Title 



'Big Bang' tomography as a new route to atomicresolution electron tomography
 
Author 



 
Abstract 



Until now it has not been possible to image at atomic resolution using classical electron tomographic methods(1), except when the target is a perfectly crystalline nanoobject imaged along a few zone axes(2). The main reasons are that mechanical tilting in an electron microscope with subangstrom precision over a very large angular range is difficult, that many reallife objects such as dielectric layers in microelectronic devices impose geometrical constraints and that many radiationsensitive objects such as proteins limit the total electron dose. Hence, there is a need for a new tomographic scheme that is able to deduce threedimensional information from only one or a few projections. Here we present an electron tomographic method that can be used to determine, from only one viewing direction and with subangstrom precision, both the position of individual atoms in the plane of observation and their vertical position. The concept is based on the fact that an experimentally reconstructed exit wave(3,4) consists of the superposition of the spherical waves that have been scattered by the individual atoms of the object. Furthermore, the phase of a Fourier component of a spherical wave increases with the distance of propagation at a known 'phase speed'. If we assume that an atom is a pointlike object, the relationship between the phase and the phase speed of each Fourier component is linear, and the distance between the atom and the plane of observation can therefore be determined by linear fitting. This picture has similarities with Big Bang cosmology, in which the Universe expands from a pointlike origin such that the distance of any galaxy from the origin is linearly proportional to the speed at which it moves away from the origin (Hubble expansion). The proof of concept of the method has been demonstrated experimentally for graphene with a twolayer structure and it will work optimally for similar layered materials, such as boron nitride and molybdenum disulphide.   
Language 



English
 
Source (journal) 



Nature.  London  
Publication 



London : 2012
 
ISSN 



00280836
 
Volume/pages 



486:7402(2012), p. 243246
 
ISI 



000305189000032
 
Full text (Publishers DOI) 


  
Full text (publishers version  intranet only) 


  
