Materials Reliability Division, National Institute of Standards and Technology, Boulder, CO, USA.
Nanotechnology. 2012 Feb 10;23(5):055702. doi: 10.1088/0957-4484/23/5/055702. Epub 2012 Jan 11.
Atomic force microscopy (AFM) methods for quantitative measurements of elastic modulus on stiff (>10 GPa) materials typically require tip-sample contact forces in the range from hundreds of nanonewtons to a few micronewtons. Such large forces can cause sample damage and preclude direct measurement of ultrathin films or nanofeatures. Here, we present a contact resonance spectroscopy AFM technique that utilizes a cantilever's higher flexural eigenmodes to enable modulus measurements with contact forces as low as 10 nN, even on stiff materials. Analysis with a simple analytical beam model of spectra for a compliant cantilever's fourth and fifth flexural eigenmodes in contact yielded good agreement with bulk measurements of modulus on glass samples in the 50-75 GPa range. In contrast, corresponding analysis of the conventionally used first and second eigenmode spectra gave poor agreement under the experimental conditions. We used finite element analysis to understand the dynamic contact response of a cantilever with a physically realistic geometry. Compared to lower eigenmodes, the results from higher modes are less affected by model parameters such as lateral stiffness that are either unknown or not considered in the analytical model. Overall, the technique enables local mechanical characterization of materials previously inaccessible to AFM-based nanomechanics methods.
原子力显微镜（AFM）方法通常用于对刚性（>10 GPa）材料进行弹性模量的定量测量，需要针尖-样品接触力在数百到数微牛顿之间。如此大的力可能会导致样品损坏，并且无法直接测量超薄薄膜或纳米结构。在这里，我们提出了一种接触共振光谱 AFM 技术，该技术利用悬臂梁的更高挠曲本征模式，即使在刚性材料上，也可以实现低至 10 nN 的接触力的模量测量。对于在接触中具有柔韧性的悬臂梁的第四和第五挠曲本征模式的光谱进行简单的分析性梁模型分析，与在 50-75 GPa 范围内的玻璃样品的体模量的批量测量吻合良好。相比之下，在实验条件下，对传统使用的第一和第二本征模光谱的相应分析给出了较差的一致性。我们使用有限元分析来了解具有物理真实几何形状的悬臂梁的动态接触响应。与较低的本征模式相比，来自较高模式的结果受模型参数的影响较小，这些参数在分析模型中要么未知，要么未被考虑。总的来说，该技术使以前无法通过基于 AFM 的纳米力学方法进行局部材料力学特性分析的材料成为可能。
