STUDY ON ENERGY DISSIPATION IN THE DYNAMIC SYSTEM OF TAPPING MODE ATOMIC FORCE MICROSCOPE
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摘要:原子力显微镜是一种典型的微纳谐振器, 其核心部件是一个对微弱力极敏感的微悬臂梁探针, 当它在不同的环境工作时, 存在着各种不同形式、不同性质的能量耗散, 这些能量耗散与系统的相位图像有着密切的联系. 在众多的耗散机制中, 只有针尖与样品的黏附接触耗散才能真正反映样品的性质, 其他耗散会降低黏附接触耗散在系统总耗散中的占比, 使得图像中的有效信息被削弱. 因而, 明确其他耗散对系统品质因数的量级贡献是十分重要的, 这有助于提高图像的品质. 为了研究这些耗散, 本文根据耗散机理产生的原因对不同的能量耗散进行了细致的分类, 系统总结了各种能量耗散的类型. 之后, 通过理论、实验和仿真的方法探究了在不同环境下、不同位置处微悬臂梁探针的能量耗散, 明确了不同耗散对系统品质因数的量级贡献. 然后, 对于不同流体环境下的能量耗散, 对比了它们的作用机理及量级大小. 最后, 对于在大气环境下工作的原子力显微镜探针, 研究了它在振动过程中从高于样品表面到下降并接触样品这一连续过程中不同阶段存在的能量耗散, 分析表明, 在这些能量耗散中对系统品质因数影响最大的是由空气引起的耗散, 包括空气黏性阻尼, 压膜阻尼及液桥耗散.Abstract:Atomic force microscope is a typical micro-nano resonator and its core component is a micro-cantilever beam probe, which is extremely sensitive to weak force. When it works in different environments, there are various forms and characteristics of energy dissipation mechanisms. These energy dissipations are closely related to the phase image of the system. Among the many dissipation mechanisms, we believe that only the adhesive contact dissipation between the tip of the probe and the sample can truly reflect the nature of the sample, and the other dissipations will reduce the proportion of adhesive contact dissipation in the total dissipation of the system, thus weakening the effective information in the phase image. Therefore, it is important to clarify the quantitative contribution of other dissipations to the quality factor of the system, which helps us to improve the quality of the phase image. In order to study these dissipations, in this paper, we meticulously classify different energy dissipations according to the causes of the dissipation mechanism and systematically summarize the different types of energy dissipations. Then, we study the energy dissipation of micro-cantilever beam probe in different environments and at different positions by theoretical, experimental and simulation methods, and the magnitude contribution of different dissipation to the quality factor of the system is also clarified. Then, for the energy dissipation in different fluid environments, we compare their mechanism of action and their magnitude contribution to the quality factor of the system. Finally, for an atomic force microscope probe operating in an atmospheric environment, we investigate the energy dissipation at different stages of the vibration process from above the sample surface to descending and touching the sample, and the analysis shows that the most significant impact on the system quality factor is caused by the air, including air viscosity damping, squeeze film damping and liquid bridge dissipation.
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Key words:
- atomic force microscope/
- energy dissipation/
- phase/
- quality factor
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图 1支撑损耗模型和仿真网格示意图
Figure 1.Schematic diagram of support dissipation model and simulation grid
图 4空气中相对位置与品质因数的关系
Figure 4.Relationship between relative position and quality factor in air
图 7理论、实验品质因数与探针位置的关系
Figure 7.The relationship between the quality factor and position of the probe in theory and experiment
图 8液膜厚度与相对湿度的关系
Figure 8.Relationship between water film thickness and relative humidity
图 10相对湿度与耗散能的关系
Figure 10.Relationship between relative humidity and dissipation energy
图 11不同相对湿度下品质因数的关系
Figure 11.Relationship of quality factor under different relative humidity
图 12微悬臂梁在液体中振动示意图
Figure 12.Schematic diagram of vibration of micro-cantilever beam in liquid
图 13典型轻敲式AFM探针品质因数量级分布图
Figure 13.Order of magnitude distribution of quality factor for a typical tapping mode AFM probe
表 1支撑损耗的理论及仿真结果
Table 1.Theoretical and simulation results of support dissipation
Parameter Value $l \times b \times h/{\text{μm} }$ 135 × 40 × 4 $ {h}_{\text{s}}/\text{μm} $ 400 material Si E/GPa 169 theoryQ $35\;538.75$ simulationQ $32\;294$ 
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表 2探针各项参数值
Table 2.Parameter values of the probe
Parameter Value $l \times b \times h/{\text{μm}}$ 135 × 40 × 4 tip height/μm 10 material Si E/GPa 169 ${m_{\text{e}}}$/kg $1.21 \times {10^{ - 11}}$ ${\omega _{n} }/({ {\rm{rad} } }\cdot{ {\rm{s} } }^{-1})$ $1.69 \times {10^6}$ ${c_{ {\text{e1} } } }/({{\rm{N}}} \cdot {{\rm{s}}} \cdot { {{\rm{m}}}^{ - 1} })$ $4.33 \times {10^{ - 8}}$ 下载:
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表 3液体中梁的参数及品质因数
Table 3.Parameters and quality factor of beam in liquid
Parameter Value $l \times b \times h/{\text{μm} }$ 135 × 40 × 4 $ {\text{material}} $ Si $ E/\text{GPa} $ 169 ${m_{{\text{liquid}}}}/{\text{kg}}$ $5.7 \times {10^{ - 11}}$ ${f_{\text{n} } }/{{\rm{kHz}}}$ 150.5 ${c_{ {\text{e} }3} }/({{\rm{N}}} \cdot {{\rm{s}}} \cdot { {{\rm{m}}}^{ - 1} })$ $5.67 \times {10^{ - 6}}$ ${Q_{{\text{liquid}}}}$ 8.83 下载:
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表 4不同环境条件下其他耗散类型及量级对比
Table 4.Comparison of other dissipation types and magnitudes under different environmental conditions
Ultrahigh vacuum Nitrogen environment Atmospheric environment Liquid environment dissipation types ${Q_{ {\text{in} } } }{ {\text{(intrinsic dissipation)} }^{\text{*} } }{\text{, } }{Q_{ {\text{sup} } } }$ $ {Q_{{\text{in}}}},{\text{ }}{Q_{{\text{sup}}}},{\text{ }}{Q_{{\text{vis}}}},{\text{ }}{Q_{{\text{squ}}}} $ $ {Q_{{\text{in}}}},{\text{ }}{Q_{{\text{sup}}}},{\text{ }}{Q_{{\text{vis}}}},{\text{ }}{Q_{{\text{squ}}}},{\text{ }}{Q_{{\text{liq}}}} $ $ {Q_{{\text{in}}}},{\text{ }}{Q_{{\text{sup}}}},{\text{ }}{Q_{{\text{liquid}}}} $ magnitude $ Q \sim {10^4} $ $ Q \sim {10^2} $ $ {\text{ }}Q \sim {10^2} $ ${\text{ } }Q \sim (0 \sim 10)$ *includes${Q_{{\text{the}}}},{\text{ }}{Q_{{\text{son}}}},{\text{ }}{Q_{{\text{sur}}}}{\text{, }}{Q_{{{\rm{int}}} }}$ 下载:
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