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We present a simple and fast method for thickness characterization ofsuspended graphene flakes that is based on transmission electron microscopy(TEM) techniques. For this method, the dynamical theory of electron diffraction(Bloch-wave approach in two-beam case approximation) was used to obtain ananalytical expression for the intensity of the transmitted electron beam I0(t),as function of the specimen thickness t for thin samples (t<< {\lambda}; where{\lambda} is the absorption constant for graphite). We show that in thingraphite crystals the transmitted intensity is a linear function of thethickness. To obtain a more quantitative description of I0(t), high resolution(HR) TEM simulations are performed using the Bloch wave approach of the JEMSsoftware. From such calculations, we obtain {\lambda} for a 001 zone axisorientation, in a two-beam case and in a low symmetry orientation.Subsequently, HR (used to determine t) and bright-field (to measure I0(0) andI0(t)) images were acquired to experimentally determine {\lambda}. We obtainthat the experimental value in the low symmetry orientation is close to thecalculated value (i.e. {\lambda}=225 nm for 300 kV accelerating voltage and 3mrad collection angle). The simulations also show that the linear approximationobtained from the analytical expression is valid up to a sample thickness ofseveral ten nanometers, depending on the orientation. When compared to standardtechniques for thickness determination of graphene/graphite, the method wepropose has the advantage of being relatively simple and fast, requiring onlythe acquisition of bright-field images.

A simple TEM method for fast thickness characterization of suspended graphene flakes