Strain Measurement Method Based On Transmission Electron Microscope Lattice Image Digital Moiré

The measurement method of the strain or stress at micro/nano-scale is one of the important directions in the research field of experimental mechanics.In recent years,quite a few new methods with different spatial resolution have been developed.Among them,micro-Raman spectroscopy is regarded as an effective method to study mechanical behaviors at the micro-scale.The techniques combining the high resolution microscopy,including SPM,SEM and TEM,with the principles of optic mechanics are applicable for the full-field deformation measurement with nanometer and even sub-nanometer resolution.However,in the transitional scale of 10 nm to 100 nm,there is still a lack of effective method.Consequently,in the cross-scale analysis of experimental mechanics,it is difficult to establish the quantitative association of the experimental results at nano-scale and micro-scale.In this work,a new digital moiré method for strain measurement was presented.This method was based on the lattice images of high-resolution transmission electron microscope(TEM).The TEM images were processed by Fourier transform-inverse Fourier transform to generate a set of TEM grating images with three different inclination angles of the gratings.The TEM grating image with a known strain state was used as the reference grating,and that a unknown strain state was regarded as specimen grating.Logistic calculation was performed on the reference and specimen grating images with different inclination angles,achieving a set of digital moiré images.Based on the principle of geometric moiré,an analytical relationship between the angle increment of the grating inclination(viz.grating rotation angle),?,the fringe inclination angle,?,and the normal strain of the grating,?,was established.By quantify the ? and ? in the digital moiré images and the grating images,the normal strains along the three inclination angles of the gratings was detected,hence all of the in-plane strain components were acquired.The proposed method obtains the average strain of the high-resolution TEM image,hence it has a spatial resolution in ten nanometer magnitude.To verify the accuracy of the RST method and exclude the influence of the rigid body rotation,experiments including uniaxial tension,bidirectional tension and rigid rotation were performed.Then,the RST method was applied to analyzed the strain inside the multi-layer semiconductor heterostructure and MOS structure,achieving the detail information of the three in-plane strain components in a spatial resolution of 10 nm magnitude.