During conventional nanoindentation measurements, the indentation depths are usually larger than 1–10 nm, which hinders the ability to study ultra-thin films (<10 nm) 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. Now, by using extremely small amplitude oscillations (<<1 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 <0.05 Å, and in normal load <0.5 nN. Being implemented on a standard AFM, this method has the potential for a broad applicability.
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