Understanding the mechanics of blisters is important for studying two-dimensional (2D) materials, where nanoscale blisters appear frequently in their heterostructures. It also benefits the understanding of a novel partial wetting phenomenon known as elastic wetting, where droplets are confined by thin films. In this twopart work, we study the static mechanics of nanoscale blisters confined between a 2D elastic sheet and its substrate (part 1) as well as their pinning/depinning dynamics (part 2). Here, in part 1, we investigate the morphology characteristics and hydrostatic pressures of the blisters by using atomic force microscopy (AFM) measurements and theoretical analysis. The morphology characteristics of the blisters are shown to be the interplay results of the elasticity of the capping sheet, the adhesion between the capping sheet and the substrate, and the interfacial tensions. A universal scaling law is observed for the blisters in the experiments. Our analyses show that the hydrostatic pressures inside the blisters can be estimated from their morphology characteristics. The reliability of such an estimation is verified by AFM indentation measurements of the hydrostatic pressures of a variety of blisters.

To meet the surging demands for quantitative and nondestructive testing at the nanoscale in various fields, ultrasonic-based scanning probe microscopy techniques, such as contact-resonance atomic force microscopy (CR-AFM), have attracted increased attention. Despite considerable success in subsurface nanostructure or defect imaging, the detecting capabilities of CR-AFM have not been fully explored yet. In this paper, we present an analytical model of CR-AFM for detecting subsurface cavities by adopting a circular freestanding membrane structure as an equivalent cavity. The parameters describing the detection limits of CR-AFM for such structures include the detecting depth and the detectable area. These parameters are systematically studied for different cantilever eigenmodes for structures of different sizes and depths. The results show that the detecting depth depends on the structure size. The higher eigenmodes generally provide better detecting capabilities than the lower ones. For an experimental verification, samples were prepared by covering a polymethylmethacrylate (PMMA) substrate with open pores at its surface with HOPG flakes. CR-AFM imaging on the HOPG-covered area was carried out using different eigenmodes in order to detect the pores in the PMMA. In addition, the influence of the applied tip load is also discussed.

Subsurface metrology techniques are of significant importance at the nanoscale, for instance, for imaging buried defects in semiconductor devices and in intracellular structures. Recently, ultrasonic-based atomic force microscopy has attracted intense attention also for subsurface imaging. Despite many applications for measuring the real and imaginary part of the local surface modulus, the physical mechanism for subsurface imaging is not fully understood. This prevents accurate data interpretation and quantitative reconstruction of subsurface features and hinders the development of an optimized experimental and engineering setup. In this paper, we present quantitative depth-sensing of subsurface cavity structures using contact-resonance atomic force microscopy (CR-AFM) imaging and spectroscopy. Our results indicate that for imaging subsurface cavity structures using CR-AFM, the induced contact stiffness variations are the key contrast mechanism. The developed algorithm based on this mechanism allows one to precisely simulate the experimental image contrasts and give an accurate prediction of the detection depth. The results allow a better understanding of the imaging mechanism of ultrasonic-based AFM and pave the way for quantitative subsurface reconstruction.

As one of the fundamental sources of noise in atomic force microscopy (AFM), thermal fluctuations of the cantilever have been studied for the case of a free tip but not much for cantilevers in contact. In this paper, using the equipartition theorem, we calculated the thermal deflection amplitude for all normal modes of an elastically supported AFM cantilever, including the free cantilever as a special case. With increasing contact stiffness, the mean thermal fluctuation amplitude decreases for all cantilever modes when in the elastic contact. In addition, considering the optical lever detection scheme used in most AFMs, we calculated the corresponding output thermal noise amplitude. The experiments validated our theoretical calculations. Our investigation facilitates a more comprehensive understanding of the thermal noise in AFM. It provides guidance for thermally excited contact-resonance AFM, which is promising for quantitative viscoelastic measurements.