High Energy Density, High Operating Frequency and Energy Efficient On-Chip Inductors based on Coiled Carbon Nanotubes (C
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High Energy Density, High Operating Frequency and Energy Efficient On-Chip Inductors based on Coiled Carbon Nanotubes (CCNTs) H. Faraby1 and P. R. Bandaru2 1 Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, California 92093-0407, USA 2 Department of Mechanical and Aerospace Engineering, Materials Science Program, University of California, San Diego, La Jolla, California 92093-0411, USA ABSTRACT We demonstrate the superior inductive properties of coiled carbon nanotubes (CCNTs) through numerical computation and analytical modeling, for the next generation of nanoscale, on-chip inductors. Taking advantage of the kinetic inductance (Lk), particularly evident at the nanoscale we find that the inductance can be increased by three orders of magnitude through changing the tube radius as well as the coil radius while the device footprint of the CCNTs can be reduced by 60%. By varying the geometric parameters of the coiled structure, the external magnetic inductance (LM,ext) can be as high as 20% of the Lk. We also report that the self resonant frequency (fSR) of CCNTs can be as much of the order of THz whereas the fSR of conventional copper(Cu) spiral inductors are limited to around 40GHz. Moreover when the material volume is considered, CCNTs have the potential to achieve Quality Factor (Q) eight times as Cu and when the footprint volume is considered Q can be twice as Cu All these promising properties of CCNTs make them a potential candidate for the entire frequency spectrum. INTRODUCTION Inductors, one of the three fundamental components in any electrical circuit, have historically been very expensive and bulky element because of their reduced scalability at high power and frequency[1]. These components are particular to high frequency circuits, incorporating power amplifiers, low noise amplifiers, matching networks, on-die antennas, tank circuits, etc[2, 3]. However, it has been often discussed that there has been essentially no change in inductor design over the past 40 years[1]. This paper discusses a potentially new type of inductor element, using quantum mechanical characteristics of rationally synthesized coiled carbon nanotubes (CCNTs) to harness high inductor performance, with small device footprint. The detailed synthesis procedures and mechanisms of CCNT formation have been reported previously[4]. There are three parameters that characterize an inductor at a given frequency (f= ωΤ2π) - the magnitude (L), quality factor (Q= ωLΤR), and self resonant frequency (fSR = 1Τ2πξLC). While Q is inversely proportional to the resistance/power loss, fSR (the self resonant frequency) denotes the highest operating frequency, i.e., for f > fSR, the parasitic capacitance is dominant. The parasitic resistance, R, could arise as a result of the (i) DC resistance, in addition to frequency dependent contributions from (ii) the skin effect, and (iii) eddy currents and dielectric losses from the substrate. To reduce the DC component, conventional copper based on chip inductors presentl
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