1 Introduction

Diamond has very high thermal conductivity, second only to that of carbon nanotubes (CNTs) [1,2,3,4,5,6]. However, the thermal conductivity of CNTs is also highly anisotropic due to their unique structure [2]. In contrast, diamond particles typically have a granular morphology and exhibit more isotropic thermal conductivity. For this reason, diamond particles are expected to be applicable as raw materials for the preparation of high thermal conductivity composite materials, and there has been much research regarding the fabrication of composites comprising diamond together with Al [7, 8], Ag [9], or Cu [10,11,12,13,14,15,16,17]. Sintering and infiltration have traditionally been used to form such materials, although both methods require the application of extremely high temperatures and pressures. Moreover, metals such as Ag and Cu in the molten state are not able to readily wet diamond. Consequently, gaps or cracks tend to form between the metal matrix and the diamond particles in the composite, such that the resultant thermal conductivity is lower than that of the original metal. Both the wettability and thermal conductivity can be improved by pre-coating the diamond particles with the metal [2, 18,19,20,21,22], although the formation process is complicated and still requires the application of extremely high temperatures and pressures.

Electrodeposition could potentially be used to form metal layers on solid materials at ambient temperature and pressure, and thus could be advantageous. An investigation on the thermal conductivity of Cu/diamond composite materials fabricated using this technique has been reported recently [23]. Our group has also reported the excellent thermal conductivity of Cu/diamond composites formed by electrodeposition [24]. In both studies, the electrodes were arranged horizontally with the cathode at the bottom of a plating bath. Diamond particles were first precipitated on the cathode, after which copper was electrodeposited on the cathode to fill the gaps between the precipitated diamond particles, as well as between the substrate and the diamond particles. Furthermore, in both reports, electrodeposition was performed under galvanostatic conditions; i.e., the current density changes during electrodeposition. In some cases, the current density becomes sufficiently high to allow hydrogen gas evolution, which disturbs the arrangement of the precipitated diamond particles. Therefore, a copper electrodeposition technique that avoids hydrogen gas evolution is required.

In this study, the copper electrodeposition behavior, i.e., the current density, on a cathode with precipitated diamond particles was studied electrochemically under galvanostatic conditions. High thermal conductivity Cu/diamond composites were then fabricated without the evolution of hydrogen gas under potentiostatic conditions.

2 Experimental

Figure 1 shows the experimental procedure for the fabrication of Cu/diamond composites using electrodeposition. The electrodes were arranged horizontally with the cathode at the bottom. Diamond particles were first precipitated on the cathode, and then electrodeposition was performed to fill the gaps between the precipitated diamond particles, and between the substrate and precipitated diamond particles. Commercially available single-crystal diamond particles with various mean sizes (MMP series with 10, 25, and 45 μm sizes and SXD series with and 230 μm sizes, Changsha Xinye Co., Ltd.) were used. Scanning electron microscopy (SEM) images of the diamond particles are shown in Fig. 2. An aqueous solution containing 0.85 M CuSO4·5H2O and 0.55 M H2SO4 was employed as the copper plating bath. A pure copper plate and a copper plate containing phosphorus with an exposed surface area of 18 cm2 (3 × 6 cm), were used as the cathode and anode, respectively. The electrolytic cell was constructed of an acrylic resin and its internal dimensions were 3.5 × 7 × 6 cm. The masses of the 10, 25, 45, and 230 μm diamond particles added to the bath were approximately 0.11, 0.28, 0.50, and 2.53 g, respectively, which correspond to two layers of particles (a bilayer) on the cathode. In the case of a monolayer, half the amount of diamond particles was added to the bath. These masses were estimated using the diamond density and the diamond particle sizes. Before electrodeposition, the diamond particles were dispersed homogeneously using a stirring bar and left undisturbed to allow the diamond particles to precipitate, i.e., to arrange diamond particle layer(s) on the cathode. In the case of a bilayer, the quantities of electrical charge passed through the cell were 54, 135, 243, and 1240 C cm−2.

Fig. 1
figure 1

Schematic illustration of the process for fabrication of Cu/diamond composites using electrodeposition

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Fig. 2
figure 2

SEM images of diamond particles used: a 10 μm, b 25 μm, c 45 μm, and d 230 μm

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The electrodeposition process fills the gaps between the precipitated diamond particles, and between the substrate and precipitated diamond particles; therefore, the surface area of deposited copper, and thus the current density, should change during electrodeposition under galvanostatic conditions. Electrochemical measurements were conducted at 25 °C using an electrochemical measurement system (HZ-5000 Hokuto Denko Co. Ltd.) to estimate the current densities during electrodeposition under galvanostatic conditions. Measurements of the rest potential and current-potential curve, and chronoamperometry were conducted using a pure copper plate, a copper plate containing phosphorus, and a saturated calomel electrode (SCE) as the working, counter, and reference electrodes, respectively. Current-potential curves were obtained at 50 mV min−1. Chronoamperometry was performed in the overpotential range of 50–260 mV for 600 s to obtain steady-state current densities that corresponded to the overpotentials. Chronopotentiometry was conducted for the cathode with a diamond particle layer under galvanostatic conditions (90 mA: 5 mA cm−2 for the cathode substrate without diamond particle layers). Electrodeposition of copper was also conducted under potentiostatic conditions at − 0.20 V vs. SCE (0.0412 V vs. standard hydrogen electrode (SHE), at which hydrogen evolution cannot occur) on the cathode with a diamond particle layer.

The diamond content (vol%) in each composite formed was determined by directly weighing the specimens after removal of the copper matrix with HNO3. The surface and cross-sectional morphologies of the composites were examined using field-emission SEM (FE-SEM, SU-8000, Hitachi High Technologies Co.), with samples prepared using a cross-section polisher (SM-09010, JEOL Ltd.). The thermal diffusivity (α) of each specimen was measured with a xenon laser flash thermal properties analyzer (LFA 447-2 Nanoflash, Netzsch Co., Ltd.). The α values of the Cu/diamond composite samples fabricated with 10, 25, and 45 µm diamond particles were measured in the thin film, in plain mode, while the specimen formed with 230 µm particles was assessed in the bulk, in normal mode. The density (ρcomp) and specific heat capacity (Ccomp) of each composite were calculated using the following equations: [10,11,12,13]

$$\rho _{{{\text{comp}}}} = \rho _{{{\text{dia}}}} \cdot V_{{{\text{dia}}}} + \rho _{{{\text{Cu}}}} \cdot V_{{{\text{Cu}}}}$$
(1)

and

$$C_{{{\text{comp}}}} = \frac{{C_{{{\text{dia}}}} \cdot V_{{{\text{dia}}}} \cdot \rho _{{{\text{dia}}}} + C_{{{\text{Cu}}}} \cdot V_{{{\text{Cu}}}} \cdot \rho _{{{\text{Cu}}}} }}{{\rho _{{{\text{comp}}}} }} ,$$
(2)

where ρdia and ρCu are the densities of diamond (3.52 g dm−3) and Cu (8.94 g dm−3), Vdia and VCu are the experimentally determined volume percentages of diamond and copper, and Cdia and CCu are the specific heat capacities of diamond (0.512 J g−1 K−1) and copper (0.385 J g−1 K−1), respectively. The thermal conductivity (λcomp) of each sample was calculated as according to

$$\lambda _{{{\text{comp}}}} = \alpha \cdot \rho _{{{\text{comp}}}} \cdot C_{{{\text{comp}}}} .$$
(3)

3 Results and discussion

Figure 3 shows an overpotential-current density curve for the electrodeposition of copper on a copper substrate without a diamond particle layer measured in the sulfate plating bath. The limiting current density was ca. − 120 mA cm−2, and significant hydrogen evolution began at overpotentials greater than ca. − 0.6 V. Hydrogen evolution during electrodeposition on the cathode with diamond particle layers would disturb the layer arrangement; therefore, electrodeposition should be conducted at a current density of less than − 120 mA cm−2 or at an overpotential lower than − 0.6 V. During the electrodeposition of copper on the cathode with diamond particle layers under galvanostatic conditions, the cathode surface area changes, which results in a change in the current density. Diamond particles with undefined shape were used in this study (Fig. 2); therefore, the surface area of the electrodeposited copper was unclear, and consequently, the current density was ambiguous. Electrochemical techniques were employed to estimate the current density during copper electrodeposition. Figure 4 shows a Tafel plot for the electrodeposition of copper on a copper cathode without diamond particle layers. The plot was linear in the overpotential range of − 0.05 to ca. − 0.20 V, whereas good linearity was not obtained at overpotentials higher than ca. − 0.20 V. Therefore, a charge transfer process is considered to be the main rate-limiting step in the potential range up to ca. − 0.20 V, while both mass transfer and charge transfer processes significantly affect the electrodeposition rate of copper at potentials greater than ca. − 0.20 V. It is generally accepted that copper electrodeposition from acidic sulfate solutions proceeds as follows:

Fig. 3
figure 3

Overpotential-current density curve for the electrodeposition of copper on a copper substrate without a diamond particle layer measured in the acidic copper plating bath

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Fig. 4
figure 4

Tafel plot for the electrodeposition of copper on a copper cathode without diamond particle layers

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$${\text{Cu}}^{{2 + }} + {\text{e}}^{ - } \rightleftharpoons {\text{Cu}}^{ + } \quad E^{ \circ } = 0.16\;{\text{V}}\;{\text{vs}}.\;{\text{SHE}}$$
(4)
$${\text{Cu}}^{ + } + {\text{e}}^{ - } \rightleftharpoons {\text{Cu}}\quad E^{ \circ } = 0.52\;{\text{V}}\;{\text{vs}}.\;{\text{SHE}}$$
(5)

where the first process is the rate-determining step [25]. In the case of large cathode overpotentials over − 0.12 V (– 0.05 V is acceptable), the following relationship exists between the current density (j) and overpotential (η):

$$\ln \left( { - j} \right) = \frac{{ - \alpha nF}}{{RT}}\eta + \ln j_{0} ,$$
(6)

where α is the transfer coefficient, n is the number of electrons involved in the rate-determining step (in this case n = 1), F is the Faraday constant, R is the gas constant, T is the absolute temperature, and j0 is the exchange current density. Least-squares fitting of the Tafel plot in the potential range of − 0.05 to − 0.125 V to Eq. 6 yielded values of α = 0.47 and j0 = 1.7 mA cm−2, which were almost the same as those previously reported in the literature [26]. The value of j0 obtained in this study is somewhat larger than the previously reported values (1.1–1.4 mA cm−2), which is most likely due to the difference in the concentrations of Cu2+ ions in this study (0.85 M) and those in the previous study (0.25 M). The Tafel slope was 124 mV/decade, which is also similar to the literature values [27,28,29]. Substituting the obtained kinetic parameter values of α and j0 into the Butler–Volmer equation, the relationship between j (mA cm−2) and η (V) was obtained as follows:

$$j = 1.7\left( {e^{{20.6\eta }} - e^{{ - 18.2\eta }} } \right).$$
(7)

Figure 5 shows the overpotential transitions during copper electrodeposition on the copper substrate with diamond particle layer(s) at a current of 90 mA (5 mA cm−2 for the substrate without diamond particle layer). The overpotential during copper electrodeposition on the copper substrate without a diamond particle layer was ca. − 0.05 V. In the case of the monolayer (Fig. 5a), the overpotentials were greater than − 0.05 V. Accordingly, the overpotentials for all substrates with diamond particle monolayers were increased to some extent compared to that without a diamond particle layer. However, the overpotentials were lower than − 0.20 V, and the fluctuations were relatively small for all diamond particle sizes. In contrast, for the bilayer (Fig. 5b), the overpotentials and fluctuations were considerably larger than those for the monolayer. The overpotential for the substrate with 230 µm size diamond particle layers was occasionally greater than − 0.50 V, at which there is a risk of considerable hydrogen evolution. Therefore, in the case of the monolayer where the overpotentials for all diamond particles sizes were lower than − 0.20 V, the electrodeposition of copper should proceed mainly as a charge transfer process. Consequently, the conversion of the overpotentials to current densities is possible using Eq. 7. In contrast, the overpotentials for bilayers were considerably large (greater than − 0.20 V), so that the electrodeposition of copper proceeds not only in charge-transfer mode but also in mass-transfer mode; therefore, Eq. 7 cannot be used to convert the overpotentials to current densities.

Fig. 5
figure 5

Overpotential as a function of time during copper deposition on the substrate with diamond particle layer(s) at 5 mA cm−2 for various diamond particle sizes: a monolayer and b bilayer

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Figure 6 shows the estimated current density transition during the electrodeposition of copper on a substrate with a diamond monolayer using the data from Fig. 5a and Eq. 7. The estimated current density during the electrodeposition of copper on the substrate without diamond layers was ca. 4 mA cm−2. For the 10 µm diamond particles, the current density reached 50 mA cm−2, which is 10 times higher than that for the copper substrate without diamond particles (5 mA cm−2). Therefore, the electrodeposition of copper under galvanostatic conditions on the substrate with a diamond particle layer(s) was difficult to control, so that copper electrodeposition under potentiostatic conditions was examined. Figure 7 shows current-potential curve for copper electrodeposition, where the x-axis has been converted to the potential versus SHE from SCE (Fig. 3). To completely avoid hydrogen evolution during copper deposition, the potential was set to 0.0412 V vs. SHE (– 0.200 V vs. SCE). The corresponding current density was ca. − 55 mA cm−2.

Fig. 6
figure 6

Estimated current densities as a function of time during copper deposition on a substrate with a diamond monolayer at 5 mA cm−2

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Fig. 7
figure 7

Current-potential curve for copper deposition. The x-axis has been converted from potential vs. SCE to potential vs. SHE

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Figure 8 shows surface SEM images of Cu/diamond composites fabricated under potentiostatic conditions. The diamond particles are a bilayer. The deposited copper fills the gaps between the diamond particles, which resulted in Cu/diamond composites for all diamond sizes. Figure 9 shows a cross-sectional SEM image of the Cu/diamond composite, where the dark regions are the 45 µm diamond particles. The diamond particles were embedded in the deposited copper, and there were no gaps between the copper matrix and diamond particles. Therefore, the Cu/diamond composites fabricated by electrodeposition under potentiostatic conditions are considered to have a dense morphology.

Fig. 8
figure 8

Surface SEM images of Cu/diamond composites with various diamond particle sizes fabricated by electrodeposition under potentiostatic conditions (– 0.200 V vs. SCE, or − 0.0412 V vs. SHE): a 10 µm, b 25 µm, c 45 µm, and d 230 µm

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Fig. 9
figure 9

Cross-sectional SEM image of a Cu/diamond composite with 45 µm diamond particles prepared under potentiostatic conditions (–0.200 V vs. SCE, or − 0.0412 V vs. SHE)

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Table 1 shows the composition of the Cu/diamond composites formed and their thermal conductivities. Theoretical values were calculated using the Hasselman–Johnson equation: [30]

$$\lambda _{{{\text{sim}}}} = \lambda _{{{\text{Cu}}}} \left\{ {\frac{{2\left( {\frac{{\lambda _{{{\text{dia}}}} }}{{k_{{{\text{Cu}}}} }} - \frac{{\lambda _{{{\text{dia}}}} }}{{ah_{{\text{c}}} }} - 1} \right)V_{{{\text{dia}}}} + \frac{{\lambda _{{{\text{dia}}}} }}{{\lambda _{{{\text{Cu}}}} }} + \frac{{2\lambda _{{{\text{dia}}}} }}{{ah_{{\text{c}}} }} + 2}}{{\left( {1 - \frac{{\lambda _{{{\text{dia}}}} }}{{\lambda _{{{\text{Cu}}}} }} + \frac{{\lambda _{{{\text{dia}}}} }}{{ah_{{\text{c}}} }}} \right)V_{{\text{d}}} + \frac{{\lambda _{{{\text{dia}}}} }}{{\lambda _{{{\text{Cu}}}} }} + \frac{{2\lambda _{{{\text{dia}}}} }}{{ah_{{\text{c}}} }} + 2}}} \right\},$$
(8)

where λsim is the simulated thermal conductivity of the Cu/diamond composite, λdia is the thermal conductivity of diamond, λCu is the thermal conductivity of Cu, a is the mean radius of the diamond particles, Vdia is the volume percentage of the diamond particles, and hc is the boundary conductance between the Cu matrix and diamond particles. In this simulation, λdia, λCu, and hc were assumed to be 1300 W m−1 K−1 [10, 18], 400 W m−1 K−1, and 8.86 × 108 W m−2 K−1 [31]. The thermal conductivities of Cu/diamond composites with diamond particle sizes larger than 25 µm were higher than that of pure copper (400 W m−1 K−1). In particular, the thermal conductivity of the Cu/diamond composite with 230 µm diamond particles (49 vol%) reached 600 W m−1 K−1, which is 1.5 times that of pure copper. Experimentally measured thermal conductivities roughly corresponded to the simulated thermal conductivities, which indicates that the Cu/diamond composites fabricated in this study have close to ideal textures for use as high thermal conductivity materials. Electrodeposition under potentiostatic conditions can thus be considered as an excellent method for the fabrication of high thermal conductivity Cu/diamond composites, and this strategy could be extended to other metal/diamond composites.

Table 1 Compositions and thermal conductivities of Cu/diamond composites fabricated under potentiostatic conditions (0.0412 V vs. SHE)
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4 Summary

Cu/diamond composites with high thermal conductivities were fabricated using an electrodeposition technique. The electrodes were arranged horizontally and the cathode was positioned at the bottom of the plating bath. Diamond particles (10–230 µm) were first precipitated on the cathode substrate, and copper was then electrodeposited to fill the gaps between the precipitated diamond particles, and between the substrate and the diamond particles, which resulted in Cu/diamond composites. The current densities during electrodeposition on the substrate with a diamond particle layer(s) were estimated electrochemically under galvanostatic conditions. The measured current densities for a substrate with a diamond monolayer were several times higher than that for a substrate without a diamond particle layer, which implies the risk of hydrogen evolution. The Cu/diamond composites formed under potentiostatic conditions where hydrogen evolution cannot occur (+ 0.0412 V vs. SHE) had compact morphologies with no gaps between the copper matrix and the diamond particles. The highest thermal conductivity measured was that for the Cu/diamond composite containing 49 vol% of 230 µm diamond particles, which reached 600 W m−1 K−1 or 1.5 times that of pure copper.