Cantilever tilt causing amplitude related convolution in dynamic mode atomic force microscopy.

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 The classical convolution model was established in contact mode assuming a static probe, but it is no longer valid in dynamic mode AFM.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 SiO(2)/Si super-lattice structure. Our model is useful for quantitative characterizations in dynamic mode, especially in probe characterization and critical dimension measurements.