[论文解读] A comparative study of force sensors for scanning probe microscopy based on quartz tuning forks and length extensional resonators

Franz J. Gießibl, Florian Pielmeier+3 more|arXiv (Cornell University)|Apr 15, 2011

Force Microscopy Techniques and Applications被引用 1

一句话总结

本研究比较了原子力显微镜中石英音叉与长度伸展谐振器力传感器的性能，分析了四种噪声源——偏转检测器噪声、热噪声、振荡器噪声和热漂移噪声——在刚度、带宽和振幅下的表现。研究证实，当振荡振幅与作用力范围相当时，信噪比达到最优，并提出了通过最小化与刚度相关的噪声源来进一步提升传感器性能的策略。

ABSTRACT

The force sensor is key to the performance of atomic force microscopy (AFM). Nowadays, most AFMs use micro-machined force sensors made from silicon, but piezoelectric quartz sensors are applied at an increasing rate, mainly in vacuum. These self sensing force sensors allow a relatively easy upgrade of a scanning tunneling microscope to a combined scanning tunneling/atomic force microscope. Two fundamentally different types of quartz sensors have achieved atomic resolution: the 'needle sensor' that is based on a length extensional resonator and the 'qPlus sensor' that is based on a tuning fork. Here, we calculate and measure the noise characteristics of these sensors. We find four noise sources: deflection detector noise, thermal noise, oscillator noise and thermal drift noise. We calculate the effect of these noise sources as a factor of sensor stiffness, bandwidth and oscillation amplitude. We find that for self sensing quartz sensors, the deflection detector noise is independent of sensor stiffness, while the remaining three noise sources increase strongly with sensor stiffness. Deflection detector noise increases with bandwidth to the power of 1.5, while thermal noise and oscillator noise are proportional to the square root of the bandwidth. Thermal drift noise, however, is inversely proportional to bandwidth. The first three noise sources are inversely proportional to amplitude while thermal drift noise is independent of the amplitude. Thus, we show that the earlier finding that quoted optimal signal-to-noise ratio for oscillation amplitudes similar to the range of the forces is still correct when considering all four frequency noise contributions. Finally, we suggest how the signal-to-noise ratio of the sensors can be further improved and briefly discuss the challenges of mounting tips.

研究动机与目标

• 评估并比较两种自传感石英力传感器在原子力显微镜中的噪声特性：基于音叉的qPlus传感器与基于长度伸展谐振器的针尖传感器。
• 识别并量化四种不同噪声源——偏转检测器噪声、热噪声、振荡器噪声和热漂移噪声——对传感器性能的贡献。
• 确定每种噪声源对传感器刚度、振荡带宽和振幅的依赖关系，以确立最佳工作条件。
• 提供通过参数优化改善自传感石英AFM传感器信噪比的设计指南。

提出的方法

• 基于物理原理建立噪声贡献的理论模型，包括布朗运动引起的热噪声和电子反馈引起的振荡器相位噪声。
• 推导每种噪声源作为传感器刚度、带宽和振幅函数的解析表达式。
• 在受控条件下对音叉和长度伸展谐振器传感器进行噪声特性实验测量。
• 系统性地改变传感器刚度、带宽和振幅，以隔离各参数对信噪比的影响。
• 将信噪比作为主要指标，评估不同配置下的传感器性能。
• 将理论预测与实验数据进行对比，以验证噪声模型并识别主要噪声源。

实验结果

研究问题

• RQ1 在基于石英的AFM传感器中，偏转检测器噪声、热噪声、振荡器噪声和热漂移噪声如何随传感器刚度、带宽和振幅变化？
• RQ2 当同时考虑四种噪声源时，信噪比最大的最优振荡振幅是多少？
• RQ3 传感器刚度如何影响每种噪声源对整体传感器性能的相对贡献？
• RQ4 通过优化带宽和振幅等传感器参数，能否进一步提升信噪比？
• RQ5 在不降低噪声性能的前提下，如何实际实现这些自传感石英传感器的探针安装？

主要发现

• 偏转检测器噪声与传感器刚度无关，但随带宽的1.5次方增加。
• 热噪声和振荡器噪声与带宽的平方根成正比，并随刚度增加而增大。
• 热漂移噪声与带宽成反比，且与振幅无关。
• 热漂移噪声不受振幅影响，而其他三种噪声源随振幅增加而减小。
• 当同时考虑四种噪声源时，先前认为最优信噪比出现在振幅与作用力范围相当时这一结论依然成立。
• 提高信噪比需要最小化与刚度相关的噪声源，并通过优化带宽和振幅来平衡相互竞争的噪声贡献。