A system and method (referred to as the system) fabricates controllable atomic assemblies in two and three dimensions. The systems identify by a non-invasive imager, a local atomic structure, distribution of vacancies, and dopant atoms and modify, by a microscopic modifier, the local atomic structure, via electron beam irradiation. The systems store, by a knowledge base, cause-and-effect relationships based on a non-invasive imaging and electron scans. The systems detect, by detectors, changes in the local atomic structure induced by the electron irradiation; and fabricate, a modified atomic structure by a beam control software and feedback.