@article{2607a00004fc40f6850cefbd7f0c7561,
title = "Material dissipation of graphene resonators",
abstract = "Graphene resonators hold a promising potential to be integrated into nanoscale sensors and electronic devices. Therefore, understanding the physics underlying their dissipation mechanisms is essential. Here we investigate the dissipation of graphene through a study of graphene foam (GF) resonators. We show that intrinsic material dissipation, related to interlayer friction, is a primary source of energy dissipation in graphene. We fabricated GFs with varying wall thicknesses and characterized their frequency responses under ambient and vacuum conditions. Additionally, we investigated their atomic structure by using Raman analysis, high-resolution scanning electron microscopy, and transmission electron microscopy. While air losses are considered the primary dissipation source of micro- and nano-electromechanical systems (M/NEMS) operating under ambient conditions, we show that friction between graphene layers is a comparable source for energy dissipation and, thus, it limits the dynamic amplification of multilayer graphene resonators even when they are operated under high-vacuum conditions. We show that the friction between the layers is enhanced when multiple layers exist and that dissipation is further amplified by microscopic defects, such as cracks and grain boundaries, or by the existence of amorphous carbon. Thus, we uncover the fundamental physical behavior of graphene.",
keywords = "Energy dissipation, Graphene, Graphene foam, NEMS, Resonators",
author = "Yahav Ben-Shimon and Anway Pradhan and Assaf Ya'akobovitz",
note = "Funding Information: The authors acknowledge the Israeli Science Foundation (ISF) for supporting this study (grant no. 194/21 ). The authors are thankful to Dr. Eran Edri and his students for their assistance in the etching process of the nickel scaffold. We thank Dr. Alexander Upcher and Dr. Nitzan Maman for their help with the high-resolution imaging of our devices. Funding Information: We fabricated GF resonators by growing graphene layers on a porous nickel scaffold with a porosity of 95% and an average pore size of several tens of microns in a chemical vapor deposition (CVD) process, after which we etched the nickel structure by dipping the graphene-nickel structure in HCl so we were left only with GF that has the same porosity and pore size as the porous nickel. During the growth process, we placed the nickel scaffold in a tube furnace (860°C) while continuously flowing helium (He,500 SCCM) and hydrogen (H2,200 SCCM) gases. These conditions were maintained for 40 min to anneal the nickel and improve the crystallinity of the GF. Then, we grew the graphene by introducing ethylene (C2H4, 30 SCCM). To achieve GFs with different thicknesses, we varied the growth duration by applying the ethylene flow for 15 min, 30 min, or 60 min. Finally, we etched the nickel, dried the GF on a hot plate for several minutes to remove water residuals, cut the GF into slander strips, and connected them to square glass slides for support using a conductive silver paste, thereby creating GF cantilevers, Fig. 2a. Before connecting the devices to the glass, we measured their mass and extracted their mass density, which showed that longer growth time is associated with higher mass density (see Supporting Information). Our material characterization analyses (shown below) demonstrate that despite the complex 3D structure of the GFs, they all share similar structure and morphology and differ mostly by their wall thickness.Optical and scanning electron microscope (SEM) images of a GF cantilever are shown in Fig. 2b and c, respectively. Additional side-view SEM images show that our devices are straight (see Supporting Information), implying that there is negligible pretension in the GF cantilevers. Electron dispersive X-ray spectroscopy (EDS) analysis confirmed that the nickel scaffold was fully etched and other chemicals that took part in the process were fully removed, such that we were left only with carbon atoms, Fig. 2d. Notably, EDS peaks related to silicon and oxygen were also observed, as the GF was anchored to a silicon dioxide substrate.Clamping dissipation is associated with the radiation of energy to the substrate, which is proportional to the ratio between Young's moduli of the GF and the glass substrate. Since GF is relatively soft, the energy radiation is low (see an estimation of Qclamping in the Supporting Information). In addition, another means of clamping dissipation stems from imperfect clamping of the GF that can result in dissipation of energy to modes known as “spurious edge modes” [34] and are characterized by vibrations on the clamping. We ruled out the existence of such clamping dissipation by measuring the vibrations on the clamp (see the relevant frequency responses in the Supporting Information).To assess the impact of material damping on the dynamics of GF resonators, we grew and characterized several batches of GF (5–6 resonators per batch), each with a different growth duration (tgrwoth=15 min, 30 min, and 60 min; Table 1), and characterized them under high vacuum to eliminate Qair, such that QTot≈Qmaterial (equation (3) when Qair→∞). In addition, we extracted Qair from the differences between the ambient and vacuum quality factors. The average quality factor values of each GF batch obtained under ambient and vacuum conditions are shown in Fig. 5a and b, respectively (the values of all devices are shown in the Supporting Information), and Qair is shown in Fig. 5c. In parallel, we investigated the crystallinity and wall thickness of the devices by using high-resolution scanning electron microscopy (HR-SEM) and transmission electron microscopy (TEM), Fig. 6 (see the Supporting Information for more images). These analyses yielded thicknesses of 40−100 nm (tgrwoth=15 min), 200−300 nm (tgrwoth=30 min), and 500−1000 nm (tgrwoth=60 min).The air-loss quality factor, Qair, ranging between 5 and 45, indicates that air losses are highly significant and are responsible for the dissipation of a considerable amount of energy. Additionally, our measurements show that thicker GF devices (i.e., devices with higher mass densities, see Supporting Information for estimation of the mass densities) have a higher air-loss quality factor (i.e., less air losses). This observation is in agreement with a previous study, which showed that the air quality factor is proportional to the square root of the density, Qair∝ρ [36].To clarify the sources of the dissipation under vacuum operation, we investigated the atomic structure of the GF walls by using HR-SEM (Fig. 6a–c, see more images in the Supporting Information) and TEM (Fig. 6d–g, and more images in the Supporting Information). Devices with a growth duration of tgrwoth=30 min showed the lowest dissipation, Fig. 5b. Devices with a growth duration of tgrwoth=60 min, by contrast, showed only a slight increase in the quality factor with respect to their ambient operation. TEM images revealed that, due to their excessive growth time, devices with tgrwoth=60 min have very thick walls with multiple graphene layers, and the existence of many layers encourages significant sliding of these layers. We also observed multiple grain boundaries in these samples, which also enhanced sliding, Fig. 6f. In addition, TEM images of these devices revealed that they bear amorphous carbon, which was observed only on the outer surface of the graphene, Fig. 6g. The long duration of the growth in these samples results in the deposition of amorphous carbon on the graphene layers. Notably, we were not able to observe the Raman modes of amorphous carbon, which indicates that its amount is rather small compared to the organized graphene. Nevertheless, the amorphous carbon increases the dissipation, due to its disorganized structure that enhances atomic friction.Assaf Yaakobovitz reports financial support was provided by Israel Science Foundation.The authors acknowledge the Israeli Science Foundation (ISF) for supporting this study (grant no. 194/21). The authors are thankful to Dr. Eran Edri and his students for their assistance in the etching process of the nickel scaffold. We thank Dr. Alexander Upcher and Dr. Nitzan Maman for their help with the high-resolution imaging of our devices. Publisher Copyright: {\textcopyright} 2023 Elsevier Ltd",
year = "2023",
month = sep,
day = "1",
doi = "10.1016/j.carbon.2023.118185",
language = "English",
volume = "213",
journal = "Carbon",
issn = "0008-6223",
publisher = "Elsevier Ltd.",
}