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 MoS nanosheet can be quantitatively analyzed at the subnanometer scale. Furthermore, by analyzing the observed ripple structure of the MoS 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.