$Å$ -压痕法，用于支持超硬超薄膜和纳米结构的非破坏性弹性模量测量
$Å$-Indentation for non-destructive elastic moduli measurements of supported ultra-hard ultra-thin films and nanostructures
摘要：
在传统的纳米压痕测量中，压痕深度通常大于1-10 nm，这阻碍了研究超薄膜（$<$ 10 nm）和支撑的原子级薄的二维（2D）材料的能力。在这里，我们讨论了调制压痕的发展，以实现在力压痕测量过程中的亚压痕深度，同时也成像材料的纳米级分辨率。调制纳米压痕（MoNI）最初被发明用于测量多壁纳米管的径向弹性。现在，通过在高频下使用极小振幅振荡（$\ll$ 1 μ m）和刚性杠杆，我们展示了调制纳米/纳米压痕（MoNI/MoNI）如何实现超薄超硬薄膜（包括CVD金刚石薄膜（模量$\sim$ 1000 GPa））的接触刚度和压痕模量的非破坏性测量，以及2D材料的横向模量。我们的分析表明，在存在标准实验室噪声基底的情况下，用商业原子力显微镜（AFM）实现的MoNI/MoNI I的信噪比使得用商业锁定放大器$-$可实现的80 dB $-$的动态范围足以观察到优异的压痕曲线，压痕深度小至0.3 μ m，压痕分辨率$<$ 0.05 μ m，在正常载荷下$<$为0.5 nN。在标准AFM上实现，该方法具有广泛的适用性。
英文摘要：
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.
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