Analytical Sciences

Cantilever Tilt Causing Amplitude Related Convolution in Dynamic Mode Atomic Force Microscopy

Chunmei WANG,*1 Jielin SUN,*1 Hiroshi ITOH,*2 Dianhong SHEN,*3 and Jun HU*4

*1 School of Life Science and Biotechnology & Ministry of Education, Key Laboratory for Systems Biomedicine, Shanghai Jiaotong University, 800 Dongchuan Road, Shanghai 200240, P. R. China
*2 Research Institute of Instrumentation Frontier, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
*3 National Center for Nanoscience and Nanotechnology, No. 2 ZhongGuanCun BeiYiJie, Beijing 100080, P. R. China
*4 Shanghai Institute of Applied Physics, Chinese Academy of Sciences, 2019 Jialuo Road, Jiading District, Shanghai 201800, P. R. China

It is well known that the topography in atomic force microscopy (AFM) is a convolution of the tip’s shape and the sample’s geometry. The classical convolution model was established in contact mode assuming a static probe, but it is no longer valid in dynamic mode AFM. It is still not well understood whether or how the vibration of the probe in dynamic mode affects the convolution. Such ignorance complicates the interpretation of the topography. Here we propose a convolution model for dynamic mode by taking into account the typical design of the cantilever tilt in AFMs, which leads to a different convolution from that in contact mode. Our model indicates that the cantilever tilt results in a dynamic convolution affected by the absolute value of the amplitude, especially in the case that corresponding contact convolution has sharp edges beyond certain angle. The effect was experimentally demonstrated by a perpendicular SiO₂/Si super-lattice structure. Our model is useful for quantitative characterizations in dynamic mode, especially in probe characterization and critical dimension measurements.

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