Energy Stored and Capacitance of a Circular Parallel Plate Nanocapacitor

Abstract

Nanocapacitors have received a great deal of attention in recent years due to the promises of high energy storage density as device scaling continues unabated in the nanoscale era. High energy storage capacity is a key ingredient for many nanoelectronic applications in which the significant consumption of energy is required. The electric properties of a nanocapacitor can be strongly modified from the expected bulk properties due to finite-size effects which means that there is an increased need for the accurate characterization of its properties. In this work, we considered a theoretical model for a circular parallel plate nanocapacitor and calculated exactly, in closed analytic form, the electrostatic energy stored in the nanocapacitor as a function of the size of the circular plates and inter-plate separation. The exact expression for the energy is used to derive an analytic formula for the geometric capacitance of this nanocapacitor. The results obtained can be readily amended to incorporate the effects of a dielectric thin film filling the space between the circular plates of the nanocapacitor.

Interaction energy between two identical hemispherical surfaces with uniform surface charge density

“…Assume that the two electrodes are very close to each other in such a way as to closely resemble the geometry of figure 1 with the only difference of charges being +Q and −Q. This would be a neat experimental realization of the present model where the experimentally measured capacitance can be compared with the one expected which can calculated by following established recipies [37,38]. Lastly, the result obtained in equation ( 28) can be useful to computational physicists to gauge the efficacy of numerical methods.…”

Imaging microwave field of chip surfaces based on scanning microwave microscopy

“…By combining microwave measurement techniques, near-field scanning microwave microscopy (NSMM) is derived as a new method of evaluating electrical parameters. It uses microwave to scan the sample surface, which enables two-dimensional semiconductor material characterization [27], quantitative measurement of dielectric constants of materials [28,29] and nanoscale capacitance measurements [30][31][32][33]. In contrast, the application of NSMM to the in-chip inspection of IC electromagnetic parameters can break through the diffraction limit and obtain micrometer or nanometer images with high spatial resolution.…”

Novel Research in Low-Dimensional Systems

“…A triangular lattice is formed by a single layer of graphene or graphite surfaces, as well as the (111) surface of face-centered cubic crystals.The author uses an extension of the lattice gas model for fermionic particles on a two-dimensional triangular (hexagonal) lattice to analyze the system within the mean field approximation. The model’s qualitative differences considering hypercubic lattices are also discussed.The third paper by Ciftja [ 15 ] represents a theoretical study of a nanocapacitor’s electric properties. Such properties can be very different from the expected bulk properties due to the finite-size effects for small length scales.…”