Graphene-Supported Thin Metal Films for Nanophotonics and Optoelectronics

Abstract

Graphene-metal hybrid nanostructures have attracted considerable attention due to their potential applications in nanophotonics and optoelectronics. The output characteristics of devices based on such nanostructures largely depend on the properties of the metals. Here, we study the optical, electrical and structural properties of continuous thin gold and copper films grown by electron beam evaporation on monolayer graphene transferred onto silicon dioxide substrates. We find that the presence of graphene has a significant effect on optical losses and electrical resistance, both for thin gold and copper films. Furthermore, the growth kinetics of gold and copper films vary greatly; in particular, we found here a significant dependence of the properties of thin copper films on the deposition rate, unlike gold films. Our work provides new data on the optical properties of gold and copper, which should be considered in modeling and designing devices with graphene-metal nanolayers.

1. Introduction

In recent years, a great deal of interest has been directed toward the use of graphene/metal hybrid nanostructures in the development of high-efficiency photonic, plasmonic, optoelectronic and nanoscale electronic devices [1,2,3]. Graphene is an atomically thin layer which therefore in practice does not affect the size of nanostructures, while possessing many remarkable properties, including broadband optical transparency [4,5,6], outstanding transport (electrical and thermal conductivity) [7,8,9,10] and record-breaking strength [11]. In addition, monolayer graphene is impermeable to atoms, molecules, ions, liquids, and standard gases [12,13,14] and exhibits superior chemical and thermal stability [15,16] together with high bioreactivity and biocompatibility [17,18]. Notably, the combination of graphene and other materials, in most cases, positively affects the entire hybrid structure. Thus, one of the most exciting characteristics of metal/graphene (plasmonic) hybrid devices is the tunability of their optical properties, which paves the way for new applications in the visible-near-IR spectral region [19,20,21,22,23,24]. Moreover, metal/graphene hybrid structures allow one to obtain a significant improvement in the strength and fatigue limit in bending compared to conventional metal structures without graphene [25,26], which allows an increase in the functionality of thin-film metal structures in relation to their use in flexible electronics applications.

Nanometric composite hybrid structures consisting of alternating thin layers of metal deposited onto a sublayer of graphene have been used to demonstrate room temperature operation of novel ultrasensitive broadband photodetectors [21,24,27], photovoltaic solar cells [19,28], hybrid graphene/metasurface systems at terahertz and infrared frequencies [24,29,30,31,32] and highly sensitive surface-enhanced Raman scattering (SERS) biosensors with the fluorescence quenching effect [33,34,35]. In addition, such novel composites can be potentially used as transparent graphene-based neural interfaces for electrophysiology, in vivo neural imaging, optogenetic applications [36,37] and brain-computer interfaces [38]. Furthermore, the combination of metallic components with other 2D materials to form a hybrid nanostructure system also provides a multifunctional platform with enhanced performance for various applications [39,40,41].

The fabrication of hybrid structures can be accomplished by transferring graphene (or a metal) to a metal (or graphene) by using a transferring method [20,42] or by the direct deposition of metals on single-layer graphene (for example by physical vapor deposition); in practice, both methods are used. In the first case, the optical, electrical and structural properties of a thin metal film cannot differ significantly from the standard tabulated values [43,44], and to our knowledge, no experimental studies have been done to clarify the second case: The effects of the graphene sublayer on the properties of the deposited metal. At present, the initial growth kinetics of nanoparticles of various metals on the surface of graphene (for both chemical vapour deposited (CVD) and mechanically exfoliated samples) [45,46] has been studied in some detail, but little attention has been paid to the deposition of thin metallic films on graphene and the study of their properties. One notable exception is the recent work of Majkova et al. [47], where the growth kinetics of copper films on CVD graphene transferred onto an oxidized silicon surface was studied in detail using the grazing-incidence small-angle X-ray scattering (GISAXS) technique, but the optical properties of these films as well as their conductivities have not been investigated. It has been noted that the ratio of the adsorption energy of copper adatoms on graphene to the bulk cohesive energy of the copper is sufficiently small, causing the graphene substrates to become non-wettable by copper. In particular, the latter circumstance (in combination with the very small diffusion barrier for copper on graphene) results in copper growing on the surface of graphene in the form of 3D islands during the initial stages according to the well-known Volmer–Weber model of thin film growth [48,49]. In addition, a 15 nm-thick copper film on graphene is close to the percolation threshold, whereas continuous films of the same thickness can be obtained for silicon, optical glass or other typical optical substrates [50].

In the present work, we have investigated the influence of a graphene underlayer on Au and Cu films properties in continuous thin films at thicknesses of 25 and 50 nm. Gold was chosen because, to date, it has been the most popular material for a variety of applications in nanoplasmonics. The optical properties of thin polycrystalline copper films are not only as good as those of noble metals [51,52,53], but unlike the noble metal components, copper-based components can easily be implemented in integrated circuits using industry-standard fabrication processes. It has been previously shown that the properties of thin-film plasmonic nanostructures depend appreciably on the film thickness [44,54,55,56], deposition rate [51,57] and ambient temperature [58]. Accurate accounting for optical constants is important for theoretical and numerical analyses (modeling) of thin-film hybrid graphene-metal nanostructures. We have undertaken numerous experiments with different deposition regimes to study the change in the optical and electrical properties of Cu and Au films with respect to differences in structural features. We focused on observing how the graphene underlayer affects the growth kinetics and characteristics of continuous thin films. All deposited films were characterized using the following techniques: Scanning electron microscopy (SEM), atomic force microscopy (AFM), and X-ray diffraction (XRD) to study the structural morphology; four-point probe measurements to determine the electrical properties; and spectroscopic ellipsometry to determine the optical constants in the spectral range from 300 to 3300 nm. The results of the experimental study are demonstrated in detail below.

2. Experimental Section

2.1. Sample Fabrication

As substrates for thin metal films deposition, we used CVD-grown monolayer graphene transferred by a poly(methyl methacrylate) (PMMA)-assisted transfer method onto silicon wafers with a 285 nm SiO₂ coating (from Graphene Laboratories Inc. (New York, NY, USA)). Monolayer graphene covered more than 90% of the substrate area, and the remaining part of the substrate was filled with a random distribution of bilayer graphene islands. Before metal deposition, graphene substrates were annealed at 250 °C in a vacuum chamber 10⁻⁶ Torr for 1 h to remove residual PMMA and water.

The crystal quality of monolayer graphene was assessed with a Thermo Scientific™ DXR™2 Raman microscope equipped with a 532 nm excitation laser working at a power of 10 mW. Raman spectra were acquired through a 50× microscope objective by means of 10 consecutive exposures, each with a duration time of 15 s. The ratio of the intensities of the D and G peaks located near 1340 and 1580 cm⁻¹, respectively, indicates the defect level in the graphene crystal [59].

Deposition of metals was made both on the graphene/SiO₂/Si and similar SiO₂/Si wafers without graphene to compare the properties of films on different substrates.

All film depositions were performed using gold and copper pellets with a purity of 99.999% (Kurt J. Lesker), and the e-beam evaporation procedure employing a Nano-Master NEE-4000 system. The base pressure of a vacuum chamber before and during the evaporation process was ~7 × 10⁻⁷ Torr and ~4 × 10⁻⁶ Torr, correspondingly. Unless mentioned otherwise, all metal depositions were performed at 20 °C. The nominal thicknesses of the deposited films are approximately 25 and 50 nm with a deposition rate in the range from 1 to 15 Å/s and were monitored by a quartz-crystal mass-thickness sensor (inside the evaporator).

2.2. Structural Characterization

X-ray diffraction (XRD) measurements of the (111) peaks of Au and Cu (Thermo ARL X’TRA X-ray diffractometer with Cu K_α radiation (λ = 0.154 nm)) were used to investigate the crystallinity of the deposited films. The Bragg reflection peak was analyzed by the Debye-Scherrer formula $\langle D\rangle =\frac{\lambda }{\sqrt{{\beta }^2-{\beta }_{\mathrm{std}}^2}\cos \theta }$ to estimate the average size of crystallites using the values of the peak width $\beta$, where $\theta$ is the diffraction peak angle and ${\beta }_{\mathrm{std}}=0.131$ is the instrumental broadening determined by the corundum single-crystal standard (SRM NIST).

Surface morphology was studied by scanning electron microscopy (SEM) (JEOL JSM-7001F with a Schottky emitter in secondary electron imaging mode, with a voltage of 30 kV, and a working distance of ~6.2–6.4 mm).

Topography measurements were performed using an atomic force microscopy (AFM, NT-MDT Ntegra) in tapping mode with a probe resonance frequency of 250 kHz. To determine the root-mean-square surface roughness of thin films, an area of 1.5 × 1.5 μm was used. The thickness of each film was obtained by direct measurement of the step height by an AFM scan of the film surface.

2.3. Optical and Electrical Characterization

To investigate the optical characteristics of thin metal films we applied ellipsometry measurements using a variable-angle spectroscopic ellipsometer VASE^® by J. A. Woollam Co. (Lincoln, NE, USA) in the wavelengths range of 300–3300 nm. Ellipsometry parameters Ψ and Δ were measured at angles of incidence of 70° and 75°, and to extract the complex effective dielectric function of metal films, ellipsometry data were analyzed by the Drude-Lorentz model fitting applying specialized spectroscopic ellipsometry software (WVASE^®, J. A. Woollam Co., Lincoln, NE, USA).

The sheet resistance of the thin metal films was measured by the four-point probe method on a Jandel RM3000 probe station using a head with a pin distance and radius of approximately 425 and 40 μm, correspondingly, both being much smaller than the area of deposited films (~1 × 1 cm²).

3. Results and Discussion

The growth and properties of thin metal films depend strongly on substrate characteristics and the use of additional coatings. In this study, we investigated metal films with thicknesses of several tens of nanometers deposited by electron beam evaporation on SiO₂/Si wafers with and without a top graphene layer (Figure 1a). Raman spectra measured at several sites on the graphene surface indicate the near-absence of D peak and, therefore, a low defect density of its crystal structure (Figure 1b and Figure A1). A quartz crystal microbalance (QCM) installed in the e-beam system provides a means to control the thickness of metal films during deposition, while the exact thicknesses were assessed with AFM measurements for each sample. Figure 1c,d shows, respectively, a polycrystalline structure of the film and typical AFM images of a scratch made on the metal film. Accurate thickness measurements of metal films are of high importance in determining their optical properties with ellipsometric measurements [44]. For convenience, in this work, we used thickness values obtained with the QCM. AFM measurements of the grain structures of all metal films provided a root-mean-square surface roughness with amplitudes of less than 1.6 nm and 0.7 nm for the SiO₂/Si substrates with and without top graphene layers, respectively.

3.1. Thin Gold Films

To study the influence of graphene on the growth of metal films, thin gold films were deposited by electron beam evaporation onto SiO₂/Si substrates with and without top graphene layers. In this section, we present the results for gold films with thicknesses of 25 nm (the results for 50 nm-thick gold films are shown in the Appendix A (Figure A2)). Figure 2a,b shows SEM images of Au films grown on SiO₂/Si and graphene/SiO₂/Si substrates at a rate of 1 Å/s in a single deposition process. These images reflect the formation of continuous polycrystalline metal films on both substrates and smaller average sizes of the in-plane grains of the gold films deposited on monolayer graphene. Gold films with the same thickness, but deposited on graphene at a higher rate of 5 Å/s, also consist of grains with smaller sizes comparing to gold films deposited on pure SiO₂/Si substrates at the same rate (Figure 2c). This indicates different kinetics of gold growth on graphene and SiO₂/Si substrates. XRD analysis of gold films reveals larger crystallite size for the films on SiO₂ than for those on graphene. It further found that the size of gold crystallites on graphene also increases as the deposition rate goes up. Thus, we obtained a mean crystallite size of 23.9 nm for the films grown on SiO₂ at both rates of 1 and 5 Å/s and mean crystallite sizes of 22.3 and 23.5 nm for the gold films on graphene deposited at 1 and 5 Å/s, respectively. A reduction of the mean crystallite size in the film results in an increase of the electron scattering losses at the crystallite boundaries, which leads to higher resistivity and optical losses. For this reason, in plasmonic and optoelectronic applications, the growth of gold films on graphene is preferred at higher deposition rates.

Next, to determine the effective permittivities of the gold films, we performed ellipsometric measurements and fitted the acquired data with a model comprising film thicknesses measured by AFM (Figure 2d). Figure 2e presents the figure of merit (FOM) for the optical quality of obtained gold films, which is the ratio of the real ${\epsilon }^{\prime }$ and imaginary ${\epsilon }^{″}$ parts of the dielectric permittivity. For wavelengths higher than 1000 nm, the FOM for the gold films deposited on pure SiO₂ is slightly higher than the FOM for the gold film deposited at the same rate on graphene with the overall difference less than 15%, which is mostly a consequence of the smaller crystallite size. This is true for deposition rates of both 1 and 5 Å/s. In addition, we performed sheet resistance measurements to characterize the electrical properties of deposited gold films. The sheet resistance of the gold films deposited on SiO₂/Si substrates does not depend on the deposition rate and equals 2.0 Ohm/sq, which is 25% and 15% lower than the sheet resistance of the corresponding films deposited on graphene at the rates of 1 and 5 Å/s, respectively (2.7 Ohm/sq and 2.3 Ohm/sq). The data obtained for the optical FOM and sheet resistance of gold films are in a good agreement with the results of XRD analysis.

3.2. Thin Copper Films

In the same manner, we studied thin copper films deposited on SiO₂/Si substrates with and without a top graphene layer. The results of the structural morphology and optical properties of copper films with a thickness of 25 nm are presented below. Additional results of 50 nm-thick copper films are given in the Appendix A. Figure 3a,b demonstrates the noticeable difference in morphology of 25 nm-thick copper films deposited at a low rate (approximately 1 Å/s) on SiO₂/Si and graphene/SiO₂/Si substrates in a single process. The copper films on a bare SiO₂/Si substrate have a continuous structure, while the ones deposited on graphene contain narrow voids between metal clusters covering the entire film. Therefore, the addition of only a single atomic layer of graphene completely changes the growth kinetics of copper films.

Nevertheless, the deposition of continuous copper films on graphene is possible by increasing a number of nucleation centers during the initial steps of film growth. According to a report by Zaporojtchenko et al. [60] and a recent report by Schwartzkopf et al. [61] increasing the deposition rate by an order of magnitude leads a two-fold increase in the number of clusters formed. Based on this assumption, we carried out a series of depositions and investigated the dependence of the optical, electrical and structural characteristics of thin copper films on the deposition rate. As a result, we found that 25 nm-thick copper films deposited on graphene at higher deposition rates of 10–15 Å/s have a continuous surface morphology without notable voids (Figure 3с). The observed difference in morphology of the Cu films shown in Figure 3a–c is also reflected in their effective dielectric functions measured by spectroscopic ellipsometry. Figure 3d,e shows the real ${\epsilon }^{\prime }$ and imaginary ${\epsilon }^{″}$ parts of dielectric functions and the FOM for copper films deposited on bare SiO₂/Si at a rate of 1 Å/s and on graphene at rates of 1 to 15 Å/s. These results reveal the large discrepancy in the optical properties of the copper films deposited under the same conditions on SiO₂/Si substrates with and without graphene, which showed poorer optical quality of the films with graphene due to presence of voids in their structure. However, an increase in the rate of copper deposition on graphene leads not only to the growth of more continuous films but also to gradual improvement in the optical FOM characterizing these films. Therefore, at a rate of 15 Å/s, the corresponding values of the FOM for copper films on graphene are quite close to those for films deposited on pure SiO₂/Si substrates. Similar dependencies were obtained for copper films with a thickness of 50 nm (Figure A3). In addition, in

Table A1. The measured real ε′ and imaginary ε″ parts of thin gold films on graphene as well as their refractive indices n and extinction coefficients k (at room temperature). The data at the most widely used laser wavelengths are in bold.

		t = 25 nm (rate = 5 A/s)				t = 50 nm (rate = 5 A/s)
E (eV)	λ (nm)	ε′	ε″	n	k	ε′	ε″	n	k
0.38	3298	−517	94.9	2.08	22.8	−528	91.3	1.98	23.1
0.45	2739	−359	55.3	1.45	19.0	−366	53.1	1.38	19.2
0.53	2343	−262	34.9	1.08	16.2	−267	33.5	1.02	16.4
0.61	2046	−199	23.5	0.83	14.1	−203	22.5	0.79	14.3
0.68	1816	−155	16.6	0.66	12.5	−158	15.8	0.63	12.6
0.76	1633	−125	12.2	0.54	11.2	−127	11.6	0.52	11.3
0.80	1550	−111	10.6	0.49	10.5	−113	10.0	0.47	10.7
0.84	1483	−102	9.24	0.46	10.1	−104	8.82	0.43	10.2
0.91	1359	−84.0	7.23	0.39	9.17	−85.7	6.88	0.37	9.27
0.95	1310	−77.5	6.53	0.37	8.81	−79.1	6.21	0.35	8.90
0.99	1253	−70.3	5.79	0.34	8.39	−71.8	5.50	0.32	8.48
1.07	1163	−59.5	4.75	0.31	7.72	−60.8	4.50	0.29	7.80
1.14	1085	−50.7	3.98	0.28	7.13	−51.9	3.76	0.26	7.21
1.16	1064	−48.0	3.76	0.27	6.93	−49.1	3.54	0.25	7.01
1.22	1017	−43.5	3.41	0.26	6.60	−44.6	3.21	0.24	6.68
1.30	956.7	−37.6	2.98	0.24	6.13	−38.5	2.79	0.22	6.21
1.37	903.3	−32.5	2.65	0.23	5.71	−33.4	2.47	0.21	5.79
1.45	855.5	−28.3	2.41	0.23	5.32	−29.1	2.23	0.21	5.40
1.53	812.5	−24.6	2.23	0.22	4.97	−25.4	2.05	0.20	5.04
1.59	780.0	−22.0	2.12	0.23	4.69	−22.7	1.94	0.20	4.77
1.60	773.7	−21.4	2.11	0.23	4.64	−22.2	1.92	0.20	4.71
1.68	738.3	−18.7	2.03	0.23	4.33	−19.4	1.83	0.21	4.41
1.76	706.1	−16.2	1.99	0.25	4.04	−16.9	1.78	0.22	4.12
1.83	676.6	−14.1	1.98	0.26	3.76	−14.8	1.76	0.23	3.85
1.91	649.4	−12.2	2.01	0.29	3.50	−12.8	1.77	0.25	3.59
1.96	633.0	−10.8	2.06	0.31	3.30	−11.5	1.76	0.26	3.39
1.99	624.3	−10.4	2.08	0.32	3.25	−11.1	1.81	0.27	3.34
2.06	601.1	−8.87	2.18	0.36	3.00	−9.49	1.88	0.30	3.10
2.14	579.6	−7.44	2.32	0.42	2.76	−8.05	1.99	0.35	2.86
2.22	559.5	−6.14	2.52	0.50	2.53	−6.73	2.14	0.41	2.63
2.29	540.8	−4.95	2.76	0.60	2.30	−5.52	2.35	0.49	2.40
2.33	532.0	−4.27	2.95	0.68	2.18	−4.83	2.50	0.55	2.27
2.37	523.3	−3.87	3.08	0.73	2.10	−4.42	2.62	0.60	2.19
2.45	506.9	−2.90	3.48	0.90	1.93	−3.41	2.98	0.75	1.99
2.52	491.5	−2.06	3.96	1.10	1.81	−2.53	3.43	0.93	1.84
2.60	477.0	−1.39	4.53	1.29	1.75	−1.81	3.99	1.13	1.76
2.68	463.3	−0.94	5.14	1.46	1.76	−1.34	4.61	1.32	1.75
2.75	450.4	−0.71	5.73	1.59	1.80	−1.13	5.21	1.45	1.80
2.83	438.2	−0.71	6.18	1.66	1.86	−1.20	5.60	1.50	1.86
2.91	426.7	−0.82	6.42	1.68	1.91	−1.32	5.71	1.51	1.89
2.98	415.7	−0.90	6.47	1.68	1.93	−1.33	5.62	1.49	1.88
3.06	405.3	−0.87	6.43	1.68	1.92	−1.17	5.49	1.49	1.84
3.14	395.4	−0.73	6.39	1.69	1.89	−0.90	5.43	1.52	1.79
3.21	385.9	−0.53	6.43	1.72	1.87	−0.60	5.49	1.57	1.75
3.29	376.9	−0.34	6.57	1.77	1.86	−0.34	5.66	1.63	1.73
3.37	368.4	−0.20	6.80	1.82	1.87	−0.16	5.92	1.70	1.74
3.44	360.2	−0.17	7.10	1.86	1.91	−0.10	6.22	1.75	1.78
3.52	352.3	−0.30	7.42	1.89	1.97	−0.20	6.53	1.78	1.84
3.60	344.8	−0.58	7.70	1.89	2.04	−0.44	6.79	1.78	1.90
3.67	337.6	−0.97	7.90	1.87	2.11	−0.77	6.96	1.77	1.97
3.75	330.7	−1.46	7.98	1.82	2.19	−1.19	7.02	1.72	2.04
3.83	324.1	−2.01	7.85	1.75	2.25	−1.64	6.89	1.65	2.09
3.90	317.7	−2.53	7.60	1.65	2.30	−2.07	6.65	1.57	2.13
3.98	311.6	−2.99	7.19	1.55	2.32	−2.43	6.29	1.47	2.14
4.06	305.7	−3.32	6.68	1.44	2.32	−2.69	5.84	1.37	2.14
4.13	300.0	−3.59	6.13	1.33	2.31	−2.89	5.37	1.27	2.12

and

Table A2. The measured real ε′ and imaginary ε″ parts of thin copper films on graphene as well as their refractive indices n and extinction coefficients k (at room temperature). The data at the most widely used laser wavelengths are in bold.

		t = 25 nm (rate = 15 A/s)				t = 50 nm (rate = 15 A/s)
E (eV)	λ (nm)	ε′	ε″	n	k	ε′	ε″	n	k
0.38	3298	−456	99.5	2.32	21.5	−502	97.3	2.16	22.5
0.45	2739	−318	58.4	1.63	17.9	−349	56.9	1.52	18.7
0.53	2343	−233	37.1	1.21	15.3	−255	36.0	1.12	16.0
0.61	2046	−177	25.1	0.94	13.4	−194	24.3	0.87	14.0
0.68	1816	−139	17.7	0.75	11.8	−152	17.2	0.70	12.3
0.76	1633	−111	13.1	0.62	10.6	−122	12.7	0.57	11.0
0.80	1550	−99.7	11.3	0.57	10.0	−109	10.9	0.52	10.5
0.84	1483	−90.8	10.0	0.52	9.54	−99.3	9.66	0.48	9.98
0.91	1359	−75.2	7.87	0.45	8.68	−82.3	7.60	0.42	9.08
0.95	1310	−69.4	7.14	0.43	8.34	−76.0	6.89	0.39	8.73
0.99	1253	−63.0	6.35	0.40	7.94	−69.0	6.13	0.37	8.31
1.07	1163	−53.3	5.26	0.36	7.31	−58.4	5.08	0.33	7.65
1.14	1085	−45.5	4.46	0.33	6.75	−49.9	4.30	0.30	7.07
1.16	1064	−43.0	4.23	0.32	6.57	−47.3	4.08	0.30	6.88
1.22	1017	−39.0	3.87	0.31	6.26	−42.9	3.73	0.28	6.56
1.30	957	−33.7	3.43	0.29	5.81	−37.1	3.31	0.27	6.10
1.37	903	−29.2	3.10	0.29	5.41	−32.2	3.00	0.26	5.68
1.45	856	−25.4	2.87	0.28	5.04	−28.1	2.77	0.26	5.31
1.53	813	−22.1	2.71	0.29	4.71	−24.5	2.61	0.26	4.96
1.59	780	−19.7	2.62	0.29	4.45	−21.9	2.53	0.27	4.69
1.60	774	−19.2	2.61	0.30	4.39	−21.4	2.52	0.27	4.64
1.68	738	−16.8	2.56	0.31	4.11	−18.8	2.47	0.28	4.34
1.76	706	−14.6	2.56	0.33	3.83	−16.4	2.48	0.31	4.06
1.83	677	−12.6	2.62	0.37	3.58	−14.3	2.52	0.33	3.80
1.91	649	−10.9	2.72	0.41	3.33	−12.4	2.62	0.37	3.55
1.96	633	−9.71	2.84	0.45	3.15	−11.1	2.74	0.41	3.36
1.99	624	−9.37	2.89	0.47	3.10	−10.8	2.78	0.42	3.31
2.06	601	−8.00	3.13	0.54	2.88	−9.26	3.00	0.49	3.08
2.14	580	−6.78	3.45	0.64	2.68	−7.92	3.31	0.58	2.87
2.22	560	−5.74	3.88	0.77	2.52	−6.76	3.71	0.69	2.69
2.29	541	−4.95	4.39	0.91	2.40	−5.81	4.21	0.83	2.55
2.33	532	−4.60	4.71	1.00	2.36	−5.35	4.56	0.92	2.49
2.37	523	−4.46	4.91	1.04	2.35	−5.14	4.79	0.97	2.47
2.45	507	−4.25	5.31	1.13	2.35	−4.80	5.33	1.09	2.45
2.52	492	−4.23	5.45	1.16	2.36	−4.74	5.66	1.15	2.46
2.60	477	−4.17	5.32	1.14	2.34	−4.79	5.67	1.15	2.47
2.68	463	−3.96	5.08	1.11	2.28	−4.73	5.44	1.11	2.44
2.75	450	−3.63	4.84	1.10	2.20	−4.50	5.13	1.08	2.38
2.83	438	−3.22	4.70	1.11	2.11	−4.14	4.87	1.06	2.29
2.91	427	−2.82	4.64	1.14	2.03	−3.73	4.70	1.07	2.21
2.98	416	−2.45	4.65	1.19	1.96	−3.32	4.62	1.09	2.12
3.06	405	−2.14	4.72	1.23	1.91	−2.96	4.61	1.12	2.05
3.14	395	−1.89	4.82	1.28	1.88	−2.65	4.65	1.16	2.00
3.21	386	−1.70	4.94	1.33	1.86	−2.40	4.71	1.20	1.96
3.29	377	−1.58	5.06	1.36	1.85	−2.22	4.79	1.24	1.94
3.37	368	−1.52	5.17	1.39	1.86	−2.09	4.87	1.27	1.92
3.44	360	−1.52	5.26	1.41	1.87	−2.02	4.93	1.29	1.92
3.52	352	−1.57	5.31	1.41	1.88	−2.00	4.96	1.29	1.92
3.60	345	−1.65	5.32	1.40	1.90	−2.02	4.97	1.29	1.92
3.67	338	−1.75	5.30	1.38	1.92	−2.06	4.94	1.28	1.93
3.75	331	−1.87	5.23	1.36	1.93	−2.12	4.88	1.26	1.93
3.83	324	−1.99	5.11	1.32	1.93	−2.18	4.76	1.24	1.93
3.90	318	−2.10	4.95	1.28	1.93	−2.24	4.63	1.20	1.92
3.98	312	−2.20	4.77	1.24	1.93	−2.29	4.46	1.17	1.91
4.06	306	−2.26	4.55	1.19	1.92	−2.32	4.27	1.13	1.90
4.13	300	−2.32	4.33	1.14	1.90	−2.34	4.07	1.08	1.88

in the Appendix A, we summarize the dielectric constants of thin metal films, both Cu and Au, as well as their refractive indices n and extinction coefficients k acquired from ellipsometry measurements in a wavelength range of 300–3300 nm with a step of 10 nm.

Here, we analyze in more detail the dependence of electrical and optical properties of copper films as well as their crystalline structure on the film deposition rate. Figure 4 indicates the sheet resistance and FOM (at 1500 nm) of the 25 nm-thick copper films grown on SiO₂/Si substrates with and without graphene at deposition rates ranging from 1 to 15 Å/s. Copper films deposited on graphene demonstrate noticeable improvements in sheet resistance as well as FOM for higher deposition rates (7.5- and 18-fold, respectively), while measurements of films on pure SiO₂/Si substrates show only slight changes. Let us keep in mind that the deposition process determines the effective dielectric function of the film in two different ways: Influencing the crystallinity of the metal films and inducing the formation of voids in the film morphology. To analyze these impacts on the optical properties of the deposited films, we performed XRD measurements to determine the crystallinity of the films, where the average sizes of the crystallites were determined from the width of the XRD peaks using the Debye-Scherrer formula. Figure 5 shows an increase in the average crystallite size D with deposition rate for copper films with and without graphene. These results are consistent with those obtained in previous works for Au films on Si [62,63]. However, the crystallite sizes show the same dependencies on the deposition rate for both types of copper films, and therefore, the sheet resistance and FOM of copper films deposited on graphene at low rates are primarily defined by the presence of voids in percolated films. These film parameters become comparable with those of the films on SiO₂/Si substrates only at high deposition rates when a more continuous film structure is formed. In addition, an increase in the crystallite sizes for higher deposition rates explains the corresponding improvement of 40% and 10% in electrical conductivities and optical response, respectively, of copper films on pure SiO₂/Si substrates because of lower electron scattering at the crystallite boundaries.

3.3. Growth Mechanisms of Thin Metal Films on Graphene

Kinetics mechanisms of metal growth strongly influence both optical and electrical properties of metal films deposited on graphene. The formation of nuclei and the increase in the size of metal islands are competing processes in the initial growth of metal films, and those processes depend on a number of factors, such as deposition rate, surface temperature, a number of surface defects, and parameters of adatom-surface interactions [45,48,49]. In turn, the interaction of metal atoms with a substrate surfaces is determined by the diffusion barrier $E_{\mathrm{d}}$ and the ratio of the adsorption energy $E_{\mathrm{a}}$ of the metal atom on the substrate to the metal cohesive energy $E_{\mathrm{c}}$.

Several research papers provide an extensive overview of the influence of deposition rate and surface diffusion on the growth of thin films [64,65]. According to the proposed model, the island density increases as a power law of the deposition rate $n_{\mathrm{i}}\sim R^p$ $(0<p<1)$. Therefore, faster deposition leads to the formation of more nucleation sites, resulting in a smaller grain size and allowing a smaller percolation thickness during film growth [50]. Increasing the deposition rate is a useful technique to grow continuous ultrathin metal films on surfaces, which are non-wettable by metal and characterized by low values of $E_{\mathrm{a}}/E_{\mathrm{c}}$ and $E_{\mathrm{d}}$.

Recent research reports of Liu et al. present experimental data on the interaction of various metal adatoms with freestanding graphene [45,48]. We also used these data for the description of graphene monolayers deposited on SiO₂/Si substrates because their weak interaction causes negligible impact on the electronic properties of graphene [66]. The ratio $E_{\mathrm{a}}/E_{\mathrm{c}}$ is quite low for the considered metallic adatoms on graphene and equals 0.024 and 0.090 for gold and copper, respectively, which demonstrates that adatoms interact more strongly among themselves than with graphene, and therefore, the growth of metal films on graphene can be described by the Volmer–Weber model [67]. The difference in morphology of copper and gold films can be explained by different diffusion barriers, which are 0.0037 and 0.0074 eV for copper and gold, respectively, and an almost three-fold difference in the corresponding atomic weights. Therefore, copper adatoms have higher mobility and diffuse faster on graphene compared to gold, which follows the Arrhenius equation for the hopping rate: $\upsilon ={\upsilon }_0\exp \left(-E_{\mathrm{d}}/kT\right)$, where ${\upsilon }_0\sim 1/\sqrt{m}$, $m$ is the adatom mass, $k$ is the Boltzmann constant, and $T$ is the absolute temperature [68,69]. Higher mobility lowers the number of secondary nucleation sites that are mainly responsible for overgrowing gaps between metallic islands. This process leads to enlargement of metallic islands and formation of wide gaps between them, which is shown in Figure 3b for 25 nm-thick copper films.

Higher growth temperatures increase the mobility of adatoms, which in specific cases, can lead to quasi-columnar growth. This type of growth differs from traditional Volmer–Weber growth by a steadily rising ratio of the film thickness to the filling of the substrate surface by the metal. We observed quasi-columnar growth during the deposition of copper at a rate of 1 Å/s on the graphene-covered SiO₂/Si substrate heated at 150 °C (Figure 6). The metal filling factor for 25 nm-thick copper films deposited at 150 °C equals 84%, while the one obtained at 20 °C equals 92%. Both these films are percolated; however, the sheet resistance of the film deposited at 20 °C is 20% lower (19.0 Ohm/sq).

4. Conclusions

We studied the growth and properties of continuous thin films of gold and copper on monolayer graphene transferred onto silicon dioxide substrates. We presented experimental measurements for films with thicknesses of 25 and 50 nm to provide their optical, electrical, and structural properties. Table A1 and Table A2 in the Appendix A summarize the optical constants of the corresponding thin films in the wavelength range of 300–3300 nm. The results for thin gold films on graphene are not significantly different from those for gold films grown on pure thermally oxidized silicon. The variation in FOM $\left(-{\epsilon }^{\prime }/{\epsilon }^{″}\right)$ obtained for these samples deposited at the rate of 1 and 5 Å/s is less than 15%. In addition, the properties of gold films show only a weak dependence on the evaporation rate. The situation is drastically different for thin copper films, whose properties strongly depend on both the type of substrate (SiO₂/Si substrates with or without graphene) and the evaporation rate. We could not grow a continuous 25 nm-thick copper film on graphene without voids at low rates (~1 Å/s). However, higher evaporation rates (>10 Å/s) provide continuous and conductive films on graphene, which is explained by the growth kinetics of this metal. Increasing the evaporation rate from 1 to 15 Å/s improved the optical FOM and reduced the sheet resistance of copper films on graphene by 18- and 7.5-fold, respectively.

The deposition of continuous thin copper films on graphene requires high evaporation rates owing to the fast mobility of copper adatoms. Higher evaporation rates produce more initial nucleation centers, which compensates for the diffusion of copper atoms and allows the deposition of continuous films without voids. In contrast, the mobility of copper adatoms increases with increasing growth temperature. We demonstrated that substrate heating leads to quasi-columnar growth of copper on graphene, which is the limiting case of Volmer–Weber-type growth. Therefore, control of the growth temperature and evaporation rate provides an effective way to grow thin copper films with a predefined ratio of film thickness to the fraction of metal filling. In addition, due to higher adatom mobility, the formation of metal films on graphene occurs for thicknesses much higher than those on other types of substrates. This makes graphene a convenient model surface to study the kinetics of metal growth, including such processes as coalescence and percolation.

In summary, our data on the structure of thin films of copper and gold deposited on graphene as well as their optical and electrical properties will help researchers to simulate and develop various photonic, plasmonic, and optoelectronic devices. Although graphene-nanometallic structures are of high importance for practical applications, the deposition of high-optical-quality metal films on graphene still requires some technological effort. We believe that our results will make an impact in this area. In our work, we performed a comprehensive study of the properties of metal films deposited using different regimes and discussed the underlying kinetics mechanisms of their growth. In addition, the described percolated metal films with high aspect ratios can form the foundation for future devices utilizing optical resonant phenomena.