Hierarchical Multi-scale Physical Unclonable Functions Based on Colloid Lithography and Block Copolymer Directed Self-Assembly

Encoding device-unique cryptographic responses from fabrication disorder requires structural randomness that can be formed reproducibly but cannot be replicated deterministically. We present a hierarchical multi-scale material platform that combines colloidal lithography with polystyrene-b-polydimethylsiloxane (PS-b-PDMS) block-copolymer directed self-assembly on a common substrate. Stochastic colloidal assembly forms a microscale grain-boundary network and defines confined wells, while PS-b-PDMS self-assembles inside the wells into nanoscale lamellar patterns. These coupled self-assembly processes introduce structural variation at two distinct length scales.

The microscale morphology is characterised by analysing the spatial density distribution of the colloidal grain-boundary network. The nanoscale morphology is characterised by extracting orientation fields of lamellar domains inside each confined well. This field-based approach describes the local structural state of the self-assembled patterns without relying on manually segmented objects such as individual grains or isolated defects.

Directed self-assembly provides geometrically isolated analysis regions within the wells, enabling consistent domain-level comparison across the substrate. Lamellar domain orientation and local order parameters are used to classify the confined lamellar structures, while topological defect density serves as a supporting structural indicator. The resulting methodology links microscale colloidal morphology and nanoscale block-copolymer ordering, providing a route to hierarchical material authentication based on sequentially compatible self-assembly processes.