Energy Stored and Capacitance of a Circular Parallel Plate Nanocapacitor.

Orion Ciftja

doi:10.3390/nano11051255

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.

Highlights

We introduce a model for a circular parallel plate nanocapacitor consisting of two identical circular plates placed face-to-face opposite to each other at an arbitrary separation distance
We found that the relative energy difference between them is about 8% [32]. Based on these general physical considerations, we expected that the results for the electrostatic energy stored and/or capacitance obtained from our model would likely be not very different from this order of accuracy if compared to numerical values found for the same system
We introduced a model for a circular parallel plate nanocapacitor consisting of two identical uniformly charged circular plates opposite to each other at an arbitrary separation distance

Summary

Introduction and Capacitance of a Circular Parallel

Extensive research efforts in nanotechnology during the last two decades have led to great advances in the fabrication of novel materials such as carbon nanotubes, single electron transistors, nanowires, semiconductor nano dots, to mention a few, with length scales in the nanometer range [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. The fabrication and characterization of nanocapacitors are a required step to build prototypes of functional nanocircuits Energy storage devices such as supercapacitors and batteries have always drawn much attention for their potential applications [23]. One expects the properties of this nanocapacitor to be very sensitive to the geometry and depend in a non-obvious way on the size of the circular plates and inter-plate separation distance For such a model, we do not consider any quantum effects and/or material-dependent properties that do affect realistic experimentally manufactured nanocapacitor-related systems [26,27,28,29]. The focus of this work was to introduce a model for a nanocapacitor that would allow us to obtain an exact expression for the energy stored and/or its capacitance as a function of size and geometry.

Theory and Model

Energy

Capacitance

Discussions

Findings

Conclusions