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.
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