Researches On Exit-wave's Phase Retrieval For A High-resolution Transmission Electron Microscopy Image Of Two-dimensional Crystals

Transmission electron microscope?TEM?is one of the most important observation tools in the fields of materials,biology,physics and chemistry research fields,which is generally applied for structural researches at the atomic scale.High-resolution electron microscopy?HRTEM?can achieve high resolution in imaging,and current advanced electron microscopes have been able to reach a resolution of 0.5 angstroms.Although the HRTEM image contains enough high-frequency information,the crystal lattice on the HRTEM image may be distorted due to the inevitable aberrations in the imaging.Therefore,the image-processing techniques are required to further quantify information at high-frequencies.The gradient descent method is one of the most important optimization algorithms for solving unconstrained optimization problems.In the image-processing methods for TEM,the exit-wave reconstruction method from a series of defocus images is solved by gradient descent method.It usually requires the input of more than a dozen or more images,because the electrons may cause the crystal-structural damage during image acquisition.Therefore,in this article,we will study the algorithm and method for reconstructing the phase of the exit-wave function from one single image.Based on the algorithm of the exit-wave reconstruction from a series of defocus images,the number of input variables and imaging formula in the case of the weak phase object,we prove this algorithm is available to reconstruct the exit-wave function from a single HRTEM image for the weak-phase object,called as one-image exit-wave reconstruction algorithm.By using the simulated images,we prove it can reconstruct the exit-wave function.We also find the two-step procedure is necessary,while not one-step procedure.The latter procedure wants to remove the effects of the spherical aberration,defocus,and all aberrations at once in the iterative calculations.Essentially,we find that the HRTEM images can be reconstructed if they are:under the optimal focal condition and affected by all aberrations;and greatly deviating from the optimal focal condition and affected by only asymmetric aberration.Started from the imaging formula of the HRTEM image in the image space and based on the gradient descent method,a relatively different phase-retrieval algorithm can also be obtained for the weak phase object,called as one-image phase-retrieval algorithm.In this article,we compare this algorithm with the former one,and find that this algorithm should remove the spherical aberration,defocus and all aberrations on the image at one time to retrieve the phase of the exit-wave function that correctly reflecting the crystal structure.Most importantly,this algorithm has no additional requirements on the symmetry of aberrations.To employ these algorithms involved in this article for a weak phase object,we perform researches on a two-dimensional?2D?crystal of molybdenum disulfide?MoS₂?.First,we use chemical vapor deposition to synthetize the MoS₂ crystal on our own experimental platform to research the various factors to obtain the optimal experimental conditions.The optimum synthesis conditions are as follows:the experiment should be in the environment of high-purity argon and exclude the miscellaneous gas,such as oxygen and water vapor;the amount of the reactant molybdenum trioxide powder and sulfur powder are 0.1 mg and 100 mg,respectively;the reaction temperature is 700?,the flow rate of a carrier gas in the experimental device is 100 sccm,and the substrate is best to be silicon dioxide/silicon.Characterized by optical microscopy,Raman spectroscopy,Photoluminescence spectroscopy,TEM,and scanning TEM,et.al,we prove the prepared sample contains 2D structural MoS₂ crystal.Then,we take images in a Cs-corrector TEM with a monochromator?FEITitan G280-300?operated at 80kV.In the periodic region of the HRTEM image,we successfully retrieve the phase of the exit-wave function by using the algorithms mentioned in this article.On the retrieved phase,the double-sulfur and molybdenum atoms are clearly visible.We compare these two methods and find that the one-image phase-retrieval algorithm is better than the one-image exit-wave reconstruction algorithm due to its relatively weaker contrast of artifact atoms on the retrieved phase.In summary,this project successfully synthesizes the 2D structural MoS₂ crystal in experiments and completes phase retrieval on the HRTEM image.This sample is one of the currently popular two-dimensional crystals,and we prove the practical application of the proposed algorithms.