Two-dimensional (2D) materials have properties that are often different from their three-dimensional (3D) bulk form. Many of these materials are stable at ambient conditions, which allows them to be integrated with other 2D- or 3D-materials to form heterostructures. Integration of various dimensional materials attains unique electrical and optical properties that aid in developing novel electronic devices. The interface of the heterogeneous integration of these films can exhibit a weak van der Waals-like bonding. In this thesis, an advanced characterization (from atomic to millimeter resolution) of various dimensional materials with weakly bonded interfaces is developed and employed to understand their behavior at scale. First, a large-area single-crystal cadmium telluride thin film is grown incommensurately and strain-free to a sapphire substrate despite a significant 3.7% lattice mismatch. The film remarkably delaminates as a bulk single crystal film due to an atomically thin tellurium that spontaneously forms at the interface. Aberration-corrected electron microscopy and spectroscopy reveal both the van der Waals-like structure and bonding at the film/substrate interface. Second, a large-area atomically thin gallium is intercalated at the interface of epitaxial graphene. Correlative microscopy workflows are applied to understand the thickness uniformity and area coverage of the 2D–gallium over few millimeters of the sample. Utilizing multiple correlative methods, SEM image contrast is found to be directly related to the presence of the intercalated gallium. The origin of the SEM contrast is investigated as a function of the surface potential. Then, the heterostructure characterization is scaled up over a few square millimeter areas by segmenting SEM images, each acquired with nanometer-scale resolution. Additionally, transmission electron microscopy is applied to investigate the interface of gallium–SiC, the gallium air–stability, and the role of the substrate on the heteroepitaxial growth of 2D–gallium, which charts a path for further development of these materials. / Thesis / Doctor of Philosophy (PhD)