Continuum-Spectral Modeling of Surface Roughness in Electron-Beam-Deposited GO/Ag Nanocomposite Thin Films

This study investigates the structural, chemical, and morphological characteristics of electron-beam–deposited GO/Ag nanocomposite thin films and establishes a compact continuum–spectral framework for quantifying their post-deposition roughness. Since atomic force microscope (AFM) measurements provide only the final, frozen morphology and no direct temporal information, distinguishing between transient and stationary spectra is not experimentally feasible within the limited AFM wavenumber band. In practice, the accessible power spectral densities (PSDs) show no resolvable deviation from the stationary form, and transient contributions cannot be uniquely identified. The stationary PSD is fitted directly to azimuthally averaged AFM spectra, allowing the smoothing coefficients, noise intensity, correlation length, and crossover scale to be extracted in a fully data-driven manner. The fitted model accurately reproduces the characteristic dual (k−2)/(k−4) spectral scaling and predicts the scan-size dependence of root-mean-square roughness, typically achieving logarithmic determination coefficients above 0.98. The close agreement among parameters obtained from spatially separated sampling points confirms the lateral uniformity of the deposited films and highlights the robustness of the continuum–spectral approach for data-guided roughness control in electron-beam-grown nanocomposite coatings.