We introduce a method for the evaluation of singular integrals arising in the discretisation of integral equations. The method is based on the idea of repeated subdivision of domains. The integrals defined on these subdomains are classified. Each class can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the relations between the classes. Therefore the approximate value of the singular integral only depends on the accuracy of the calculation of regular integrals.
The present study covers the nanoanalysis methods for four key material characteristics: electrical and electronic properties, optical, stress and strain, and chemical composition. With the downsizing of the geometrical dimensions of the electronic, optoelectronic, and electromechanical devices from the micro to the nanoscale and the simultaneous increase in the functionality density, the previous generation of microanalysis methods is no longer sufficient. Therefore, the metrology of materials' properties with nanoscale resolution is a prerequisite in materials' research and development. The article reviews the standard analysis methods and focuses on the advanced methods with a nanoscale spatial resolution based on atomic force microscopy (AFM): current-sensing AFM (CS-AFM), Kelvin probe force microscopy (KPFM), and hybrid optical techniques coupled with AFM including tip-enhanced Raman spectroscopy (TERS), photothermal-induced resonance (PTIR) characterization methods (nano-Vis, nano-IR), and photo-induced force microscopy (PIFM). The simultaneous acquisition of multiple parameters (topography, charge and conductivity, stress and strain, and chemical composition) at the nanoscale is a key for exploring new research on structure-property relationships of nanostructured materials, such as carbon nanotubes (CNTs) and nano/microelectromechanical systems (N/MEMS). Advanced nanocharacterization techniques foster the design and development of new functional materials for flexible hybrid and smart applications.
Herein, the evolution of carbon nanotubes (CNTs) as functional material in nano‐ and microelectromechanical systems (N/MEMS) is featured. Introducing material morphologies for the CNTs in a homologue series (single CNTs—bundles, fibers, yarns—networks and thin films), different concepts for mechanical sensors based on the intrinsic and extrinsic properties of the CNT materials are introduced (piezoresistive effect, strain‐induced band bending, charge tunneling). In a rigorous theoretical treatment, the limits of the achievable sensor performance (i.e., gauge factor) are derived and discussed in the context of applications. A careful literature survey shows that highest sensitivity is reached for devices exploiting the intrinsic transport properties of single CNTs. For reliability tests of such sensor systems made from nanomaterials and classical MEMS, the specimen‐centered approach (SCA) is introduced to give viable insights into the structure property relationships and failure modes of CNT mechanical sensors. CNT actuation occurs on the macro‐, micro‐, and nanoscales via atomic force microscopy, electrostatic gating, integration in N/MEMS systems, or through substrate bending.
Carbon nanomaterials are important for future sensors and electronics. Defects determine the material properties, therefore, it is critical to find new ways to investigate defects at the nanoscale. In this context, Raman spectroscopy (RS) is the tool of choice to study defects in carbon nanomaterials. On the other hand, Kelvin probe force microscopy (KPFM) provides structural and surface potential information at the nanoscale. Here, the authors demonstrate the synergistic application of these methods in the investigation of ion-beaminduced defects in graphite. KPFM and RS imaging are used for visualizing ioninduced defects in a wide range of ion doses from 10 10 to 10 16 ions cm À2 . For the lower range of ion dose, the authors find that RS provides image contrast for the different defect regions in graphite up to a dose of 5 Â 10 13 ions cm À2 . For higher doses, the sp 2 carbon concentration becomes so small that the Raman spectra get dominated by broad amorphous carbon bands. For this dose range, the KPFM contrast allows the defective regions to be differentiated. This contrast in KPFM originates from sp 3 carbons that act as charge traps. The results show that KPFM and Raman microscopy make a powerful and necessary combination for studying the spatial distribution of defects in carbon.
This paper reports on concepts, technology, integration aspects, and results of a MEMS-based test platform for reliability tests of micro and nano objects.Building blocks of this platform to be used in in-plane push-pull-configurations are a thermal actuator, a force sensor, and a displacement sensor as well as several types of samples to be integrated directly or indirectly. The technology concept is proven for aluminum wires as a first demonstrator for an integrated specimen. The modular concept enables the adoption of the platform for further types of samples and test configurations. The building blocks are simulated using a Finite-Element approach and the results are compared to experimentally obtained data sets. According to the specifications, the thermal actuator is capable of providing displacements up to 1.5 μm. The displacement and the force sensor are specified to provide sensitivities of 3 fF nm À1 and 2.5 μV nN À1 , respectively. SEM image of a piezoresistive force sensor attached to an integrated Al wire as test sample À building blocks of MEMS-based test platforms.
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