'Big Bang' tomography as a new route to atomic-resolution electron tomography

摘要

Until now it has not been possible to image at atomic resolution using classical electron tomographic methods, except when the target is a perfectly crystalline nano-object imaged along a few zone axes. The main reasons are that mechanical tilting in an electron microscope with sub-angstrom precision over a very large angular range is difficult, that many real-life objects such as dielectric layers in microelectronic devices impose geometrical constraints and that many radiation-sensitive objects such as proteins limit the total electron dose. Hence, there is a need for a new tomographic scheme that is able to deduce three-dimensional 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 sub-angstrom 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 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 point-like 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 point-like 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 two-layer structure and it will work optimally for similar layered materials, such as boron nitride and molybdenum disulphide.%最先进的电子显微镜能够轻而易举以亚原子分rn辨率解析结构，但要获得具有相似分辨率的三rn维图像却是一个更大的挑战。在这项研究中，rnDirk Van Dyck和Fu-Rong Chen描述了一个原rn始图像重建方法，它仅仅从一次投射便能在平rn面上以及在垂直方向上提取到关于所有原子去rn向的信息。该概念是基于这样的假设：每个原rn子作为一个“点源”(point source)来行动，散rn射出向探测器传播的球面波，在探测器上它们rn与来自其他原子的球面波相互干涉。所观测到rn的“出来的波”(exit wave)包含样品中所有原rn子的信息，可以用适当的算法进行调用。该方rn法对一个两层的石墨烯样品进行了实验演示。rn本文作者指出，他们的重建方法与宇宙学家用rn来构建“哈勃图”(Hubble plot)的方法相似，rn所以将其称之为“大爆炸断层扫描”(Big Bang rntomography)。