Graphene
The theory of graphene was first explored by Wallace in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by Semenoff, DiVincenzo and Mele. The earliest TEM images of few-layer graphite were published by Ruess and Vogt in 1948. An early, detailed study on few-layer graphite dates to 1962 when Boehm and colleagues reported producing monolayer flakes of reduced graphene oxide. Efforts to make thin films of graphite by mechanical exfoliation started in 1990, but nothing thinner than 50 to 100 layers was produced before 2004. Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained.
Graphene production techniques
Transmission electron microscopy (TEM) uses electrons to generate high-resolution images as using electrons allows to overcome limitations of visible light wavelengths. TEM on graphene should be done with electron energy less than 80 keV to induce a smaller amount of defects, because this energy is the threshold electron energy for damaging a single-wall carbon nano-tube. There are some other difficulties in the study of graphene by TEM, e.g., in a plane-view geometry (top-view graphene) the substrate causes strong electron scattering, and a thick substrate makes it impossible to detect the graphene layer. For a cross-section view, detecting a monolayer graphene is a difficult task as it needs simulation of the TEM images.