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多频原子力显微术(MF-AFM)是近些年发展的包含一大类先进原子力显微术的新技术,具有很高的空间分辨率,不仅可以实现更多样品物性的表征,还具有时间分辨的非线性力的探测能力.MF-AFM的基本原理是对微悬臂探针的多个振动频率进行激励和探测,而这些振动频率通常与微悬臂的高次谐波振动或本征模式有关,因此,实现这一新技术的关键是设计特殊的微悬臂.传统AFM中应用较为广泛的颇具代表性的传统微悬臂有硅微悬臂与石英音叉微悬臂等.传统矩形硅微悬臂的二阶弯曲本征模式与基础模式的频率比为6.27,而石英音叉微悬臂的二阶弯曲本征模式与基础模式的频率之比无统一的值,但均为非整数,直接利用传统微悬臂去探测高次谐振信号是非常困难的.基于微悬臂的共振放大效应,本文通过改变微悬臂的质量分布,讨论了传统硅微悬臂和石英音叉微悬臂本征模式的变化,调谐其高阶本征模式与基础模式间频率的耦合关系.通过理论计算和有限元分析,设计了二阶弯曲本征模式与基础模式的频率比为整数倍关系的特殊硅微悬臂与石英高次谐振型微悬臂,部分特殊微悬臂还涉及了一阶扭转模式与基础模式的耦合.
Multi-frequency atomic force microscopy (MF-AFM) is a new technology developed in recent years that includes a large group of advanced atomic force microscopy, with high spatial resolution, not only to achieve more characterization of sample properties, but also has Time-resolved detection of nonlinear force.The basic principle of MF-AFM is to stimulate and detect multiple vibration frequencies of micro-cantilever probe, and these vibration frequencies are usually associated with the micro-cantilever harmonic oscillation or eigenmode Therefore, the key to realize this new technology is to design a special micro-cantilever.The traditional AFM widely used representative of the traditional micro-cantilever with silicon micro-cantilever and quartz tuning fork micro-cantilever etc .. The traditional rectangular silicon micro-cantilever two The frequency ratio of the stepwise bending eigenmode to the fundamental mode is 6.27, while the frequency ratio of the second order bending eigenmode and the fundamental mode of the quartz tuning fork micro-cantilever has no uniform value, but both are non-integer, and the traditional micro-cantilever is used directly It is very difficult to detect high-order resonant signals.Based on the resonant effect of micro-cantilever, this paper discusses the micro-cantilever eigen-mode of silicon cantilever and quartz tuning fork by changing the mass distribution of micro-cantilever , Tuning the coupling between the high-order eigenmode and the fundamental mode frequency.According to the theoretical calculation and finite element analysis, a special silicon micro-cantilever and quartz with the frequency ratio of the second order bending eigenmode to the fundamental mode High-order resonant micro-cantilever, part of the special micro-cantilever also involves the first order torsional mode and the basic mode of coupling.