title: A Simple Transmission Electron Microscopy Method for Fast Thickness Characterization of Suspended Graphene and Graphite Flakes.
abstract: We present a simple, fast method for thickness characterization of suspended graphene/graphite flakes that is based on transmission electron microscopy (TEM). We derive an analytical expression for the intensity of the transmitted electron beam I 0(t), as a function of the specimen thickness t (t<<λ; where λ is the absorption constant for graphite). We show that in thin graphite crystals the transmitted intensity is a linear function of t. Furthermore, high-resolution (HR) TEM simulations are performed to obtain λ for a 001 zone axis orientation, in a two-beam case and in a low symmetry orientation. Subsequently, HR (used to determine t) and bright-field (to measure I 0(0) and I 0(t)) images were acquired to experimentally determine λ. The experimental value measured in low symmetry orientation matches the calculated value (i.e., λ=225±9 nm). The simulations also show that the linear approximation is valid up to a sample thickness of 3-4 nm regardless of the orientation and up to several ten nanometers for a low symmetry orientation. When compared with standard techniques for thickness determination of graphene/graphite, the method we propose has the advantage of being simple and fast, requiring only the acquisition of bright-field images.
authors.affiliation: 1Department of Engineering Sciences,Uppsala University,Box 534,SE-751 21 Uppsala,Sweden.
authors.forename: Stefano
authors.identifier: http://orcid.org/0000-0001-5738-0591
authors.initials: S
authors.lastname: Rubino
authors.affiliation: 1Department of Engineering Sciences,Uppsala University,Box 534,SE-751 21 Uppsala,Sweden.
authors.forename: Sultan
authors.initials: S
authors.lastname: Akhtar
authors.affiliation: 1Department of Engineering Sciences,Uppsala University,Box 534,SE-751 21 Uppsala,Sweden.
authors.forename: Klaus
authors.initials: K
authors.lastname: Leifer
mesh_terms: D006108:Graphite; D046529:Microscopy, Electron, Transmission / Q000379:methods*; D055585:Physical Phenomena
chemical_list: D006108:Graphite
keywords: TEM; bright field; graphene; thickness maps