The Fukui function and its associated potential serve as essential descriptors of chemical reactivity within the framework of conceptual density functional theory (c-DFT). While c-DFT is well-established for molecular systems, it encounters formal and technical challenges when applied to extended systems. This comprehensive study addresses the complexities involved in calculating the Fukui function and its potential in systems with periodic boundary conditions (PBC). We specifically investigate the introduction of a fictitious potential associated with a compensating background of charge (CBC) in these calculations, examining its implications for the reliability of these reactivity descriptors. To explore this issue, we analyze a diverse range of metallic and semiconductor surfaces, including elemental metals such as Ti and Pt, metal oxides like TiO