Enhanced electrical conductivity in graphene–copper multilayer composite

Copper has the second-highest electrical conductivity of all metals (58 MS/m at 20 °C).¹ It is the preferred electrical conductor material in most electrical wiring applications. Wind power generators and electric vehicle (EV) traction motors use copper to conduct the high current required to generate a strong magnetic field. Thus, even a small improvement in copper’s conductivity will have a tremendous impact on global power generation and electricity consumption.² Electrical conductivity of a metal depends on the free charge carrier density and mobility. Improving electrical conductivity requires increasing one of these two factors without significantly decreasing the other. The carrier density of a metal is determined by the number of valence electrons of the constituent atoms, and the carrier mobility is affected by defects, such as impurities, inhomogeneities, and grain boundaries. Efforts have been devoted to purifying copper to achieve impurity levels less than 10 ppm and to grow single crystals. The conductivity of copper has been improved to 109% that of the international annealed copper standard (IACS).³ However, with the conductivity approaching its theoretical limit, room for further improvement is vanishing and costs are increasing. A viable approach to increase conductivity is to composite copper with a material with higher carrier mobility, such as graphene or carbon nanotubes (CNTs).

Graphene and CNTs have remarkable carrier mobility^4–6 and long mean free paths,⁷ making them appealing for electronic applications.^8,9 However, the electrical properties of CNTs are sensitive to the wall numbers, diameter, and chirality.^10–12 This complication leads to a challenging purification process for making metallic single-walled carbon nanotubes, which are ideal as filler material in the copper matrix.^13,14 In contrast, graphene’s electrical properties are determined by its layer numbers,¹⁵ structural integrity,¹⁶ adsorption atoms¹⁷ or intercalation molecules,¹⁸ and the substrate material.^19–22 With the realization of large-area, uniform, single-layer graphene grown on copper foil by chemical vapor deposition (CVD),²³ graphene’s quality and properties can now be well-controlled. As a result, graphene is preferable to CNTs as filler material to enhance copper’s electrical conductivity.

A number of groups have studied the electrical conductivity of the graphene–copper composite with negative or limited improvement. Some of these works focused on studying the carbon source used for growing and distributing graphene [for example, reduced graphene oxide,^24–29 graphene nanoplatelets,^30–33 pristine graphene,^34–36 hydrogenated graphite,^3,37 or polymers like polymethyl methacrylate (PMMA)],^38,39 while others focused on graphene–copper composite fabrication methods, such as hot-pressing,^{3,25,31,32,36,38,39} spark plasma sintering,^{26–30,34,35} and electrodeposition.^24,33 Among these reported results, the highest conductivity achieved was 117% IACS. The bulk specimen was fabricated by Cao et al.³ using the hot-pressing method to consolidate copper foils with CVD-grown graphene. To isolate graphene’s effect, they synthesized the graphene–copper composite foil, removed the graphene layer using oxygen ions, hot-pressed the graphene-free copper foil into a bulk sample, and measured its conductivity. The result was 112% IACS. It shows that graphene contributed 5% improvement in conductivity while the microstructural changes associated with the high-temperature treatment during the CVD process contributed to the remaining 12% improvement. More interestingly, the conductivity of the copper foil before and after the CVD of graphene remained the same. It appears that hot-pressing may activate the coupling between graphene and copper, resulting in a 17% improvement in total conductivity. Li et al.²⁹ achieved a 108% IACS by ball-milling copper powder together with reduced graphene oxide, followed by spark plasma sintering. However, the two-point probe method they used to measure the conductivity convoluted their results with contact resistance. Huang et al.³³ reported 103% IACS conductivity in a graphene–copper composite film fabricated by electrodeposition on a patterned substrate. However, were the film’s tapered cross-sectional shape is considered, the conductivity would be corrected to 96.5% IACS.

Two requirements must be simultaneously satisfied for the added graphene to have a meaningful impact: (1) the graphene layer must be uniformly distributed and aligned parallel with the applied electrical current and (2) the graphene must be in direct contact with the copper (i.e., free of any oxide or dielectric materials at the interface).⁴⁰ The weak van der Waals bonding between graphene and copper not only preserves the electronic structure of pristine graphene²² but also results in low adhesion energy of the monolayer graphene on the copper surface,⁴¹ making it difficult to embed graphene into the copper matrix. Most of the composite fabrication processes reported in the previous studies satisfy only part of the two requirements, which explains why most of the reported results show statistically negligible improvement in electrical conductivity.

To achieve a clean and intimate interface between graphene and copper, we used sequential multilayer deposition to fabricate the composite in the present work. Alternate graphene and copper films were deposited on a 23.6-µm-thick copper foil using the plasma-enhanced CVD (PECVD) and electron-beam deposition methods. The sample has six layers of copper and six layers of graphene, with a total thickness of 1.3 µm excluding the substrate, and the graphene volume fraction is estimated to be 0.008%. The graphene layers are aligned in-plane and equally spaced by the copper layers. The electrical conductivity of the multilayer composite was measured from room temperature to 200 °C using the four-wire method. A conductivity of 104.2% IACS was measured on the sample at room temperature. The sample thickness used by the measurement was 24.9 mm. If the substrate thickness is discounted using the parallel resistance model, the conductivity of the 1.3-µm-thick composite with six layers of graphene and six layers of copper is estimated to be 185% IACS. This result is a significant improvement from Cao’s results of 117% IACS³ due to the much-reduced copper lamella thickness (from 9 to 0.2 µm). It proves that embedding graphene in the copper matrix is effective in enhancing copper’s electrical conductivity. In addition, if the copper lamella thickness can be further reduced to 100 nm, the conductivity could exceed 256% IACS based on the simple rule of mixture.

Copper–graphene multilayer composite was fabricated via sequential deposition of copper film and graphene on a copper foil (AlfaAesar 10950, 5N pure) using electron-beam deposition and PECVD, respectively. The thickness of the purchased copper foil varies from batch to batch, and it is lower than the nominal thickness of 25 μm. Before the graphene deposition, the copper substrate was cleaned with acetone in an ultrasonic bath for 10 min and then dried by blowing with nitrogen gas. The cleaned Cu substrate was placed in the CVD chamber, which was then pumped down to a pressure of 50 mPa. The temperature in the CVD chamber was then ramped to 650 °C at a rate of 10 °C/min. An RF plasma (13.5 MHz, 50 W) was used to synthesize the graphene under a gas flow of CH₄ (99.99%, 1 SCCM) mixed with H₂ (15 vol. % in argon, 99.99%, 10 SCCM) for 10 min. Next, the furnace was moved away from the CVD chamber to allow the Cu substrate with the just-deposited graphene layer to cool quickly. The cooled sample was then removed from the CVD chamber and was ready for the copper-layer deposition.

The copper film was deposited by using an electron-beam evaporator (e-beam Temescal BJD-1800). Copper slugs (AlfaAesar 39675, 4N) serving as metal source were loaded into a molybdenum crucible, and the electron-beam chamber was pumped down to 0.1 mPa before deposition. The electron power was set for a deposition rate of 10 Å/s. During deposition, the film thickness and deposition rate were monitored by using a quartz crystal microbalance placed next to the rotating substrate holder. The film thickness was subsequently verified by a surface profilometer (Ambios Tech, XP-100). Graphene deposition by CVD and copper deposition by electron-beam were alternated to obtain a multilayer graphene–copper composite. Figures 1(a) and 1(b) show schematic illustrations of the PECVD setup and the electron-beam chamber, respectively.

For consistency of the electrical measurements, copper foil (Alfa Aesar, 10950, 5N pure) was heat-treated under the similar thermal conditions of the PECVD process and used as a reference for electrical resistivity measurement. It is noteworthy that the change in thickness of the foil during the heat treatment was negligible. Both graphene–copper composite foil (Sample ID: PECVD6L) and pure copper foil (Sample ID: annealed Cu) were cut into strips (3 × 25 mm²) for resistivity measurements. The four-wire method was used to eliminate the effect of contact resistance. Four 50-μm-diameter gold wires were attached to the sample with silver paint as electrodes. The distance between the two inner wires was about 14 mm. Figure 1(c) shows the setup for measuring the electrical resistivity. To measure the resistance, 100 mA current was applied by using a Keithley 6220 precision current source, and the voltage drop was read by a Keithley 2182A nanovoltmeter. To eliminate thermal offsets, Delta mode was used where the current polarity switched back and forth, and the average voltage drop over five power line cycles (PLC, where 1 PLC is 16.67 ms) was taken. The sample was enclosed in a tube furnace, and a thermocouple was placed under the sample holder to measure the resistivity as a function of temperature. After the chamber was purged four times with argon, the sample was heated at a rate of 5 °C/min under 40 SCCM Ar flow. At each target temperature, the furnace dwelled for 20 min before a measurement was made. Three samples were cut from the PECVD6L sample and the annealed Cu sample. The average thickness of the samples was measured by dividing the sample volume measured using Archimedes’ method by the sample area measured using an optical camera. The electrical resistivity was calculated by Ohm’s law, $ρ=RwtL$⁠, where R is the measured resistance, w is sample width, t is sample thickness, and L is the distance between inner wires. The error in resistance measurement generally increases with temperature but is less than 0.01% in all cases. Measured by an optical microscope, the ratio of sample width and inner wire distance has an error of less than 0.2%, and the error of thickness measurement is about 0.5%.

The Raman spectrum of the graphene sample was collected by using an inVia 488 nm Renishaw Coherent Laser Raman microscope spectrometer. The instrument was calibrated with a standard internal silicon reference centered at 520 cm⁻¹ (±1). The sample was measured in the range of 1200–3000 cm⁻¹ by using a 50× objective lens, a 20 s laser exposure per accumulation, with up to 30 accumulations, and at a laser power of 5 mW. For each sample, three scans were averaged to improve the signal-to-noise ratio. To prepare the sample for Raman spectroscopy, the PECVD-grown graphene was chemically etched from the copper foil by dissolving copper in an iron-nitrate solution (0.05 gm/ml). Before the wet etching of copper, one side of the copper substrate was spin-coated with PMMA. The PMMA-coated copper substrate was baked at 90 °C on a hot plate for 10 min. The non-coated side of the substrate was then treated with diluted (5% HNO₃) nitric acid to remove the graphene layer. After the acid treatment, the copper substrate was placed overnight in an iron-nitrate solution. Once the copper substrate had dissolved, the PMMA-coated graphene film was fished out from the solution, washed in deionized water, and transferred to a Si/SiO₂ substrate. The transferred film was dried in ambient air and on a hot plate at 120 °C to ensure proper adhesion of the graphene film to the Si/SiO₂ substrate. Later, the PMMA coating was dissolved overnight in 70 °C acetone, followed by baking in a tube furnace at 400 °C for 1 h in Ar gas.

To observe the graphene layers, a focused ion beam (FIB) was used to cut the cross section of the sample. The sample was initially cut with a razor blade to expose a fresh edge. It was then mounted on a standard 45° pre-tilted stub and loaded into the dual-beam instrument (FEI/Thermo-Fisher Helios Nanolab G3 UC.) A protective layer of carbon was deposited, and FIB cross-sectioning proceeded using standard techniques.⁴² Care was taken to situate the FIB cross-sectional well away from the edge deformed by the razor blade.

The Raman spectrum (Fig. 2) has two typical intense Raman bands centered around 1590 and 2701 cm⁻¹. These Raman bands are assigned as G and 2D bands and attributed to the E_2g optical phonon mode and to the overtone of the A_1g optical phonon mode, respectively. In addition, a weak combinational Raman band appears at 2452 cm⁻¹. This phonon mode was previously assigned to the D + D″ band, arising from the combination of the longitudinal acoustic phonon branch at 1100 cm⁻¹ and D phonons at the K point of the Brillouin zone. Generally, the intensity ratio of the G band to the 2D band [I(G)/I(2D) ∼ 0.5 for monolayer graphene] along with the shape of the 2D band is used to determine the number of layers.²³ Evidently, the magnitude of I(G)/I(2D) and the symmetric shape of the 2D band confirm the single-layer graphene deposition on the copper foil. Moreover, the near-background level of the D band at 1353 cm⁻¹ is further evidence of the low defect density in the PECVD-synthesized graphene sample. The uniformity of graphene quality is assured by acquiring Raman spectra from five randomly selected spots. The results are found qualitatively consistent (Fig. S3).

Figure 3(a) shows the SEM image of the PECVD6L cross-sectional cut by FIB. The sample thickness is about 24.9 µm, including 23.6-µm pure copper foil and 1.3-µm Cu-Gr multilayer film, which can be seen in Fig. 3(b). There are six layers of copper films in total with one layer of graphene between each copper layer. The average thickness of the copper film is about 215 nm. The interfaces are not smooth, and there are occasional pores embedded at the interface, which may be related to the surface roughening during the PECVD heating process. Interestingly, the first two layers show minimum grain contrast, and the layers are mostly merged with the copper foil without an obvious interface. The first copper layers underwent five heating cycles during the PECVD process for growing five layers of graphene, and the grains inevitably grow. Carbon is known to have limited solubility in copper (<8 at. ppm) even annealed at over 1000 °C for a prolonged time.⁴³ It is postulated that the grains grow across graphene, forming an atomic level intimate contact between graphene and copper lattice. This is the ideal structure for facilitating electron transport.

Figure 4 plots the electrical resistivity of the samples, PECVD6L and annealed Cu, as a function of temperature. From 20 to 200 °C, the PECVD6L sample has about 4.5% higher conductivity than the annealed Cu sample. It is significant to mention here that we did not observe in texturing (Fig. S1) stemming from heat treatment, facilitating the electrical conductivity of the composite. The temperature coefficient of electrical resistivity (TCR) is the same as that of pure copper. Table I summarizes the relevant electrical properties of the samples.

A moderate improvement in conductivity of 4.5% occurs with low graphene content, about 0.008 vol. % (assuming a monolayer graphene thickness of 0.335 nm).⁴⁴ Figure 5 compares the electrical conductivity of this work with the results reported in the literature, as a function of graphene content. This result is consistent with that of Cao,³ who attributed a 5% conductivity improvement to 0.008 vol. % graphene in a multilayer graphene–copper architecture. The PECVD6L sample consists of a 23.6-µm pure copper substrate and about 1.3-µm graphene–copper composite film. When the current is applied in the plane of the foil, the parallel resistance model (Fig. S2) can be applied to calculate the resistivity of the composite film. Using the data in Table I, the resistivity of the composite film was calculated to be 0.933 × 10⁻⁸ Ω m at room temperature and 1.587 × 10⁻⁸ Ω m at 200 °C, about 185% IACS at 0.15 vol. % graphene content. Applying the same calculation method, the conductivity of the composite film will be 256% IACS if the copper film thickness is reduced to 100 nm. The present result demonstrates that even with low graphene loading, macroscopic electrical conductivity enhancement could be achieved, providing that layers of high-quality graphene are embedded in the copper matrix in a parallel manner.

Density-functional theory calculations have shown that, despite weak bonding between graphene and copper, the Fermi level of graphene shifts up, indicating that copper electrons are donated to the graphene.^21,22 The linear band dispersion of graphene at the K point remains unchanged after doping, offering high carrier mobility with increased electron density. Near the graphene–Cu interface, the local conductivity is reportedly over 3000 times greater than that of the Cu matrix.³ The overall improvement in conductivity can be understood as due to a small fraction of the copper electrons near the graphene entering the graphene π orbit and being significantly accelerated.

The electron donors, which are the copper atoms near the graphene–Cu interface, are only localized within a few atomic layers from the graphene sheet. We may hypothesize that, with the spacing between graphene layers reduced to several tens of nanometers, the overall conductivity may increase and approach the conductivity measured at the interface until the copper layer thickness reaches its 39 nm electron mean free path.⁴⁵ At such a high graphene content, the TCR may also decrease significantly due to the suppressed electron–phonon coupling.⁴⁶ A viable method of fabrication is to incorporate more multilayers and use thinner copper film and copper substrate. However, a thinner copper layer per electron-beam deposition would require more electron-beam deposition runs to fabricate a sample with the desired final thickness. In addition to increased cost, repetitive heating during graphene growth increases the surface roughness of copper,⁴⁷ which may adversely affect the subsequent graphene deposition.⁴⁸ To mitigate this problem, we used herein PECVD to lower the graphene growth temperature from about 1000 to 650 °C.⁴⁹ This method is useful for proving the concept and probing scientific principles. However, for the copper–graphene composite to become widely deployed, a novel fabrication method is required to cost-effectively impregnate copper with finely separated graphene layers.

We synthesized the multilayer graphene–copper composite foil containing 0.008 vol. % graphene by using an alternate deposition process involving PECVD and electron-beam deposition. The composite’s electrical conductivity reaches 104.2% IACS and is about 4.5% better than that of the copper substrate in the temperature range 20–200 °C. The improvement is attributed to charge transfer from copper to graphene, whose high carrier mobility is preserved when embedded in the copper matrix. The multilayer sample-fabrication method enables graphene to be incorporated into the copper matrix in a well-controlled manner. Much higher conductivity is expected by increasing the graphene content without losing its structural integrity.

See the supplementary material for the x-ray diffraction pattern of the copper foils, the derivation of the parallel resistance model, and Raman spectra of graphene.

This work was supported by Dr. Jun Cui’s startup fund at Iowa State University.