Fundamental investigations on non-linearity and noise distribution in co-resonantly coupled cantilever sensors with piezoelectric excitation and readout

动态悬臂梁传感器作为敏感的质量和力传感器用于许多不同的应用，例如在材料表征和气体传感中。持久的要求是在保持可靠的振荡检测的同时提高灵敏度的需求。为了应对这一挑战，开发了一种基于高灵敏度纳米悬臂和微悬臂共振耦合的概念来进行检测。该方法的关键是两个谐振器之间的本征频率匹配。传感器的制造是这一概念的主要挑战之一，因为(I)悬臂梁的几何性质通常非常不同，(Ii)特征频率匹配需要精确控制悬臂梁的尺寸。单片几何本征频率匹配共振悬臂梁传感器批量制造工艺的研究是当前研究的重点。此外，通过一个耦合谐振子模型对共振概念的含义进行了解析研究，得到了传感器的有效特性及其估计的解析表达式。在该项目中进行的理论和实验工作中的观察提出了许多关于传感器线性、稳定性和噪声的新问题，这些问题无法用目前关于共振耦合引起的复杂相互作用的理论知识来回答。然而，这些都是传感器应用中非常重要的考虑因素。此外，对基本方面的更深层次的理解不仅限于悬臂式传感器，还可以扩展到关于耦合谐振荡器的基本物理知识。因此，拟议项目的一个重点是扩大理论分析和建模，特别是关于非线性振荡和噪声的分析和建模，并在此基础上考虑探测的基本限度。拟议项目的第二个主要目标是扩大共振悬臂式传感器的用例。到目前为止，它们仅被用于相当大且需要许多附加部件的光学检测设置中。因此，我们计划开发一种制造工艺，通过将压电极组集成到微悬臂梁中来实现自感知/自激励共振悬臂梁传感器。这将降低微悬臂梁的灵敏度，因为它变得更厚和更硬。然而，共振概念在这方面提供了独特的优势，因为总体灵敏度主要由纳米悬臂的性质决定。通过将实验研究和理论建模相结合，我们期待着对共振态与(非线性)非线性振荡行为和传感应用的检测极限有关的许多新的基本见解，以及对自感知/自激励方法对这一概念的适用性的评估。

Dynamic-mode cantilever sensors are used as sensitive mass and force sensors for many different applications, e.g. in material characterization and gas sensing. A persisting requirement is the demand for increased sensitivity while maintaining a reliable oscillation detection. To address that challenge, a concept based on co-resonant coupling of a highly sensitive nanocantilever and a microcantilever for detection has been developed. The key aspect of the approach is the eigenfrequency matching between both resonators. Sensor fabrication is one of the main challenges of the concept since (i) the cantilevers are usually very different in their geometric properties and (ii) the eigenfrequency matching requires a precise control of the cantilever dimensions. The development of a batch-fabrication process for monolithic geometrically eigenfrequency matched co-resonant cantilever sensors was the main focus of the current research project. Furthermore, the implications of the co-resonant concept have been studied analytically by a coupled harmonic oscillator model which led to the derivation of effective sensor properties and analytical expression for their estimate. Observations during the theoretical and experimental work conducted in the project raised many new questions with regard to sensor linearity, stability and noise which cannot be answered with the current theoretical knowledge about the complex interplay induced by the co-resonant coupling. However, these are very important considerations for sensor applications. Furthermore, a deeper understanding of the fundamental aspects is not limited to cantilever sensors but can be extended towards basic physical knowledge about coupled harmonic oscillators. Consequently, one focus of the proposed project is on extending the theoretical analysis and modelling, especially with regard to non-linear oscillations, noise and, based on that, consideration for the fundamental limit of detection. The second main aim of the proposed project pertains the expansion of used cases for co-resonant cantilever sensor. So far, they have only be employed in optical detection settings which are rather large and require many additional components. We therefore plan on developing a fabrication process for implementation of a self-sensing/self-actuating co-resonant cantilever sensor by integrating a piezoelectric electrode stack into the microcantilever. This will reduce the microcantilever’s sensitivity as it becomes thicker and stiffer. However, the co-resonant concept offers a unique advantage in that regard, as the overall sensitivity is mainly determined by the nanocantilever’s properties. By combining experimental studies and theoretical modelling, we expect many new fundamental insights into the co-resonant state with regard to (non)linear oscillation behavior and limits of detection for sensing applications, and an evaluation of the suitability of the self-sensing/self-actuation approach for this concept.