Multiscale Fractal Characterization of Substrate-Controlled Surface Morphology Evolution in 2,6-Diphenyl Anthracene Thin Films

Complex surfaces exhibit hierarchical morphological organizations that cannot be fully described by conventional roughness parameters alone. In this study, a fractal–statistical framework is proposed to elucidate the substrate-controlled morphological evolution of 2,6-diphenyl anthracene (DPA) thin films deposited on chemically modified dielectric substrates, including hexamethyldisilazane (HMDS), octyltrimethoxysilane (OTMS), octadecyltrichlorosilane (OTS), and bare silicon dioxide (SiO2). A multidimensional morphological descriptor vector (MDPA) is introduced by integrating ISO 25178 areal surface parameters (HISO), fractal dimension (Df), texture direction parameters (Td), power spectral density (PSD), and scale-sensitive fractal analysis (SSFA) descriptors to quantify amplitude-based, spatial-frequency, and scale-dependent morphological information. Atomic force microscopy (AFM) topographies of 5 nm and 50 nm thick films were analyzed using complementary approaches, including ISO 25178 areal surface parameters, texture direction analysis, peak statistics, morphological envelope fractal analysis, two-dimensional Fourier analysis, power spectral density (PSD), and scale-sensitive fractal analysis (SSFA). The results demonstrate that substrate chemistry governs not only the amplitude of surface roughness but also the lateral organization, spatial frequency distribution, and scale-dependent fractal complexity of DPA morphologies. The fractal dimension analysis revealed substrate-dependent variations in surface complexity, with values ranging from 2.11 to 2.45 for 5 nm films and from 2.19 to 2.52 for 50 nm films. PSD analysis identified distinct substrate-induced modifications in spectral organization, while SSFA revealed significant changes in smooth–rough crossover scales, maximum complexity scales, and fractal surface complexity during film growth. In particular, OTMS promoted the strongest hierarchical organization for thicker films, exhibiting the highest scale-sensitive fractal complexity, whereas OTS generated highly developed but less hierarchically correlated rough structures. The integrated fractal–spectral methodology establishes quantitative relationships between substrate functionalization and multiscale surface evolution, demonstrating that morphological complexity cannot be described solely by conventional height parameters. This framework provides a robust approach for characterizing hierarchical thin-film architectures and can be extended to other organic semiconductor systems where substrate-driven morphological control is critical.