Discovering the Electron Beam Induced Transition Rates for Silicon Dopants in Graphene with Deep Neural Networks in the STEM

The atom-sized electron beam in the scanning transmission electron microscope (STEM) has been used as an imaging tool for atomic structures, as an analytical tool for energy loss spectroscopy and 4D-STEM, and in far fewer scenarios, as a manipulation tool at the atomic scale. The motion of gold atoms [1] was initially observed shortly after aberration correction became available, prompting researchers into a new field of atomic manipulation. It was realized that a model system for beam control is graphene containing dopant atoms, e.g., silicon. By placing the electron beam on or near neighbor carbon atoms, the dopant atom has a probability to move throughout the lattice, by effectively exchanging places with its neighboring carbon atom. This effort was spearheaded by several groups [2,3], initially by manual placement of the electron beam, followed by more complex beam control routines, but ones that do not consider the atomic lattice (i.e., blind patterning). Up to this point, the “rules” of atomic manipulation, however, have mostly been based on physical intuition: knock-on displacement is the primary damage mechanism for damage in graphene. Therefore, it is thought that the best strategy to cause a transition of silicon to a new atomic site is by placing the electron beam directly on the center of the neighboring carbon atom of that desired new location. However, this is purely anecdotal, and the true mechanism for manipulating dopant atoms in a lattice is not well-understood, even for 3-fold coordinated substitutions. Consequently, it is unlikely to be valid for more complex silicon bonding configurations where additional topological defects are present. Here, we discuss an automated data-driven experiment where a large variety of state-action pairs are collected. The state is the image and coordinates of the atomic lattice, and the action is the location and dwell time of the electron beam relative to the silicon atom. For accurate and reliable beam placement, the coordinates of both the carbon and silicon must be known in real time, where ensemble neural networks are used to provide a robust and fast prediction of these coordinates [4]. By analyzing these causal relationships, the electron beam induced transition rates for silicon in graphene can be extracted using a deep neural network. Further, in configurations different from the pristine 3-fold coordinated silicon (e.g., 4-fold coordinated silicon, or with other topological defects present), transition rates and optimal beam positions can be discovered for these non-trivial configurations. Provided these rates, a more effective control of silicon dopant manipulation throughout graphene is envisioned [5]. Annular dark field (ADF)-STEM image of graphene with silicon dopant (a), followed by real-time predicted coordinates in (b). Distribution of possible beam locations shown around dopant atom in (b). The learned rates of 3-fold coordinated silicon (c) where center of contours show optimal beam locations to promote a transition. Scalebar in (a) 5 Å. ADF-STEM images of graphene with silicon dopant (a,b) with additional topological defects present. Real-time predicted coordinates in (c,d). Distribution of possible beam locations shown around dopant atom in (c,d). Scalebars in (a,b) 5 Å.