Practical procedure for retrieval of quantitative phase map for two-phase interface using the transport of intensity equation

Atomic resolved phase map of monolayer MoS2 retrieved by spherical aberration-corrected transport of intensity equation

An atomic resolution phase map, which enables us to observe charge distribution or magnetic properties at an atomic scale, has been pointed out to be retrieved by transport of intensity equation (TIE) when taking two atomic-resolved transmission electron microscope (TEM) images of small defocus difference. In this work, we firstly obtained the atomic-resolved phase maps of an exfoliated molybdenum disulfide sheet using spherical aberration-corrected transmission electron microscope. We successfully observed 60° grain boundary of mechanically exfoliated monolayer molybdenum disulfide sheet. The relative phase shift of a single molybdenum atomic column to the column consisting of two sulfur atoms was obtained to be about 0.01 rad on average, which was about half lower than the simulated TIE phase map, indicating that the individual atomic sites can be distinguished qualitatively. The appropriate condition for retrieving atomic-resolved TIE phase maps was briefly discussed.