thermal gap conductance between conforming rough surfaces, AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, St. Louis, Missouri, 1982, AIAA-82-0888. [11] M. Bahrami, J.R. Culham, M.M. Yovanovich, Thermal resistance of gaseous gap for conforming rough contacts, 42nd AIAA Aerospace Meeting and Exhibit, Reno, 2004, AIAA-2004-0821. [12] M.M. Yovanovich, Thermal contact correlations, Prog. Astronaut. Aeronaut. Spacecraft Radiat. Transfer Temp. Control 83 (1982) 83–95.
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[13] G.P. Peterson, L.S. Fletcher, Measurement of thermal contact conductance and thermal conductivity of anodized aluminum coatings, ASME J. Heat Transfer 112 (3) (1990) 579–585. [14] L.S. Fletcher, A review of thermal enhancement techniques for electronic systems, IEEE Trans. Compon. Hybrids Manuf. Technol. 13 (4) (1990) 1012– 1021. [15] K-.C. Chung, Experimental study on the effect of metallic-coated junctions on thermal contact conductance, JSME Int. J. B 38 (1) (1995) 100–107. [16] L.S. Fletcher, M.A. Lambert, E.E. Marotta, Thermal enhancement coatings for microelectronic systems, ASME J. Electron. Packag. 120 (3) (1998) 229–237. [17] T.K. Kang, G.P. Peterson, L.S. Fletcher, Effect of metallic coatings on the thermal contact conductance of turned surfaces, ASME J. Heat Transfer 112 (4) (1990) 864–871. [18] V.W. Antonetti, M.M. Yovanovich, Using metallic coatings to enhance thermal contact conductance of electronic packages, Heat Transfer Eng. 9 (3) (1988) 85–92. [19] P. Misra, J. Nagaraju, Test facility for simultaneous measurement of electrical and thermal contact resistance, Rev. Sci. Instrum. 75 (8) (2004) 2625– 2630. [20] P. Misra, Simultaneous studies of electrical contact resistance and thermal contact conductance across metallic contacts, PhD Thesis, Indian Institute of Science Bangalore, India, 2009. [21] B. Kshirsagar, J. Nagaraju, M.V.K. Murthy, Thermal conductance across oxygenfree high-conductivity copper contacts in different environments, J. Thermophys. Heat Transfer 17 (3) (2003) 540–542. [22] B. Kshirsagar, J. Nagaraju, M.V.K. Murthy, Thermal contact conductance of silicon nitride-coated OFHC copper contacts, Exp. Heat Transfer 16 (4) (2003) 273–279. [23] B. Kshirsagar, P. Misra, J. Nagaraju, M.V.K. Murthy, Thermal contact conductance across gold coated OFHC Cu contacts in different media, ASME J. Heat Transfer 127 (2005) 657–659. [24] S. Song, M.M. Yovanovich, Correlation of thermal accommodation coefficient for engineering surfaces, in: Proceedings of 24th National Heat Transfer Conference and Exhibition, Pittsburgh, 1987, pp. 107–116. [25] M. Antler, Materials, coatings, and platings, in: P.G. Slade (Ed.), Electrical Contacts: Principles and Applications, Marcel Dekker, New York, 1999, pp. 155–277.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal gap conductance at low contact pressures (<1 MPa): Effect of gold plating and plating thickness Prashant Misra, J. Nagaraju * Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
a r t i c l e
i n f o
Article history: Received 26 May 2009 Received in revised form 12 May 2010 Accepted 20 June 2010 Available online 5 August 2010 Keywords: Thermal gap conductance OFHC Cu Brass Thin gold plating
a b s t r a c t Thermal contact conductance (TCC) measurements are made on bare and gold plated (60.5 lm) oxygen free high conductivity (OFHC) Cu and brass contacts in vacuum, nitrogen, and argon environments. It is observed that the TCC in gaseous environment is significantly higher than that in vacuum due to the enhanced thermal gap conductance. It is found that for a given contact load and gas pressure, the thermal gap conductance for bare OFHC Cu contacts is higher than that for gold plated contacts. It is due to the difference in the molecular weights of copper and gold, which influences the exchange of kinetic energy between the gas molecules and contact surfaces. Furthermore, the gap conductance is found to increase with increasing thickness of gold plating. Topography measurements and scanning electron microscopy (SEM) analysis of contact surfaces revealed that surfaces become smoother with increasing gold plating thickness, thus resulting in smaller gaps and consequently higher gap conductance. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Engineering surfaces are never absolutely smooth and the surface irregularities become apparent when observed under a microscope. As a result, when two solids are pressed together, actual contact is made only at a few discrete points separated by relatively large gaps. Due to the reduction in heat transfer area at the interface, there exists an extra resistance to heat flow, known as thermal contact resistance. A more popular term for it is the thermal contact conductance (TCC), defined as the inverse of thermal contact resistance. Heat transfer across the interface can take place by means of conduction through solid-to-solid contact spots and conduction through the gaps. Heat transfer through the interfacial gaps gives rise to thermal gap conductance (hg ), which together with the conductance of contact spots (hc ) decides the overall joint conductance (hj ) of a thermal contact. Therefore, for all thermal contacts
hj ¼ hc þ hg
ð1Þ
In vacuum environment, the thermal gap conductance is negligible and the joint conductance is predominantly the conductance of contact spots only (hj hc ). Radiative heat transfer across the gaps is insignificant at moderate temperatures, and needs to be considered only if interface temperatures are above 300 °C [1]. In a gaseous environment, heat transfer through gas filled interfacial gaps is possible by either conduction or convection. Considering the small * Corresponding author. Tel./fax: +91 80 22932273. E-mail address: [email protected] (J. Nagaraju). 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.06.052
thickness of interfacial gaps (typically less than 10 lm), possibility of convective heat transfer is also neglected due to the fact that the Grashof number (the ratio of buoyant to viscous forces) is generally below 2000 [2]. Therefore, conduction remains the dominant mode of heat transfer across the gas filled interfacial gaps. Conduction across the gaps is particularly important when the contact pressure is relatively low, and/or the interstitial gaseous medium is relatively good thermal conductor [3]. It has been shown that, at low contact pressures (<1 MPa), very little heat passes through the solid contact spots, and the major portion of heat transfer occurs through the gas even when the solids are relatively soft and good thermal conductors such as aluminum [4]. In many practical applications, especially in electronic components, the operating contact pressures are in low or moderate range (for instance, average contact pressure in the case of a bolted thermal contact between the base plate and the heat sink of a multiple chip unit (MCU) in a computer is about 0.9 MPa). As a result, in such cases, the gaseous gap conductance plays a more significant role than the solid spot conductance. The thermal resistance at the interface can often lead to thermally induced failure of a component or a system as has been frequently observed in the case of electronic systems. As a result, enormous research has been done in this field and a substantial amount of data is available on the solid spot conductance [5–7]. However, there is comparatively little information on thermal gap conductance, especially of an experimental nature. Gaseous heat transfer across the interfacial gaps depends upon a number of parameters, such as, thermal properties of solids and gases, surface roughness characteristics, applied contact load, micro-hardness of
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Nomenclature erfc–1 H h k M Mg Ms Mg P Pr T TAC TCC Y
Greek symbols ratio of specific heats of gas K mean free path l ratio of molecular weights of gas and solid (=Mg/Ms) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r combined rms roughness ¼ r21 þ r22
inverse complementary error function Vickers micro-hardness thermal conductance thermal conductivity gas parameter molecular weight of gas molecular weight of solid for monoatomic gases Mg ; ¼ 1:4M g ; for dia=polyatomic gases contact pressure Prandtl number temperature thermal accommodation coefficient thermal contact conductance mean surface plane separation
c
Subscripts 1, 2 contact surfaces 1 and 2 c contact g gas j joint s solid
solids, etc. Because of the large number of parameters involved, numerous attempts by various researchers to model the thermal gap conductance have not been completely successful. While analytical models tend to neglect some of the important parameters, experimental correlations are valid only for limited ranges of these parameters. Song [8] and Hegazy [9] studied the gap conductance in N2, Ar and He environments across nickel and stainless steel contacts. Yovanovich et al. [10] developed a sophisticated statistical model (popularly known as the integral model) to predict thermal gap conductance between conforming rough surfaces, which was later presented in a simplified form by Song [8]. Bahrami et al. [11] presented a new approximate comprehensive, yet simple model for determining the heat transfer through the gap between conforming rough surfaces. The model is based on the general expression for heat transfer between two isothermal parallel plates proposed by Yovanovich [12], and covers the four regimes of heat conduction of gas, i.e., continuum, temperature-jump or slip, transition, and free molecular. It is easy to evaluate and accounts for gas and solid mechanical and thermal properties, gas pressure and temperature, surface roughness, and the applied load. According to this model, the thermal gap conductance is expressed as a function of the thermal conductivity of gas, gas parameter, and mean surface plane separation
kg hg ¼ MþY
ð2Þ
Where the gas parameter depends on the properties of gas and the mean plane separation depends on the properties of contact surfaces and applied contact pressure. The simple relationship for thermal gap conductance expressed in Eq. (2) is obtained by simplifying the gap thermal resistance problem with the help of the following assumptions: (i) the gas and microcontacts thermal resistances are in parallel at the interface; (ii) the gap heat transfer area is identical to the apparent area; (iii) temperatures for the contacting surfaces are uniform; and (iv) heat transfer through the interstitial gas in the gaps occurs by conduction. Bahrami et al. [11] compared his model (Eq. (2)) with the experimental data of Song [8] and Hegazy [9], obtained from SS 304 and Ni 200 contacts in Ar, He and N2 gases. The data covered a wide range of surface characteristics, applied load, thermal and mechanical properties, and the gas pressure. The model showed good agreement with the data over entire range of comparison with the rms relative difference between the data and the model to be approximately 7.8%. Techniques for enhancement of thermal performance of contacts are continuously being researched to overcome some of the challenging thermal problems posed by the progressive miniaturi-
zation of electronic components and systems. Use of soft surface coatings is one such technique that has been suggested for better thermal management in electronics [13,14]. Chung [15] studied the variation of contact resistance with indium, lead, and aluminum coatings on metals. Fletcher et al. [16] used both the vapor deposited silver and electroplated silver coatings in electronic components for the enhancement of TCC. Kang et al. [17] experimentally studied the enhancement in contact conductance across aluminum contacts coated with materials such as lead, tin, and indium. Antonetti and Yovanovich [18] gave a thermomechanical model according to which the thermal contact conductance across metallic coated contacts depends on the effective hardness and thermal conductivity ratio of that substrate–layer combination. Present work deals with experimental measurements of thermal gap conductance across bare and gold plated (with different plating thickness) OFHC Cu and brass (Cu/Zn 30) contacts. Gold is a relatively softer material with a reasonably high value of thermal conductivity. It offers a stiff resistance to oxidation in normal conditions. The obtained experimental data is analyzed with the help of surface topography, micro-hardness, and SEM measurements conducted on the contact surfaces. 2. Experimentation The test setup developed for simultaneously measuring electrical contact resistance and thermal contact conductance [19] is used for the experimentation. However, only thermal contact conductance measurements are made in the present study. Schematic of the setup is shown in Fig. 1a. It consists of various subsystems including a contact conductance cell, a vacuum system, a loading system, heating–cooling systems, and sophisticated instrumentation for temperature and low level electrical resistance measurements. The contact conductance cell can either be evacuated with the help of vacuum system, or can be pressurized by introducing a gas. The cell houses the contact specimens in a triangular frame attached to its lid. The top half of the triangular frame stays outside the contact conductance cell and holds a hydraulic jack and a compression type load cell. Hydraulic jack is a part of the hydraulic loading system, with which specimens are subjected to different contact loads. The axial contact load acting on the specimens is measured with the help of the load cell. The bottom half of the frame, which stays inside the contact conductance cell, accommodates the contact specimens in the form of a stacked assembly known as the test column. Fig. 1b shows the details of the test column. It consists of two contact specimens, two identical heat-flux meters, and two identical heater–cooler blocks. Heater–cooler
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Fig. 1a. Schematic of test setup.
blocks have vacuum compatible heaters powered by a stable output voltage from a variac, as well as cooling coils connected to a constant temperature liquid bath. The heater and the cooler blocks act as heat source and sink, respectively, and maintain a steady heat flow through the test column. Heat-flux meters are used for measuring the heat flow rate in the test column. The test column is balanced on a pair of ball and conical seating arrangements placed at both ends to ensure that the compressive load is always applied parallel to the axis of the test column. Instrumentation for temperature measurement includes multiple T-type thermocouples connected to a multi-channel DAQ hardware interfaced with a PC. These thermocouples measure temperatures at different axial locations in the heat-flux meters and contact specimens, and the collected data is used for heat flow rate and interface temperature drop estimations. Steady state temperature data obtained from the heat-flux meters is used for calculating the heat flow rate (Q) by using the Fourier’s law of heat conduction. Temperature data obtained from the contact specimens is used for estimating the temperature drop (DT) at the contact interface. Thermal conductance of the joint is then calculated as hj ¼ Q =ADT, where A is the apparent area of the contact. Uncer-
tainty in any single TCC measurement can be calculated from the relative uncertainties associated with the heat flow rate (±5%, obtained from the uncertainties in thermal conductivity and temperature measurements), apparent contact area (±0.13%), and interface temperature drop measurements (±3.4%). Therefore, the relative uncertaintyp inffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a typical TCC measurement made with the ffi present setup is 0:052 þ 0:00132 þ 0:0342 ffi 0:06 ¼ 6%. A complete description of the setup, its functioning, methodology used for TCC measurements, and detailed uncertainty analysis is provided elsewhere [19,20]. All the experiments are conducted on OFHC Cu and brass specimens prepared from respective single bar stocks to ensure identical material properties. Cylindrical specimens of 40 mm length and 16 mm diameter are prepared. To insert the thermocouples, three holes (1.2 mm diameter, 8 mm deep, and 10 mm apart) are drilled in each specimen along its length. All contact surfaces are optically polished to have a smooth surface finish. Three different thicknesses of gold layers (0.1, 0.3, and 0.5 lm) are obtained on three pairs of specimens by electrodeposition technique. A 2 lm thick nickel underlayer is given between the OFHC Cu/brass substrate and the gold layer in all the gold plated specimens. A nickel under-
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different experiments. On each specimen pair, measurements are made in vacuum, followed by nitrogen and argon environments (gas pressure of 2 bar). Properties of the used gases are given in Table 2. Detailed experimentation and data reduction procedure is provided in [20]. 3. Results and discussion
Fig. 1b. Details of test column.
plate in gold coated contacts is very common in commercial contacts as it acts as a diffusion barrier, provides mechanical backing, and improves the adhesion of the gold coating. Topography measurements on contact surfaces are made with the help of a stylus based profilometer (Taylor–Hobson Form Talysurf Intra). Microhardness measurements on bare and plated contact surfaces are made with the help of a Vicker’s micro-hardness tester (Zwick Roell ZHV1), at a constant indenter load of 10 gf. These measurement results from all the specimens are summarized in Table 1. SEM images of contact surfaces are taken after conducting the experiments. TCC measurements on all specimen pairs are made at different contact pressures in the range of 0–1 MPa. Interface temperature is maintained constant for facilitating easy comparison of data from
Table 1 Properties of contact surfaces. Contact
Bare OFHC Cu 0.1 lm Au plated 0.3 lm Au plated 0.5 lm Au plated 0.1 lm Au plated 0.3 lm Au plated 0.5 lm Au plated
OFHC Cu OFHC Cu OFHC Cu brass brass brass
Combined rms roughness qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ r21 þ r22 [lm]
Vicker’s micro-hardness [kg/mm2]
0.55 0.50 0.37 0.22 0.59 0.39 0.28
130 380 349 312 390 352 319
Fig. 2 shows the comparison of thermal conductance for bare OFHC Cu contacts in different environments. For vacuum environment, the plotted conductance is the measured joint conductance, which is nothing but the conductance of contact spots. For gaseous environments, the plotted conductance is the thermal gap conductance, which is obtained by subtracting the conductance of contact spots (thermal conductance in vacuum) from the measured joint conductance in these environments (according to Eq. (1)). Experimentally obtained gap conductance data is compared with the theoretical model [11]. The data agrees well with the model and the rms relative difference between the present experimental data and the model is less than 7%. It can be observed from Fig. 2 that the magnitude of thermal gap conductance for both N2 and Ar is higher than that of contact spot conductance, thus confirming that heat transfer through gas filled interfacial gaps is dominant in thermal contacts operating at low or moderate contact pressures. Furthermore, the thermal gap conductance for a given gas pressure is higher in N2 compared to that in Ar, because of relatively higher thermal conductivity of N2 (Table 2). A similar trend of gap conductance has been reported by other researchers [21–23] at higher contact pressures (few MPa) too. This validates the assumption that conduction is the dominant mode of heat transfer across the interfacial gaps. Figs. 3a and 3b show the comparison of thermal gap conductance in bare and gold plated OFHC Cu contacts in N2 and Ar environment, respectively. In both environments, it is observed that the thermal gap conductance for bare OFHC Cu contacts is higher than that for all the gold plated contacts. The magnitude of gap conductance is governed by the amount of thermal energy exchanged between the gas molecules and contact surfaces. For a given gas–solid combination, the degree to which the kinetic energy of a gas molecule is exchanged while in collision with the solid wall depends on a parameter known as the thermal accommodation coefficient (TAC), which depends on the molecular weights of the gas and the solid. A correlation for predicting the TAC for a given gas–solid combination is given by Song and Yovanovich [24], as
! Mg T s 273 TAC ¼ exp 0:57 273 6:8 þ Mg
2:4l T s 273 1 exp 0:57 þ 273 ð1 þ lÞ2
ð3Þ
It can be seen from Eq. (3) that the TAC strongly depends on the factor 2.4l/(1 + l)2, which is a function of the ratio of molecular weights of gas and solid (l). Higher the value of l, higher is this factor and consecutively, higher will be the value of TAC. Now; for N2 —OFHC Cu :
l¼
M N2 28 2:4l ffi 0:44 ) ¼ ffi 0:51 2 M OFHC Cu 64 ð1 þ lÞ
and; for N2 —Au :
l¼
M N2 28 2:4l ffi 0:14 ) ¼ ffi 0:26 M Au 197 ð1 þ lÞ2
Assuming that all other conditions are same, the TAC for N2–OFHC Cu combination should be more than for N2–Au. Using the same approach, it can be shown that the TAC for Ar–OFHC Cu is more than that for Ar–Au combination (l = 0.63 and 0.20 for Ar–OFHC Cu and Ar–Au, respectively). As a result, transfer of thermal energy
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Table 2 Properties of gaseous media. Property Thermal conductivity (kg) [W/mK] Molecular weight (Mg) Mean free path (K) [nm] @ 288 K and 760 torr Ratio of specific heats (c) Prandtl number (Pr)
N2
Ar 5
kg(T) = 0.028 + 5.84 10 27 6 T 6 400 °C 28 62.8 1.41 0.69
T;
kg(T) = 0.018 + 4.05 105T; 27 6 T 6 400 °C 40 66.6 1.67 0.67
Fig. 2. Contact spot conductance and gap conductance in OFHC Cu contacts.
Fig. 3b. Thermal gap conductance in bare and gold plated OFHC Cu contacts in Ar.
Fig. 3a. Thermal gap conductance in bare and gold plated OFHC Cu contacts in N2.
Fig. 4a. Thermal gap conductance in gold plated brass contacts in N2.
across the gaps will be relatively more in OFHC Cu contacts. This explains the observed high thermal gap conductance for bare OFHC Cu contacts compared to gold plated ones in both environments. It is also observed in Figs. 3a and 3b that the gap conductance for gold plated contacts increases with increasing thickness of gold plating. Gold plated brass contacts also exhibit an exactly similar kind of behavior, as shown in Figs. 4a and 4b in N2 and Ar environments, respectively. The transfer of heat from one solid surface to another through a gas filled gap depends on the thickness of the gap. As discussed earlier, given the very small size of interfacial gaps, the prevailing mode of heat transfer through the gas is
conduction. Under such circumstances, smaller be the thickness of gap, more efficient is the heat transfer through it. The thickness of interfacial gaps is estimated by a parameter known as the mean surface plane separation (Y), given as [11]
Y¼
pffiffiffi 1 2P 2rerfc H
ð4Þ
For a given contact pressure, the mean surface plane separation depends on the inherent roughness and hardness of contacting surfaces. Rougher be the contacting surfaces, higher is the mean plane separation. Similarly, for a given roughness and contact pressure,
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[25]. SEM images of various contact surfaces shown in Fig. 5 clearly indicate that the gold plated surfaces become smoother with increasing plating thickness. With decreasing surface roughness the mean surface plane separation or the thickness of interfacial gaps decreases, thus resulting in increased heat transfer through gaps and thereby an enhanced thermal gap conductance. Micro-hardness measurements on contact surfaces indicate that the surface micro-hardness also decreases with increasing gold plating thickness. This also has an effect on the enhancement of thermal gap conductance observed in Figs. 3 and 4 (in accordance with Eq. (4)). However, as discussed earlier this effect of hardness will be very small compared to that of surface roughness. Similarly, higher micro-hardness of gold plated surfaces (due to the underlying layer of nickel) is also responsible for the reduced thermal gap conductance observed in gold plated contacts compared to bare OFHC Cu contacts.
4. Conclusions Fig. 4b. Thermal gap conductance in gold plated brass contacts in Ar.
lower be the surface micro-hardness, smaller is the mean plane separation. However, by evaluating Eq. (4) using the approximate expressions given for erfc–1 [11], it can be easily seen that the roughness is the dominant term in Eq. (4). This indicates that the thickness of interfacial gaps is highly influenced by the roughness of contacting surfaces, while surface micro-hardness has a relatively smaller effect. Topography measurements on contact surfaces reveal that the roughness of gold plated surfaces decreases as gold plating thickness increases (Table 1). This is particularly true for thin gold coatings, which tend to be porous and discontinuous
Thermal conductance data obtained at low contact pressures in vacuum and gaseous environments shows that the conductance of gaps is much higher than the conductance of contacting spots, asserting the fact that bulk of heat transfer across the interface takes place through gas filled interfacial gaps. The thermal gap conductance in gold plated OFHC Cu contacts is lower than that in bare contacts because of the higher molecular weight of gold compare to OFHC Cu. For a given gas–solid combination, a higher gas to solid molecular weight ratio results in higher gap conductance. In gold plated contacts, thermal gap conductance shows an increase with increasing gold plating thick-
Fig. 5. SEM images of different contact surfaces showing the effect of gold plating thickness on surface topography.
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ness. Topography measurements and SEM analysis of contact surfaces indicate that thin gold platings tend to become smooth as plating thickness increases, resulting in smaller interfacial gaps and thereby enhanced thermal gap conductance.
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