Atomic-scale physical unclonable functions in solids.

The rapid development of the Internet of Things and the digital information era has intensified the demand for secure hardware and information systems. Physical unclonable functions (PUFs) provide a hardware-based approach by exploiting fabrication-induced randomness to generate unique, unclonable labels. Concurrently, advances in deterministic nanofabrication increasingly challenge the unclonability of conventional micro- and nanoscale PUFs, motivating the exploration of more fundamental sources of physical randomness. Here, we demonstrate an atomic-scale PUF architecture that leverages intrinsic randomness in solids through lattice and defect engineering. The resulting PUFs exhibit both three-dimensional spatial variability and atomic-scale configurational complexity, yielding extraordinary encoding space and uniqueness. For a characteristic feature size of 1 nanometer, the Shannon entropy is estimated at 17.49, underscoring the encoding capacity. Moreover, the embedded structure ensures intrinsic unclonability and robustness against environmental perturbations. These results establish atomic-scale PUFs as a fundamentally secure and scalable platform for next-generation hardware and information security.