$\mathring{A}$-Indentation for non-destructive elastic moduli measurements of supported ultra-hard ultra-thin films and nanostructures

Abstract

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 indentation 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 ($\ll$ 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 (modulus $\sim$ 1000 GPa), 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.

37 pages, 12 figures

References in corpus (2)

• Atomically thin p-n junctions with van der Waals heterointerfaces
• Mechanical Properties of Atomically Thin Boron Nitride and the Role of Interlayer Interactions