Å-Indentation for non-destructive elastic moduli measurements of supported ultra-hard ultra-thin films and nanostructures

During conventional nanoindentation measurements, the indentation depths are usually larger than 1–10 nm, which hinders the ability to study ultra-thin films (\u3c10 \u3enm) and supported atomically thin two-dimensional (2D) materials. Here, we discuss the development of modulated Å-indentation to achieve sub-Å indentations depths during force-indentation measurements while also imaging materials with nanoscale resolution. Modulated nanoindentation (MoNI) was originally invented to measure the radial elasticity of multi-walled nanotubes. w, by using extremely small amplitude oscillations (\u3c\u3c1 Å) at high frequency, and stiff cantilevers, we show how modulated nano/Å-indentation (MoNI/ÅI) enables non-destructive measurements of the contact stiffness and indentation modulus of ultra-thin ultra-stiff films, including CVD diamond films (~1000 GPa stiffness), as well as the transverse modulus of 2D materials. Our analysis demonstrates that in presence of a standard laboratory noise floor, the signal to noise ratio of MoNI/ÅI implemented with a commercial atomic force microscope (AFM) is such that a dynamic range of 80 dB –– achievable with commercial Lock-in amplifiers –– is sufficient to observe superior indentation curves, having indentation depths as small as 0.3 Å, resolution in indentation \u3c0.05 Å, and in normal load \u3c0.5 nN. Being implemented on a standard AFM, this method has the potential for a broad applicability