Effects of Process Parameters on Graphene Growth Via Low-Pressure Chemical Vapor Deposition

As a material with enormous potential, graphene has been fabricated through both physical and chemical processes, including mechanical exfoliation, liquid-phase exfoliation, graphene oxide reduction, epitaxial growth, and chemical vapor deposition (CVD). Among these methods, CVD on copper has become the prevalent method for large-scale monolayer and few-layer graphene growth because of its cost-effectiveness of both the growth substrate and carbon source material. Depending on the chamber pressure and the presence of plasma, chemical vapor deposition for graphene fabrication can be further divided into atmospheric CVD, plasma-enhanced CVD (PECVD), and low-pressure CVD (LPCVD). PECVD allows a lower growth temperature, because energetic electrons produced by the plasma help to enhance the ionization, excitation, and dissociation of hydrocarbon precursors at relatively low temperatures [1]. However, the graphene grown by atmospheric CVD and PECVD has relatively low quality compared with LPCVD, because the processes are easily affected by environmental conditions such as humidity and the ion bombardment effect. To date, LPCVD remains the most efficient and scalable method to produce high-quality and cost-effective graphene in large size.

Graphene growth in LPCVD is affected by both the growth substrate and process conditions. Different substrates yield different graphene quality and the number of graphene layers in the CVD process. Because of different catalytic activities, the growth mechanism of graphene on various substrates may be different. Many researchers have conducted graphene growth on different substrates, such as Cu [2], Ni [3], Pd [4], Ru [5], and Ir [6]. The graphene growth on these metal substrates largely follows two different routes. When the carbon solubility in the substrate is low, the graphene growth is basically through surface adsorption [7,8]. When the carbon solubility is high, the graphene growth goes through a series of activities, including dissolution, surface segregation, and precipitation. In an extremely well-controlled process, the graphene growth could be limited to one route; however, both routes could be in play in a CVD graphene growth process. By carefully controlling the process parameters, monolayer as well as few-layer graphene could be obtained depending on the growth time [9].

For a given substrate and carbon source, five key process parameters have been identified in the past in the LPCVD graphene growth process to achieve high graphene quality. These parameters are methane/hydrogen (CH₄/H₂) ratio, time, pressure, temperature, and cooling rate. It has been shown that these parameters could significantly influence the graphene nucleation density, graphene grain size, and graphene grain shape. Table 1 summarizes the effects of these parameters from previous studies. Zhang et al. [10] has found that the shape of graphene grains changes with the increasing CH₄/H₂ ratio. For example, the graphene grains change from a hexagonal shape at CH₄/H₂ = 1:30 to mostly a four-lobe structure at CH₄/H₂ = 1:20. This study also showed that the morphology of graphene grains would change with increasing growth pressure. Graphene grains changed from small irregular flakes at 80 mTorr to mostly four-lobed grains at 100 mTorr, and eventually to almost continuous film when the pressure was increased to 400 mTorr. Regmi et al. [11] showed that the growth time had a relatively high impact on graphene grain size, but low impact on nucleation density and grain shape. After nucleation occurred, the graphene grains continued to grow laterally as growth time increased. The graphene grain size increased until the grain edges merged with each other. Monolayer graphene covering more than 95% of the surface was obtained. Double-layer (2 L) and multilayer graphene flakes appeared before the monolayer was completed. The 2 L and multilayer flakes seemed to appear at the initial nucleation sites. Vlassiouk et al. [12] found that growth temperature had high impact on nucleation density and graphene grain size, but relatively low influence on the grain shape. The graphene nucleation density decreased dramatically with increasing temperature, while the graphene grain size increased with increasing temperature. Choi et al. [13] showed that the cooling rate had a strong impact on nucleation density, but a weaker effect on graphene grain size and grain shape.

Although important process parameters of LPCVD graphene have been identified, most of the previous studies have focused on individual and independent effects of these process parameters ranging from CH₄/H₂ ratio to cooling rate one at a time. This approach does not provide an estimation of interaction effects among the input factors. In order to produce graphene with high quality, a statistical analysis through a design of experiment approach is required [14,15]. Shanmugam et al. [16] conducted a design of experiment study on CVD graphene growth; however, only three process parameters, carbon source, growth temperature, and mass flow rate of the carbon source, were included in the study.

In this study, we conduct a design of experiment study on LPCVD graphene growth with all the five major process parameters that have been identified in literature. A fractional factorial design was selected to minimize the experimental resource and time required for the study. A statistical analysis on both the main effects and second-order interaction effects of experiment was conducted to reveal the interplay of process parameters. The study considers a larger set of process parameters including their interaction effects than existing studies. It provides guidelines to control the quality of graphene grown via LPCVD focusing on the number of graphene layers and the graphene grain size.

The experiment was conducted with a LPCVD system, as shown in Fig. 1. The LPCVD system consisted of flow controllers, a quartz tube of one-inch diameter, a high-temperature tube furnace, a moving platform, a pressure gage close to the gas outlet, a computer for gas and motor control, and a vacuum pump to draw vacuum in the quartz tube. The furnace was mounted on a moving platform, such that the heating zone of the furnace could be moved away rapidly from the sample to control the cooling rate of the growth process. The moving platform was assembled with four V-type rail rollers and a gear rack under an aluminum plate. Two V-type rails were located under the four rollers. A stepper motor with a spur gear was connected to a motor drive controlled by an Arduino microcontroller and a DC power supply. The amount of methane and hydrogen were controlled through the flow controllers connected to the computer.

Commercially available copper foils with 125 μm thickness were used as the substrate for graphene growth. The copper foil was cut into 1 × 2 in.² samples and chemically treated in a 0.5 M ammonium persulfate solution for 20 min to remove the native oxide layer and other contaminations that existed on the copper foil. The copper foil was sequentially cleaned with acetone, isopropyl alcohol, and de-ionized water. The treated copper foil was placed in the middle of the one-inch quartz tube. Graphene growth consisted of the following steps: (1) The pressure in the quartz tube was pumped down to 5 mTorr; (2) the temperature of the furnace was ramped up to 1030 °C with H₂ flow at 10 sccm in the quartz tube for 50 min in order to further remove the oxide layer of the copper and to recrystallize the copper grains; (3) the required growth temperature was set and maintained for 10 min to reach a temperature steady-state; (4) the growth pressures was set by controlling the down flow valve of the LPCVD system under a constant H₂ flow (10 sccm) environment; (5) one minute after the growth pressure was achieved, the carbon precursor CH₄ was introduced under a constant H₂ flow (10 sccm) rate; (6) after a controlled graphene growth time, the sample is allowed to cool down to ambient temperature at a controlled cooling rate by moving the furnace away from the sample; and (7) the flow of the gases and the furnace were turned off at 300 °C of the copper foil temperature.

The process parameters of the LPCVD process are illustrated with Fig. 2. The overall LPCVD process can be largely divided into four phases: ramping, annealing, growth, and cooling. In the ramping phase, the temperature sharply increases from room temperature to 1030 °C within 20 min at 140 mTorr under 10 sccm H₂. In the annealing phase, the temperature is maintained at 1030 °C for 40 min at 140 mTorr under 10 sccm H₂. In the growth phase, the temperature is set at 1030 °C for 10 min, but the pressure is varied from 300 mTorr to 1000 mTorr under a constant H₂ flow (10 sccm) and different CH₄ flows (1–10 sccm). In the cooling phase, the temperature decreases from 1030 °C to room temperature in 50 min with the corresponding pressure in the growth phase under the constant H₂ flow (10 sccm) and different CH₄ flows (1–10 sccm).

Table 2 shows the experimental factors and their ranges selected for this study. Growth time is defined as the time from the start of CH₄ flow to the start of the cooling process. Growth pressure is defined as the pressure at the start of CH₄ flow and can be manually controlled by the gas valve. Growth temperature is the highest temperature in the LPCVD growth period. Cooling rate is achieved by controlling the speed of the moving platform. The maximum flow rates of CH₄ and H₂ were limited to 10 sccm due to equipment capability. Other factors including ramp time, annealing time, annealing temperature, and the H₂ flow rate of 10 sccm were all fixed.

A two-level fractional factorial design of experiment is conducted in this study. The fractional factorial design has the tradeoff between the number of runs and the resolution of the design. A 2⁵⁻¹ resolution V matrix (16 run) was chosen with I = ABCDE. Each main effect is aliased with a four-factor interaction effect (i.e., A = BCDE, B = ACDE, C = ABDE, D = ABCE and E = ABCD), and each two-factor interaction effect is aliased with a three-factor interaction effect (i.e., AB = CDE, AC = BDE, AD = BCE, AE = BCD, BC = ADE, BD = ACE, BE = ACD, CD = ABE, CE = ABD, and DE = ACB).

The samples were characterized with Raman spectroscopy and scanning electron microscopy (SEM). Raman spectroscopy (WITec Alpha 300 micro-Raman confocal microscope, λ = 488 nm) is used as a common tool to determine graphene defects using the I_D/I_G ratio and the number of graphene layers with the I_2D/I_G ratio [17–19], where I_2D/I_G is the ratio of the intensities of the 2D to G peak in the Raman spectrum of the graphene grown on copper foil. The relative intensity of the I_2D/I_G ratio increases with decreasing layer numbers. SEM (FEI Quanta 650, Hillsboro, OR) is used to characterize the number of graphene grains on the copper foil [20]. Statistical analysis software jmppro 14 was used to analyze the experimental data.

Figure 3 shows the Raman spectroscopy indicating defect (D), graphene (G), and two-dimensional (2D) peaks, 30 × 30 μm² SEM, and 10 × 10 μm² scale I_2D/I_G Raman mapping images of a typical sample (DoE case 2). The Raman spectroscopy shows monolayer graphene with few defects based on the presence of G peak, high 2D peak, and very low D peak intensities. The SEM image shows several wrinkles and graphene grain boundaries. The white dots in the SEM image are due to silicon contaminations in the bulk copper foil when they segregated to the surface. In the I_2D/I_G Raman mapping image (Fig. 3(c)), the bright yellow regions indicate monolayer graphene and the dark brown regions indicate multilayer graphene, while the black regions indicate the presence of voids. An averaged I_2D/I_G ratio was calculated from 900 measurement points on the Raman mapping image. An I_2D/I_G ratio value over two was used to detect the presence of monolayer graphene [21]. For this particular sample, a value of 2.6 was obtained, indicating almost the entire copper surface was covered with monolayer graphene [22].

Table 3 shows the results from total 19 cases, including 16 cases from the fractional factorial design of experiment and three trial cases (cases 17–19). The I_D/I_G ratio, I_2D/I_G ratio, and the number of graphene grains within the same 30 × 30 μm² area were determined as response variables to examine the graphene quality in terms of graphene defect, the number of graphene layers, and graphene grain size, respectively.

An analysis of variance study was conducted to detect the goodness of fit of a statistical model. The coefficient of determination (R²), adjusted coefficient of determination (R²_adj), and probability (P) of the model are shown in Table 4. With low R² and R²_adj values and a probability over 0.05, it shows that the model does not fit the I_D/I_G data well, which indicates that the tested process conditions do not affect the amount of graphene defects. In fact, all the samples obtained in this experimental study had good coverage and little defects. On the other hand, the I_2D/I_G ratio and the number of grains had a good fit with the experimental data, with high R² and R²_adj values and a P-value under 0.05. This means that the number of graphene layers and number of graphene grains can be optimized through the adjustment of processing conditions. Therefore, further statistical analyses were performed on the number of graphene layers and the number of graphene grains.

Process parameter effects on graphene layers are shown in Fig. 4. As shown in Fig. 4(a), in the range studied, a higher growth time was favorable for the graphene growth with a higher number of layers (I_2D/I_G ratio value between 1 and 2). Similarly, a lower pressure and a lower temperature were favorable for the graphene growth with a higher number of layers. CH₄/H₂ ratio and cooling rate are not statistically significant for the I_2D/I_G ratio, as confirmed by the parameter estimates in Fig. 4(c). A higher growth time allows a longer carbon source reaction time, promoting the formation of more graphene layers on the copper surface.

The interaction plots shown in Fig. 4(b) indicate strong interaction effects between growth pressure and growth temperature and between the CH₄/H₂ ratio and cooling rate. When the growth temperature was low, multilayer graphene was obtained with a low growth pressure, whereas monolayer graphene was obtained at a high growth pressure. On the other hand, when the growth temperature was high, both low and high growth pressures resulted in monolayer graphene. This phenomenon is consistent with the general CVD kinetics, which divides the growth rate into two regions, mass transport limited and surface-reaction limited, based on the growth temperature and pressure. The CVD growth of graphene on copper in a tube furnace basically involves two processes: (1) the mass transport process where diffusion of the carbon species pass through a boundary layer to reach the substrate surface and (2) the surface reaction process of the active carbon species forming the graphene lattice [23]. At high temperatures, there is a stable growth region for both low and high pressures, because the surface reaction rate is fast and the carbon species can be converted to graphene efficiently. At low temperatures, there may be a stable graphene growth region with high growth pressure due to the limiting mass transport process; however, with low growth pressure where more carbon species could diffuse through the boundary layer, the growth is in an unstable region, resulting in the growth of additional graphene layers. This phenomenon was also observed in previous studies [12,23,24].

The interaction plot between CH₄/H₂ ratio and cooling rate for the I_2D/I_G ratio response shows that at high CH₄ flow (10 sccm) with slow cooling rate (0.5 °C/s), the I_2D/I_G ratio decreases, indicating the formation of graphene with multiple layers. This is because high CH₄ flow and slow cooling rate increase the amount of carbon source and the reaction time, respectively, both leading to the growth of additional graphene layers.

The effects of process parameters on the number of graphene grains are shown in Fig. 5. As shown in Fig. 5(a), the graphene growth with a higher number of graphene grains is resulted from a longer growth time and a lower growth pressure. CH₄/H₂ ratio, growth temperature, and cooling rate are not statistically significant for the number of graphene grains, as confirmed by the parameter estimates in Fig. 5(c). The physical phenomena regarding the major factors such as growth time and growth pressure can be explained as follows. First, the nucleation density of graphene is increased by increasing growth time. This is because a longer growth time leads to an extended reaction time in which CH₄ as the carbon supply in the CVD chamber is catalytically decomposed on the copper surface to create new nucleation sites of graphene. Therefore, a higher nucleation density of graphene with a longer growth time is expected [11]. Second, at a high pressure copper evaporation is suppressed, and the activation energy is assigned to the desorption energy of carbon species [12]. Therefore, a lower nucleation density of graphene is expected with a high growth pressure. Conversely, a low growth pressure leads to an increase of graphene grain nucleation.

The interaction plots highlighted in a box in the first row in Fig. 5(b) indicate that there are strong interaction effects among CH₄/H₂ ratio, growth time, growth pressure, and growth temperature on the number of graphene grains. It shows that with low CH₄ flow (1 sccm), a higher number of graphene grains is obtained with a longer growth time (30 min) and a lower growth pressure (300 mTorr). This is because at a lower CH₄ flow, the amount of available carbon species is limited, making the effects of reaction time and growth pressure more pronounced. At a high CH₄ flow (10 sccm), a higher number of graphene grains are obtained with a lower growth temperature (950 °C). This is because the high carbon supply (CH₄) is catalytically decomposed on the copper surface to create more nucleation sites of graphene [10]. Moreover, at a low temperature, the desorption of carbon species adsorbed on copper surface is suppressed [12]. Therefore, a high CH₄/H₂ ratio and low temperature are expected to increase the number of graphene grains. The interaction plot between CH₄/H₂ ratio and growth temperature also shows that at a low CH₄ flow (1 sccm), a higher number of graphene grains are obtained with a higher growth temperature (1030 °C), because more reaction will happen, resulting in more free carbon species to form nuclei. The interaction plot highlighted in the box in the second row between growth time and growth pressure for the number of graphene grains shows that a long growth time (30 min) and a low pressure (300 mTorr) lead to a higher number of graphene grains. The interaction plot between growth time and cooling rate (also shown in a red box) shows that a long growth time (30 min) and a fast cooling rate (5 °C/s) yield a higher number of graphene grains. This is because that copper would form small grains due to a fast cooling rate, leading to a large number of smaller graphene grains. The interaction plot highlighted in the fourth row between cooling rate and growth temperature shows that a low growth temperature (950 °C) and a slow cooling rate (0.5 °C/s) or a high growth temperature (1030 °C) and a fast cooling rate (5 °C/s) would lead to a high number of graphene grains.

Table 5 provides a summary of the effect of each factor on the above two response variables. To obtain monolayer graphene with large grain size and fewer graphene grain boundaries, it is desirable to have fewer graphene grains and a higher I_2D/I_G ratio (i.e., # of grains↓ and I_2D/I_G↑). Based on the significance of the major factors and interaction effects, a favorable condition with low CH₄/H₂ ratio, short growth time, high growth pressure, high growth temperature, and slow cooling rate can be suggested to obtain monolayer graphene with large grain size.

Graphene quality in a LPCVD process is investigated in this study through a fractional factorial design of experiment method. Five key process parameters are identified as CH₄/H₂ ratio, growth time, growth pressure, growth temperature, and cooling rate. The graphene quality is examined as not only the number of graphene layers through the I_2D/I_G ratio, but also the number of graphene grains through SEM images. Statistical analysis reveals the interaction effect as well as the major and minor factors for each response. For the I_2D/I_G ratio response, the major factors are growth time, growth pressure, and growth temperature. There are strong interaction effects among growth pressure, growth temperature, CH₄/H₂ ratio, and cooling rate. For number of graphene grains, the major factors are growth time and growth pressure. The interaction plots show that there are interaction effects among CH₄/H₂ ratio, growth time, growth pressure, growth temperature, and cooling rate. For monolayer graphene growth with larger grain size, conditions with low CH₄/H₂ ratio, short growth time, high growth pressure, high growth temperature, and slow cooling rate are generally favored. This study examines a large set of process parameters of LPCVD graphene growth and reveals the interaction effects among the process parameters. It provides guidelines to control the quality of graphene for large-scale fabrication.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

• National Science Foundation under Cooperative (Agreement No. EEC-1160494; Funder ID: 10.13039/100000001).