Persistent Homology Analysis of Graphene Surface Morphology Toward Carrier Mobility Evaluation

ABSTRACT A comprehensive prediction of the electrical properties of graphene, independent of field‐effect transistor (FET) fabrication, could accelerate the development of graphene wafers and electronic materials. Such a capability may also enable the implementation of in‐line inspection techniques during production. In this study, as a preliminary step toward predicting electrical properties solely from images, the relationship between carrier mobility and graphene surface roughness using atomic force microscopy (AFM) is investigated. Although no correlation is observed between carrier mobility and conventional roughness metrics such as arithmetic mean roughness (S _a ) and maximum height (S _z ), persistent homology analysis—a mathematical framework that captures topological connectivity—revealed distinctly different persistence diagrams for samples with nearly identical S _a values but differing carrier mobilities. It is found that graphene structures conforming to pronounced substrate undulations, rather than convex features such as wrinkles or bubbles, led to decreased carrier mobility. This study serves as a foundational investigation, demonstrating the potential to predict the electrical properties of graphene using only surface morphology images, made possible through the application of persistent homology analysis.