Quantitative estimation of atom-scaled ripple structure using transmission electron microscopy images

Atom-scaled ripple structure can be intrinsically formed because of thermal instability or induced stress in graphene or two-dimensional (2D) materials. However, it is difficult to estimate the period, amplitude, and shape of such a ripple structure. In this study, by applying the geometrical phase analysis method to atomically resolved transmission electron microscopy images, we demonstrate that the atom-scaled ripple structure of MoS₂ nanosheet can be quantitatively analyzed at the subnanometer scale. Furthermore, by analyzing the observed ripple structure of the MoS₂ nanosheet, we established that it is inclined by approximately 7.1° from the plane perpendicular to the incident electron beam; it had 5.5 and 0.3 nm in period and amplitude, respectively. For quantitative estimation of ripple structure, our results provide an effective method that contributes to a better understanding of 2D materials in the sub-nanometre scale.