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 < < lambda; where lambda 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 lambda 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 lambda. The experimental value measured in low symmetry orientation matches the calculated value (i.e., lambda = 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.