Atomic force microscopy (AFM) plays a critical role in the characterization of two-dimensional materials such as graphene and transition metal dichalcogenides (TMDCs). Its ability to provide high-resolution topographical data makes it indispensable for studying thickness, surface defects, and heterostructure interfaces. AFM operates by scanning a sharp probe across a sample surface, detecting interatomic forces between the tip and the material. This allows for non-destructive imaging at the nanoscale, essential for analyzing atomically thin layers.

One of the primary applications of AFM in 2D material research is thickness measurement. Since graphene and TMDCs are often only a few atomic layers thick, precise thickness determination is crucial for understanding their electronic and mechanical properties. AFM measures height differences between the substrate and the material, providing sub-nanometer resolution. For example, single-layer graphene typically exhibits a height of approximately 0.34 nm when measured by AFM, corresponding to its interlayer spacing in bulk graphite. Similarly, TMDCs like MoS2 show step heights of around 0.65 nm per monolayer. However, factors such as tip-sample interactions and surface contaminants can influence these measurements, necessitating careful calibration and environmental control.

Defect identification is another area where AFM excels. Point defects, step edges, and grain boundaries in 2D materials can significantly alter their electronic properties. AFM's high spatial resolution allows for direct visualization of these features. For instance, atomic vacancies in graphene appear as depressions in topography scans, while adatoms or adsorbates manifest as protrusions. In TMDCs, defects such as sulfur vacancies in MoS2 can be detected through variations in surface morphology. Beyond topography, advanced AFM modes like conductive AFM (C-AFM) and Kelvin probe force microscopy (KPFM) provide additional insights into electronic inhomogeneities caused by defects. These techniques map local conductivity and work function variations, respectively, revealing how defects influence charge transport and doping.

Heterostructure analysis is a third key application of AFM in 2D material research. Van der Waals heterostructures, formed by stacking different 2D materials, exhibit unique properties dependent on interfacial quality and layer alignment. AFM helps characterize these structures by mapping surface roughness, layer continuity, and interlayer spacing. For example, in graphene-hBN heterostructures, AFM can identify regions of clean interfaces versus those with trapped contaminants or bubbles. Phase imaging, an AFM mode sensitive to variations in material properties, further distinguishes between different layers in a heterostructure based on their mechanical or adhesive characteristics.

Despite its strengths, AFM has limitations that necessitate complementary techniques. One major challenge is the convolution of topographic and material contrast. Surface features and actual material properties can be difficult to disentangle, especially in heterogeneous samples. Additionally, AFM measurements can be affected by tip artifacts, such as tip broadening, which distorts lateral dimensions. Slow scan speeds also limit its use for large-area characterization or dynamic processes.

Raman spectroscopy is often paired with AFM to overcome these limitations. While AFM provides topographical and mechanical data, Raman offers chemical and structural information through vibrational modes. For graphene, the G and 2D peaks in Raman spectra indicate layer number and strain, complementing AFM thickness measurements. In TMDCs, Raman modes like E2g and A1g provide insights into layer thickness and doping. Together, AFM and Raman enable a more comprehensive analysis of 2D materials by correlating physical morphology with electronic and vibrational properties.

Another complementary technique is scanning electron microscopy (SEM), which provides faster large-area imaging but lacks AFM's height resolution. Transmission electron microscopy (TEM) offers atomic resolution and detailed defect analysis but requires destructive sample preparation. AFM bridges the gap by providing non-destructive, high-resolution imaging under ambient conditions.

Quantitative analysis with AFM requires careful consideration of experimental parameters. For example, force-distance curves can measure mechanical properties like Young's modulus of 2D materials. Studies have reported graphene's Young's modulus to be around 1 TPa, consistent with its theoretical strength. Similarly, AFM-based nanoindentation has been used to probe the elasticity of MoS2 monolayers, revealing a modulus of approximately 270 GPa. These measurements are sensitive to tip calibration and loading conditions, emphasizing the need for standardized protocols.

Environmental factors also influence AFM performance. Humidity can cause capillary forces between the tip and sample, altering measured heights and forces. Vacuum or inert gas environments minimize these effects but add complexity to experiments. Dynamic AFM modes, such as tapping mode, reduce lateral forces and sample damage compared to contact mode, making them preferable for delicate 2D materials.

In summary, AFM is a versatile tool for characterizing 2D materials, providing essential data on thickness, defects, and heterostructures. Its nanoscale resolution and ability to operate under various conditions make it indispensable for research on graphene, TMDCs, and related materials. However, its limitations highlight the importance of combining AFM with techniques like Raman spectroscopy, SEM, and TEM for a complete understanding of 2D material properties. Future advancements in AFM technology, such as higher speed imaging and improved tip functionalization, will further enhance its capabilities in this rapidly evolving field.