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Generalized Scattering Matrix Method For Electrostatic Calculations Of Nanoscale Systems

机译:纳米系统静电计算的广义散射矩阵法

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摘要

We present a theoretical formalism specially suited for the simulation of electrostatic force microscopy (EFM) magnitudes. The method allows for an exact three-dimensional description of the electrostatic interaction. Furthermore, any other calculation that involves different interactions may also be considered since the theory is developed specifically from the Sturm-Liouville equation. The main advantage of this technique is that the influence of the sample, included in the scattering matrix, must be calculated only once at the beginning of the simulation. Once the scattering matrix has been obtained, sources can be moved easily without calculating the whole system again. This characteristic allows us to simulate full scans of magnitudes directly measurable by an electrostatic force microscope such as the capacitance between a metallic tip and a dielectric nanowire. Additionally, the formalism goes beyond standard tip-sample geometries by considering the presence of point charges inside the sample.
机译:我们提出一种理论形式主义,特别适合于静电力显微镜(EFM)大小的模拟。该方法允许对静电相互作用进行精确的三维描述。此外,由于该理论是根据Sturm-Liouville方程专门开发的,因此也可以考虑涉及不同相互作用的任何其他计算。该技术的主要优点在于,在仿真开始时,必须只计算一次包含在散射矩阵中的样本的影响。一旦获得散射矩阵,就可以轻松移动光源,而无需再次计算整个系统。此特性使我们能够模拟可通过静电力显微镜直接测量的幅值的完整扫描,例如金属尖端与电介质纳米线之间的电容。此外,考虑到样品内部存在点电荷,形式主义超越了标准的尖端样品几何形状。

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