Analysis of atomic distortion distributions in thin film and invisible substrate by FT-moiré inversion method

This study proposes the FT-moiré inversion method for accurately measuring and analyzing the atomic arrays in thin films and invisible substrates. The atomic arrays at the bottom of the structure cannot be directly observed in a scanning tunneling microscope (STM), but only the moiré pattern generated by their interference is visible. To overcome this limitation, the FT-moiré inversion method retrieves the characteristic parameters and compares the possibilities of all the interference combinations of moiré patterns in multilayer atomic structures, identifies the correct two atomic species, and then analyzes them to obtain the periodic characteristics of the potentially invisible atomic arrangements. The validity and accuracy of the FT-moiré inversion method are verified. Moreover, the FT-moiré inversion method is successfully applied to analyze the distortion distributions of thin-film atoms and invisible substrate atoms in the Fe₂N-Cu(111) atomic structure. This method can probe underlying atomic features in structures that are not visible with STM and can be generalized to other atomic structure studies of thin films and substrates to achieve improved optoelectronic and mechanical properties through precise detection of lattice defects and tuning of strain fields.