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UNIVERSITY OF SHEFFIELD Large Field of View Electron Ptychography Shaohong Cao Supervised by Prof. John M Rodenburg and Dr. Andrew M Maiden A thesis submitted for the degree of Doctor of Philosophy August 2017 1 Abstract Electron ptychography can overcome the limits of the conventional electron microscopy in terms of both resolution and phase quantitative measurements. There are two ways to implement ptychography with electrons. One employs a focused probe and the other uses a large probe. The advantage of focused probe electron ptychography is allowing to analyse spectrum while collecting the data. The biggest advantage of large probe electron ptychography is much larger field of view with the same scanning positions. In this thesis, we investigate the applications of the large probe ptychography in three modes, which are a transmission electron microscope in the selected area diffraction mode (SAD ptychography), a scanning electron microscope in the transmission mode (SEM ptychography), and a scanning transmission electron microscope (STEM ptychography). The thesis includes the detailed experimental procedures to collect ptychographic data in the three modes, as well as the investigation and evaluation of the experimental parameters. It presents extensive experimental data and results, which includes the decomposition of a partially coherent electron source via the modal decomposition ptychography with the SAD ptychography, the improvement of the delocalization issue with the SEM ptychography, and the atomic resolution reconstruction with the STEM ptychography. The challenges of the implementation and the reconstruction of ptychography in the three modes are also discussed. The main achievement of the thesis is the modal decomposition of matter wave, which has never been done before. 2 3 Declaration I confirm that all the work in this thesis is my own research. I confirm that all the work in this thesis is original except where the reference is explicitly given. Shaohong Cao 15/08/2017 4 5 Acknowledgements Now, it comes to the end of my PhD. I was full of joy the moment when I finished the last chapter of this thesis and put the whole thesis together. A lot of feeling has come to me and a lot of people I want to express my acknowledgments to. I would like to express my sincere gratitude to my supervisor Prof. John Rodenburg. I have received tremendous support from John during my PhD. John has transferred me not only a vast amount of knowledge about the scientific research, but also a solid attitude to conduct scientific research. It has been a great pleasure to work with John together; he is always calm, patient and very easy-going; he is a supervisor who would like to spend time with students. We have had numerous discussion in the pub called Red Deer, or at the dining table in some Café or restaurant. John’s influence on me from day by day, from conversation by conversation; it will stay with me for the rest of my life. I would like to express my special thanks to my second supervisor, Dr. Andrew Maiden. I was Andy’s first PhD student, so I have got the special attention that the first ‘child’ always has. In my first year, Andy has spent a lot of time to supervise my algorithms and to make sure that I have an extensive literature review. Andy has given me great support in the 6 research projects in this thesis. He is a supervisor who involved experiments with students together, debugged algorithms with students together, who supports students a lot and is very patient in supervising. It is my great luck to have supervisors like John and Andy. I would like to express my thanks to my colleague Dr. Peng Li. Peng has helped me considerably. Peng sat next to me in the office; I cannot count how many times in a day that I just turned my head to him, to begin a question, a discussion or a complaint. Peng has given me a lot of very useful suggestion on coding, data processing and the experimental design. He is like a third supervisor to me. I would like to express my special thanks to Dr. Ian Ross for his patient and detailed training on the JEOL R005. I would like to express my special thanks to Dr. Pieter Kok, who has given the exhaustive nomenclature of the quantum mechanics derivation of the modal decomposition. I would like to express my thanks to my previous colleagues Dr. Darren Batey, Dr. Tega Edo and Dr. Francis Sweeney, for the helpful conversations and the encouragements. I would like to give my special thanks to my colleagues Danny Johnson and Samuel McDermott for the discussion we have had in the office, and especially for your grammar review on Chapter 4 and Chapter 5 of this thesis. It is really a pleasant experience to be working in the office with you people together. I would like to express my thanks to my friends and my family, thank you for giving me the strength when sometimes I nearly ran out, for your being there to share my joy, for encouraging me when I felt I was small, for helping me clear my mind when I felt lost. Last but not least, I am truly grateful to Phase Focus Ltd. and the Electrical and Electronic Engineering department of the University of Sheffield for funding my PhD. Phase Focus Ltd 7 also gave me quite significantly technical support during my first year. I sincerely appreciate it. 8 List of Symbols P the complex illumination/probe function O the complex object transmission function 푃푒 extra mode of the probe function 푂푒 extra mode of the object function L camera length 휓 complex exit wave Ψ the Fourier transform of 휓 ℱ Fourier transform 휆 wavelength ℎ Planck’s constant 푚0 rest mass of electron d lattice spacing R the radius of the diffraction ring x, y real space coordinates 9 u, v Fourier space coordinates H transfer function j register of scanning positions Γ mutual coherence function 훼 object function update scale 훽 probe function update scale G Gaussian profile 퐼푐표ℎ coherent diffraction intensities 퐼푚 partially coherent diffraction intensities c detector pedestal 10 Table of Contents Abstract ...................................................................................................................................... 2 Declaration ................................................................................................................................. 4 Acknowledgements .................................................................................................................... 6 List of Symbols .......................................................................................................................... 9 Chapter 1 Introduction ............................................................................................................ 16 1.1 Motivation ...................................................................................................................... 16 1.2 Thesis Outline ................................................................................................................ 20 Chapter 2 Background ............................................................................................................ 23 2.1 The Fourier transform and its properties ....................................................................... 23 2.2 Electrons and electron waves ......................................................................................... 26 2.2.1 Definition of the electron wave............................................................................... 26 2.2.2 Description of electron waves and wave propagation ............................................ 27 2.2.3 Diffraction approximations ..................................................................................... 29 2.3 Partially Spatially Coherent illumination....................................................................... 34 2.3.1 van Cittert-Zernike theorem .................................................................................... 35 11 2.3.2 Density matrix ......................................................................................................... 36 2.4 Wave front aberrations and the transfer function .......................................................... 39 2.4.1 Perfect lens function ............................................................................................... 39 2.4.2 Aberrations .............................................................................................................. 41 2.5 Electron specimen interaction ........................................................................................ 44 2.5.1 Elastic scattering and inelastic scattering ............................................................... 44 2.5.2 Diffraction ............................................................................................................... 45 2.5.3 Weak Phase Object Approximation ........................................................................ 48 2.5.4 WPOA image .......................................................................................................... 48 2.5.5 Contrast transfer function ....................................................................................... 50 2.6 Electron microscopy ...................................................................................................... 52 2.6.1 Why use an electron microscope ............................................................................ 52 2.6.2 The components of an electron microscope ............................................................ 55 2.6.3 TEM and