Free-standing Graphene Sheets Research Articles

Ultraflat graphene

Graphene, a single atomic layer of carbon connected by sp(2) hybridized bonds, has attracted intense scientific interest since its recent discovery. Much of the research on graphene has been directed towards exploration of its novel electronic properties, but the structural aspects of this model two-dimensional system are also of great interest and importance. In particular, microscopic corrugations have been observed on all suspended and supported graphene sheets studied so far. This rippling has been invoked to explain the thermodynamic stability of free-standing graphene sheets. Many distinctive electronic and chemical properties of graphene have been attributed to the presence of ripples, which are also predicted to give rise to new physical phenomena that would be absent in a planar two-dimensional material. Direct experimental study of such novel ripple physics has, however, been hindered by the lack of flat graphene layers. Here we demonstrate the fabrication of graphene monolayers that are flat down to the atomic level. These samples are produced by deposition on the atomically flat terraces of cleaved mica surfaces. The apparent height variation in the graphene layers observed by high-resolution atomic force microscopy (AFM) is less than 25 picometres, indicating the suppression of any existing intrinsic ripples in graphene. The availability of such ultraflat samples will permit rigorous testing of the impact of ripples on various physical and chemical properties of graphene.

Free-Standing Epitaxial Graphene

We report on a method to produce free-standing graphene sheets from epitaxial graphene on silicon carbide (SiC) substrate. Doubly clamped nanomechanical resonators with lengths up to 20 microm were patterned using this technique and their resonant motion was actuated and detected optically. Resonance frequencies of the order of tens of megahertz were measured for most devices, indicating that the resonators are much stiffer than expected for beams under no tension. Raman spectroscopy suggests that the graphene is not chemically modified during the release of the devices, demonstrating that the technique is a robust means of fabricating large-area suspended graphene structures.

Edge-Stress-Induced Warping of Graphene Sheets and Nanoribbons

We show that edge stresses introduce intrinsic ripples in freestanding graphene sheets even in the absence of any thermal effects. Compressive edge stresses along zigzag and armchair edges of the sheet cause out-of-plane warping to attain several degenerate mode shapes. Based on elastic plate theory, we identify scaling laws for the amplitude and penetration depth of edge ripples as a function of wavelength. We also demonstrate that edge stresses can lead to twisting and scrolling of nanoribbons as seen in experiments. Our results underscore the importance of accounting for edge stresses in thermal theories and electronic structure calculations for freestanding graphene sheets.

Buckle or break

The isolation of free-standing graphene sheets seems to contradict common belief about the existence of two-dimensional crystals. Monte Carlo simulations confirm that the sheets may be stabilized by the formation of finite-sized ripples.

Thermal desorption of hydrogen from carbon nanosheets

Carbon nanosheets are a unique nanostructure that, at their thinnest configuration, approach a single freestanding graphene sheet. Temperature desorption spectroscopy (TDS) has shown that the hydrogen adsorption and incorporation during growth of the nanosheets by radio frequency plasma-enhanced chemical vapor deposition are significant. A numerical peak fitting to the desorption spectra (300-1273 K) via the Polanyi-Wigner equation showed that desorption followed a second order process, presumably by the Langmuir-Hinshelwood mechanism. Six peaks provide the best fit to the TDS spectra. Surface desorption activation energies were determined to be 0.59, 0.63, and 0.65 eV for the external graphite surface layers and 0.85, 1.15, and 1.73 eV for desorption and diffusion from the bulk. In contrast to TDS data from previously studied a-C:H films [Schenk et al. J. Appl. Phys. 77, 2462 (1995)], a greater amount of hydrogen bound as sp(2) hybridized carbon was observed. A previous x-ray diffraction study of these films has shown a significant graphitic character with a crystallite dimension of L(a)=10.7 nm. This result is consistent with experimental results by Raman spectroscopy that show as-grown carbon nanosheets to be crystalline as commercial graphite with a crystallite size of L(a)=11 nm. Following TDS, Raman data indicate that the average crystallite increased in size to L(a)=15 nm.

Cluster expansion method for adsorption: Application to hydrogen chemisorption on graphene

A systematic method is presented for determining the ground state of absorbed species on a substrate based on a cluster expansion of the configurational energy. It is shown that the method can determine the ground state of a strongly relaxing system using a few first-principles total energy calculations of small cells only. The method is applied to a particularly challenging case, the two-sided hydrogen chemisorption on a free standing graphene sheet, where, as a function of hydrogen coverage, the carbon hybridization goes from ${\mathrm{sp}}^{2}$ to ${\mathrm{sp}}^{3}.$ The method should require still fewer calculations and yield still more accurate results in the case of physisorption where longer-ranged strain effects are less important.